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Course Requires a Media Kit to be Purchased by Course Sponsor (see additional details below): No Description: The course emphasizes the relationships among geometric figures and concepts and applies them to real world applications. The concepts of points, lines, planes, parallel lines, congruence, similarity, polygons, coordinate geometry, area, volume, circles, and right triangle trigonometry will be explored. Students will apply logical thinking throughout the course, without an emphasis on formal proofs. Students are expected to have, and be able to use, solid algebra skills to solve problems in each topic area. Internet resources are used throughout the course to explore and instruct the topics presented. Media: There is no text for this course. All instruction materials are either provided in the course or located on content related websites. Geogebra, a free geometry software application, will be downloaded and used for constructions and investigations
Discrete Math Dis­crete math­e­mat­ics, broadly speak­ing, is the "study of dis­crete objects." As opposed to objects that vary smoothly, such as the real num­bers, dis­crete math­e­mat­ics has been described as the math­e­mat­ics of count­able sets. Because of the absence of an all-encompassing def­i­n­i­tion, the best way to under­stand what dis­crete math­e­mat­ics entails is to enu­mer­ate some of the top­ics it cov­ers: graph the­ory, com­bi­na­torics, set the­ory, logic, dis­crete prob­a­bil­ity the­ory, num­ber the­ory, cer­tain top­ics in alge­bra (numer­i­cal semi­groups and monoids, for instance), dis­crete geom­e­try, and sev­eral top­ics in game theory. Of these top­ics, Prince­ton offers sep­a­rate courses on graph the­ory, com­bi­na­torics, logic, dis­crete geom­e­try, and game the­ory. Set the­ory, num­ber the­ory, prob­a­bil­ity, and the "dis­crete" top­ics in alge­bra come up in their own right in var­i­ous other courses, where they can be stud­ied in more depth. Finally, it should be stated that dis­crete math­e­mat­ics is very closely asso­ci­ated with com­puter sci­ence. As a result, many of the top­ics can be stud­ied as inte­gral parts of either of the two dis­ci­plines. In fact, there are a cou­ple of courses offered by Princeton's COS depart­ment which are really dis­crete math­e­mat­ics courses in dis­guise. Stu­dents major­ing in either of the two also often end up tak­ing courses from the other, and as a result there is con­stant exchange and col­lab­o­ra­tion between the two departments. Dis­crete Math Courses [Show]Dis­crete Math Courses [Hide] MAT 375: Intro­duc­tion to Graph The­ory This course, taught by Pro­fes­sor Sey­mour, serves as the "stan­dard" Prince­ton intro­duc­tion to dis­crete math­e­mat­ics. The course cov­ers the fun­da­men­tal the­o­rems and algo­rithms used in graph the­ory. Since there is not enough time to build the deeper results in graph the­ory, the course is based on breadth rather than depth, and there­fore goes through a host of top­ics. These include con­nec­tiv­ity, match­ing, graph col­or­ing, pla­narity, the cel­e­brated Four Color The­o­rem, extremal prob­lems, net­work flows, and many related algo­rithms which are often of sig­nif­i­cance to com­puter sci­ence. Pro­fes­sor Sey­mour is one of the great­est graph the­o­rists that the world has ever seen, and the course is designed and taught by him; it is, con­se­quently, a unique expe­ri­ence that not many other uni­ver­si­ties can pro­vide. He uses his own course notes, which have evolved through the last cou­ple of decades, and are noto­ri­ous for their terse expo­si­tions ("Proof: Triv­ial.") as well as the large amount of mate­r­ial con­densed into them. Pro­fes­sor Sey­mour also rec­om­mends Dou­glas West's clas­sic graph the­ory text­book, although he rarely con­sults it after the first lec­ture. The course is meant for a wide range of stu­dents. Since it assumes no back­ground except with the basics of math­e­mat­i­cal rea­son­ing, it is one of the largest depart­men­tal courses offered by Prince­ton Math­e­mat­ics. Stu­dents tak­ing the course range from the math­e­mat­ics majors who intend to spe­cial­ize in graph the­ory to stu­dents who need a "the­o­ret­i­cal" require­ment for their Prince­ton aca­d­e­mic career. A huge con­tin­gent of the class is com­prised of com­puter sci­ence majors, who are inter­ested in the con­nec­tions between graph the­ory and com­puter sci­ence. It is impor­tant to note that the course is cross-listed with COS 342, and is there­fore also a com­puter sci­ence depart­men­tal. The class starts slowly, but picks up very fast as it goes into more and more mate­r­ial. Although it is almost uni­ver­sally agreed as a "fun" class, doing well can be chal­leng­ing, since there is a scram­ble for the higher grades – the class is noto­ri­ous for yield­ing medi­ans of 9.8 out of 10 in its weekly prob­lem sets. The grade is based on eleven prob­lem sets through the semes­ter, and on a ten-problem take-home final exam. The prob­lem sets are instruc­tive, and often end up teach­ing new mate­r­ial out­side of class. Pro­fes­sor Sey­mour always goes over all the home­work prob­lems every week after they are handed in. Col­lab­o­ra­tion is allowed, and heav­ily encour­aged. All in all, the course is well-organized, bril­liantly taught, and extremely fun and acces­si­ble to stu­dents of all lev­els. How­ever, doing well in the course requires hard work and a some­what sub­stan­tial time com­mit­ment. Col­lab­o­ra­tion is encour­aged and ask­ing the TAs for help is not at all uncom­mon. MAT 377: Com­bi­na­to­r­ial Math­e­mat­ics This course is taught by Pro­fes­sor van Zwam, and func­tions as the stan­dard under­grad­u­ate intro­duc­tion to non-graph-theoretic com­bi­na­torics. Com­bi­na­torics, the the­ory of "count­ing," is an indis­pens­able tool and inte­gral com­po­nent of many areas of math­e­mat­ics; but more impor­tantly, it has recently, in light of mod­ern research, grown into a fun­da­men­tal math­e­mat­i­cal dis­ci­pline in its own right. This mod­ern the­ory relies on deep, well-developed tools, some of which the course gets into. In essence, the course cov­ers over a dozen vir­tu­ally inde­pen­dent top­ics illus­trat­ing some of the most pow­er­ful the­o­rems of mod­ern com­bi­na­torics, such as Ram­sey The­ory, Turan-type the­o­rems, extremal graph the­ory, prob­a­bilis­tic com­bi­na­torics, alge­braic com­bi­na­torics, and spec­tral tech­niques in graph the­ory. This course is meant pri­mar­ily for math­e­mat­ics majors look­ing for an intro­duc­tion to the the­ory of com­bi­na­torics. The class, there­fore, is typ­i­cally much smaller than its "pre­de­ces­sor," MAT 375. Pro­fes­sor van Zwam uses his own notes and sup­ple­ments them with some of the clas­sic expos­i­tory texts in com­bi­na­torics, such as Peter Cameron's notes or Richard Stanley's book. Stu­dents are highly encour­aged to take notes dur­ing lec­tures, since they are usu­ally not put up online. Another use­ful resource is Jacob Fox's notes from the same course, which was taught by him in ear­lier years. There are about six prob­lem sets spread evenly through the semes­ter. Each con­tains about five or six prob­lems, which get steadily more and more chal­leng­ing. Col­lab­o­ra­tion, there­fore, is an impor­tant part of the course. Stu­dents have been known to stay up for sev­eral nights work­ing on a cou­ple of seem­ingly impos­si­ble prob­lems towards the end. How­ever, this is an effort to intro­duce stu­dents to basic com­bi­na­torics research, and is an impor­tant part of the course; solu­tions are dis­cussed in depth after the prob­lems are handed in. There is a take-home final with six prob­lems, which col­lec­tively involve tech­niques learned through­out the semes­ter. As a reca­pit­u­la­tion of these broad tech­niques, the final is a bril­liant but com­pletely rea­son­able test of what the stu­dents are expected to have taken out of the course. There­fore, it is easy to do well on the course as long as a stu­dent has attended the lec­tures and learned the gen­eral prin­ci­ples. An impor­tant part of the course is the last two or three weeks, when it departs from the tra­di­tional top­ics taught in sim­i­lar courses in other uni­ver­si­ties, and delves into some of the mod­ern research in com­bi­na­torics. In par­tic­u­lar, the lec­tures on spec­tral graph the­ory and the basic intro­duc­tion to matroid the­ory are extremely reward­ing, since Pro­fes­sor van Zwam him­self is a matroid the­o­rist. There is usu­ally less home­work assigned from this part, but the mate­r­ial is won­der­fully pre­sented by Pro­fes­sor van Zwam; these last cou­ple of lec­tures also serve as suf­fi­cient back­ground to the grad­u­ate course on matroid the­ory, MAT 595. MAT 378: Game The­ory Pro­fes­sor van Zwam's course on game the­ory the only class that the math­e­mat­ics depart­ment offers on the sub­ject (there are other classes on game the­ory offered by other depart­ments). Game the­ory is the for­mal math­e­mat­i­cal study of strate­gic decision-making; con­se­quently it deals with a num­ber of sce­nar­ios where one person's suc­cess depends on oth­ers' choices, and there­fore choos­ing the "right" course of action is a com­plex cal­cu­la­tion. Game the­ory is not entirely a sub­set of dis­crete math­e­mat­ics, since a lot of the more mod­ern results in it are much more con­tin­u­ous in nature; how­ever, given the large dis­crete com­po­nent of the dis­ci­pline, it deserves men­tion in this cat­e­gory. MAT 584: Inci­dence The­o­rems and their Appli­ca­tions This is Pro­fes­sor Dvir's grad­u­ate course on Inci­dence The­o­rems and their appli­ca­tions. The tit­u­lar the­o­rems are a way of for­mally describ­ing how dis­crete shapes such as lines, points and var­i­ous other geo­met­ric objects inter­sect each other. These the­o­rems have recently risen in impor­tance because of their tremen­dous appli­ca­tions. The course serves as a rig­or­ous intro­duc­tion to this vast and won­der­ful the­ory, prov­ing some of its major results. The course delves into prob­lems such as Szemeredi-Trotter prob­lems ("How many inci­dences can a set of lines have with a set of points?"), Kakeya prob­lems ("What are the prop­er­ties of sets in Euclid­ean space con­tain­ing line seg­ments in each direc­tion?"), as well as Sylvester-Gallai prob­lems ("Is it pos­si­ble to have a non-collinear set of points such that a line through any two of them must go through a third?"). The top­ics cov­ered in this grad­u­ate course have far-reaching con­se­quences in some of the most impor­tant areas of mod­ern research, such as addi­tive com­bi­na­torics, cod­ing the­ory and com­pu­ta­tional com­plex­ity. Pro­fes­sor Dvir fol­lows his own excel­lent notes, which are avail­able on his web­site. The same page also details some addi­tional read­ings for the inter­ested reader. The course is aimed pri­mar­ily at grad­u­ate stu­dents, although under­grad­u­ates with suf­fi­cient back­ground in math­e­mat­ics and com­puter sci­ence are encour­aged to try it as well. As with all math­e­mat­ics grad­u­ate courses, the under­grad­u­ates have to solve a few prob­lems in order to pass the course, though typ­i­cally this is more a for­mal­ity than a strin­gent require­ment. The course is reward­ing but chal­leng­ing, and any under­grad­u­ate stu­dent plan­ning on tak­ing it is advised to read up as much back­ground mate­r­ial as pos­si­ble in order to fol­low the lec­tures eas­ily. It also helps to be inter­ested in com­puter sci­ence, as then the moti­va­tion behind much of the mate­r­ial becomes evi­dent. MAT 595: Top­ics in Dis­crete Math­e­mat­ics This grad­u­ate top­ics course is usu­ally offered by Pro­fes­sor Sey­mour (the matroid the­ory course has also been offered by Pro­fes­sor van Zwam). The course changes from semes­ter to semes­ter, but is usu­ally one of the three fol­low­ing top­ics. Matroid The­ory: This class is offered by either Pro­fes­sor Sey­mour or Pro­fes­sor van Zwam, and serves as a rig­or­ous intro­duc­tion to matroids, which are dis­crete struc­tures sim­i­lar to graphs that exhibit prop­er­ties of rank and lin­ear inde­pen­dence. This the­ory is young and excit­ing, and the course cov­ers most of its sem­i­nal results in addi­tion to going into cur­rent research top­ics. The instructor's notes are usu­ally used in con­junc­tion with Oxley's clas­sic text­book. Struc­tural Graph The­ory – Induced Sub­graphs: This course is an intro­duc­tion to the the­ory of induced sub­graphs, build­ing up grad­u­ally to the cel­e­brated 2002 proof of the Strong Per­fect Graph The­o­rem (a graph is per­fect if and only if it is a Berge graph). Like its coun­ter­part, the Graph Minors course, this course is about struc­tural graph the­ory, which is tra­di­tion­ally one of the "hard­est" branches of com­bi­na­torics, and hence stu­dents are expected to be com­fort­able with long proofs and extremely intri­cate argu­ments. Struc­tural Graph The­ory – Graph Minors: This course is a fast but inten­sive run through some of the results of the famous Graph Minors Project of Sey­mour and Robert­son. The course builds up a lot of the the­ory behind con­tain­ment rela­tions such as minors, sub­graphs, immer­sions and topo­log­i­cal con­tain­ment, and then goes into struc­ture the­o­rems and many forbidden-minor char­ac­ter­i­za­tions. Using path­width, treewidth and branch­width, the course then devel­ops most of the nec­es­sary tools for attack­ing Sey­mour and Robertson's cel­e­brated Graph Minor The­o­rem (graphs are well-quasi-ordered under minors), and sketches the proof. The dis­crete math­e­mat­ics grad­u­ate course is reward­ing in the extreme, since it is taught by the best in the world. Any stu­dent plan­ning on tak­ing it, how­ever, should be pre­pared to put in a lot of time for the prob­lem sets. Some of the home­work prob­lems, be warned, have been unsolved and are (still) open. Another point that should be kept in mind is that know­ing the mate­r­ial from MAT 375 is really a pre-requisite to tak­ing this course. The first lec­ture is some­times a refresher, but unless a stu­dent already knows some stan­dard tech­niques in graph the­ory before­hand, even the refresher does not help. This should be kept in mind because of the fre­netic nature of the course; it delves into quite advanced mate­r­ial from the sec­ond lec­ture onwards. COS 488: Ana­lytic Com­bi­na­torics This course of Pro­fes­sor Sedgewick's serves as an intro­duc­tion to one of the most pow­er­ful recent tech­niques in algo­rithm analy­sis. The dis­ci­pline of ana­lytic com­bi­na­torics rep­re­sents many decades of col­lab­o­ra­tion between Pro­fes­sor Sedgewick and Phillipe Fla­jo­let. Essen­tially, the course is divided into two halves. In the first half, the course cov­ers tech­niques from clas­si­cal com­bi­na­torics to tackle "hard" approx­i­ma­tion prob­lems that come up in com­puter sci­ence (par­tic­u­larly in the analy­sis of cer­tain recursion-based algo­rithms), and then in the sec­ond half, it goes into deeper math­e­mat­ics in order to deal with more gen­eral classes of prob­lems by using tech­niques from com­plex analy­sis. This course is very unique, in that it really is a math­e­mat­ics class; there is next to no cod­ing, and not much men­tion of com­puter sci­ence. How­ever, unlike most math­e­mat­ics classes, it switches gears in the mid­dle, and moves from dis­crete to con­tin­u­ous math­e­mat­ics, but with the same end in sight. Not much back­ground is required for the class, though some famil­iar­ity with algo­rithm analy­sis helps dis­tinctly. Fur­ther­more, a stu­dent who knows com­plex analy­sis is at a great advan­tage towards the begin­ning of the sec­ond half of the course. Pro­fes­sor Sedgewick encour­ages col­lab­o­ra­tion and is one of the most orga­nized lec­tur­ers at Prince­ton, so the course ends up being acces­si­ble to any­one inter­ested in tak­ing it. He is also known to be very gen­er­ous with his final grades. Although the "dis­crete" part of this course is con­fined to the first half, it is a course worth tak­ing. Pro­fes­sor Sedgewick loves teach­ing the class, and takes great care to ensure that the con­tent is well under­stood by every­one. Fur­ther­more, it is use­ful in sim­pli­fy­ing a num­ber of prob­lems that come up a lot in "real-life com­puter sci­ence," and solv­ing them with the aid of the beau­ti­ful but counter-intuitive approaches aris­ing from mathematics.
How do I go about studying Further Mathematics? If possible you should study Further Mathematics through timetabled classes at your school or college. Where this is not possible, with the cooperation of your school or college, the Further Mathematics Support Programme can help you, either by providing all of your Further Mathematics tuition, or by sharing the teaching with your school or college. Taking AS Further Mathematics in year 13 is an excellent option if you have decided during year 12 that you are going to apply to for a mathematics-rich degree course at university. It will really help you on your university degree course and will look very impressive on your university application form. If you are able to enrol in a Further Mathematics class at your school or college, but cannot access all of the options you would like to study, you could share your tuition between your school/college class and tuition through the FMSP. The flowchart below will help you to decide how best to access Further Mathematics tuition. Updated by CS 02/08/09 Quotes "It's been an excellent experience, introducing me to some more interesting mathematics, and making my regular Maths stronger."
Seat Lookup for math exams Using this form, you may look up seating assignement for upcoming exams from math classes such as Calculus 131 and 132. Please input your last name, the course number (e.g. 131,132), and the exam number (f for final).
Mathematica Mathematica is a program and computer language for use in mathematical applications. More information Mathematica can be used as a calculator with a much higher degree of precision than traditional calculators. Mathematica can perform operations on functions, manipulate algebraic formulas, and do calculus. Mathematica is also able to produce both two- and three-dimensional graphs.
Complete Idiot's Guide to Calculus (Complete Idiot's Guides) Synopses & Reviews Publisher Comments: According to figures released by ACT Inc., many more U.S. high school students are taking courses in mathematics than was the case a decade ago. In fact, the portion of college-bound students taking calculus increased from 16 percent in 1987 to 27 percent in 2000. Let's face it, most students and adults who take calculus do so not for the fun of it, but rather to advance within a job or fulfill a degree requirement. The Complete Idiot's Guide to Calculus will take the sting out of this complex math by putting its uses, functions and limitations in perspective of what is already familiar to readers-algebra. Once readers have brushed up on their algebra and trigonometry skills, they'll be eased into the fundamentals of calculus. Synopsis: Cast off the curse of calculus!About the Author W. Michael Kelley is a former award-winning calculus teacher and the author of The Complete Idiot's Guide to Calculus, The Complete Idiot's Guide to Precalculus, and The Complete Idiot's Guide to Algebra.
Electromagnetics Size: 1.14 MB Licence: Shareware Price: 40 USD Description: ElectPanageos Size: 0.67 MB Licence: Shareware Price: 35 USD Description: PanChemLab Size: 2.64 MB Licence: Shareware Price: 32.99 USD Description:MathProf Size: 9.82 MB Licence: Shareware Price: 45.00 USD Description: MathMechanics Size: 1.81 MB Licence: Shareware Price: 50 USD Description: MechanicsMathematics Saving Greendale Size: 10 MB Licence: Demo Price: 68 USD Description: An game that teaches mathematics whilst being fun and rewarding. The interactive content of the computer game teaches the student to really see how mathematic skills can help to solve daily problems and how it helps to play along in the game. The game mix the classic platform genre with interactive problems and practice sessions. The software contains simulations of a calculator, sketch pad, graphs and adds the ability to construct objects. RubricBuilder Size: 14.36 MB Licence: Shareware Price: 62.00 USD Description: The. Solving Triangles Size: MB Licence: Shareware Price: 15 USD Description: The program provides detailed, step-by-step solutions in a tutorial-like format to the problems of solving triangles in elementary geometry. The program is designed for high school students and teachers.
Graphing Calculators Replace PCs For Mathematics Instruction 04/01/97 Looking at the Texas Instruments TI-92 mathematics instructional tool, itís easy to see why both students and teachers like it so much. For students who grew up handling video game controllers , the unit fits comfortably in both hands, with a horizontal orientation that suits its 240 x 128-pixel display. It even has an eight-direction thumbpad like many video game controllers, complementing its full QWERTY keyboard, separate function keys and numeric keypad. For teachers, the TI-92ís functionality and versatility are just some of the reasons for its popularity. It handles a broad range of math from algebra through calculus including interactive geometry, symbolic manipulation, statistics and even 3D graphing. Best of all, the TI-92 has been priced with the notion of giving each student their own, powerful mathematics tool. Sounds great, right? But d'es it all come together in the classroom? Can this hand-held unit replace, or even supplement, traditional PC-based mathematics instruction? In answer to these very important questions, Kathy Longhart, mathematics teacher at Flathead High School in Kalispell, Montana, would give a resounding ìYes!î PCs vs. Calculators In 1992, while teaching a new curriculum that had been specifically written to take advantage of technology, Longhart and the teachers at Flathead High School tried using traditional computers in a lab-based setting to teach mathematics. However, this initial effort did not prove to be a very successful experiment. With four kids to a computer, each student had to share time and space, making sure the technologically adept or mathematically inclined didnít ìhogî the machine. The more reticent students would sit back and, while not participating, let those so inclined make good use of the lab time. And when class was over, the computers, with their math software, stayed put, while the students who needed them went home. Enter the TI-92. Now, Flathead High School has three classroom sets of these mathematics tools, which works out to about 80 or 90 calculators. Longhart uses them in all three of the mathematics classes she teaches, starting with her Math 2 class. ìThe TI-92 has a symbolic manipulator, data package, geometry package and graphing package in one unit, and I like to pick problems where we do a lot of moving between the packages,î she says. ìBy incorporating all of the packages, we can look at more powerful problems.î The calculator even has a two-graph mode for creating separate graphing environments, letting one compare different functions and graphs. Longhart mentions that the unit acts as a kind of ìelectronic chalkboard, where students can manipulate problems by hand.î They type problems into the calculator using its standard-style keyboard and keypad, and the calculator lets them do the same manipulations that they would do on paper, with one important difference: it lets them instantly see if they are correct. Instead of shuffling through a time-consuming calculation, marking up an entire page and finally realizing that a minor arithmetic mistake screwed up what was otherwise a correct procedure, the calculator simply d'esnít make these kinds of errors, letting students concentrate on learning procedures and formulas rather than worrying about every arithmetic problem that needs to be solved. Students Vote with Own Money After getting used to the TI-92s, students actually ask Longhart to go get them, she says. "At first, my Math 2 class was a bit frustrated because I hadnít given them enough guidance," she admits. But after showing them how helpful the calculators could be, her students had a change of heart. About 40 or 50 students have even purchased their own TI-92, which speaks spades about the students' opinions of the calculator. For those who donít have their own, the school lets them check out calculators to take home for homework. "I love [the TI-92], I think it's great. It's easy to learn, very user-friendly," mentions Longhart. "You don't get bogged down teaching a machine, you can focus on teaching math."
Designed to help Advanced Placement students succeed in their studies and achieve a '5' on the AP Exam, AP Achiever for European History provides: A thorough explanation of course expectations, exam parameters, preparation suggestions, as well as comprehensive tips on writing essays for the document-based and free-response section of the Exam, all to help your students maximize studies and time. Each chapter includes a thorough ... Glencoe Pre-Algebra is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation. We learn often in life, but only once as a child. This popular book will help future teachers make the most of this special time. Here is complete coverage of how children learn, what they can learn, and how to teach them. The focus is on creating a child-centered curriculum that addresses children's needs in all developmental areas—physical, social, emotional, creative, and cognitive. The authors provide a wealth of meaningful teaching ... Six-Way Paragraphs , a three-level series, teaches the basic skills necessary for reading factual material through the use of the following six types of questions: subject matter, main idea, supporting details, conclusions, clarifying devices, and vocabulary in context. THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! Glencoe Pre-Algebra is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments. Chemistry: Matter and Change is a comprehensive chemistry course of study, designed to for a first year high school chemistry curriculum. The program incorporates features for strong math-skill development. The Princeton Review has review and authenticated all in-text assessment items to validate them to be unbiased. Applying AutoCAD 2008 introduces new features and enhancements to existing capabilities. What's New in 2008? * A new default workspace called 2D Drafting & Annotation has been added. * The new 2D Drafting and Annotation workspace employs a new Dashboard containing panels and toolbars for drawing and dimensioning in two dimensions, while new panels and features improve the Dashboard for the 3D Modeling workspace. * New dimensioning ...
Calculus AB is designed to be taught over a full high school academic year. Calculus AB can be covered within a year even while spending some time on elementary functions. Adequate preparation for Calculus AB, however, requires dedicated time on topics in differential and integral calculus. AP exams lay special emphasis on these topics. Calculus BC is designed to be offered by schools that are able to complete all the prerequisites before the course. Calculus BC spans one full year in the calculus of functions of a single variable. The course content for Calculus BC has certain additional topics apart from the same for Calculus AB. Prerequisites (for both Calculus AB and Calculus BC) algebra geometry trigonometry analytic geometry elementary functions properties of functions algebra of functions graphs of functions Before studying calculus, all students must complete four years of secondary mathematics designed for college-bound students in topics such as: Topics covered in Calculus AB and Calculus BC Functions, Graphs, and Limits Derivatives Integrals Polynomial Approximations and Series For detailed description of course content under each topic,Click Here. AP Calculus Exam Pattern (AP Calculus AB and AP Calculus BC) Each exam runs 3 hours and 15 minutes and covers topics typically included in about two-thirds of a full-year college level Calculus sequence (Calculus AB) or those included in a full-year, college-level calculus sequence (Calculus BC). Students taking Calculus BC will receive a sub-score grade for the AB portion of the exam in addition to the overall composite grade. Both AP Calculus courses require a similar depth of understanding of common topics, and graphing-calculator use is an integral part of the courses. Both exams contain: 1 hour and 45 minutes of multiple-choice questions that tests proficiency on a wide variety of topics. 1 hour and 30 minutes of free-response questions that allows the students to demonstrate their ability to solve problems using an extended chain of reasoning. Both the multiple-choice and free-response sections contain sections where a graphing calculator is required and parts where calculator use is prohibited. List of AP approved graphing calculators can be seen on collegeboard.com. Section I - Multiple-Choice: This section has two parts - Part A - 55 minutes - 28 questions without calculator Part B - 50 minutes - 17 questions using a graphic calculator Random guessing can hurt the final score of student. While there is nothing to lose for leaving a question blank but one quarter of a point is subtracted for each incorrect answer on the test. Section II - Free Response: This section also has two parts - Part A - 45 minutes - 3 questions using a graphic calculator Part B - 45 minutes - 3 questions without calculator During Part B, one is permitted to continue work on problems in Part A but use of calculators is prohibited during this time. Scoring Scheme: AP Calculus Each section (Multiple choice & free response) accounts for one-half of the final exam grade. It is not expected that all questions will be answered to, since there is full coverage of the subject matter. TransWebTutors.com provides the students an excellent platform to learn about function theory using various existing mathematical techniques and graphing calculator, the rules of differentiation and their applicability, integration techniques their applications. We customize the package based on your availability and performance in the diagnostic test. TransWebTutors.com provides online tutors who are experts in analyzing the student's strengths and weaknesses, and thus design the package so that students can master every section. AP Calculus AB Packages * Fast Track Course for 30 hrs (Price : $ 299) Exhaustive Course for 60 hrs (Price : $ 599) Fast Track Course The duration for this course is 30 hrs. Intensive coverage of each section is carried out. Free Diagnostic test Free Discussion based on the diagnostic test and choosing strong and weak area's 1.0hour Functions, Graphs & Limits Analysis of Graphs 1.0 hour Functions, Graphs & Limits Limits of Functions (incl. one-sided limits) 1.0 hour Functions, Graphs & Limits Asymptotic and Unbounded Behavior 1.0 hour Functions, Graphs & Limits Continuity as a Property of Functions 2.0 hour Derivatives Concept of the Derivative 1.0 hour Derivatives Derivative at a point 2.0 hour Derivatives Derivative as a Function 2.0 hour Derivatives Second Derivatives 2.0 hour Derivatives Applications of Derivatives 2.0 hour Derivatives Computation of Derivatives 2.0 hour Integrals Interpretations and Properties of Definite Integrals 2.0 hour Integrals Applications of Integrals 2.0 hour Integrals Fundamental Theorem of Calculus 2.0 hour Integrals Techniques of Anti-differentiation 2.0 hour Integrals Applications of Anti-differentiation 2.0 hour Integrals Numerical Approximations to Definite Integrals 1.0 hour Full Course 1st Review after Differentiation 1.0 hour Full Course 2nd Review after Integration 1.0 hour Full Course Overall Review in the end Free Final Assessment test Free Detailed discussion on the attempt of AP Calculus AB Exam Exhaustive Course The duration for Exhaustive course for AP Calculus AB preparation in different topics is given below. Each topic and subtopic is exhaustively and comprehensively taught. Online tutoring was never a positive word for us; it always signified negative until it happened to our daughter Katherine who's in 10th grade. The service from TransWebTutors was so good and cheap that our connotation of online tutoring has changed completely now. Smith family My son was not doing well in his studies, particularly mathematics and science; I couldn't afford the $60-70 per hour online tuitions that were available in the market. I then came to learn about TransWebTutors offering online tutoring. I thought of giving it a try and today I am a happy and satisfied man. Mr. Bishop, father of an eighth grader at Chicago Katie was a good sportsperson, but she was not particularly good in her studies. She wanted to devote her evenings to her passion for sports and her school classes were not enough for her. She had started lagging in math but didn't want to part from her evening sports. Online classes with TransWebTutors late in the evening were what we could have asked for. Now she can pursue her passion along with her studies and it's easy on our pocket too! Ms. Rosemary, mother of Katie I love to see my daughter enjoying studies these days. Thanks to her online tutoring sessions with TransWebTutors which have now become even more affordable for me. She enjoys the new model which is flexible for her and economical for me. Nancy, mother of a fifth grader "Thanks to TransWebTutors, my sons can be flexible about their tutorial timings and I can be relaxed about my spending on their tutoring. It has even reduced the costs for me without compromising on the quality; I am a happy man now." Mr. Clark, father of two school going kids "I do not care if the teacher teaches my son online! As long as my son can understand and score good grades in his exams using the tuitions, I am least bothered. 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Welcome to Trimester 3 of the 2012-2013 school year. Just a few things to help you navigate my site. 1. There is a link to each subject matter that will have: A) The assignment list B) copy of the course syllabus. 2. Grades will be updated on "Infinite Campus" 3. Extra Help: I am available for extra help both before (except Wednesdays) and after school in room 161 or library (on some Thursdays). Students are welcome to stop by, but it is best for them to sign up on the "extra help" clipboard found in the back of the room. If I have meetings scheduled (listed on the "extra help" clipboard) I will not be available. Trigonometry The major topics covered in this course are Right Triangle and Non-Right Triangle Trigonometry, Unit Circle Trigonometry, Graphing of Trigonometric Functions, Trigonometric Identities, and Solving Trigonometric Equations. Other skills emphasized include improving arithmetic skills, algebraic manipulation, solving equations without calculators. The textbook used is, Algebra and Trigonometry for College Readiness: Lial, Hornsby (Addison Wesley Publication). The replacement cost for a lost book is $100.00. TEST/QUIZ DATES (may be subject to change depending on progression of the classes) March 26: Quiz 1 (rt triangles trig and convert D-M-S to deceimal form and visa-versa Course designed to better prepare students for College Algebra or Precaclulus. The major topics covered in this course are graphs of parent functions and their transformations; sequence and series; factoring methods; linear, quadratic, exponential, logarithmic, polynomial, rational and radical functions.Other skills emphasized include improving arithmetic skills, algebraic manipulation, solving equations without calculators. Test(s)/Quiz Date: (may be subject to change depending on progression of the classes) The course content includes algebraic, exponential, logarithmic, trigonometric, and polar equations and their graphs, analytic geometry and trigonometry, as well as matrices and determinants. This course is a college preparation course. Success in college level mathematics begins with a good understanding of algebra and trigonometry. The goal of this course is to help students gain that understanding. The text we will be using is Precalculus, 6th Edition, Larson/Hostetler: Houghton Mifflin 2004. (Replacement cost is $85.00) Please see attached syllabus for materials needed, classroom procedures, grading policies, and extra help availability. TEST/QUIZ DATES (may be subject to change depending on progression of the classes)
Fill out this form to do the assignments or see your scores. Login Course: First Name:Last Name:Student ID: Email address on record at the beginning of the term: Assignment Schedule General Instructions for Assignments Your browser must be configured to accept cookies, to allow pop-up windows and, to use JavaScript. Generally, it is a good idea to set up your browser to verify each document every time it is loaded, rather than to use a cached copy. That will ensure that you have the most up-to-date version of every assignment. SticiGui assignments combine forms, instructions, and interactive tools to reinforce the material presented in the chapters and to assess your understanding. The assignments use two frames. The upper frame has the instructions and a form for your responses; the bottom frame has tools you might need to solve the problems, such as graphs, calculators, etc. To access the assignments, you must provide the following identifying information: last name, first name, student ID, email address. At the bottom of the instruction frame, after all the questions, there are three buttons: one to submit the assignment for grading, one to save your intermediate results on your computer, and one to clear the answer form. You must click the submit button to send your answers to be graded. After you click the submit button, you must click another button to confirm that you really want to submit your answers for grading. Click the "OK" button once only—if you double-click, it will submit your answers twice and you will lose one of your chances to submit the assignment. The window that contained the problem set will show a confirmation screen (from AutoGrader) giving your score and telling you how many times you have submitted the problem set so far. It might take up to 30 seconds for the confirmation screen to appear, depending on web and server traffic. Be patient. If you get the confirmation screen, the server definitely received your submission. You can also see your scores by clicking the "My Scores on Past Assignments" button near the top of this page, just below where you type in your login information. If you open the problem set after the due date, there will be no "submit" button. To see your grades, you need to enter your name, email address, and SID, to protect your privacy. Click the button just under the assignment list, near the top of this page. Also, if you go back to the assignment after the due date, you can see the correct answers to your unique version of the assignment. Many of the questions and data in assignments have a random component. Different students get different questions and different data. You are graded based on the questions and data you receive. Differences in question wording can be subtle: If you work with other students, be sure to answer your version of the question. You can save intermediate results on the assignment using a button at the bottom of the instruction page—sort of. The assignments also save themselves as a cookie on your computer when you submit them. Because the cookie is stored on your computer, you cannot access the answers from a different computer (or even a different browser on your computer). Warning: Cookies are volatile, not reliable. Some events will cause or require your cookies to be deleted. And they "expire" after a few days. Always write down your answers on paper in case the cookie is deleted. You've been warned. You can use different computers for different assignments. After filling out the identifying information at the top of this page to access the assignments, your browser will look for a cookie with a record of your previous work on the assignment on your computer. If it finds a cookie, the assignment will fill in your previous answers. That is the last thing that happens when the assignment loads. Be patient. Do not scroll, click or type while the assignment page is still loading. If the computers does not find a cookie, the answer fields will be blank. Questions with multiple-choice answers. There are two types of questions with multiple-choice answers. The first kind allows you to select only one response. The second kind asks you to "select all that apply." How to select more than one answer depends on the computer operating system and browser. In Firefox on unix and linux systems, click each answer you want to select; clicking an answer again de-selects it. On Windows systems, hold down the control (ctrl) key while clicking each response to select more than one. On Macintosh systems, hold down the "command" key while you click to select multiple responses. In such "multiple-multiple-choice" questions, if you select an answer that is not correct, or fail to select one that is correct, you will not receive credit—there is no partial credit. Numerical answers. The grader strips commas from numbers, so you are free to punctuate numerical responses. If your response includes a percent sign at the end, your numerical answer will be converted to a percentage (divided by 100). Scientific notation (e.g., 4.23e-7 as shorthand for 0.000000423) will work; do not put a space between the digits and the letter "e." Questions that do not have an exact numerical answer accept a small range of answers as correct. The precision required depends on the problem statement. When in doubt, don't round off your final answer. In this class, there is no such thing as an answer that is "too precise." Never round off intermediate calculations. The chapter exercises accept arithmetic expressions as answers, but these submitted homework assignments, graded by the server, do not. For instance, if the answer is supposed to be 50%, the SticiGui in-chapter exercises will accept 50%, 0.5, 1/2, 50/100, 1/sqrt(4), etc., as correct. But the homework assignments—the problems you access through this login page—will only accept 50% or 0.5. The server will count 50/100 or 1/sqrt(4) as wrong answers. Troubleshooting Most technical problems with the online book and assignments have one of three causes: Scrolling, clicking or typing before the assignment page is fully loaded. Be sure to wait until the page has loaded completely before you do anything. The cursor should be normal, no hourglass or spinning wheel. The status bar should have a message like "done" or "loaded." If you can't log in, be sure you selected your course from the drop-down menu. If the server says you have submitted the assignment more times than you remember submitting it, you might have double-clicked the "OK" button. The server cannot mis-count the number of times you submitted the assignment. If, when you try to access the problem sets, you get an error message that starts like this, delete the cookies (see below): Bad Request Your browser sent a request that this server could not understand. Size of a request header field exceeds server limit. Cookie: 0x.... Cookies Cookies are small text files stored on your computer. SticiGui uses cookies to store your answers to assignments to homework assignments on your computer and to remember your student ID when you log in to do an assignment or check your scores. Cookies are not reliable: many things will cause them to be deleted or require them to be deleted. 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Course Descriptions Mathematics Course Listings - Fall 2012 MATH 118 Mathematics for Elementary and Middle School Teachers (4 credits) Post, Regina Prerequisite: Math Placement Level 22 or higher Study of number systems, number theory, patterns, functions, measurement, algebra, logic, probability, and statistics with a special emphasis on the processes of mathematics: problem solving, reasoning and proof, communicating mathematically, and making connections within mathematics and between mathematics and other disciplines. Open only to students intending to major in education. Every year. Mathematical-reasoning intensive. Prerequisite: MATH 118 Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry with a special emphasis on the processes of mathematics: problem solving, reasoning and proof, communicating mathematically, and making connections among mathematical ideas, real-world experiences, and other disciplines. Includes computer lab experiences using Geometer's Sketchpad. Open only to students majoring in education. Every year. Mathematical-reasoning intensive. Prerequisite: Math Placement Level 24 or higher This is a standard pre-calculus (4 credits) Shelburne, Brian Prerequisites: Math Placement Level 23 or higher A study of statistics as the science of using data to glean insight into real-world problems. Includes principles andMATH 131 Essentials of Calculus (4 credits) Shelburne, Brian Prerequisite: MATH 120 or Math Placement Level 25 1 171 Discrete Mathematical Structures (4 credits) Burke, Kyle Prerequisite: Math Placement Level 25, the course will cover relations and functions, counting arguments, discrete probability, number theory and graph theory. The course is required for the major in computer science and can be used as an elective for the computer science minor. The course grade will be determined by quizzes, graded homework assignments, in-class tests and a comprehensive final. Mathematical-reasoning intensive. MATH 201 Calculus I (4 credits) Parker, Adam and Stickney, Alan Prerequisite: MATH 120 or Math Placement Level 25 in mathematics, computer science (B.S.), physics, or chemistry, or minoring in mathematics. MATH 201 and MATH 202 can also count as supporting science "Essentials of Calculus". Talk with your advisor or with any math professor for advice on which calculus course is most appropriate for you. Students (4 credits) Sancier-Barbosa, Flavia Prerequisite: MATH 201 This is the second course in Wittenberg's three semester calculus sequence. MATH 202 is primarily concerned with integration and power series representations of functions. Topics covered include indefinite and definite integrals, the Fundamental Theorem of Calculus, integration techniques, approximations of definite integrals, improper integrals, applications of integrals, power series, Taylor series will be based on quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive. MATH 205 Applied Matrix Algebra (4 credits-The final grade in this course is based on quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive. MATH 227 Data Analysis (4 credits) Andrews, Douglas Prerequisite: MATH 131 or MATH 201 This introductory statistics course is designed not only for students majoring or minoring in math, but for any student who would benefit from a more substantial introduction to the field - especially prospective teachers of mathematics or statistics, as well as students considering careers as statisticians or actuaries. Students will learn general principles and techniques for summarizing and organizing data effectively, and will explore the connections between how the data was collected and the scope of conclusions that can be drawn from the data. Also emphasized are the logic and techniques of formal statistical inference, with greater focus on the mathematical underpinnings of these basic statistical procedures than is found in other introductory statistics courses. Software for probability and data analysis is used daily. Note: A student may not receive credit for more than one of the following: MATH 127, MATH 227, PSYC 107, or MGT 210. Mathematical-reasoning intensive. MATH 228 Univariate Probability (4 credits) Andrews, Douglas Prerequisite: MATH 131 or MATH 202 Probability is the branch of math in which we study randomness and quantify uncertainty. This course introduces some of the theory and applications of probability for a single variable. Topics include combinatorics, probability axioms, discrete and continuous random variables. This material constitutes one third of the first actuarial exam. Anyone interested in pursuing actuarial science or statistics should certainly take this course, and it would be a great elective for any math major or minor. Mathematical-reasoning intensive. MATH 360 Linear Algebra (4 credits) Stickney, Alan C. Prerequisites: MATH 205 and MATH 210 Introduction to abstract vector spaces. Topics include Euclidean spaces, function spaces, linear systems, linear independence and basis, linear transformations and their matrices. Students are required to have a TI-83, TI-84, or TI-86 graphing calculator for use in class, for homework, and on tests. A TI-89, TI-92, or Voyage 200 is also acceptable. The final grade in the course is based on written assignments, quizzes, tests, and a comprehensive final exam. Writing intensive. Mathematical-reasoning intensive. MATH 370 Real Analysis (4 credits) Parker, Adam Prerequisite: MATH 210 Through a rigorous approach to the usual topics of one-dimensional calculus - limits, continuity, differentiation, integration, and infinite series - this course offers a deeper understanding of the ideas encountered in calculus. The course has two important goals for its students: the development of an accurate intuitive feeling for analysis and of skill at proving theorems in this area. The final grade in this course is based upon written assignments, tests, and a comprehensive final exam. Writing intensive. Mathematical-reasoning intensive. MATH 460 Senior Seminar (2 credits) Shelburne, Brian Prerequisite: Senior math major or permission of instructor This is a capstone course for mathematics majors. Its purpose is to let participants think about and reflect on what mathematics is and to tie together their years of studying mathematics at Wittenberg. The structure of the course will be taken from the book Journey Through Genius by W. Dunham which covers the story of mathematics from the 5th century B.C.E. up to the 20th century C.E. by looking at some of the famous problems, theorems, and "colorful" mathematical characters who worked on them. The course is a seminar where participants are expected to research areas of interest in mathematics and present their findings to the rest of the seminar. The grade will be based on class discussions and presentations. Mathematical-reasoning intensive.
This Algebra Essentials Practice Workbook with Answers provides ample practice for developing fluency in very fundamental algebra skills - in particular, how to solve standard equations for one or more unknowns. These algebra 1 practice exercises are relevant for students of all levels - from grade 7 thru college algebra. With no pictures, this workbook is geared strictly toward learning the material and developing fluency through practice. This workbook is conveniently divided up into seven chapters so that students can focus on one algebraic method at a time. Skills include solving linear equations with a single unknown (with a separate chapter dedicated toward fractional coefficients), factoring quadratic equations, using the quadratic formula, cross multiplying, and solving systems of linear equations. Not intended to serve as a comprehensive review of algebra, this workbook is instead geared toward the most essential algebra skills. Each section begins with a few pages of instructions for how to solve the equations followed by a few examples. These examples should serve as a useful guide until students are able to solve the problems independently. Answers to exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes. The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient for parents/teachers who have multiple children/students or if a child/student needs additional practice. An introduction describes how parents and teachers can help students make the most of this workbook. Students are encouraged to time and score each page. In this way, they can try to have fun improving on their records, which can help lend them confidence in their math skills. Customer Reviews: just what i needed. By Daniel - January 15, 2012 Was into advanced math in early college and high school but got out of it further in degree. I'm going back to school now and this book helped me prepare for an intermediate algebra course. It's foundation learning in which each section builds upon previous sections. Instructions are also very clear. Plan on many hours of work. Also to note, the author allows use of problems for students, such as if one were a math teacher needing extra equations for assignments. problems By Anne - November 3, 2010 Having been a high school math teacher since 1972, I believe in homework and lots of examples and samples, but this book has way too many of only a few problems. If I had seen it in a store, I would not have bought it. I will use it, but only a page or two at a time. I do NOT recommend it for parents who do not know algebra. Algebra workbook By Duane Drake - December 8, 2012 This is used as part of a homeschooling algebra course for our ninth grader. The algebra problems have been great. The only drawback is that the problems aren't numbered on the pages or on the answer key & so it's a little bit if a challenge trying to decipher what each answer is. Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of creative applications and thoroughly integrating the graphing calculator. Written in a ...
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Understandable Statistics (Hardcover) 9780618949922 ISBN: 0618949925 Edition: 9 Publisher: Houghton Mifflin Company Summary: This algebra based text is a thorough yet approachable statistics guide for students. The new edition addresses the growing importance of developing students' critical thinking and statistical literacy skills with the introduction of new features and exercises.
Almost all adults suffer a little math anxiety, especially when it comes to everyday problems they think they should be able to figure out in their heads. Want to figure the six percent sales tax on a $34.50 item? A 15 percent tip for a $13.75 check? The carpeting needed for a 12½-by-17-foot room? No one learns how to do these mental calculations in school, where the emphasis is on paper-and-pencil techniques. With no math background required and no long list of rules to memorize, this book teaches average adults how to simplify their math problems, provides ample real-life practice problems and solutions, and gives grown-ups the necessary background in basic arithmetic to handle everyday problems quickly. This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems. "An understanding of the relationship between the product and the process in election polling is often lost. This edited volume unites ideas and researchers, with quality playing the central role." --J. Michael Brick, PhD, Director of the Survey Methods Unit, Westat, Inc. Elections and Exit Polling is a truly unique examination of the specialized surveys that are currently used to track and collect data on elections and voter preferences. Employing modern research from the past decade and a series of interviews with famed American pollster Warren Mitofsky (1934-2006), this volume provides a relevant and groundbreaking look at the key statistical techniques and survey methods for measuring voter preferences worldwide. Drawing on the most current studies on pre-election and exit polling, this book outlines improvements that have developed in recent years and the results of their implementation. Coverage begins with an introduction to exit polling and a basic overview of its history, structure, limitations, and applications. Subsequent chapters focus on the use of exit polling in the United States election cycles from 2000-2006 and the problems that were encountered by both pollsters and the everyday voter, such as how to validate official vote count, confidentiality, new voting methods, and continuing data quality concerns. The text goes on to explore the presence of these issues in international politics, with examples and case studies of elections from Europe, Asia, and the Middle East. Finally, looking to the upcoming 2008 U.S. presidential election, the discussion concludes with predictions and recommendations on how to gather more accurate and timely polling data. Research papers from over fifty eminent practitioners in the fields of political science and survey methods are presented alongside excerpts from the editors' own interviews with Mitofsky. The editors also incorporate their own reflections throughout and conclude eaNew probabilistic model, new results in probability theoryOriginal applications in computer scienceApplications in mathematical physicsApplications in finance use back cover copy A 'down-to-earth' introduction to the growing field of modern mathematical biology Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra The 11th International Workshop on Dynamics and Control brought together scientists and engineers from diverse fields and gave them a venue to develop a greater understanding of this discipline and how it relates to many areas in science, engineering, economics, and biology. The event gave researchers an opportunity to investigate ideas and techniques from outside their own fields of expertise, enabling a cross-pollination of dynamics and control perspectives. Now there is a book that documents the major presentations of the workshop, providing a foundation for further research. The range and diversity of papers in Dynamical Systems and Control demonstrate the remarkable reach of the subject. All of these contributed papers shed light on a multiplicity of physical, biological, and economic phenomena through lines of reasoning that originate and grow from this discipline. The editors divide the book into three parts. The first covers fundamental advances in dynamics, dynamical systems, and control. These papers represent ideas that can be applied to several areas of interest. The second part deals with new and innovative techniques and their application to a variety of interesting problems, from the control of cars and robots, to the dynamics of ships and suspension bridges, and the determination of optimal spacecraft trajectories. The third section relates to social, economic, and biological issues. It reveals the wealth of understanding that can be obtained through a dynamics and control approach to issues such as epidemics, economic games, neo-cortical synchronization, and human posture control. This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the Écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated.Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field. This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stability. Of paramount importance in their own right, the results presented also offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results in this monograph are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications. Each chapter contains a section of open problems and conjectures that will stimulate further research interest in working towards a complete understanding of the dynamics of the equation and its functional generalizations-many of them ideal for research projects or Ph.D. theses. Clear, simple, and direct exposition combined with thoughtful uniformity in the presentation make Dynamics of Second Order Rational Difference Equations valuable as an advanced undergraduate or a graduate-level text, a reference for researchers, and as a supplement to every textbook on difference equations at all levels of instruction. Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research. Engage students in grades K–1 and build their confidence using Early Graphing: Hidden Pictures. This 64-page resource teaches essential early graphing skills through hands-on activities using popular kindergarten and first-grade themes. Students work to reveal hidden pictures while practicing reading order, fine-motor skills, attention to detail, concentration, and color words. They take pride in the finished product and look forward to the next one lesson. The lessons are ideal for independent practice, centers, and homework. This book aligns with state, national, and Canadian provincial standards. Because elementary mathematics is vital to be able to properly design biological experiments and interpret their results. As a student of the life sciences you will only make your life harder by ignoring mathematics entirely. Equally, you do not want to spend your time struggling with complex mathematics that you will never use. This book is the perfect answer to your problems. Inside, it explains the necessary mathematics in easy-to-follow steps, introducing the basics and showing you how to apply these to biological situations. Easy Mathematics for Biologists covers the basic mathematical ideas of fractions, decimals and percentages, through ratio and proportion, exponents and logarithms, to straight line graphs, graphs that are not straight lines, and their transformation. Direct application of each of these leads to a clear understanding of biological calculations such as those involving concentrations and dilutions, changing units, pH, and linear and non-linear rates of reaction. Each chapter contains worked examples, and is followed by numerous problems, both pure and applied, that can be worked through in your own time. Answers to these can be found at the back. Though Economics as a discipline arose in Great Britain and France at the end of the eighteenth century, it has taken two centuries to reach the threshold of scientific rationality. Previously, intuition, opinions, and conviction enjoyed equal status in economic thought; theories were vague, often unverifiable. It is no wonder, then, that bad economic policies ravaged entire nations during the twentieth century. In Economics Does Not Lie, noted French journalist Guy Sorman examines the state of economic affairs today. Virtually everywhere, the public sector has given ground to privatization and market capitalism. The results have been breathtaking. Opening economies and promoting trade have helped reconstruct Eastern Europe after 1990 and lifted 800 million people out of poverty across the globe. Economics Does Not Lie reveals that behind all this unprecedented growth is not only the collapse of state socialism but also a scientific revolution in economics–one that is as of yet dimly understood by the public but increasingly embraced by policymakers around the globe. No longer does economics lie; no longer would Baudelaire be able to write that "economics is a horror." For the mass of mankind, on the contrary, economics has become a source of hope.—whether it is a Fortune 500 company, a small accounting firm or a vast government agency—This books holds the keys to success for systems administrators, information security and other IT department personnel who are charged with aiding the e-discovery process.Comprehensive resource for corporate technologists, records managers, consultants, and legal team members to the e-discovery process, with information unavailable anywhere elseOffers a detailed understanding of key industry trends, especially the Federal Rules of Civil Procedure, that are driving the adoption of e-discovery programsIncludes vital project management metrics to help monitor workflow, gauge costs and speed the processCompanion Website offers e-discovery tools, checklists, forms, workflow examples, and other tools to be used when Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology. Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics. Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion. Effective Experimentation is a practical book on how to design and analyse experiments. Each of the methods are introduced and illustrated through real world scenario drawn from industry or research. Formulae are kept to a minimum to enable the reader to concentrate on how to apply and understand the different methods presented.The book has been developed from courses run by Statistics for Industry Limited during which time more than 10,000 scientists and technologists have gained the knowledge and confidence to plan experiments successfully and to analyse their data. Each chapter starts with an example of a design obtained from the authors' experience. Statistical methods for analysing data are introduced, followed, where appropriate, by a discussion of the assumptions of the method and effectiveness and limitations of the design.The examples have been chosen from many industries including chemicals, oils, building materials, textiles, food, drink, lighting, water, pharmaceuticals, electronics, paint, toiletries and petfoods.This book is a valuable resource for researchers and industrial statisticians involved in designing experiments. Postgraduates studying statistics, engineering and mathematics will also find this book of interest.The EPUB format of this title may not be compatible for use on all handheld devices.
Linear algebra and abstract algebra simultaneously? Linear algebra and abstract algebra simultaneously? Is this a good idea (provided the university will allow it)? I'll be going into my sophomore year at my university. But I'm unfamiliar with exactly how much linear algebra an intro course in abstract algebra would require. In hindsight I probably should have taken linear last semester, but scheduling issues meant that I would have had to sacrifice a lot to do it. I'm interested in doing a major in pure math and maybe going to grad school, and thus I want to get involved with research as early as possible. For this reason I want to start taking advanced courses soon, and abstract felt like a good place to start. There are other math courses I could take instead, but most of them seem to require linear algebra, and the ones that don't either interfere with my schedule or are only offered spring semester. Since abstract algebra seems to build from fundamentals, it felt like a good option. Thoughts? I think you hit a key point with "provided the university will allow it". Why would you take the recommendations of a bunch of folks on the internet over those of the university? Courses in Linear vary from "a bag of computational tricks" all the way to "abstract lite". We can't tell how much rigor your particular university's version has, and we can't tell how much prior knowledge the abstract professor expects the students to walk in with. That's what prereqs and co-reqs are for. Taking them concurrently might work out, or you might get squashed like a bug.
The Bridge Designer is a web-based program that allows the user to design and analyze 2-Dimensional statically determinate trusses. The user can specify support types (fixed or rolling) and locations, as well as the locations of various truss nodes and members. This virtual laboratory, which accompanies the Johns Hopkins University course "500.101 What is Engineering?" uses JAVA interactive technology to offer students experiment-oriented problems via the WWW or CD-ROM. The objective of the course and the virtual laboratory is to introduce beginning science and engineering students to eCourses web portal is designed to assist both students and professors in basic engineering courses. The web site includes all instructional material to conduct a course and there is no cost to either the instructor or student. Features include eBook, database of homework/quiz/test problems, solutions to all problems, lectures in both Quicktime and Flash format, computer grading, and utilities. To help facilitate communications between students, instructors, and TAs there is an integrate web board and collaborative drawing board. Each web-based course is controlled and administered by the instructor. There are six complete engineering eBooks available directly without having to register or set up any class. The eBooks cover Statics, Dynamics, Thermodynamics, Fluids, Math, and Multimedia. The eBooks are also searchable using a Google-Mini for fast and accurate indexing. The NSDL was created by NSF to provide organized access to high quality resources and tools that support innovations in teaching and learning at all levels of science, technology, engineering, and mathematics (STEM) education. To futher our knowledge of science and engineering, we try to formulate mathematical models that quantify behaviors. We trust these models only when they predict observed behavior. Normally this requires the solution of the unknown quantities in our model when written in a system of equations. What is a vector? The answer may surprize you. But let's start with the simplest view of a vector. It is an arrow that records distance and direction. By stringing together a sequence of arrows we can provide detailed directions for a journey, or outline an object. It is the way we add arrows to produce a new arrow that really identifies what a vector is. We can incorporate this addition property to other quantities such as velocities, forces, and even functions. What quickly emerges is that it is the linear combination of vectors that allows great diversity in applications and provides deep understanding to the nature of solutions to linear problems. This module starts with the basic Description of vectors and then proceeds to elucidate their role in the Formation of systems of linear equations. The SOCR Database contains a number of datasets that may be used for demonstration purposes in probability and statistics education. There are two types of data - simulated (computer-generated using random sampling) and observed (research, observationally or experimentally acquired). The Probability and Statistics EBook is an internet-based electronic textbook. The materials, tools, and demonstrations presented in this EBook would be very useful for advanced-placement (AP) statistics educational curriculum. The EBook was initially developed by the UCLA Statistics Online Computational Resource (SOCR). However, all statistics instructors, researchers, and educators are encouraged to contribute to this project and improve the content of these learning materials. There are four novel features of this specific Statistics EBook: it is community-built; completely open-access (in terms of use and contributions); blends information technology, scientific techniques, and modern pedagogical concepts; and is multilingual. finite difference discretization and the stable upwind method.
MINOS: Steps Towards a Syntax-free Computer Algebra Program The idea of Mathematical Interface with Natural Object Syntax, or MINOS for short, was a product of the author's increasing concern about the shortcomings of leading symbolic calculus software, such as Maple or Mathematica, as a tool for instruction of mathematics. After running several Maple-assisted laboratories for calculus and algebra, first at University of California, Irvine, and then at Uppsala, he arrived at a viewpoint that no pedagogic effort can focus the freshman's attention away from the intricacies of the command syntax and back to the mathematical content, so there is an urgent need for a more user-friendly software package. Even regular users of Maple have difficulty remembering most of its commands accurately. Ask a mathematics teacher after the summer vacation what Maple command draws a circle as a curve t->(cos(t),sin(t)) and you will probably be told to look up the manual. It is not enough to replace the command line interface, like Derive does, by menus (that point to the same old commands) and uniform dialog boxes (for input of arguments of the commands). Although this protects the user from typing errors in the keywords and saves him from remembering the sequences of brackets, braces, commas, colons and semicolons that follow the keyword in the command line interfaces, the treatment of mathematical objects by the existent menu-dialog interfaces still imposes on the user a non-mathematical semantic environment. The author has also found that the record of computations in the form of a log also forces on the user non-mathematical semantics. Consider for example the two following lines: x = a+2 a = 3 For a mathematician they mean two equations that one is free to interpret as a system or as two separate statements. However, for a typical mathematical software package these lines represent two assignment operators, and after they are executed the variable x either contains the value 5 or resides in a state of "suspended evaluation" and yields 5 after one types in something like eval(x). Add another line, x = sin(x) and it becomes a recurrent assignment that makes x equal sin(5). We rest our case on a belief that computer aided instruction of mathematics should not put a first year student into this alien environment. This is not the opinion that most proponents of computer aided mathematics instruction hold today. The prevailing opinion says that the syntax of Maple or Mathematica is something a technical student has to learn anyway, that these programs are here to stay as a part of the new scientific and engineering culture, together with Emacs and TeX, and so the effort spent by a mathematics instructor on teaching the command syntax of Maple alongside mathematics is effort wisely spent. However, it has often happened that consensus lasts only as long as the current level of functionality is the best one available. Our objection to the existent high-end mathematical programs is restricted only to the first year or two of college instruction. After a couple of years most students become proficient enough in programming in general to master Mathematica or Maple as their fifth or so computer language, and may use them for projects in, say, differential equations or Fourier analysis. The underlying idea of MINOS is to take full advantage of object oriented programming and populate the screen with visual mathematical objects with robust behavior that matches the way a mathematician relates to a mathematical object. MINOS employs Microsoft's metaphor of a file system (the technical name is ListView ActiveX control), but it uses the standard 32x32 icons with a name box underneath, not for handling files, but for representation of mathematical variables, vectors, matrices, sequences and whatever else might be beneficial for a mathematician to see as a conceptional unit. Figure 1 shows a screenshot of MINOS (draft 009) with function f(x,y) = sin(x*y) and its two partial derivatives, calculated by pressing the differentiation button; one of the derivatives is plotted. Operations with visual objects (we tentatively call a MINOS object eidolon) are performed with a mouse, for example by highlighting the icons of arguments or by dragging one of them onto another. Each object type has its own context menu with the main operations specific to this object (a matrix should have a determinant on its menu) as well as a few common ones (delete, copy and paste). Plotting is one of the easiest accessible features of MINOS: marking a check-box near an eidolon results in an automatic plotting, whenever the eidolon has a graphic representation. Plot types can be changed and the range of arguments readjusted by self-explanatory buttons and boxes on the graphics window. Figure 2 shows an overlay of graphs for a function f(x) = x sin(x) and its derivative. Several functions dependent on the same variable can be graphed in the same axes merely by marking the check boxes. Figure 1. A screenshot of MINOS (draft 009) with function f(x,y) = sin(x*y) and its two partial derivatives, calculated by pressing the differentiation button; one of the derivatives is plotted Figure 2. An overlay of graphs for a function f(x) = x sin(x) and its derivative The main benefit of the new interface is a level of fluency - the student is now free from the concern of "how shall I do it?" and can better concentrate on the question "what does it mean?". Representation of the workspace as a log is abandoned: pedagogic research shows that the sequential approach to problems is inferior to the structural approach, and MINOS provides the latter. One enters the problem's data in the form of eidola, one creates other eidola with relations that seem relevant to the problem, and performs the calculations that output further eidola which can be stored in the same workspace. There is no chronological dependence between eidola: in our example above eidola x=a+2, a=3 and x=sin(x) coexist without affecting each other. One can substitute a=3 into x=a+2 by dragging one icon onto the other, and one has to decide oneself if x=sin(x) is to mean an equation or an iterative assignment. A finer tuning between the interface and the needs of instruction will still be needed: although the software is tested as it is written, most teachers prefer to evaluate only a completed work. MINOS is not meant to be a pedagogic solution by itself, only a better platform that allows teachers to develop more efficient laboratory sessions and project assignments. This organization requires that the user executes commands step-by-step, not as program code (for program writing we find Maple and Mathematica less objectionable). We found this limitation bearable, as very few instructors of calculus or linear algebra give programming assignments in the freshmen computer laboratory sessions. MINOS is expected to be used also as a presentation tool for mathematical lectures: it can be used dynamically to discuss students' spontaneous suggestions and examples, while existent programs are hard to use in class in a spontaneous manner - advance preparation is recommended. A tentative prototype of MINOS was developed at Uppsala in 1997-1998 with a small intramural grant from the Unit for Instructional Development. Its interface was employing MathEdge (a developer edition of Maple V, release 3) for all computational tasks. However, the program was aborted because of licensing problems: Waterloo Maple Software has discontinued MathEdge and never offered us a license that would allow us to use it on a regular basis in a laboratory, not to say, to distribute MINOS elsewhere. The project took an unpredictable turn: keeping the word "interface" in the name, we decided to rebuild MINOS completely as a program with its own computation engine. This was not without benefit, as instead of the string-exchange API (Application Program Interface) offered by Maple's computation engine, MINOS integrates data structures of its computation engine into the visual mathematical objects of the interface as interoperable COM objects. At this risky stage financing of the project switched to private sources. Since the fall of 1998 MINOS has been supported by a grant of SKR 700 000 from The Foundation for Knowledge and Competence Development (KKS) matching the equal amount of private investment. Under the terms of the sponsorship the first release of MINOS, the School Edition, due in February 2000, will be aimed at the high schools, covering the Swedish national curriculum for mathematics. The School Edition will be capable of algebraic manipulations of expressions, equation solving (mostly numerical, with symbolic solutions limited to equations used at school) integration and differentiation, vector algebra, a variety of 2D and 3D plotting modes, including animated plots, and elements of differential equations. At the same time, the School Edition of MINOS is being developed as a platform capable of supporting add-on programs that are necessary for the university courses of calculus and linear algebra. Under favourable circumstances a college edition of MINOS may be finished within months after the release of the School Edition. It is not unlikely that MINOS will be used on both sides of the school-college divide as well as in adult and distance education. Building in an "object mail" capability, so that several participants could collaborate on the same mathematical assignment via Internet, is a part of the MINOS project as well. The interface of MINOS has been tested with several groups of last year high school students. The following pattern has emerged: teachers opt for a five minutes introduction of the interface, and students need an average of fifteen minutes to handle MINOS with confidence (add-on libraries might need additional five minutes each). Students with time left eagerly engage in experimentation on their own and, when the teacher permitted, productively collaborated with each other on solving the problems. The testing at schools will continue in the fall 1999, and in 2000 we will begin testing MINOS in university instruction as well. Development versions of MINOS are available to educational institutions upon registration with Eidonome, the commercial arm of the MINOS project, without cost. The company's address is Upon receiving the password one can download the current MINOS distribution, a 5MB zip file over a fast connection (a modem connection, presumably from a residence, will be timed out). This arrangement remains in force until the beginning of the beta testing program in November. English and Swedish versions of MINOS are being developed and will be released simultaneously.
Programs Math resources for grades 9-12 Building Your Future Financial Literacy Curriculum Resource Grades 9-12 Help your students prepare for life on their own! The award-winning Building Your Future helps students easily grasp the essentials of personal finance, gives them multiple opportunities to practice core skills and showcases the real-world impact of the financial decisions they make Probability & Statistics: Modular Learning Exercises Grades 9-12 WEB VERSION NOW AVAILABLE! The Actuarial Foundation is proud to launch the web version of an excitingNEWcurriculum resource aimed at engaging accelerated math students while also introducing them to the core principles of probability and statistics. Students take on the role of an actuary as they help an insurance company estimate the risk of storm activity and calculate potentially costly damages.
A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices
Syllabus Calculators and computers You are free to use any scientific, non-graphing calculator for quizzes and exams. You may not use any graphing calculator. Many computer programs (such as Mathematica and MATLAB) can perform a wide variety of calculations. You may wish to use a program to check your homework, but you will still be expected to write out the steps involved in solving each problem.
books.google.co.uk - The Fundamental Theorem of Algebrastates that any complex polynomial must have a complex root. This basic result, whose first accepted proof was given by Gauss, lies really at the intersection of the theory of numbers and the theory of equations, and arises also in many other areas of mathematics. The... fundamental theorem of algebra
Commercial site with one free access per day. Students can vary a, h and k to explore the effects on the graph. An exploration guide is available to help guide the students through an acitivty. By cli... More: lessons, discussions, ratings, reviews,... Commercial site with one free access per day. Students are given a set of points and are asked to "zap" as many points as possible. They can use either polynomial form or vertex form. Students can ge... More: lessons, discussions, ratings, reviews,... This file describes an experimental setup (using a motion detector) in which a ball's distance from start is recorded as the ball rolls up then down an inclined plane. It includes a simulation applet... More: lessons, discussions, ratings, reviews,... Guided activities with the Graph Explorer applet, designed to let students learning about quadratic functions explore: the parabolic shape of the graphs of quadratic functions; how coefficients affect
Students find data on sunrise and sunset times for some locale over the course of a year, then graph the length of the day as a function of the day of the year. They are asked to find a trigonometric function that models the data and to comment on such characteristics as amplitude and period. Data from locales at other latitudes are also investigated. In the solution section, the graphs of the sine waves generated through these experiments are analyzed in detail. This problem is an open-ended assessment task from the Balanced Assessment in Mathematics Program at the Harvard Graduate School of Education. (author/th) Ohio Mathematics Academic Content Standards (2001) Patterns, Functions and Algebra Standard Benchmarks (11–12) A. Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. Grade Level Indicators (Grade 11) 4. Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology. Grade Level Indicators (Grade 12) 3. Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior. Principles and Standards for School Mathematics Algebra Standard Understand patterns, relations, and functions Expectations (9–12) understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;
Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on... The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the... more... A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics... more...
Microsoft Mathematics is a piece of software you might have never heard of, but can prove to be tremendously useful for your high school or college homework. It is not advanced as a full blown suite like Matlab, but is definitely a step up to the Windows Calculator if you find it inadequate for your needs and don't want to invest time to learn a new software. The screen looks like a typical graphing calculator and a worksheet window to the right. The various sets of functions spanning calculus, trigonometry, statistics, linear algebra etc. ensure that a number of problems can be easily solved. Microsoft had updated the software with the Ribbon interface in this fourth iteration. The options there allow you to easily switch between operations on real and complex numbers, radians and angles etc. Pen Input is also supported (but wasn't something I could test properly owing to the lack of tablet PC) A number of inbuilt tools make certain kinds of calculations easy to perform. The equation solver does exactly what it says. The formulas and equations drop down lets you work with some standard formulae of science, and lets you even plot them and see the variation with change in variables! The unit converter is pretty handy for converting values in different units in physics and engineering. The insert tab lets you quickly insert matrices for linear algebra, a number of variables, and data sets for easy manipulation. The graphing capabilities of the software are also impressive. Just switch from Worksheet mode to Graphing mode to get started. You can plot equations, data sets, inequalities and parametric equations. The most handy part is the graph control tool, which allows you to manipulate the graph variables. Graph display settings can be changed from the context-sensitive Format tab. The graph can also be exported as a picture. Microsoft Mathematics also has a Word and OneNote add-in to seamless integrate a lot of the features into the respective documents. Do you like this post? Mrinal Mohit is an engineering undergraduate. His interests revolve around robotics, photography, internet, gadgets and technology. He loves to share everything he comes across with others, and that's how he learns. Wow! this is really a great software for our own computer. I never knew about this before all I know is the Microsoft office can you please tell me where to download this software, this can be very useful specially teaching our child basic mathematics.
Store Maths Education Books Each book in the Lesson for Every Day series includes 190 creative activities for Literacy or Maths lessons, one for each day of the teaching year. They provide a comprehensive and balanced resource to support teaching all year round.Eager to develop embedded systems? These systems don't tolerate inefficiency, so you may need a more disciplined approach to programming. This easy-to-read book helps you cultivate a host of good development practices, based on classic software design patterns as well as new patterns unique to embedded programming. You not only learn system architecture, but also specific techniques for dealing with system constraints and manufacturing requirements. Written by an expert who's created embedded systems ranging from urban surveillance and DNA scanners to children's toys, Making Embedded Systems is ideal for intermediate and experienced programmers, no matter what platform you use. * Develop an architecture that makes your software robust and maintainable * Understand how to make your code smaller, your processor seem faster, and your system use less power * Learn how to explore sensors, motors, communications, and other I/O devices * Explore tasks that are complicated on embedded systems, such as updating the software and using fixed point math to implement complex algorithms Part of a series of books that match the AQA specifications for Maths A-level. This book has been produced in consultation with a Senior Examiner to ensure complete and authoritative coverage of the Statistics 2 module. It contains all the pure... This is a practical book. It shows you how to typeset your mathematics, from a simple equation to a complex mathematical treatise. As a reference book it contains a list of mathematical symbols, and covers a wide range of additional math packages... A good chef needs a firm grasp of basic math skills in order to cook well and achieve financial success. Ideal for students and working professionals, this book explains all the essential mathematical skills needed to run a successful...
A First Course in Discrete Mathematics Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules
Navigating Through Probability - With Cd - 03 edition Summary: This book helps students develop their probabilistic thinking by introducing them to the notion of sample space and the use of tree diagrams and geometric regions to represent sample spaces. Many activities present probability in the context of the fairness of games, a topic of great interest to middle-grades students. Notions of population samples, prediction over the long term, and the law of large numbers are reinforced through games and engaging problems. Edition/Copyright: 03 Cover: Paperback Publisher: National Council of Teachers of Mathematics Published: 01/28/2003 2003 Paperback Still in original package4.71
Synopsis Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics. The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world. At the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics. In a concise and easy-to-read style, each chapter of this book introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion website includes interactive Excel spreadsheet examples and templates. This comprehensive resource covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing. Widely used risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing are also explored. A chapter on time series analysis introduces interest rate modeling, GARCH, and jump-diffusion models. Bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics are covered as well. If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no
Specification Aims To discuss the basic ideas associated to simple polytopes in all dimensions, To explain the context and applications of toroidal symmetry in topology and geometry, To explore the relationship between 1) and 2), To introduce students to a subject which is currently under rapid development. Brief Description of the unit Problems connected with torus actions arise in different areas of mathematics and mathematical physics. So the theory is always fashionable, and is a constant source of novel applications; it also regularly contributes new ideas to topology. The course is intended as a systematic but elementary introduction to toric topology, with emphasis on the more accessible aspects related to discrete mathematics.
South Gibsonalgebra courses introduce students to mathematical concepts beyond that of basic arithmetic. Students first learn about integers, exponents and equations in a pre-algebra course. While most people find they do not need the concepts learned in higher math courses such as calculus, the concepts taught in pre-algebra are used in everyday life
The student calculator graphically displays many of the standard mathematical formulae and has the ability to edit graphically, lines, circles, triangles and many other standard images, thus providing an insight into the basic structure of mathematic formulae. The student calculator has hundreds of science, astronomy, physics data and mathematical formulae built in and can be easily accessed and used in calculations. No longer do you have to search the text books for that common formula or data. The student calculator has built in conversion tool facilities, ideal for engineering and physics projects. Double click on the dowloaded file to let windows install the full version calculator for you. Dovada student calculatorMaTris is a nice program for practicing the basic operations of arithmetic. The calculation method is preselectable. It includes simple counting exercises, addition with symbols, addition/subtraction, multiplication and division.
of Use of Mathematics Introduction The course is suitable for students who attained a grade D or lower at GCSE in their secondary school. It provides an ideal opportunity for students to improve their mathematical skills. The course has an emphasis on the everyday application of mathematics. It consists of two Free Standing Mathematics Qualifications (FSMQs) in Money Management and Using Data, as well as a broader Core unit. Further Details This is an alternative to the GCSE Mathematics re-sit course and, with its emphasis on using mathematics in real life, enables students to develop skills that are highly regarded by employers. Progression Options Successful students would be able to attempt the GCSE Mathematics course. Additional Info Qualification:AQA Certificate of Use of Mathematics and FSMQ Entry Requirements:College entry requirements including Grade C or better at English GCSE. Duration:1 year Assesment:The course is taught and assessed in 3 modules with each being assessed by a written calculator exam taken in June. Each examination is based on some pre-release material.
We think the best approach is to buy the best calculator for the long haul – the one that will get you all the way through high school math and science as well as the ACT and/or SAT and into your college math and science courses. Therefore, we recommend a good graphing calculator - such as the TI-83 Plus (made by Texas Instruments) or better. (We are referring to the TI series since they are the most popular calculator at this level. Other companies such as Casio and Hewlett- Packard also make excellent calculators.) Need even more? Calculators for high school and college math come in three major varieties. Scientific calculators have the basic functions used for algebra and trigonometry. They work well for many students and are cheap ($5-$20). The TI-30 series is a good example. However, courses such as trigonometry, algebra II, and calculus often require graphing functions. So we recommend scientific calculators for algebra 1 only. Graphing calculators allow the student to graph equations. The graphing element is powerful since an understanding of what math equations look like graphically can be crucial to understanding the topic of math. Also graphical approaches top math problems can be useful to get a quick answer without having to do a bunch of grueling math, which may be critical for the SAT and ACT exams where you have one minute to answer. The TI-83, TI-84, and TI-89 series are all graphical calculators. Prices are usually in the $90 to $150 range. Computer Algebraic Systems (CAS) calculators provide the ability to graph AND the ability to actually solve algebraic (and often calculus) equations. These calculators are very powerful – and as such are NOT allowed on the ACT. (CAS calculators are allowed on the SAT!) CAS calculators provide all the tools needed for the most high powered math courses – including college calculus and engineering. The TI-89 series is perhaps the most popular of these (and my pick) with prices in the $150+ range. Other hints!!!! Most students do not know how to use 1/10 of the power in their calculator. I encourage them to get out the manual and play with it. See what it will do. Then keep the manual handy for reference. When you get to the ACT and SAT use all the power you have at your disposal. The exams allow them – so use them to your advantage.
Aimed at students requiring a fundamental introduction to mathematical analysis, this text is suitable for self-study and covers key topics from convergence to the Riemann integral. Exercises, illustrations and examples throughout bring the subjects alive. Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites. Real Number System.- Sequences: Convergence and Divergence.- Limits, Continuity, and Differentiability.- Applications of Differentiability.- Series: Convergence and Divergence.- Definite and Indefinite Integrals.- Improper Integrals and Applications of Riemann Integrals.- Power Series.- Uniform Convergence of Sequences of Functions.- Fourier Series and Applications.- Functions of Bounded Variation and Riemann-Stieltjes Integrals.- References.- Index of Special Notations.- Hints for Selected Questions and Exercises.- Index. From the reviews: "The book is intended for undergraduate students and beginning graduate students of mathematics. It can be used in the classroom or as a self-study guide. ... The text is organized in a classical way, each section is followed by a set of questions that stimulate the reader to think about the deeper nature of definitions or the background of theorems and exercises, which vary from routine to simple proofs." (Vladimir Janis, Zentralblatt MATH, Vol. 1236, 2012)
4-color hardback text w/complete text-specific instructor and student print/media supplement package AMATYC/NCTM Standards of Content and Pedagogy integrated in Exercise Sets, Sourced-Data Applications (students are also asked to generate and interpret data), Scientific and Graphing Calculator Explorations Boxes, Mental Math exercises, Conceptual and Writing exercises, geometric concepts, Group Activities, Chapter Highlights, Chapter Reviews, Chapter Tests, and Cumulative Reviews 6 step Problem-Solving Approach introduced in Chapter 2 and reinforced throughout the text in applications and exercises helps students tackle a wide range of problems Early and intuitive introduction to the concept of graphing reinforced with bar charts, line graphs, calculator screens, application illustrations and exercise sets. Emphasis on the notion of paired data in Chapters 1 and 2 leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 3. Graphing and concepts of graphing linear equations such as slope and intercepts reinforced through exercise sets in subsequent chapters, preparing students for equations of lines in Chapter 7
Finished the exercise we had started in class. Showed how this problem related to the take home questions. Day 55: Monday, 4/29 Covered section 11.4 - and demonstrated the earlier sections by going through an example very thoroughly using the programs on the graphing calculator: Slopes, Euler, and Euler2. Day 54: Friday, 4/26 Covered section 11.2 and 11.3. Discussed the principles behind Euler's method, and showed how to use it with a particular differential equation. Day 53: Thursday, 4/25 Worked in lab on Slope Fields. Had emailed students a mathematica file that had the command lines that would allow them to define a particular differential equation, create the general solutions to the DE, create a slope field, and then create solution curves superimposed on the slope field. Day 52: Wednesday, 4/24 Began chapter 11. Discussed what a Differential Equation was, and how we could test to see if a specific function was a solution to a differential equation. Finished section 8.2 - Did a problem of building a set of semicircles on a particular region, and finding the volume of that solid. Also developed the concept of arc length - developing the formula with the class - and then applying the formula for a specific exercise. Continued work on section 8.2. Did another exercise involving washers - revolving around a horizontal line. Day 49: Thursday, 4/18 Had students complete the Survey of Teaching forms at the beginning of class. Students worked on Graded Work 6 in the lab. Extended the due date for Graded Work 6 until Monday, 4/22. Day 48: Wednesday, 4/17 Began section 8.2. Worked on several examples, showing how to find volumes of solids of revolution by the disk method. Began one problem that involved a washer. Will complete that problem on Friday, as well as begin the problems dealing with arc length. Handed out Graded Work 6. Students should be working on this material during class time while I am away. Students spent the remainder of the class working on the quiz. Day 43: Monday, 4/8 Discussed section 10.2 and 10.3 more, showing a demonstration on mathematica that helped us see the error in the TP approximation compared to the function value. Showed how to determine if a Taylor Series converges or diverges by using the ratio test. Day 42: Friday, 4/5 Discussed Sections 10.1 and 10.2, showing students the pattern for how you generate a Taylor Series centered at a. Worked through exercise 2 from section 10.2. We will continue to discuss Taylor Series on Monday. Quiz/Test on Chapter 9 will be on Wednesday - worth 60 points. It will contain 6 problems, a different type of test for each problem. We have covered 7 types of test. The problems will be in random order, not in the order that we covered the tests. Day 41: Thursday, 4/4 Finished discussing exercise 12, showing how to prove that the series converged for a finite interval. Gave students time to work together on the sheet of series. Handed out my solutions to these problems. Day 40: Wednesday 4/3 Discussed Power Series. Emphasized how power series differed from our numerical series. Handed out a sheet that showed tables for Exercise 12. Focused on 3 specific values for x, and showed clear evidence of convergence for two of them, though the power series clearly converged more slowly for one point than the other. For the third x value, the series clearly diverged. Test on Chapter 9, sections 1 - 4 will be next Wednesday. Day 39: Monday 4/1 Teacher out sick. Sent students a sheet to work on for series over email. Collected Graded Work 6. Finished section 9.3. Emphasized the requirements for the integral test. Did a number of examples. Day 35: Monday 3/25 Discussed section 9.3. Worked through the harmonic series, and showed how you can compare to an improper integral that diverges. Spent a lot of time helping students see how they had to thoughtfully read the book to pick up some of the essential details. Day 34: Friday, 3/22 Handed back GW 4 and partial answers. Discussed question 3 in some detail. Answered some questions from practice exercises in section 9.2. Lively discussion of # 17! Will start section 9.3 on Monday. Students should make sure they are working on graded work and practice exercises from 9.1 and 9.2. Day 33: Thursday, 3/21 Students worked on GW 6. Day 32: Wednesday, 3/20 Gave students a chance to review and redo the mathematica part of graded homework for Friday, in case the feedback from the test would influence their explanations to the homework. Changed test to Wednesday! GW 4 will be ALL due on Friday, 3/8. We will start Chapter 9 on Monday. Day 25: Thursday 2/28 Worked in computer room on GW 4. Showed students how to work with tables in the most effective way in terms of presenting their work in a professional way. Created the first set of tables together with the class. Students continued work on the second set of tables. Day 24: Wednesday 2/27 Worked through one of the practice exercises from section 7.7. Answered some other conceptual questions that students had about the material. Talked about the composition of the test on Monday. Handed out GW 4 & 5. Spent some time talking about what I was looking for. Please notice that the material is due in two pieces. Only question 4 must be done using mathematica. Worked on another problem from section 7.8. Day 23: Monday 2/25 Finished working on the third scenario for the general improper integral below. Walked through section 7.8, asking students to pay particular attention to key information. Worked on some examples from section 7.8. Encouraged students to begin working on discovering the patterns of convergence and divergence of the integral from 0 to 1 of 1/x^p. This proof will follow the same type of pattern as our work for the integral from 1 to infinity. There will again be 3 cases to consider. This will be part of the next turn in homework assignment. Day 22: Friday 2/22 Answered some questions from section 7.7. Completed # 18 from section 7.7 - which was an improper integral that diverged. Began working through Example 3 from section 7.7 to consider what happens to the improper integral from 1 to infinity of 1 / x^p. Showed that there were three distinct cases.... when p > 1, when p < 1 and when p = 1. We got through the first two cases, and will finish this work on Monday. Day 21: Thursday 2/21 Began section 7.7. Walked students through the section pointing out some very important ideas. Students should take additional notes from the book, as the work I will do in class will be to clearly demonstrate the core ideas - but I will not be writing out all the the definitions and background material. Worked on two specific exercises # 6 and # 16. #6 was improper because one of the limits was infinite. # 16 was improper because the integrand was boundless at one of the endpoints. We will continue work with these ideas tomorrow. Day 20: Wednesday, 2/20 Handed back tests and answer key. Handed out Practice Exercises for Unit 3 Reviewed material we had covered for section 7.5 on approximation techniques. Continued to work with this material. Did an example from section 7.5 and and example from 7.6. Day 19: Friday, 2/15 Test # 1. Day18: Thursday 2/14 Spent the class reviewing by answering questions students had on practice exercises. Test # 1 tomorrow. Day 17: Wednesday 2/13 Answered several questions on the practice exercises. Presented the core ideas in section 7.4 on the use of Left and Right hand rectangle sums, Midpoint Rectangle sums, and sum of areas of trapezoids. Discussed which were overestimates and which were underestimates, and what controlled that - i.e. increasing, decreasing, or concavity. Showed how to use the Integral program on the calculator to create the results for these rules. Notice, there will be a test on Friday that covers chapt 6 and chapt 7 sections 1, 2, 4. Answered some questions on practice problems. Discussed Integration by partial fractions, showing two examples: One with 2 linear factors in denominator, and one with a linear factor and a quadratic factor. Day 15: Friday 2/8 Class cancelled due to impending snow storm. Day 14: Thursday 2/7 Collected GW 3. Began section 7.2 - Integration by Parts. Showed how the formula was developed by working from the derivative of a product. Showed the short cut form. Did problems 10 and 4. Then showed students how to access Wolfram Alpha, and how they could use this with the "Show Steps" feature to help them work their way through integration problems that caused them trouble. We will do a problem with a "repeated integral" in the next class. Day 13: Wednesday 2/6 Spent some time reviewing some of the questions that students had asked me during my office hours in relation to the turn in assignment which is due tomorrow. Answered several questions on the practice exercises from 7.1, pointing out that not every problem that was presented could be done by substitution, and that students needed to be aware that they might have to use other approaches, including simplifying the integrand before doing the integration. Finished section 7.1 - discussed two different approaches to completing a definite integral problem when using substitution. One approach changes to u, and changes the limits of integration accordingly. The problem is then completed using the variable u. The other approach uses u to help find the antiderivative, but then reverts to the original variable, and uses the original limits of integration. Students should work on exercises 47 - 53 odd, and then 55, 59, 63, 67. I will get the next practice exercise sheet out as soon as possible. Day 12: Monday 2/4 Finished discussing # 30 from section 6.4. Began section 7.1 - Integration by substitution. Pointed out key ideas in the book, and discussed how the book structured the examples, giving the first few worked out by trial and error, and then honing in on the actual technique of substitution. Students should work on exercises 3 - 39 odd. We will continue with this section on Wednesday. Day 11: Friday 2/1 Went over the GW 3 sheet, making some points to students about what level i was looking for, and where on the sheet they would be using the capabilities of Mathematica other than as a word processor. Worked on section 6.4, doing problems 10, 16, and almost finishing 30. I will put the finishing touches on #30 on Monday, and will be starting Chapter 7. Day 10: Thursday 1/31 Quiz on sections 6.1 and 6.2. Handed out GW 3, and reminded students that they should first work through Section 17 of Part 3 Mathematica instructions before trying to work on the table asked for on the assignment. Day 9: Wednesday 1/30 Handed back GW 2 with answers. Discussed what students should do each time they get a graded assignment back. If anyone has questions on their paper, please come and talk to me about it as soon as possible. Handed out Part 3 mathematica instructions, and asked students to make sure to bring the packets with them to lab tomorrow. After the quiz, students should go through section 17 of these instructions in preparation for the next graded homework assignment. Quiz tomorrow will cover sections 6.1 and 6.2. The practice exercises for Success Strategies will NOT be due tomorrow. I will let you know a future date for that material, since we are not where I predicted we would be because of the storm on Monday. Answered some questions on practice homework. Began section 6.4. Did exercise 6. Will finish the discussion of this section on Friday. Day 8: Monday 1/28 Answered some questions on 6.2. Spent time doing work with some of the definite integrals in this section, emphasizing the notation used, and need to make sure that parentheses were used appropriately. Worked on 3 specific practice problems. Reminded students that there was a quiz on Thursday on sections 6.1 and 6.2. Handed out attendance cards with grades indicated for GW1 to make sure that all students agreed with their grade. Asked students to write their grade on the back of their Success Strategies grade sheet ( turquoise). Day 7: Friday 1/25 Answered some questions on section 6.1 practice problems. Discussed the concept that a general antiderivative or indefinite integral resulted in a family of functions that were only different by the constant. Went over how to find the antiderivative of a power function where the exponent was not equal to -1. Discussed the situation where the exponent was -1, so the integrand would be 1/x. Showed that the antiderivative would be ln |x| + C. Students should read the material in 6.2 and work with the practice exercises from this section. Day 6: Thursday 1/24 Collected GW 2. Worked on section 6.1. Talked about the examples that were in the text book, pointing out some specifics that students should focus on as part of their work for this material. Worked through Exercises 4, 6 and 10 in class, emphasizing what the examples were demonstrating, how they were similar and how they were different. Students should work on some of the practice exercises from the Practice Exercises for Unit 1 sheet for tomorrow. Reviewed the last question on the Derivative Review Material from the first day. Handed out a Review Sheet on Integration, and gave students time to discuss some of the material together. Reviewed questions 1 and 3 together as a class. Students should work on 3 things before the next class: 1) Continue work on Graded Work 2. 2) Complete problem 4 on the review sheet on Integrals, and 3) Work on the specific exercises listed on the Practice Work for Week 1 sheet. On Wednesday, I will answer any questions on review material, and also begin Chapter 6. Day 3: Thursday 1/17 Meet in Lab. Handed out Graded Work 2 (Green). Handed out Part 1 and Part 2 of Basic Instructions for Mathematica. (Extra copies in bin outside my door.) These instructions have been significantly revised from the ones you may have received last semester, so you should use these as reference. Gave students time to work on Graded Work 2 in the lab. The intent of the assignment is to have you review key ideas from Calculus 1 while also honing your skills on Mathematica.
Workbook in Polygons and Space figuresPresentation Transcript contents next A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly Asian Countries. contents back next The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technologies and other related fields. It shall also undertake research and extension services and provide progressive leadership in its areas of specialization. contents back next In pursuit of the college vision/mission the College of Education is committed to develop the full potentials of the individuals and equip them with knowledge, skills and attitudes in Teacher Education allied fields to effectively respond to the increasing demands, challenges and opportunities of changing time for global competitiveness. contents back next Produce graduate who can demonstrate and practice the professional and ethical requirement for the Bachelor of Secondary Education such as: 1. To serve as positive and powerful role models in pursuit of learning thereby maintaining high regards to professional growth. 2. Focus on the significance of providing wholesome and desirable learning environment. 3. Facilitate learning process in diverse type of learners. 4. Use varied learning approaches and activities, instructional materials and learning resources. 5. Use assessment data plan and revise teaching – learning plans. 6. Direct and strengthen the links between school and community activities. 7. Conduct research and development in Teacher Education and other related activities. contents back next This Teacher"s "Module in solving Polynomials" is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies. The students are provided with guidance and assistance of selected faculty members of the College on the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kinds of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation and utilization of instructional materials. The output of the group"s effort on this enterprises may serve as a contribution to the existing body instructional materials that the institution may utilize in order to provide effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students. REVELLAME, JEZREEL A. Workbook Developer MAGAYON, LOUIE M. Workbook Developer contents back next This Teacher"s "Module in solving Polynomials" is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies. The students are provided with guidance and assistance of selected faculty members of the College on the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kinds of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation and utilization of instructional materials. The output of the group"s effort on this enterprise may serve as a contribution to the existing body instructional materials that the institution may utilize in order to provide effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students. FOR-IAN V. SANDOVAL Computer Instructor/Adviser Educational Technology 2 DELIA F. MERCADO Workbook Consultant ARLENE G. ADVENTO Workbook Consultant LYDIA R. CHAVEZ Dean College of Education contents back next The authors wish to express their sincerest gratitude and appreciation to the support of those who assisted them to this requirement for their time and effort to finish their workbook. Without their cooperation, all of these have not been possible. First, the authors want to express their deepest gratitude to our Lord Jesus Christ, who serves as the greatest inspiration, for all the strength and wisdom that He had gave to enhance their spiritual parts for carrying in times of trouble for still giving hope. Mr. For – Ian V. Sandoval, who spent his time in giving instruction and sharing his knowledge in the production of this activity workbook. Prof. Lydia R. Chavez, Dean of College of Education, for her generous assistance. Mrs. Arlene G. Advento and Mrs. Delia F. Mercado, consultants and major teachers, for their valuable comments, suggestions, ideas and for sharing their knowledge which made this workbook of more substance and more meaningful. Parents for their love, moral and financial supports in making this workbook. Classmates and friends, whose served as an inspiration and shared their ideas on this workbook. Someone special for support, love and inspiration. The Authors contents back next Polygons are very useful graphical tool. Three- - dimensional shapes solids can easily be approximated with few polygons, and, when good shading and texturing are applied, they can look reasonably realistic. They can be drawn quickly and cover up very little storage space. Polygons are enclosed area bounded by at least three sides. A polygon can be defined as a set of points or a set of line segments. The order in which the set of points are listed is important. Different orders mean different polygons. These two polygons are made from the same set of points, listed in a different order. Space figures are figures whose points do not all lie in the same plane. In this unit, we'll study the polyhedron, the cylinder, the cone, and the sphere. Polyhedrons are space figures with flat surfaces, called faces, which are made of polygons. Prisms and pyramids are examples of polyhedrons. Cylinders, cones, and spheres are not polyhedrons, because they have curved, not flat, surfaces. A cylinder has two parallel, congruent bases that are circles. A cone has one circular base and a vertex that is not on the base. A sphere is a space figure having all its points an equal distance from the center point. The space that we live in have three dimensions: length, width, and height. Three-dimensional geometry, or space geometry, is used to describe the buildings we live and work in, the tools we work with, and the objects we create. First, we'll look at some types of polyhedrons. A polyhedron is a three-dimensional figure that has polygons as its faces. Its name comes from the Greek "poly" meaning "many," and "hedra," meaning "faces." The ancient Greeks in the 4th century B.C. were brilliant geometers. They made important discoveries and consequently they got to name the objects they discovered. That's why geometric figures usually have Greek names! We can relate some polyhedrons--and other space figures as well--to the two-dimensional figures that we're already familiar with. For example, if you move a vertical rectangle horizontally through space, you will create a rectangular or square prism. If you move a vertical triangle horizontally, you generate a triangular prism. When made out of glass, this type of prism splits sunlight into the colors of the rainbow. Now let's look at some space figures that are not polyhedrons, but that are also related to familiar two-dimensional figures. What can we make from a circle? If you move the center of a circle on a straight line perpendicular to the circle, you will generate a cylinder. You know this shape--cylinders are used as pipes, columns, cans, musical instruments, and in many other applications. A cone can be generated by twirling a right triangle around one of its legs. This is another familiar space figure with many applications in the real world. If you like ice cream, you're no doubt familiar with at least one of them! A sphere is created when you twirl a circle around one of its diameters. This is one of our most common and familiar shapes--in fact, the very planet we live on is an almost perfect sphere! All of the points of a sphere are at the same distance from its center. There are many other space figures--an endless number, in fact. Some have names and some don't. Have you ever heard of a "rhombicosidodecahedron"? Some claim it's one of the most attractive of the 3-Dimensional figures, having equilateral triangles, squares, and regular pentagons for its surfaces. Geometry is a world unto itself, and we're just touching the surface of that world. In this unit, we'll stick with the most common space figures. contents back next At the end of the workbook, students are expected to: 1. define what polygon is; 2. know the different formulas in areas of polygons, surface areas and volumes of space figures; 3. exercise the ability of the student in solving problem; 4. solve the areas of polygons; 5. solve the surface areas and volumes of space figures; 6. develop the skills of the students in solving problems involving different formulas; 7. solve practical problems dealing with the different formulas in polygons in easy way and less hour; and 8. formulate their own formulas in getting the areas of polygons, surface areas and volumes of space figures. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 17 Instruction: Solve the following. 1. One angle of a rhombus is 88. What are the measures of the exterior angles? 2. A polygon has 22 sides. Find the sum of the measure of the exterior angles. 3. An interior angle of a regular polygon is 120. How many sides does the polygon have? 4. The measure of each interior angle of a regular polygon is 8 times that of an exterior angle. How many sides does the polygon have? 5. In heptagon, the sum of the six exterior angles is 297. What is the measure of 7 th exterior angle? 6. The sum of the angles of polygon is 1620. How many sides does the polygon? 7. What is the measure of each interior angles of a regular 20-sided polygon? contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 23 Instruction: Answer the following questions. Give the reason. 1. Are all squares similar? 2. Are all rectangles similar? 3. Are all equilateral triangles similar? 4. Two rhombuses each has 60˚ angle. Must they be similar? 5. Two isosceles trapezoids each has 100˚ angle. Must they be similar? 6. The length and width of one rectangle are each 2cm more than the length and width of another rectangle. Are they similar? 7. If two figures are congruent, are they also similar? 8. If two figures are similar, are they also congruent? 9. Are equiangular triangles similar? 10. The length and width of a rectangle are 20 cm and 15cm respectively. Is a rectangle whose length and width are 12cm and 9cm respectively, similar to the given rectangle? contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 24 Instruction: Solve the following problems. 1. Two isosceles triangles are similar and the ratio of corresponding sides is 3 to 5. If the base of the smaller triangle is 18cm, find the base of the bigger triangle. 2. Given two similar triangles, triangle UST and triangle PLU with US = 8 cm, ST = 12 cm and UT = 16cm. If PL = 12 cm, find the lengths of the other two sides. 3. What is the length of longer leg of a triangle whose shorter leg is 24 cm, if the ratio of the shorter leg to the longer leg of a similar triangle is 5/6? 4. A copier machine is to reduce a diagram to 75% of its original size. The size of rectangle in the diagram after it has been reduced is 9 cm by 12 cm. What are the dimensions of the bigger rectangle? 5. Stan and Gina created a design 6 inches by 8 inches for a piece of cloth that is 1 ft wide. They plan to cross-stitch the same design on a piece of cloth that is 18 inches wide. What should be the measurement of the new design? contents back next Part II "A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. " David Hilbert contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 27 Instruction: Answer the following problems. 1. The measure of a basketball court is 26 cm by 14 cm, find its area. 2. Find the area of a baseball court with the measure of 90 ft by 60 ft. 3 . One face of chalk box has a length 60 cm and its width is 30 cm, find its area. 4. If the measure of a volleyball court is 50ft by 70 ft, what is area. 5. The measure of a floor is 26 m by 78 m, find its area. 6. Find the floor area of the gymnasium whose length and width is 65 m and 45 m respectively. 7. A badminton court has a measure of 27 m by 36 m, find its area. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 28 Instruction: Solve the following problems. 1. Find the length of the base of a rectangle with the area of 186 square yards and a length of the altitude of 13 yards. 2. One dimension of rectangular pool table is 76 cm. Its area is 8664 cm 2, find the other dimension. 3. The length of the base of the table in the canteen is 15 m and the length of the diagonal is 17 m. Find its area. 4. Find the area of a rectangle if the length of the base is 5 m and the length of the diagonal is 13 m. 5. Find the area of a rectangle ABCD where AB = 5 cm and BC = 8 cm. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 33 Instruction: Solve the following problems. 1. How many 6 – inch square bricks are needed to fill in a square window frame whose area is 900 sq. in.? 2. Find the dimension of a square field whose area is 196 square meters. 3. The area of a square is 675 cm2. Find the length of its side. 4. The coordinates of the vertices of a square are (0 , 5), (5, 0), (0 , - 5) and ( - 5, 0). What is the area of th square? 5. Find the area of a square LOVE with LO = 10 cm and OV = 10 cm. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 48 Instruction: Find the L.A and T.A for each right rectangular prism. 1. 12 2. 15 9 10 10 9 3. The perimeter of the base of a right prism is 12cm and the height is 6cm. Find the L.A.. 9 4. The perimeter of the base of a right prism is 8m and the height is 3m. Find the L.A. 5. Find the L.A. and the T.A. of the cube. 5cm 6. The edge of a cube is 7cm. find the L. A. and T.A. 7. The perimeter of the base of a cube is 16cm. Find the T.A. 8. The perimeter of the base of a cube is 24m. Find the T.A. 9. Find the L.A. and T. A. of a right prism whose base is a square. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 50 Instruction: Complete each statement with always, sometimes, or never. 1. The lateral faces of a pyramid are_________ triangle regions. 2. The number of lateral edges is _________ the number of vertices of the base of regular pyramid. 3. The lateral faces of a pyramid are _________ congruent. 4. The base of a regular pyramid is ___________ congruent. 5. The lateral faces of a regular pyramid are _________scalene triangles. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 53 Instruction: Find the total surface area of each polygon using the given conditions. 1. Regular pyramid, whose base is a square of side 10 inches and whose altitude is 12 inches. 2. A regular pyramid, whose base is a hexagon of side 10 inches and whose altitude is 20 inches. 3. Frustum of a regular square pyramid, whose base has sides 20 inches each long, respectively, and whose altitude is 12 inches. 4. The base of square pyramid is 5 ft, the area of the base is 25 ft 2, the perimeter is 20 ft and the altitude is 4 ft. 5. The perimeter of the base is 34 cm and the altitude is 14 m. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 55 Instruction: Solve the following problems. Use the figures at the right side. 1. The height of the smaller cylinder is 8. What 10 m is the height of the larger cylinder? 5m 8m 2. The surface area of the larger cylinder is 288п. What is the surface area of the smaller cylinder? 3. The diameter of the larger cylinder is 10. 10 m What is the diameter of the smaller cylinder? 10 m 4. The surface area of the smaller cylinder is 5m 25 m 75п. What is the surface area of the larger cylinder? 5. The radius of the smaller cylinder is 5. What is the radius of the larger cylinder? contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 62 Instruction: Solve the following. 1. The surface area of a great circle of a sphere is 6900 cm2 .What is the surface area of the sphere? 2. The surface area of the great circle of a sphere is 1m2.What is the area of the sphere? 3. The area of a sphere is 476m2 .What is the surface area of a great circle of the sphere? 4. A soccer ball has a diameter 0f 9.6 inches. Find the surface area of the sphere. 5. Consider the earth as a sphere with a radius of 4000 miles. Find its surface area. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 64 Instruction: Solve the following problems. 1. The height of a right circular cylinder is 20 cm and the radius of the base is 10 cm. Find the total area. 2. The height of a right circular cylinder is 10 cm and the diameter of the base is 18 cm. Find the lateral area. 3. A cylinder tank can hold 1540 m3 of H2O is to be built on a circular base with the diameter of 7 m. What must be the height of the tank? 4. A right circular cylinder has a lateral area of 2480 cm2. If the height of the cylinder is 16 cm, what is the radius of the base? 5. Find the total area of a right circular cylinder having a height of 5 m and the base has a radius of 1.5 m. contents back next Part IV "The intelligence is proved not by ease of learning, but by understanding what we learn. " Joseph Whitney contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 68 Instruction: Match each item with the best estimated volume. 1. Swimming pool a. 120 cm3 2. Soap box b. 750 cm3 3. Test tube c. 380 m3 4. Bar soap d. 500 mm3 Complete the statements with the most appropriate units (m3, cm3, mm3) 1. The volume of a 10-gallon fish tank is about 40___. 2. The volume of a gymnasium is about 30,000___. 3. The volume of a refrigerator is about 30,000___. 4. The volume of a ca condensed milk is about 354 ___. 5.v The volume of a an allergy capsule is about 784___ contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 69 Instruction: Solve the following problems. 1. How many cubic meters of concrete will be needed for a ratio 12 m long, 8 m wide, and 12cm deep? 2. A prism has a square base and a volume of 570 cm3, if it is 9 cm high, how long is a side of a base? 3. Find the volume of a regular triangle prism whose height is 15 cm and whose base has side that each measure 20 cm. 4. Find the volume of a prism whose base has an area of 24 cm2 and whose height is 8 cm. 5. Find the volume of a prism with a trapezoidal base and a height of 35 cm. The lengths of the parallel sides of the trapezoid are 40 cm and 95 cm. The altitude of the trapezoid is 5 cm. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 71 Instruction: Solve the following word problems. 1. The great pyramid in Egypt is approximately 137 m tall, the square base measures 225 m on each edge. Find the volume of the pyramid. 2. The area of the base of a pyramid is 237 cm2, and the height of the pyramid is 1 m. Find the volume in cubic centimeters. 3. The height of the pyramid is 15 ft, the base is a right triangle whose legs is 9 in and 12 in long. Find the volume of the pyramid in cubic inches. 4. A regular pyramid has a base area of 289 ft2 and a volume of 867 ft. What is the height of the pyramid? 5. If the area of the base of a pyramid is doubled, how does that affect the volume? contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 74 Instruction: Use mathematical reasoning in answering the following questions. 1. A regular pyramid has the base area of 389 ft2 and a volume of 867 ft2. What is the height of the pyramid? 2. Two regular pyramids have square bases and equal heights. If the length of a side of one of the bases is 1 m, and the length of a side of the other is 3 , how will the volumes compare? 3. A cube is broken into six identical pyramids as shown. Each face of the cube is a base of a pyramid. An edge of the cube is 10 cm. What is the volume of pyramid? contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 76 Instruction: Solve the following problems. 1. The radii of two spheres are 5 cm and 9.8 cm, respectively. What is the ratio of their volumes? 2. The diameters of two spheres are 12 m and 19 m, respectively. What is the ratio of their volumes? 3. A soccer ball has a diameter of 9.6 inches. Find its volume. 4. Find the volume of sphere whose radius is 15 cm. 5. Consider the earth as a sphere with the radius of 4000 miles, find its volume. contents back next Name:_______________________________ Score: ____ Year/section: ____________ Date: _____ ACTIVITY 83 Instruction: Solve the following problems. 1. The volume of a circular cone is 1005 cm3 and the height is 25 cm, find the radius of the base. 2. A gas storage tank has a radius of 4 m and a height of 8 m, find the volume of the cylinder. 3. Find the volume of a right circular cylinder having a height 0f 60 m and with a base whose radius is 20 m. 4. The height of a circular cylinder is 180 in and the radius of the base is 90 in. Find the volume. 5. If the volume of a circular cylinder is 72 cm3 and the radius of the base is 90 cm, find the volume. contents back next Jezreel Astejada Revellame is the eldest son of Mr. Emmanuel B. Revellame Sr. and Mrs. Eterna A. Revellame. He was born on February 13, 1992 at Infanta, Quezon. He finished his elementary in General Nakar Central School and finished his high school in Mount Carmel High School in General Nakar, Quezon. He finished his tertiary level in 2012 at Laguna State Polytechnic University with the Degree of Bachelor of Secondary Education major in Mathematics. Louie Magracia Magayon is the youngest son of Mr. Samuel M. Magayon and Mrs. Amalia M. Magayon. He was born on April 30, 1990 at San Agustin, Romblon. He finished his elementary in Pang- ala alang Paaralang Severina M. Solidum and finished his high school in Mabitac National High School. He finished his tertiary level in 2012 at Laguna State Polytechnic University with the Degree of Bachelor of Secondary Education major in Mathematics. contents back next
Hi all, I just began my free algebra equation calculator class. Boy! This thing is really difficult! I just never seem to understand the point behind any topic. The result? My grades go down. Is there any guru who can lend me a helping hand? Algebrator is what you are looking for. You can use this to enter questions pertaining to any math topic and it will give you a step-by-step solution to it. Try out this software to find answers to questions in angle-angle similarity and see if you get them done faster. I agree, a good software can do miracles . I tried a few but Algebrator is the best. It doesn't make a difference what class you are in, I myself used it in Pre Algebra and Basic Math too, so you don't have to be concerned that it's not on your level. If you never had a software before I can tell you it's not hard, you don't need to know much about the computer to use it. You just have to type in the keywords of the exercise, and then the software solves it step by step, so you get more than just the answer. I remember having often faced problems with angle-angle similarity, adding numerators and trigonometry. A truly great piece of math program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many math classes – Remedial Algebra, Algebra 2 and Intermediate algebra. I greatly recommend the program.
Math Professional Development What do the measures of central tendency (mean, median, and mode) tell you about the data? Teach your students how to answer that question and encourage them to look beyond calculations and individual data points. Explain how the measures are related to the whole set and see the data as an aggregate; help students perform higher-order statistical thinking. Develop strategies for teaching students how to represent and manipulate linear equations. Examine the rationale behind the symbol manipulation that maintains an equality or corresponding inequality. Use symbolic and graphic techniques to solve equations. Discover a fresh approach to teaching linear functions through the use of real-world problems that generate varied approaches and solutions. Learn how multiple representations and solutions strengthen students' understanding of functions, equations, and problem solving. Discover techniques to successfully guide your students through the critical transition from elementary mathematics and computing to the more complex, proportional thinking of algebra. Adapt problems from your curriculum to different learning styles using graphing, multimedia technology, and other strategies. Move beyond tried-and-true quadratic equation teaching techniques and look at the big picture: what the results reveal, how to interpret them within the context of a problem, and how to find related information. Manipulate the three symbolic forms of a quadratic function in order to inspect and predict shape, orientation, and location, and connect graphic and symbolic representations
Variables, Constants, and Real Numbers Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses variables, constants, and real numbers. By the end of the module students should be able to distinguish between variables and constants, be able to recognize a real number and particular subsets of the real numbers and understand the ordering of the real numbers. Links Supplemental links Section Overview Variables and Constants Real Numbers Subsets of Real Numbers Ordering Real Numbers Variables and Constants A basic distinction between algebra and arithmetic is the use of symbols (usually letters) in algebra to represent numbers. So, algebra is a generalization of arithme­tic. Let us look at two examples of situations in which letters are substituted for numbers: Suppose that a student is taking four college classes, and each class can have at most 1 exam per week. In any 1-week period, the student may have 0, 1, 2, 3, or 4 exams. In algebra, we can let the letter xx size 12{x} {} represent the number of exams this student may have in a 1-week period. The letter xx size 12{x} {} may assume any of the various values 0, 1, 2, 3, 4. Suppose that in writing a term paper for a biology class a student needs to specify the average lifetime, in days, of a male housefly. If she does not know this number off the top of her head, she might represent it (at least temporarily) on her paper with the letter tt size 12{t} {} (which reminds her of time). Later, she could look up the average time in a reference book and find it to be 17 days. The letter tt size 12{t} {} can assume only the one value, 17, and no other values. The value tt size 12{t} {} is constant. Variable, Constant A letter or symbol that represents any member of a collection of two or more numbers is called a variable. A letter or symbol that represents one specific number, known or unknown, is called a constant. In example 1, the letter xx size 12{x} {} is a variable since it can represent any of the numbers 0, 1, 2, 3, 4. The letter tt size 12{t} {}example 2 is a constant since it can only have the value 17. Real Numbers Real Number Line The study of mathematics requires the use of several collections of numbers. The real number line allows us to visually display (graph) the numbers in which we are interested. A line is composed of infinitely many points. To each point we can associate a unique number, and with each number, we can associate a particular point. Coordinate The number associated with a point on the number line is called the coordinate of the point. Graph The point on a number line that is associated with a particular number is called the graph of that number. Constructing a Real Number Line We construct a real number line as follows: Draw a horizontal line. Origin Choose any point on the line and label it 0. This point is called the origin. Choose a convenient length. Starting at 0, mark this length off in both direc­tions, being careful to have the lengths look like they are about the same. We now define a real number. Real Number A real number is any number that is the coordinate of a point on the real number line. Positive Numbers, Negative Numbers Real numbers whose graphs are to the right of 0 are called positive real numbers, or more simply, positive numbers. Real numbers whose graphs appear to the left of 0 are called negative real numbers, or more simply, negative numbers. The number 0 is neither positive nor negative. Subsets of Real Numbers The set of real numbers has many subsets. Some of the subsets that are of interest in the study of algebra are listed below along with their notations and graphs. Natural Numbers, Counting Numbers Whole Numbers Integers The integers (ZZ): . . . -3, -2, -1, 0, 1, 2, 3, . . . Notice that every whole number is an integer. Rational Numbers (Fractions) The rational numbers (QQ): Rational numbers are sometimes called fractions. They are numbers that can be written as the quotient of two integers. They have decimal representations that either terminate or do not terminate but contain a repeating block of digits. Some examples are Notice that there are still a great many points on the number line that have not yet been assigned a type of number. We will not examine these other types of numbers in this text. They are examined in detail in algebra. An example of these numbers is the number ππ, whose decimal representation does not terminate nor contain a repeating block of digits. An approximation for ππ is 3.14. Exercise 4 Solution Exercise 5 Solution Ordering Real Numbers Ordering Real Numbers A real number bb size 12{b} {} is said to be greater than a real number aa size 12{a} {}, denoted b>ab>a size 12{b>a} {}, if bb size 12{b} {} is to the right of aa size 12{a} {} on the number line. Thus, as we would expect, 5>25>2 size 12{5>2} {} since 5 is to the right of 2 on the number line. Also, -2>-5-2>-5 size 12{"- 2 ">"-5"} {} since -2 is to the right of -5 on the number line. If we let aa size 12{a} {} and bb size 12{b} {} represent two numbers, then aa size 12{a} {} and bb size 12{b} {} are related in exactly one of three ways: Either Equality Symbol a=ba and b are equal(8=8)a=ba and b are equal(8=8) Inequality Symbols Sample Set B Example 4 What integers can replace xx so that the following statement is true? -3≤ x< 2-3≤ x< 2 size 12{"-3" <= " x"<" 2"} {} The integers are -3, -2, -1, 0, 1. Example 5 Draw a number line that extends from -3 to 5. Place points at all whole numbers between and including -1 and 3. Exercise 7 Solution Exercises For the following 8problems, next to each real number, note all collections to which it belongs by writing NN size 12{N} {} for natu­ral number, WW size 12{W} {} for whole number, or ZZ size 12{Z} {} for integer. Some numbers may belong to more than one collec­tion
Just in Time Algebra for Students of Calculus in Management and the Lifesciences Just-in-Time Algebra and Trigonometry : For Students of Calculus Just-in-Time Algebra and Trigonometry for Calculus Just-In-Time Algebra and Trigonometry for Early Transcendentals Calculus Just-in-Time Algebra and Trigonometry for Early Transcendentals Calculus Just-In-Time Algebra and Trigonometry for Students of Calculus Mymathlab Mystatlab Student Access Kit For Ad Hoc Valuepacks Summary Strong algebra skills are crucial to success in applied calculus. This text is designed to bolster these skills while students study applied calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra topics and points out potential problem spots. the table of contents is organized so that the algebra topics are arranged in the order in which they are needed for applied calculus.
Problem solving is the heart of mathematics; all the math we have now was invented to solve a particular problem. Some problems come from science, economics, or real life, while others are purely mathematical. The only way to get good at math is through problem solving. Here you will find problems from various areas of mathematics. Some are harder than others, so you should try the easier ones first and then progress on to the harder ones. Arithmetic problems do not require almost any knowledge, just intuition and determination. Algebra problems cover a wide variety of topics, including equations, systems of equations, polynomials, and series. Combinatorics is the branch of math that covers probability, permutations, and combinations. Geometry problems range from simple calculation problems to harder proof and construction problems. Whatever your math level, we hope that you will have fun solving these problems. If you give up on a problem, you can certainty look at the solution provided, and maybe try and come up with a different solution.
by Patricia W. Hammer, Department of Mathematics and Statistics and Jessica A. King, Department of Computer Science Hollins University and Steve Hammer, Department of Mathematics Virginia Western Community College In this project, students will complete a series of modules that require the use of polynomial and trigonometric functions to model the paths of straight stretch roller coasters. These modules involve the mathematical definition of thrill and calculation of thrill for several real coasters (Module A), design and thrill analysis of single drop coaster hills (Modules B and C) and design and thrill analysis of several drop coasters (Modules D and E). The ultimate goal of this interactive project is successful completion of an optimization problem (Module F) in which students must design a straight stretch roller coaster that satisfies the following coaster restrictions regarding height, length, slope and differentiability of coaster path and that has the maximum thrill (as defined below.) Roller Coaster Restrictions The total horizontal length of the straight stretch must be less than 200 feet. The track must start 75 feet above the ground and end at ground level. At no time can the track be more than 75 feet above the ground or go below ground level. No ascent or descent can be steeper than 80 degrees from the horizontal. The roller coaster must start and end with a zero degree incline. The thrill of a drop is defined to be the angle of steepest descent in the drop (in radians) multiplied by the total vertical distance in the drop. The thrill of the coaster is defined as the sum of the thrills of each drop. The path of the coaster must be modeled using differentiable functions. Students must use Maple8 (or any later version) to complete the project. Students must already be familiar with derivatives and their use in determining maximum and minimum function values. These ideas play a crucial role in the design and analysis of the coasters. To complete this project, student should work through each of the modules given below. A.Introduction to Roller Coaster Design - In this module, students use an interactive coaster window to mark peaks and valleys of real-life coasters and then calculate the thrill of each drop using the above definition. Be sure to record the x and y coordinates of the peak and valley points and the slope at the steepest point. You will need this information to complete parts B - E below. B. Design and Thrill of One Coaster Drop Using a Trig Function- In this module, students model one drop of a coaster by marking the peak and valley of the drop and then by fitting (in height and slope) a trig function of the form f(x) = Acos(Bx+C)+D to the marked points. Once the function has been determined, students then calculate the thrill of the single drop. A downloadable Maple worksheet with commands and explanation is provided. C. Design and Thrill of One Coaster Drop Using a Polynomial Function - In this module, students model one drop of a coaster by marking the peak and valley of the drop and then by fitting (in height and slope) a cubic polynomial to the marked points. Once the function has been determined, students then calculate the thrill of the single drop. A downloadable Maple worksheet with commands and explanation is provided. D. Design and Thrill of a Straight Stretch Coaster Using Trig Functions - In this module, students model a straight stretch coaster (several hills) by marking peak and valley points and then by fitting (in height and slope) a trig function to each consecutive pair of marked points. Once the functions have been determined, students then calculate the thrill of the coaster. A downloadable Maple worksheet with commands and explanation is provided. E. Design and Thrill of a Straight Stretch Coaster Using Polynomial Functions - In this module, students model a straight stretch coaster (several hills) by marking peak and valley points and then by fitting (in height and slope) a cubic polynomial function to each consecutive pair of marked points. Once the functions have been determined, students then calculate the thrill of the coaster. A downloadable Maple worksheet with commands and explanation is provided. F. Project Assignment - Design the Most Thrilling Straight Stretch Coaster - Students use the ideas from modules A- E above to design a coaster (that satisfies all restrictions) with the maximum possible thrill. Completion of this project requires ingenuity, creativity and extension/modification of many of the ideas and Maple commands presented in modules A-E.
Mathematical Applications in Agriculture the specialized math skills you need to be successful in today's farming industry with MATHEMATICAL APPLICATIONS IN AGRICULTURE, 2nd Edition. Invaluable in any area of agriculture-from livestock and dairy production to horticulture and agronomy--this easy to follow book gives you steps by step instructions on how to address problems in the field using math and logic skills. Clearly written and thoughtfully organized, the stand-alone chapters on mathematics involved in crop production, livestock production, and financial management allow you... MORE to focus on those topics specific to your area while useful graphics, case studies, examples, and sample problems to help you hone your critical thinking skills and master the concepts. Invaluable in any area of agriculture or as a hands-on learning tool in introductory math courses, the 2nd Edition of MATHEMATICAL APPLICATIONS IN AGRICULTURE demonstrates industry-specific methods for solving real-world problems using applied math and logic skills students already have.
**The statistics class invites you to take a quick on-line survey about your music listening habits. Thank you for participating! Statistics 2011-12 Instructor: Eric Rhomberg How can we understand and communicate about numbers and data that describe real, practical situations? How can we best prepare ourselves in terms of mathematics to be successful in our post-high school lives? How can we increase our comfort and confidence level in mathematics? These will be the essential questions that guide our work throughout the year. This course is for students who want an alternative to pre-calculus and calculus – students who would benefit more from solidifying basic skills, preparing to be "college ready" in terms of computational skills, and developing their practical math fluency and confidence. In this course, we will: Use Statisitics as a playing field for developing our overall math fluency. Review math skills and concepts from basic computations through algebra and geometry. Play math games, solve puzzles, engage in problem solving challenges and "number talks" in order to develop our "math minds" and our fluency with numbers. Support your peers. Do your part to create a safe and effective collaborative environment. Do 20 minutes of focused math homework each night. If you get stuck on a problem, always write it out as far as you can take it (even if that just means writing out the initial problem). Bring your homework to class everyday, and be ready to go over it and ask questions. Complete projects by the due date. Communicate with the instructor in advance to negotiate extensions. Try to have fun with all of this! The flow of the class: Our class periods will vary depending on what we are working on. We will often start class with a "Warm-up" problem or challenge to activate our math thinking. We will then divide the period up between two or three of the following: Direct skill instruction to the whole class. Individualized work and practice, with instructor(s) doing 1-on-1 coaching. Games and Puzzles that liven things up and develop our math fluency. Group problems that emphasize collaboration. "Number Talks" in which we really break down and articulate how we think about and solve math problems.
MAT-231 Calculus I An intensive, higher-level course in mathematics that helps students become efficient and creative problem solvers. Topics include the Cartesian plane, limits and continuity, problems of tangents, velocity and instantaneous rates of change, rules for differentiation, implicit differentiation, maxima and minima theory, antiderivatives and the indefinite integral, exponential and logarithmic functions, and the area between curves. Advisory: It is advisable to have knowledge in a course equivalent to MAT-129 Precalculus for Technology with a grade of C or better to succeed in this course. Students are responsible for making sure that they have the necessary knowledge. Students will need a scientific calculator; a graphing calculator is not required. Programmable calculators are not permitted in examinations.
Useful information Tests consist of both calculations and conceptual questions. The math test format typically consists of short answer, multiple choice and computation problems. Class work and homework exercises are assigned to provide practice in analyzing and formulating a problem-solving approach. At least two tests will be administered each six weeks. 6th Grade Pre-AP Math Course Description The overarching goal of Glencoe Texas mathematics Course 1 is to help students develop mathematical knowledge, understanding, and skills, as well as awareness and appreciation of the rich connections among mathematical strands and between mathematics and other disciplines. 6th grade pre-Ap Math is a fast paced, rigorous curriculum that combines the 6th grade curriculum with additional concepts from the 7th grade curriculum
Basic College engaging Martin-Gay workbook series presents a user readers' perception of math by exposing them to real-life situations through graphs and applications and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book covers topics such as multiplying and dividing fractions, decimals, ratios and proportion, percent, geometry, statistics and probability, as well as an introduction to algebra. For anyone who wishing to brush up on their basic mathematical skills.
Math 150: Business Calculus Beginning Summer 2009, this course will be known as Math 148; only the course number will change. Course Description Math 150 is a one-quarter introduction to calculus intended primarily for students in business programs; it is not intended for students pursuing degrees in science or mathematics. Who should take this course? Generally, students studying business and related disciplines are required to take Math 150, but before taking this course you should consult the planning sheet for your program and consult an advisor to determine if this course is appropriate for you. Who is eligible to take this course? The prerequisite for this course is Math 131 or Math 140 with a grade of 2.0 or higher. Students new to EdCC with an Accuplacer score high in the 66–120 range on the College Level Math test and who have a very strong high school background (high grades in math courses up to or even including calculus) may also consider taking Math 150, but any student in this situation should contact the instructor of the class for which he/she registers prior to the beginning of the quarter to determine whether or not he/she is ready for calculus. (The instructor's permission must be obtained in order for the student to remain in the class.) Is this course transferable? This course transfers to the University of Washington as UW Math 112. Consult an advisor or see the Transfer Center to determine transferability to other institutions. What textbook is used for this course? The fourth edition of Applied Calculus by Stefan Warner and Steven Constenoble. What else is required for this course? Students are required to have a graphing calculator; the TI-83 Plus or TI-84 Plus is recommended.
This course is designed for those with a strong background in mathematics. Topics covered include a thorough review of linear and quadratic functions and an in-depth study of polynomial functions. The study of functions in the abstract is facilitated through the study of their graphs using both pen and pencil and technology in the form of graphing calculators and computers. Topics covered include exponential and logarithmic functions and their applications in the real world; trigonometric functions, their equations, graphs and identities and their applications; sequences and series, functions and limits, and their relationship to calculus. Finite topics developed include matrices, combinatorics and probability.
Description Courses are continually being revised or developed to challenge all students, both those needing high level mathematics skills and knowledge and those of average/remedial performance levels. The new curriculum relates mathematics more closely to practical applications. Instructional techniques will include lecture, manipulatives, cooperative group work, and use of scientific calculators. All math courses except Algebra Support meet the UC and CSU "c" requirement. Courses Algebra 1-2 Prerequisite: None Open to grades 9-12 Course Description: This two-semester course is designed to give a foundation in basic algebraic principles which will prepare the student for advanced courses in mathematics. The student learns to work with signed numbers, fundamental operations with algebraic symbols, graphing, radicals, the solution of elementary word problems, factoring, linear and quadratic functions, and solving quadratic equations. Instructional techniques will include manipulatives, cooperative groups and the use of scientific calculators. Algebra Support Integrated 1-2 Geometry 1-2 Prerequisite: C or better in Algebra 1-2. Open to grades 9-12 Course Description: This two semester course reviews and extends the algebra concepts of Algebra 1-2 and introduces the fundamentals of geometry which will prepare students for more advanced courses in mathematics. Topics covered include perimeter, area, volume congruence, similarity, circles, patterns and spatial visualization. Emphasis is placed on making conjectures from observations and justification of reasoning. Instructional techniques include manipulatives, cooperative groups and scientific calculators. Integrated 3-4 Algebra 3-4 Prerequisite: C or better in Geometry 1-2. Open to grades 9-12 Course Description: This course expands upon the mathematical content of Algebra 1-2 and Geometry 1-2 and a review of those concepts are integrated throughout. Emphasis is placed on abstract thinking skills, the function concept, and the algebraic solution of problems in various content areas such as the solution of systems of quadratic equations, logarithmic and exponential functions, sequences, the complex number system, mathematical probability, and right and oblique triangle trigonometry. Graphing calculators will be used extensively. All of this will be done in a setting of cooperative groups exploring new concepts and reviewing previously learned material. An emphasis is placed on students organizing key concepts in a meaningful way. Pre Calculus Prerequisite: C or better in Algebra 3-4. Open to grades 9-12 Course Description: This course blends together all of the precalculus concepts and skills that must be mastered prior to enrollment in a college-level calculus course. Content includes a study of the trigonometric functions (developed using the concept of the circular functions), such as graphs, identities, the inverse trig functions, and solution of equations. It also covers applications of trigonometry in complex numbers, polar coordinates and vectors. Finally, conic sections, rational functions and their graphs, parametric equations and their graphs, lines and planes in space, the concepts of area under a curve rates of change, and statistics are studied. Calculus 1-2 AP (AB) Prerequisite: C or better in Pre Calculus or consent of the instructor. Open to grades 10-12 Course Description: Although it is a year course here at Aragon, AB Calculus covers the standard topics of differential calculus and integral calculus, which constitute one semester of calculus at most universities. Students enter the course with the understanding that they are to prepare themselves to take the Advanced Placement Test, AB version, in Calculus. Passing the test with a grade of 3, 4, or 5 can earn one semester of college credits in calculus at some universities. This course is an AP course; students should expect 45 minutes to an hour of homework nightly and will have to study quite seriously to do well. Calculus 3-4 AP (BC)Year Course Prerequisite: "C" or better in Calculus AP, "B" or better in Pre-Calculus or consent of instructor. Open to grades 9-12 Calculus BC is an extension of Calculus AB and covers the topics of integral calculus, differential calculus, polynomial approximations, and series. Although it is a year course at Aragon Calculus BC constitutes the second semester of calculus at most universities. Students enter the course with the understanding that they are to prepare themselves to take the Advanced Placement test, BC version, in calculus. Passing the test with a grade of 3, 4, or 5 can earn one semester of college credit at some universities. As with all AP classes, this course will be demanding and challenging. Finite Mathematics And Statistics Prerequisite: C or better in Algebra 3-4. Open to grades 11-12 Course Description: This two semester college preparatory math course is an alternative to Trigonometry/Math Analysis and/or Calculus. It provides 10 elective credits of mathematics for college bound students not planning to major in the sciences. Topics include review and extension of Geometry and Algebra 3-4 skills, statistics, street networks, circuits, linear programming, coding information, and apportionment. Statistics AP Course Description: This is a year long course to prepare students for the AP exam in the spring. Topics include data analysis using graphical and numerical techniques, data collection techniques, probability and statistical inference.
Note: This course serves as a pre-requisite for MATH 110 (College Algebra), MATH 130 (Introductory Statistics), or MATH 155 (Mathematics, A Way of Thinking). You must earn at least a "C" grade to qualify for the next course in your sequence. (b) Students will work through pre-algebra ALEKS modules indicated as necessary. 2. Students will improve their mastery of algebraic skills. (a) Students will take ALEKS assessment of algebra knowledge and skills. (b) Students will work through the ALEKS modules indicated as necessary. (c) Students will take indicated exams to demonstrate their learning. 3. Students will develop their ability to apply algebraic thinking and procedures to problem solving. (a) Students will work through the ALEKS modules that focus on problem solving. Course Procedures and Policies: MATH 001: Math 001, "Introductory Algebra", is a not-for-graduation-credit course intended to prepare students for the various courses for which 001 is a pre-requisite, namely MATH 110 (College Algebra), MATH 130 (Introductory Statistics), and MATH 155 (Mathematics, A Way of Thinking). The material is essentially the first year of algebra, which would typically be taken in high school, which explains why this course is numbered 001, and why the 4 credits you will earn here do not count toward graduation, even though they do count toward full-time status. Your placement score indicated that you have not mastered this content, whatever the reason. Our job here is to make the best of the situation, to finally learn this material and master the necessary skills so that you can be successful in the courses you eventually need to take as part of your college program. In an ideal world, no one would need this course – they would have learned it the first time around – but since that isn't the case we just have to do what is necessary to ensure your success in the long run. ALEKS: ALEKS (Assessment and LEarning in Knowledge Spaces) is a web-based program designed to carefully assess what students know and what they are ready to learn, and then to methodically tutor them in the given material, in this case Introductory Algebra. Probably the best thing about ALEKS is that it allows each student to take a course specifically designed for their needs – each student in the class will be working at their own pace and working on material they are ready to learn. The implication of this is that I will not be "lecturing" on textbook sections the way you might be used to seeing. My role as instructor here is to monitor your learning and to engage in individual tutoring as the need arises. Another advantage to using ALEKS is that since it is web-based you can work on your course at your convenience. ALEKS will remember where you left off and will always make sure that you have shown readiness before presenting new material. By the way, even though you will be expected to do a considerable amount of ALEKS work on your own time, it is very important to understand that it is important to DO YOUR OWN WORK! If you get someone else to do the work you will only be frustrated when ALEKS thinks you know more than you do and starts asking questions you are not ready for. Also the exams must be taken on your own so having someone work through the online material for you will not help your performance on those exams, and hence on your grade for the course. Textbook: The textbook we will be using is published by McGraw-Hill, who also handles ALEKS for institutions of higher education. Our text has been precisely integrated with ALEKS, so that you can use your book for explanations, worked examples and practice problems as we move our way through the course material. Attendance: A major factor in learning mathematics is a regular and focused schedule of practice. Can you imagine learning to play the piano by only practicing a few minutes a week! You need to practice virtually every day, and for considerable time each day. It takes the same sort of discipline to solidly learn algebra. My attendance policy is given below. Because it is so important that you put in the time, I have a system that rewards regular attendance. On the other hand, I think a person who has missed 5 classes has demonstrated a clear lack of focus and discipline and should be dropped from the course. In general I will not distinguish between "excused" and "unexcused" absences, although I do consider absences due to participation in a school event, such as an athletic trip or a theatrical production, to NOT be "absences". In this case, however, it is still important that you put in the extra time to catch up. Number of AbsencesPoints 0 +25 1 +20 2 +15 3 +10 4 +5 5 Withdrawn ALEKS Time: ALEKS keeps track of how much time you have put in as well as how much progress you have made. I will be using your ALEKS time as part of the grading scheme, as summarized below. Each week there will be a grade assigned based on the time you have spent working on ALEKS over the previous week. ALEKS hours this week Points 8 or more +5 7 or more +4 6 or more +2 5 or more +1 less than 5 -2 The times INCLUDE the 4 hours spent in class, so that 9 hours for 5 points means you would need to work five hours outside of class to earn those points. In general college students are expected to work 2 hours outside of class for each hour in class. I have made this number a little smaller because I am trying to build in some time for studying the text book. Some people will need more time to learn the material that others – life is not fair and some people learn things more quickly than others. I do expect each of you, however, to put in roughly 12 total hours per week working on learning the material. This does mean that some of you who are farther along than others might end up finishing the course at some point during the semester! ALEKS will tell you how far along you are and some of you will have a starting point farther along than others. By the way, there are several "short weeks" this fall. Labor Day (9/5) week and Mid-semester break (10/21) week have only three class meetings rather than four, so these two weeks the 9-8-7-6 will become 7-6-5-4. Thanksgiving (11/24) week is very short, only 1 class meeting, on Monday; this week the numbers are 3 hrs = 5 points, 2 hours = 3 points, 1 hour = 1 point Exams: ALEKS has the ability to construct exams at points indicated by the instructor. I tell ALEKS what material I want covered and the program constructs problems that test understanding of that material. I plan to ask ALEKS to give you an exam after you have completed every other ALEKS topic section, as numbered on the ALEKS page included here. Thus, after you have completed sections 1 and 2 you will have an exam, then after sections 3 and 4, after sections 5 and 6, and finally after sections 7 and 8. These exams will all be taken on line but you will have to take these in the classroom so that they will be supervised. It is important to know that you are actually able to do your own work. You will also take a paper and pencil exam of my design at midterm and during finals week. I imagine that some of you will not be on schedule and this will no doubt affect your performance on these two exams, but then part of success in a course is learning the material within a designated amount of time. Grading System: At present, and I want to reserve the right to make adjustments to this system as the semester wears on, I see your grade being determined by these four factors: This makes for a total of 750 points. Grades will be assigned according to the scale: A = 90% or higher, B = 80% or higher, C = 70% or higher, D = 60% or higher. You also need to complete at least 160, or 80%, of the ALEKS topics to pass the course. You need at least a "C" grade to be allowed to advance to the next course in your sequence. Schedule: Because ALEKS allows students to work at their individual pace you will be at a variety of places in the material throughout the semester. Still, in order to pass the course and move into the subsequent course you will need to finish the material within the semester's time constraints. It is possible that some of you will actually complete the ALEKS course before the calendar indicates the semester is over, and that's fine. I will still have you take the final exam with the rest of the class on 14 December. And it is possible that some of you may reach December without completing the material. ALEKS offers a guarantee that if you put in a reasonable amount of time during the semester and do not pass the course your license to use ALEKS can be extended so that you can continue to work on finishing the course during the following semester – in this case you will be given a grade of "I" (Incomplete) so that you can work on completing the course during the next semester. Of course, this is far from ideal since it means you could not yet enroll in the course you need to take for your major, so it should be your goal to see that that does not occur. Americans with Disabilities Act: If you are a person with a disability and require any auxiliary aids, services, or other accommodations for this class, please see me and/or Wayne Wojciechowski, the campus ADA coordinator (MC 335, 796-3085), within ten days to discuss your needs. ALEKS Your textbook should come with a username and password so that you can log onto ALEKS (Assessment and LEarning in Knowledge Spaces). Then to be enrolled in my specific course you need the course code, which will be given in class. The first day of class you will each log in and we will take a look at the basics of using ALEKS. I will ask you to work your way through the tutorial so that you become familiar with how to enter mathematical expressions. Then on the second day of class I will have you take the initial ALEKS assessment to get a baseline rating of your skills and readiness for the material in this course. ALEKS keeps track (and lets your instructor see the results as well) of how much you have mastered and what you are ready for. We have designed the syllabus by slightly modifying the standard ALEKS version of "Beginning Algebra" (adding or dropping a few topics), and the Viterbo version of MATH 001 now includes 202 individual topics.
Get ready to master the concepts and principles of geometry! Master Math: Geometry is a comprehensive reference guide that explains and clarifies the principles of geometry in a simple, easy-to-follow style and format. You'll begin with the language of geometry, deductive reasoning and proofs, and key axioms and postulates. And as you understand the most basic fundamental topics you'll progress through to the more advanced topics, with step-by-step procedures and solutions, along with examples and applications, to help you as you go. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up, Master Math: Geometry will help you master everything from deductive reasoning and proofs to constructions and analytic geometry. less
The "Big Idea"of high school mathematics instruction is for students to develop mathematical proficiency that will enable them to efficiently use mathematics tomake sense of and improve the world around them. To review the state of Texas' standards for these courses please visit the TEA website. Algebra 1 The main goal of Algebra 1 is to develop fluency in working with linear equations. Students will extend their experiences with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will extend their knowledge of the number system to include irrational numbers. Students will generate equivalent expressions and use formulas. Students will simplify polynomials and begin to study quadratic relationships. Students will use technology and models to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life's experiences. Algebra 2 - Spring 2012 In Algebra 2 students will build upon the concepts established in Algebra 1. We willfocus on number sense, functions, transformations and systems. Knowledge of the concepts will be explored through multiple methods (graphically, verbally, algebraically, experimentally, etc…). Additionally, students will explore making connections between these different methods and applying them to real world situations through the use of technology. Math Models - Fall 2011 Math Models is a problem-solving math course. Much of the material covered will have been touched on in a previous course; however, we will examine each topic in detail through word problems and real world situations. Students will use technology and models to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations.Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life's experiences.
Teaching algebra to be able to home school students may be any problem. Regardless of precisely what sort associated with curriculum you might become. Teaching algebra to house school students is often any problem. No matter precisely what type associated with curriculum you might always be employing, describing the functions as well as concepts involving algebra is complicated — perhaps teachers throughout regular school configurations may locate it problematic. Include for you to that the possibility that you possess forgotten about significantly about the subject your self, as well as you may see precisely how hard it can be. Even so, you will discover property college algebra courses available that will allow it to be easier and also easier for you to educate your current children this subject. The issue is that its not all programs are equal – you should guarantee that you pick the top probable class. Visual Lessons Bookwork isn't some thing that the majority college students adore. Additionally, when a few students can exceed on this manner, many come across that intimidating as well as much less than participating. On the other hand, residence school algebra programs which supply visual lessons can easily deliver your wedding that your university student requirements in order to really ""get"" the particular topic. When learning directly from a publication, college students can easily become annoyed. While your concepts might be spelled out inside black and white, this really is not really essentially the very best solution to have that facts inlayed inside your child's thoughts. You will also obtain which numerous home college algebra guides appear to depart some thing out there : that will important element that will really get this math concepts ""click"" within your kid's thoughts. Visual training support your own little one observe the particular procedure performs. Super-hero instruction walk your own little one by means of your method of dilemma solving and also show main tenets regarding algebra that will get plenty in mere wording. Enrichment Activities Another essential part involving picking the ideal residence school algebra programs would be to take into consideration the actual further work for that program. Quite a few course possibilities leave out virtually any form of enrichment activity — counting solely in bookwork or even training in order to provide your needed information. Having said that, the best remedy will provide engaging enrichment activities your child won't simply uncover pleasant, nevertheless can help to concrete ideas and operations throughout his or her mind, also. Testing Is actually Good Your kid can likely obtain that going from 1 topic in order to a different inside algebra can be frustrating. It can end up being overwhelming in order to also take into consideration. On the other hand, a few dwelling school algebra courses provide pre-testing which is developed to not dissuade your own college student, yet to be able to stimulate him or her by ""getting their particular ft wet"" using the ideas and operations which will become covered in the upcoming unit In add-on, post-tests aid to be able to assure that your university student fully is aware of your prior system just before going on to another. This may make specific that the kid has a firm understanding of the things they ought to realize in each important point in their education. Choosing the appropriate option here is actually crucial, not merely to your youngster, yet to you since the teacher. With the suitable algebra training course to assist an individual, there's absolutely no have to have to be able to be concerned that you or your own child is going to be left guiding. Feelings regarding drawback might be place to relaxation as well as the approach associated with studying may genuinely start throughout earnest. The appropriate algebra course could be almost all that you want in order to assure understanding as well as satisfaction on this subject.
Description This access kit will provide you with a code to get into MyMathLab, a personalized interactive learning environment, where you can learn mathematics and statistics at your own pace and measure your progress. In order to use MyMathLab, you will need a CourseID provided by your instructor; MyMathLab... Expand is not a self-study product and does require you to be in an instructor-led course.Collapse Used items have varying degrees of wear, highlighting, etc. and may not include supplements such as [...] Used
MATHEMATICS WORKBOOK Higher physics demands fluency and ability in physical and mathematical analysis that are not given prominence in school physics syllabii. During the SPC we shall be developing both problem solving skills and experimental techniques. In order to provide a common assumed background we have prepared a set of questions based (roughly) on the core AS-level syllabus. You may have already mastered all the material, in which case this workbook will provide a useful set of revision problems. However, if some of the material is new to you or if you are uncertain about it or get stuck on any of the questions, then we suggest that you refer to an appropriate A-level textbook. These questions are selected and adapted from the University of Cambridge Natural Sciences Tripos mathematics workbook: Any comments or queries about this workbook should be sent to spcphy@hermes.cam.ac.uk
The mathematics program at Fresno Pacific University is designed to prepare students to solve problems, communicate their understanding and appreciate the beauty of mathematics and its role in human history.
Mathematics Extension 2 tutoring - year 12 HSC Mathematics Extension 2 is often said to be the most challenging HSC course, but it scales incredibly high. For almost a decade, maths extension 2's scaled mean has hovered around the low to mid 40s (source: Table A3, UAC Scaling Report), making it the highest scaled subject commonly offered by schools. The majority of students who attain 99+ ATAR have done this course. Therefore, we strongly urge all students with at least moderate mathematical capability to consider doing this course. Dux College prides itself in the high standards of our Extension 2 classes. Course information HSC Mathematics Extension 2 will be taught by topic throughout year 12. Students who take this course should have a strong foundation in the Preliminary 2 unit and Extension 1 content. In this course, we focus on maximising our students' exposure to the largest variety of exam-style questions possible. Practice of all variations of the core topics will prepare students to get almost full marks for Questions 1 to 6. We aim higher than this. Our students are also given a variety of the more difficult, creative questions which are considered Question 7-8 standard. Theory and harder questions will be discussed in class through worked examples, paying particular attention to technique, manipulation and pattern recognisation. A common concern with this subject is the difficulty of Questions 7 and 8. Often these questions are left substantially unattempted. We've even seen school teachers advise their students to "not worry about it too much". We believe this complacent approach towards the subject is ill-advised. We disagree with the popular notion that some students are born with exceptional lateral thinking skills needed to get near full marks in this subject. It is simply a matter of experience. Students will see patterns emerge after they have done a large quantity and variety of questions. It is this skill gained from doing many Question 8 standard questions that allows students to comfortably tackle the more challenging Questions 7 and 8. Like all the other courses, we provide HSC exam style homework booklets for students to practice each week. Exposure to exam-style questions and exam conditions is the best preparation for the real thing. Questions will range in difficulty, with the bulk of questions being slightly harder than average (question 4-6 standard). There will also be challenging questions which are compulsory for all students to attempt. These will be discussed fully in class. All our homework questions will be marked and provided with teacher's comments and worked solutions where appropriate. Students are expected to use the discussion forums for homework assistance when they face any difficulty. Term 1 starts 2nd of February - for all new students interested in joining us for Term 1 2013, contact us to book a free trial lesson first. Harshala Bharath - Leumeah High School, 2010 My class teacher was very helpful and to the point when I got confused. The teaching style was methodic and simple to understand compared to school. The study notes were very helpful and easy to understand. My marks went up progressively ...
About Luke Posts by Luke: Pre-(r)amble The odds favor that by the time someone has reached this article, myself included, they have spent at least the briefest of moments (frustratedly?) questioning the practical applications for linear combination, linear independence and linear math. In a sentence, these concepts allow us to mathematically understand and represent multidimensional coordinate systems. If you're looking for a quick explanation for a homework problem feel free to skim through the bolded topics for help in specific areas of concern. Otherwise, here's something to think about. Imagine maneuvering in three dimensional space. An instantaneous position can be described using a three dimensional coordinate system. When following a consistent pattern of movement, an instantaneous position can be described with a fourth dimension, time. Suppose you have just landed the snowball throw of a lifetime and hit a target moving across your view plane, increasing the distance between you, and uphill. You have properly estimated the intersection of two moving objects in four dimensions. This is not always an easy task to execute. Now make this throw using a fifth dimension. Most people can't comprehend the existence of a fifth dimension without having to understand how to maneuver in it. With linear math we can attempt to understand and represent the relationships between these dimensions. Important Definitions Linear Independence A set of linearly independent vectors {} has ONLY the zero (trivial) solution <> <> for the equation Linear Dependence Alternatively, if or , the set of vectors is said to be linearly dependent. Determining Linear Independence By row reducing a coefficient matrix created from our vectors {}, we can determine our <>. Then to classify a set of vectors as linearly independent or dependent, we compare to the definitions above. Example Determine if the following set of vectors are linearly independent: , , , Setting up a Corresponding System of Equations and Finding it's RREF Matrix We need to understand that our vectors can be represented with a system of equations all equaling zero to satisfy the equation from our definition of linear independence. These equations will look something like this: Notice that I have simply taken the coefficients from the given vectors and multiplied them by four variables (the number of variables will equal the number of vectors in the given set). They have been set equal to zero to allow us to test for linear independence. From here, create a coefficient matrix and perform row operations to reduce the matrix to reduced row echelon form (rref) . rref = Finding the Solution of the RREF Matrix Finding the solution of the rref matrix may be the more difficult step in this process. However, it may become trivial following a few simple steps. 1) Identify the free variables in the matrix. Free variables are non-zero and located to the right of pivot variables. Pivot variables are the first non-zero entry in each row and since we have taken the rref of our matrix, all of the pivot variable coefficients are 1. By locating all free variables (or by eliminating all pivot variables) we find that is our only free variable. 2) Write free variables into your solution. The variable can be written into our solution vector as itself but we will represent it with another variable name (i.e. ) so that our solution is in parametric form. Multiple free variables are represented with multiple variables names (i.e. ). After this step your solution vector should look like this: <> <>. 3) Solve for pivot variables. The pivot variables should either be constant (i.e. 0, 6) or a function of your free variables (i.e. ). From the rref matrix we can see that , , and . Since not all of our , the given set of vectors is said to be linearly dependent. The linear dependence relation is written using our solution vector multiplied by the respective vector from the given set: . We can also conclude that any vectors with non-zero coefficients are linear combinations of each other. Therefore, and are a linear combination. TweetMatrix manipulations and properties Finding the inverse of a matrix is much more complex than finding the inverse of a number. All real numbers have an inverse (i.e. ). However, not all matrices have an inverse. There are several characteristics that allow us to visibly determine whether a matrix has an inverse but we will [...] Basic BJT Equations: It is also important to know that can be modeled as . These equations are not very informative by themselves so a few examples are demonstrated below. In both examples we will assume is very large. What this means for our calculations is . Since we also assume that . Finding missing [...]
Looking for a complete mathematical computing package? MATLAB could be the answer. MATLAB is a high-level programming language and development environment for analyzing data and developing algorithms and applications. Easy to use and learn, MATLAB integrates tools for computation, data analysis and visualization and an intuitive programming language. Simulink is an interactive environment for designing and simulating dynamic systems in every engineering discipline. An intuitive block-diagram interface lets you model, simulate and analyze multidomain control, signal processing, communications and other systems. Scientists, engineers and mathematicians at many of the world's leading universities, technology companies and government laboratories use MATLAB and Simulink to solve their most challenging technical computing problems. The Student Version of this software provides all of the features of professional MATLAB, with no limitations, and the full functionality of professional Simulink, with model sizes up to 1000 blocks. The Student Version gives you immediate access to high performance numeric computing, modelling and simulation power. The software comes with manuals for both MATLAB and Simulink. These provide easy-to-follow instructions on how to use the software. The user needs to learn the MATLAB programming language, how to create Simulink block diagrams and how to command Simulink to simulate the system being designed. These tasks are easily accomplished thanks to the user-friendly nature of the manuals, which have plenty of worked examples. MATLAB & Simulink the Student Version will run on Windows, Mac OS X and Linux systems. System requirements for Microsoft Windows are: Obviously, the better your system, the better it will run. If you wish to make enquiries or to purchase MATLAB & Simulink the Student Version, I suggest you check with you local University Union Bookshop. Students of degree awarding institutions can purchase and activate the Student Version software at a relatively low cost (around $165 Australian). Teachers and other professionals need to buy the professional version, which is more expensive. AutoSketch 9 by Autodesk Inc, USA, for use with Windows XP Professional or Home Edition or Windows 2000 Professional. This is an excellent CAD package. AutoSketch 9 is a precision drawing tool for the Microsoft Windows environment. It has been developed for anyone who needs to construct fast, accurate drawings. It is easy to learn and comes with an excellent User's Guide. Uses for AutoSketch 9 include: Conceptual sketches Scientific & engineering drawings Architectural drawings Electrical drawings Technical illustrations Product specifications Informative graphics and many others System requirements: Microsoft Windows XP Professional or Home Edition or Microsoft Windows 2000 Professional. This is an excellent read. In typical exciting, down-to-earth and informative style, Dr Karl clears up many a common myth and entertains all the way. Ever wondered what happens to all those bullets you often see fired into the air in jubilation? Can piranhas strip a human body to the bone in seconds flat? Can you re-start a flatlined heart? Lie detectors, the legendary beauty of Cleopatra, the history of the electric chair, the physics of torpedos, the reasons for the seasons, asteroids and comets, the benefits of megadoses of vitamins, myths of Titanic proportions, the great cash crash of 1929, your survival chances in the vacuum of space and many, many more topics are addressed. At 247 pages, once you start reading this book, you'll finish it in one sitting. Then, days later, you'll come back and read most of it again. This is an excellent and very up to date book on cosmic evolution. The Dutch science journalist Govert Schilling takes the reader on a whirlwind journey through time. He describes the evolution of the cosmos, from the beginning of space and time fourteen billion years ago, to the creation of the Earth and humankind. The book ends with a glance into the distant future of the universe. The book is a combination of compelling text and breathtaking photographs. The text is exciting to read and easily understandable. Any person interested in science will find this book an absolute delight to read and experience. This book is a real masterpiece. Fermat's Last Theorem by Simon Singh (ISBN 1841157910) paperback edition published by Fourth Estate, London in 2002. This is a truly marvellous book. Fermat's Last Theorem is a mathematical conundrum created in France in the 17th Century. The proof of the theorem has eluded multitudes of brilliant mathematicians from that time right up until 1993 when mathematician Andrew Wiles finally solved the problem. In presenting the story of the formulation of the theorem and the ensuing attempts to prove it, the book provides enthralling insights into the nature and history of mathematics itself and entertaining descriptions of many of the interesting characters who have added so much to our mathematical knowledge and understanding across the years. Singh's enthusiastic telling of this story captures the interest of the reader from page 1 and holds it throughout. His lucid and riveting storytelling style makes this book a very enjoyable read. Galileo's Commandment edited by Edmund Blair Bolles (ISBN 0349112460) published by Abacus, London in 2000. As it says on the front cover, this is "an anthology of great science writing". The editor has selected science literature from many authors - from Herodotus' natural history of the Nile Valley around 444BC, to Galileo's descriptions of what he saw through his telescopes, to Lavoisier's preface to "The Elements of Chemistry", to the writings of Charles Darwin, Marie Curie, Albert Einstein, Carl Sagan and many, many others. It is both fascinating and enlightening to read the thoughts of the many scientists included in this collection. "The aim behind this collection", says Bolles in his introduction, "is to show readers that science writing can be great writing in precisely the same sense that other genres are great: it has something important to say; it says it by presenting readers with unique imaginations; and readers in turn are inspired to think in ways, that by themselves, they never could." He wants readers to see "that science writing can be fresh, pleasurable and not at all like cold toast". I believe that he has succeeded in his aim. While the writings chosen reveal much about the nature of scientific method and progress in science, at the same time they reveal the very human nature of science, from the painstaking, meticulous struggles of some to the creative thinking and flashes of brilliance of others. There is a genuine human warmth, energy and excitement present in many of the writings that draw the reader in and motivate the reader to delve further into the topic under study. I would certainly recommend this book to any person, scientist or non-scientist. There is something here for everyone! Our Cosmic Habitat by Martin Rees (ISBN 0297829017) published by Weidenfeld & Nicholson, London in 2002. Sir Martin Rees is Royal Society Research Professor at Cambridge University. His central thesis in this book is that our universe is just part of a vast "multiverse" or ensemble of universes. He discusses the possibility that our cosmic habitat is a very special, perhaps unique universe in which the prevailing laws of physics allowed life to emerge. Rees examines the credibility of the Big Bang Theory and what we know of the beginning of the universe, briefly discusses black holes and their effect on time, considers possible futures for the universe, comments on the latest attempts to attain a unified theory of the cosmos and microworld and describes why he believes in the multiverse concept. Any person with an interest in astronomy or cosmology would find this book very entertaining and informative. It provides good revision and extension material for any student studying new HSC Syllabus Topics 8.4 The Cosmic Engine or 9.7 Astrophysics. It is available in the College Library. Our Final Century by Martin Rees (ISBN 0434008095) published by William Heinemann, London in 2003. Sir Martin Rees is Royal Society Research Professor at Cambridge University. In this, his latest book, he explores the downside of unpredictable science and runaway technology. He addresses the hazards of error, terror and environmental catastrophe - some familiar, others less so - emphasizing the great difficulty of countering these risks. The theme is not new - many novels and movies have been based on the same theme - think of "The Matrix" and the "Terminator" series of movies. This book however presents an up to date consideration of what are very real possibilities and dangers. Rees is concerned that before too long, maybe within twenty years at the outside, bio and cyber technologies will become so powerful that even one fanatic or social misfit could trigger a worldwide disaster of previously unimagined scale. He worries that catastrophes could arise simply from technical misadventure - mistakes do happen, even in the most well-regulated organizations. There are even fears that certain high energy experiments in particle accelerators may one day trigger some cataclysmic unraveling of the fabric of the universe, bringing everything to an untimely end. How should society guard against being unknowingly exposed by scientists to a not-quite-zero chance of an event with an almost infinite downside? What safeguards need to be put in place? If the human race is to survive this new century says Rees, it is time to make some difficult decisions about the future of science. Written in Rees' easy-to-read, authoritative and entertaining style, this book is well worth the read. Parallel Worlds by Michio Kaku (ISBN 0713997281) published by Penguin Allen Lane, London in 2005 Michio Kaku is a leading theoretical Physicist and one of the founders of String Theory, widely regarded as the strongest candidate for a Theory of Everything. Kaku is also an excellent author. "Parallel Worlds" tells the story of the latest scientific theories of the nature of creation and tells it in a lucid, entertaining, down to earth style. Using the latest astronomical data, Kaku outlines the current views of the Big Bang, theories of everything and our cosmic future. He takes us on an exciting, thought provoking tour of such concepts as Dimensional Portals, Time Travel, Parallel Quantum Universes and aspects of String and M Theory. He considers the possibility of escaping from our universe into another. He discusses some thoughts on the meaning of life, the universe and everything. Throughout the book Kaku includes interesting anecdotes to illustrate a host of points. Tales of philosophical battles between Bohr and Einstein; stories illustrating the paradoxes of time travel; and so on. For instance, imagine using a time machine to go back into the past and actually become your own father. Mind boggling!!! This is a very informative and entertaining read. Extremely good! It would be a good addition to any school library. It says on the back cover: "The greatest challenge in fundamental physics attempts to reconcile quantum mechanics and general relativity in a theory of "quantum gravity." The project suggests a profound revision of the notions of space, time and matter. It has become a key topic of debate and collaboration between physicists and philosophers. This volume collects classic and original contributions from leading experts in both fields for a provocative discussion of the issues. It contains accessible introductions to the main and less-well-known known approaches to quantum gravity. It includes exciting topics such as the fate of spacetime in various theories, the so-called "problem of time" in canonical quantum gravity, black hole thermodynamics, and the relationship between the interpretation of quantum theory and quantum gravity. This book will be essential reading for anyone interested in the profound implications of trying to marry the two most important theories in physics." This book is well worth a read for anyone interested in developments in the field of quantum gravity. Probably most appropriate for undergraduate students in Physics and/or Philosophy and graduate students. Science A History 1543-2001 by John Gribbin (ISBN 0713997311) published by Penguin, London in 2002. I cannot speak highly enough of this book. It is an excellent read. Although the title may sound a little dry, for anyone interested in the history of science, this is a "must read"! John Gribbin is currently Visiting Fellow in Astronomy at the University of Sussex. He is an accomplished astrophysicist as well as a very respected author of many books on Science. In this book Gribbin tells the story of the people who made science from the Renaissance to the present day. He shows that although we tend to think of science in terms of a few unique geniuses, more often than not it involves relatively ordinary people building step by step on the progress of previous generations. Gribbin gives us a unique insight into the minds and hearts of the scientists without whom our lives would be unrecognizable. There is one error. In the section discussing the Michelson-Morley Experiment, Gribbin writes : "Always the answer was the same - no interference between the two beams". In fact, there was always interference between the two beams of light in the interferometer. The crux of the experiment is that when the whole apparatus was rotated through 90 degrees there was no change in the interference pattern observed on the screen. Still, this book is a masterpiece. It is an epic tale that animates the history of science. It informs, excites and inspires the reader. You are left in awe at the creative genius that lies within the human soul and with a real sense of science as perhaps the greatest achievement of the human mind. Every teacher of science should read this magnificent book. It would be a great addition to any school library. The Elegant Universe by Brian Greene (ISBN 009928992X) published by Vintage, London in 2000. Brian Greene is Professor of Physics and Mathematics at Columbia University and Cornell University. He is one of the world's leading experts on "Superstring Theory", one of the main contenders for a quantum theory of gravity. In trying to fathom what happened in the first 10-43 of a second of the Big Bang (the Planck time), physicists reach a point at which the equations of General Relativity break down. At that time the universe was only about 10-35 metres in diameter (the Planck length). On such short distance scales as these, we encounter a fundamental incompatibility between General Relativity and Quantum Mechanics. Basically, the central feature of Quantum Mechanics, the uncertainty principle, conflicts directly with the central feature of General Relativity, the smooth geometrical model of spacetime. The notion of a smooth spatial geometry is destroyed by violent fluctuations of the quantum world on short distance scales. Greene firstly provides an excellent and very readable account of the main features of the Theory of General Relativity and the Theory of Quantum Mechanics, without delving into the associated mathematics. He then explains clearly, the reasons for the incompatibility between these two theories on very short distance scales. These first five chapters are probably readable by anyone with an interest in Physics. Greene uses many good analogies to get his points across. In the remaining ten chapters, Greene presents an exciting account of Superstring Theory that provides the reader with a very clear picture of the main features of the theory and of the work being done to build this theory into a successful quantum theory of gravity. Along the way we are introduced to the concept of a 10 or 11 dimensional universe, where the fabric of space tears and repairs itself, and all matter is generated by the vibrations of microscopically tiny loops of energy. We also see how Superstring Theory successfully overcomes the incompatibility between General Relativity & Quantum Mechanics. Exciting! Mind-blowing! Beautiful! But be warned - much of the material beyond chapter 6 requires a great deal of concentration to read and understand, even for someone with a solid background in Physics. The Road To Reality - A Complete Guide to the Laws of the Universe by Roger Penrose (ISBN 0224044478) published by Jonathan Cape, London in 2004. Weighing in at 1094 pages, this is a heavy book - both physically and cognitively. The book provides a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. Professor Penrose describes with clarity our present understanding of the universe. He conveys a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. In the book we learn about the roles of the different kinds of numbers in Physics; the ideas - and magic - of calculus and of modern geometry; notions of infinity; relativity theory; the foundations and controversies of quantum mechanics; the standard model of particle physics; cosmology; the Big Bang; Black Holes; the profound challenge of the second law of thermodynamics; string and M Theory; loop quantum gravity; fashions in science; and new directions. Roger Penrose is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford. He has received a number of prizes and awards, including the 1988 Wolf Prize for Physics, which he shared with Stephen Hawking for their joint contribution to our understanding of the universe. This book is awesome in its scope. Inspite of claims to the contrary by the author, you will need a degree in Physics or Mathematics to read this work from cover to cover. As one reviewer from Amazon.com wrote of this book: "The number of people in the world who can understand everything in it could probably take a taxi together to Penrose's next lecture." For most people, this book will serve as an extremely authoritative reference on matters concerning the nature of the universe. It would be a good addition to any school or university library. Three Roads To Quantum Gravity by Lee Smolin (ISBN 0297643010) published by Weidenfeld & Nicolson, London in 2000. Lee Smolin is currently Professor of Physics at the Centre for Gravitational Physics and Geometry at Pennsylvania State University and a leading contributor to the search for a unification of Quantum Theory, Cosmology and Relativity. One of the greatest challenges in modern Physics is the quest to successfully unify Einstein's Theory of General Relativity with the Quantum Theory into what has become know as the Quantum Theory of Gravity. This book is an extremely valuable, up to date report on progress towards this goal at the beginning of the 21st Century. With elegance, simplicity and clarity, Smolin describes the three main "roads" along which most progress has been made - Black Hole Thermodynamics, String Theory and Loop Quantum Gravity. The work that has been done in these three fields of research, and others that Smolin describes, is inspirational and the insights that have been gained are very exciting. The reader is presented with new insights into the nature of space and time. For instance, space could well be discrete rather than continuous on the Planck scale (10-35 metre). So just as there is a smallest unit of matter that can exist, there could well be a smallest volume of space that can exist. The reader is introduced to the "holographic principle" which may very well be the fundamental principle of Quantum Gravity. Towards the end of the book Smolin addresses the question of who or what chose the laws of nature. Throughout the book Smolin conveys the human nature of scientific research - the frustrations, worries and disappointments, as well as the joy and excitement of discovery. He stresses that research at this level has to be a community activity taking full advantage of the talents and abilities of all those involved in the struggle. He highlights the importance of communication between mathematicians and physicists. As one reads this book one experiences a sense of awe at the innate beauty and mystery of the universe created by our God and at the nobility and ingenuity of the God-given human intellect as it strives to understand the universe. I would recommend this book to any person interested in the nature of space and time and in our growing scientific understanding of these two fundamental concepts. (Also note that the material on pages 99-100 of this book can be used in relation to the Stage 6 Physics Syllabus Statement 9.4.2 Column 3 Dot Point 2 - Einstein's contribution to Quantum Theory etc.) The Grip of Gravity by Prabhakar Gondhalekar (ISBN 0521803160) published by Cambridge University Press in 2001. This is a very readable account of the development of our understanding of the force of gravity over the last two thousand years. It includes revealing biographical sketches of many of the scientists who added to our understanding and illuminating digressions on the political and cultural background of the times in which various discoveries were made. The book describes all aspects of gravity, including curved space-time, neutron stars, wormholes (and time travel), black holes, gravitational lenses and current developments in cosmology. Einstein's Theory of General Relativity is examined as well as alternative theories. In the final chapter there is a very good description of attempts to unify the four forces of nature, including a brief outline of Superstring Theory. The book is written in a logical, easy to read, entertaining style. The author's coverage of the topic is extremely thorough. He also provides a list of suggested further readings. This book is well worth a read for anyone interested in physical science and its historical development. A fantastic book! Lisa Randall is one of the world's leading theoretical Physicists and an expert on String Theory. Her work has attracted enormous interest and is some of the best cited in all of science. She was the first tenured woman in the Princeton Physics Department and the first tenured woman theorist at MIT and Harvard. In the Preface and Acknowledgements section at the start of the book Randall states that she "envisioned a book that shares the excitement that I feel about my work without compromising the presentation of the science. I hoped to convey the fascination of theoretical physics without simplifying the subject deceptively or presenting it as a collection of unchanging, finished monuments to be admired. Physics is far more creative and fun than people generally recognize. I wanted to share these aspects with people who hadn't necessarily arrived at this realization on their own." Randall has certainly achieved what she envisioned. This book is an excellent read. In this brilliant and accessible account, Randall takes us into an incredible world of warped, hidden dimensions that underpin the universe we live in. She describes how we might prove their existence. She explores what they can tell us about our existence and looks at the questions that they they still leave open. Giving an exhilarating overview of the major developments in physics over the last century, giving accessible accounts of subjects such as string theory, particle theory and brane theory and unweaving the current debates about relativity, quantum mechanics and gravity, this brilliant book demystifies the science and unravels the mysteries at the heart of our world. A must read!!! It would be an excellent addition to the science section of any school library.
Advances in technology, together with an increased interest in dynamical systems, are influencing the nature of many first courses in ordinary differential equations (ODEs). In addition, there is an increased emphasis on nonlinear differential equations, systems of differential equations, and mathematical modeling, as well as on qualitative and numerical approaches that shed light on the behavior of solutions. Analytic techniques are still important, but they no longer tend to be the sole focus. As these new directions come into classrooms, research is beginning to illuminate aspects of learning and teaching ODEs that can inform ongoing curricular innovations. In a French study aimed at exploring the teaching of qualitative solutions, Michèle Artigue conducted a three-year project with first-year students at the University of Lille I. Approximately 100 students per year received nearly 35 hours of instruction on first-order differential equations. Students attended common lecture sessions with smaller exercise sessions using computers. As evidenced by their lab reports and examinations, early on students were able to successfully complete tasks where information was given simultaneously in two settings and the problem to be solved required interpretation between the two settings. For example, one interpretation task asked students to find and justify the correct match between seven different differential equations and corresponding graphs of solution curves. With little or no intervention from the instructor, these students were successful because they were able to employ a variety of familiar criteria for determining and checking their answers. These criteria included connections between the sign of f (where dy/dx = f(x, y)) and properties of monotonicity for solution curves, zeros of f and horizontal slope, infinite limit of f and vertical slope, the value of f at a particular point and the slope of a solution curve at that point, and recognizing particular solutions associated with straight lines in the graphic setting and checking them in the algebraic setting. We would hope all students are familiar with these criteria from calculus, and thus, that such criteria can serve as a basis for further study of differential equations. [see Artigue (1992)] Michelle Zandieh and Michael McDonald also studied students' underlying understanding of solutions and equilibrium solutions. They interviewed a total of 23 students from two separate reform-oriented differential equations classes, one at a large state university in the southwest and one at a small liberal arts college on the west coast. In addition to asking students open-ended questions such as, "What is a differential equation?" and "What is a solution to a differential equation?", they posed several tasks for students to solve. One of the tasks was the same matching task used by Rasmussen and another asked students to draw representative solutions on a given slope field for dy/dt = y + 1. Much like previous research findings, 7 of the 23 students overgeneralized the notion of equilibrium solution to include all values for which dy/dt is zero. When asked to draw representative solution functions, 3 of the 23 students failed to sketch the equilibrium solution y(t) = 1. Mathematically, we would expect students' notion of equilibrium solution to be a subset of their notion of solution, but for these students this did not appear to be the case. Consistent with Rasmussen's findings, these results underscore an important conceptual difficulty that may lie beneath many correct answers. [see Zandieh & McDonald (1999)] In another task Rasmussen provided students with the autonomous differential equation dN/dt = 4N(1N/3) (1N/6) and the corresponding graph of dN/dt vs. N. He asked the following three questions: (a) What are the equilibrium solutions? (b) Which of the equilibrium solutions are stable and which are unstable? (c) What is the limiting population for N(0) = 2, N(0) = 3, N(0) = 4, and N(0) = 7? All six interview subjects figured out the correct answers to parts (a) and (b) but four of the six students were unable to address part (c). This was particularly surprising because the typical student approach to this problem was to figure out the first two parts by creating a sketch like that in Figure 1. Figure 1. Typical student sketch Why would students be able to do parts (a) and (b), but fail to "see" the connection between their sketches and the long-term behavior for various initial populations? This question is especially intriguing because these students had just created for themselves what is from our perspective a sketch like that in Figure 1 of various solution functions. During the interviews, the answer to this question became quite clear. Students did not view the sketch they had just created as a plot of the functions that solve the differential equation. In the words of one student, his sketch was "just a test for stability." These students had learned a graphical approach for determining stability where the graphs they created did not carry the intended conceptual meaning. [see Rasmussen (2001)] Research findings focusing on student understanding in courses taking new directions in ODEs indicate that graphical and qualitative approaches do not automatically translate into conceptual understanding. In a traditional course, a typical complaint is that students often learn a series of analytic techniques without understanding important connections and conceptual meanings. Care must be taken or else students are likely to supplement mindless symbolic manipulation with mindless graphical manipulation. Of course, how a student thinks and reasons is as much a reflection of his or her individual cognitive development as it is a reflection of the mathematics classroom. For example, if students are not routinely expected to explain and mathematically defend their conclusions, it is more likely that they will learn to proceduralize various graphical and qualitative approaches in ways that are disconnected from other aspects of the problem. Since graphical predictions are playing an increasingly prominent role in reform-oriented approaches to ODEs (see for example, Blanchard, Devaney, and Hall, 2002; Borrelli and Coleman, 1998; Diacu, 2000; Kostelich and Armbruster, 1997), it makes sense to explore the extent to which students are able to create geometric proofs. Artigue's work specifically examined this issue; she reported on students' work on three types of tasks — prove that a solution intersects a given curve; prove that it cannot intersect a given curve; and prove that it has an asymptote or rule out the possibility of such an infinite branch. She found that students had great difficulties generating these proofs. She attributes this to two causes. First, students had not been exposed to the delicate tools that they needed to use in qualitative proofs in the graphical setting. For example, the helpful ideas of fence, funnel, and area had not been introduced to students because, as Artigue suggests, mathematics professors have been slow to accept the graphical setting as a place for proof. Second, many students have strong monotonic conceptions that interfere with their proof efforts. For example, students had an intuitive belief in the following false statement: If f(x) has a finite limit when x tends towards infinity, its derivative f '(x) tends toward zero. Yet another reason for students' difficulty was that moving from predictions about how a solution might look to actually proving these statements requires the use of elementary analysis. [see Artigue (1992)] A different approach to proofs involves emphasizing argumentation as a routine part of everyday classroom discussions. In a multi-year project at a mid-sized university in the Midwest, researchers2 are studying student learning in a first course in ODEs as it occurs in classrooms over the course of an entire semester. An interesting example from this research related to proof involves the arguments students developed to justify that two solutions to a logistic growth differential equation with different initial conditions would never touch. Although these students had not yet studied the uniqueness theorem, they argued that since graphs of solutions to autonomous different equations were shifts of each other along the t-axis, there would never be a point in time when the solutions intersected each other. For another example of arguments involving short chains of deductive reasoning, consider the following question that students in this project asked and answered: Is it possible for a graph of a solution to an autonomous differential equation to oscillate? The typical argument these students developed to reject this possibility was to argue that since the slopes in a slope field for an autonomous differential equation would have to be the same "all the way across" the slope field, a graph of a solution would not oscillate because if it did, there would be a value for y where the slope would be both positive and negative. For students like those in this class who have little to no experience in developing mathematical arguments to support or refute claims, significant progress in their ability to create and defend short deductive chains of reasoning was observed. This progress was due in large part to the explicit attention paid to classroom norms pertaining to explanation and justification. These social aspects of the mathematics classroom are reviewed in the final section. [see Stephan & Rasmussen (2002)] In Rasmussen's study, students discussed a previously completed Mathematica assignment where they had generated and interpreted graphs of the angular position (in radians) versus time for the linear and non-linear differential equations similar to those shown in Figure 3. Each plot in Figure 3 shows a different set of initial conditions for the solutions to the undamped linear model, '' + = 0 and to the undamped nonlinear model, '' + sin = 0. Graphs of solutions to the nonlinear model are indicated with NL. Figure 3. Solution graphs for a linear and nonlinear pendulum As might be expected, students experienced the most difficulty interpreting the graphs in Plots C and D. Students tended to interpret the graph as a literal picture of the situation. For example, one student said that the graph of the solution to the nonlinear model in Plot C indicates that "it starts increasing and remains at a constant distance from, whatever, and then it would start increasing again spontaneously, plateau again and then start increasing." He also acknowledged that he had never seen a pendulum do something like that, but was unable to interpret the plot otherwise. In Plot D, this same student explained that the graph of the solution to the nonlinear model shows the pendulum "increasing and increasing and this thing wouldn't be able to hold it and it would just fly off." [see Rasmussen (2001)] The studies by Trigueros and Rasmussen suggest that developers of both curriculum and instruction need to be cautious about what is assumed will be obvious to students when dealing with rich and complex graphical representations. Perhaps further and deeper classroom conversations surrounding the interpretation of such representations might help minimize the types of student difficulties highlighted in these studies. In the study conducted by Rasmussen at the large mid-Atlantic university, students worked on CAS labs outside of class time and only rarely did class discussion focus on interpretations or analysis of their labwork. As documented by interviews and surveys, students viewed these CAS labs as unrelated to what they saw as the main ideas of the course and they did not think that the work they put into the labs furthered their understandings of important ideas or methods, which was contrary to the instructor's goals of the course. However, when technology is integrated into the course, there is some evidence that this does help promote better understandings of various graphical representations. For example, in Habre's study students used computer modules designed for specific course goals of the course and intended to introduce students to specific concepts. Although this was not the focus of his research, some of Habre's interview data suggests that these modules might have been helpful to students in their development of mathematics in the graphical setting. For example, when given a vector field for the system of ODEs x'(t) = x + 4y, y'(t) = 3xy, all the students he interviewed were able to draw an appropriate trajectory in the xy-plane and to draw reasonable x(t) and y(t) graphs corresponding to this trajectory. Some students, however, faced difficulties in drawing the 3D-parametric curve. Habre suggests that the role of such computer modules in student learning warrants further study. [see Rasmussen (1997); Habre (2000)] What this limited research does indicate is that we need to be deliberate in how and why we decide to implement technology in the classroom. It shows that students' visual understanding of phase portraits, slope fields, and solutions of differential equations is an area where we might consider integrating technology into students' experiences in the classroom. Using a computer algebra system as a separate lab component or only as a demonstration tool seems less likely to achieve the intended learning goals. Findings include the significant role of explanation and justification as a normal part of classroom discussion. The following classroom features, critical to the success of the project in terms of student learning, were initiated by the instructor and sustained throughout the semester: Students routinely explained their thinking and reasoning (versus just providing answers), listened to and tried to make sense of other students' thinking, indicated agreement or disagreement with other students' thinking, and responded to other students' challenges and questions. Such aspects of classroom social interactions involving explanation and justification that become routine are referred to as social norms. The initiation and maintenance of such norms was a challenge because students in the project classes were used to and expected traditional patterns of interaction where the instructor talked and the students listened. Given that many undergraduate students are not used to explaining their reasoning and making sense of other students' thinking, a pervasive and important question is: How can instructors (1) initiate a shift in social norms, and (2) sustain these norms over time? The studies conducted by Rasmussen and colleagues offer useful responses. For example, in the semester-long classroom studies described, the instructor devoted explicit attention to initiating the social norms described above. During an approximately twenty-minute whole class discussion on the second day of class, the instructor led a whole discussion where he offered no mathematical explanation himself. Rather, he strove to initiate new social norms by inviting students to discuss their thinking and reasoning through remarks and questions such as: Tell us how you thought about it. That's what we're interested in. What do some of the rest of you think about what Jason just said? Did anyone think about that in a different way? That's a good question. Let's put that question out to the rest of the class. What do the rest of you think about it? Tell us why you are thinking that. I'm not sure that everyone heard what you were saying. Say it again please. Say a bit more about that. Social norms are not rules set out in advance on a syllabus. Although being explicit about expectations can be useful, such explicit statements are insufficient. Norms are regularities in the ways individuals interact. As such, an instructor alone cannot establish them. They are constituted and sustained through participation and interaction over time. As students and the instructor act in ways that are consistent with new expectations regarding explanation and justification, they contribute to their ongoing constitution. Another point, which is illustrated in two case studies at two different U.S. universities, is that every class, from the most traditional to the most reform-oriented, has social norms that are operative for that particular class. It is not the presence or absence of social norms that differentiates one class from one another. Rather, it is the nature of the norms that differ from class to class. Of course the social norms pertaining to explanation and justification might apply to a history class or an English literature class, as well as a mathematics class. The term sociomathematical norm refers to the fact that the subject being learned is mathematics. The expectation that one is to give an explanation is a social norm, but what is considered to be an elegant solution, a different solution, an efficient solution, or an acceptable mathematical explanation are sociomathematical norms. For example, when students develop predictions and explanations about the future of say, the population of fish in a lake, it is imperative that these explanations move beyond conclusions based solely on contextual reasons (e.g., the fish are going to run out of food, so their numbers are going to decrease) to include reasons that rely on an interpretation of the mathematical idea of rate grounded in the differential equation. Fostering a classroom learning environment that promotes the types of explanations valued by the mathematics community is a process that evolves over time as students and instructor interact in the classroom setting. If instructors are interested in promoting a classroom environment where students routinely give and evaluate mathematical arguments, explicit attention to the processes by which norms are constituted is a first step. Finally, this research team documented how these evolving norms fostered a shift in student beliefs about their role as learners, about their instructor's role, and about the general nature of mathematical activity. These beliefs shifted from seeing their role as passive absorbers of information to active participants in knowledge creation. When the classroom is viewed as a dynamic system that includes the way in which students participate in mathematical learning, we can account not only for how student beliefs evolve and develop, we can also promote student beliefs about mathematics more compatible with the discipline itself. [see Yackel & Rasmussen (in press)]
Metadata Name: Algebraic Expressions and Equations: Combining Polynomials Using Addition and Subtraction ID: m21854 Language: English (en) Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form. Objectives of this module: understand the concept of like terms, be able to combine like terms, be able to simplify expressions containing parentheses.
Advanced Algebraic Geometry (WONDER) The goal of the course is to introduce concepts and techniques of algebraic geometry, up to a level where students can begin to study current research literature. Description This is an advanced course on algebraic geometry for students who are already familiar with some basic notions of algebraic geometry. The main focus of the course will be on the geometry of nonsingular curves and surfaces. Chapters 4 and 5 of Hartshorne's book give a good idea of what we are aiming for. Along the way we shall introduce several techniques, such as sheaves and their cohomology. Rather than developing the full theory of schemes we will focus on geometric aspects. Organization There will be a weekly 3-hour lecture. As part of their study we expect students to work through exercises on their own initiative. Also we expect them to be willing to independently study material from the literature. Examination At the end of the course there will be a take home assignment. After this there is an oral exam. Literature As a main reference we shall use Hartshorne's book 'Algebraic Geometry'. This is a classic and we recommend that students get hold of their own copy. In addition to this we shall use bits and pieces from other textbooks, to be announced during the course. Prerequisites This is an advanced course, only for students who are already familiar with some basic notions of algebraic geometry, including: affine varieties and their coordinate rings, projective varieties, irreducibility, morphisms of varieties, regular and rational functions, the function field. The mastermath course Algebraic Geometry provides sufficient background to follow this course. Remarks *This is a course offered by WONDER. It is an advanced master and beginning graduate student level course. Students cannot apply for travel costs for this course.
Beginning Algebra : Early Graphing conti... MOREnual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the first edition of Tobey/Slater Essentials of Basic College Mathematics even more practical and accessible. Normal 0 false false false MicrosoftInternetExplorer4 John continual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the first edition of Tobey/Slater Beginning Algebra: Early Graphing even more practical and accessible. Prealgebra Review; Real Numbers and Variables; Equations, Inequalities, and Applications; Graphing and Functions; Systems of Equations; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Radicals; Quadratic Equations For all readers interested in algebra.
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Prerequisites:A Math ACT of 23, a grade of C or better in MATH 1010 or equivalent. Other Materials:Graphing Calculator. Course Description: This course explores the concept of functions: polynomial, rational, inverse, logarithmic and exponential; with an emphasis on graphing. Solving systems of equations using matrix methods is covered along with conic sections. Other topics may include sequences, mathematical induction and the binomial theorem. The course involves the extensive use of graphing calculators. Objectives: Be able to solve problems with and without the use of a graphing calculator Become familiar with common functions and their graphs Solve (systems of) equations and inequalities Understand conics Work with arithmetic and geometric sequences and geometric series Use exponential and logarithmic functions. Homework: Homework assignments are listed on the next pages of this syllabus. I will collect weekly assignments on the following Tuesday. Late unexcused homework will not be accepted. Attendance:Students are expected to attend all class meetings and are responsible for all of the material covered.Students who miss a class meeting should copy a classmate's notes for that meeting. Also, there will be no "make–up" exams and quizzes. Unless a valid excuse is presented in advance, a missed exam will receive the score 0.Students must look at this syllabus carefully and plan well ahead. University Policies: Scholastic dishonesty will not be tolerated and will be prosecuted to the fullest extent. You are expected to have read and understood the current issue of the student handbook (published by Student Services) regarding student responsibilities and rights, and the intellectual property policy, for information about procedures and about what constitutes acceptable on-campus behavior. Students with medical, psychological, learning or other disabilities desiring academic adjustments, accommodations or auxiliary aids will need to contact the Southern Utah University Coordinator of Services for Students with Disabilities (SSD), in Room 206F of the Sharwan Smith Center or phone (435) 865-8022. SSD determines eligibility for and authorizes the provision of services. In case of emergency, the University's Emergency Notification System (ENS) will be activated. Students are encouraged to maintain updated contact information using the link on the homepage of the mySUU portal. In addition, students are encouraged to familiarize themselves with the Emergency Response Protocols posted in each classroom. Detailed information about the University's emergency management plan can be found at Information contained in this syllabus, other than the grading, late assignments, makeup work, and attendance policies, may be subject to change with advance notice, as deemed appropriate by the instructor.
These programs are designed to execute various calculations arising in our books in mathematical biology. They are intended for illustrative purposes only for understanding models that are always based on extensive simplifying assumptions. The MATLAB programs in this document were developed over several years, and so they use many versions of MATLAB.
This lucid and insightful exploration reviews complex analysis and introduces the Riemann manifold. It also shows how to define real functions on manifolds analogously with algebraic and analytic points of view. Richly endowed with more than 340 exercises, this book is perfect for classroom use or independent study. 1967 edition. Reprint of the 1980 Concept of a Riemann Surface by Hermann Weyl Gerald R. MacLane This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition. read more $12.95 Non-Riemannian Geometry by Luther Pfahler Eisenhart This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition. read more Riemann's Zeta Function by H. M. Edwards Superb study of the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude" traces the developments in mathematical theory that it inspired. Topics include Riemann's main formula, the Riemann-Siegel formula, more. read more Differential Manifolds by Antoni A. Kosinski Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition. read more Topology of 3-Manifolds and Related Topics by M.K. Fort, Jr. Daniel Silver Summaries and full reports from a 1961 conference discuss decompositions and subsets of 3-space; n-manifolds; knot theory; the Poincaré conjecture; and periodic maps and isotopies. Familiarity with algebraic topology required. 1962 edition. read more $16.95 $17$17
Beginning Algebra - With Cd - 4th edition Summary: For college-level courses in beginning or elementary algebra. Elayn Martin-Gay's success as a developmental math author and teacher starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions provide new pedagogy and resources to build student confidence, help students develop basic skills and understand concepts, and provide the highest ...show morelevel of instructor and adjunct support. Martin-Gay's series is well known and widely praised for an unparalleled ability to: Relate to students through real-life applications that are interesting, relevant, and practical. Martin-Gay believes that every student can: Test better: The new Chapter Test Prep Video shows Martin-Gay working step-by-step video solutions to every problem in each Chapter Test to enhance mastery of key chapter content. Study better: New, integrated Study Skills Reminders reinforce the skills introduced in section 1.1, "Tips for Success in Mathematics" to promote an increased focus on the development of all-important study skills. Learn better: The enhanced exercise sets and new pedagogy, like the Concept Checks, mean that students have the tools they need to learn successfully. Martin-Gay believes that every student can succeed, and with each successive edition enhances her pedagogy and learning resources to provide evermore relevant and useful tools to help students and instructors achieve successSusies Books Garner, NC 2004 Hardcover CD INCLUDED AND UNOPENED This book looks good. It is like any used book you would expect to find in a used book shop
Materials to be ordered via the DLD Description Algebra II is a comprehensive course that builds on the algebraic concepts covered in Algebra I and prepares students for advanced-level courses. Through a "Discovery-Confirmation-Practice" based exploration of intermediate algebra concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to Within each Algebra II lesson, students are supplied with a post-study "Checkup" activity, providing them the opportunity to hone their computational skills in a low-stakes, 10-question problem set before moving on to a formal assessment. Additionally, many Algebra II lessons include interactive-tool-based exercises and/or math explorations to further connect lesson concepts to a variety of real-world contexts. The content is based on the National Council of Teachers of Mathematics (NCTM
Graphing calculators are sophisticated devices that can run small computer programs and draw the graph represented by complex equations in an instant. In the last few years, they have become mandatory in many high school mathematics classes and can be used on the SAT and advanced placement exams and other standardized tests. This article sets forth the arguments for and against the use of these handheld computers in the classroom and during assessment. (author/sw) Ohio Mathematics Academic Content Standards (2001) Geometry and Spatial Sense Standard Patterns, Functions and Algebra Standard Data Analysis and Probability Standard Mathematical Processes Standard Benchmarks (8–10) E. Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas. Benchmarks (11–12) H. Use formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations. Principles and Standards for School Mathematics Algebra Standard Geometry Standard Data Analysis and Probability Standard Representation Standard Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena
consists of the textbook plus an access kit for MyMathLab/MyStatLab. #xA0; The Bittinger Graphs and Models Serieshelps students #x1C;see the math#x1D; and learn algebra by making connections between mathematical concepts and their real-world applications. The authors use a variety of tools and techniques-including side-by-side algebraic and graphical solutions and graphing calculators, when appropriate-to engage and motivate all types of learners. Abundant applications, many of which use real data, provide a context for learning an... MOREd understanding the math. #xA0; MyMathLabprovides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online. #xA0; 7.7 The Distance Formula, the Midpoint Formula, and Other Applications 7.8 The Complex Numbers Summary and Review Test 8. Quadratic Functions and Equations 8.1 Quadratic Equations 8.2 The Quadratic Formula 8.3 Studying Solutions of Quadratic Equations 8.4 Studying Solutions of Quadratic Equations 8.5 Equations Reducible to Quadratic Mid-Chapter Review 8.6 Quadratic Functions and Their Graphs 8.7 More About Graphing Quadratic Functions 8.8 Problem Solving and Quadratic Functions 8.9 Polynomial Inequalities and Rational Inequalities Summary and Review Test 9. Exponential Functions and Logarithmic Functions 9.1 Composite Functions and Inverse Functions 9.2 Exponential Functions 9.3 Logarithmic Functions 9.4 Properties of Logarithmic Functions Mid-Chapter Review 9.5 Natural Logarithms and Changing Bases 9.6 Solving Exponential and Logarithmic Equations 9.7 Applications of Exponential and Logarithmic Functions Summary and Review Test Cumulative Review: Chapters 1—9 10. Conic Sections 10.1 Conic Sections: Parabolas and Circles 10.2 Conic Sections: Ellipses 10.3 Conic Sections: Hyperbolas Mid-Chapter Review 10.4 Nonlinear Systems of Equations Summary and Review Test 11. Sequences, Series, and the Binomial Theorem 11.1 Sequences and Series 11.2 Arithmetic Sequences and Series 11.3 Geometric Sequences and Series Mid-Chapter Review 11.4 The Binomial Theorem Summary and Review Test Cumulative Review: Chapters 1-11 Answers Glossary Photo Credits Index Index of Applications Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters. David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master's degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary. Barbara Johnson has a B.S. in mathematics from Bob Jones University and a M.S. in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she recently earned a black belt in karate.
Author Topic: Mathematics Books (Read 829 times)Care to be a bit more specific about which math you'd like to relearn? I've found the Schaum's Outline series to be pretty useful, and have one to supplement just about every math or science class I have taken. They provide a very brief review of a topic, followed by a bunch or worked out examples. They are great if you are relearning something. Also, they are very inexpensive (a couple dollars used, maybe $25 US new). I'd recommend getting a couple of those, and then possibly an additional "real" textbook if you feel you need a more in depth treatment of the topics. Also, to the OP: check out your local library, chances are they have some math textbooks. Find a subject you are interested in, and grab as many text books on the subject as you can carry. You may find some that "click" with you better than others, and a concept that is confusing in one text may be better explained in another. Every time I've take a college math or science course, I always go to the university library and get a few additional books on the subject for these reasons. If you just want to read something about math for the joy of reading - and hey, there's no reason why you can't do that while also learning stuff - I recommend two books: The Drunkard's Walk by Leonard Mlodinow (about probability)+ The Calculus Diaries by Jennifer Oullette (about... well, guess) Both are a lot of fun and if you're like me will spur you on to learning moar I would NOT go for a text book. if you are looking for high school level math, get yourself the Martin Gardner Sci-Am collection. There are 15 of them, most go for under $3 as used (in amazon or abebooks). there's loads and loads of interesting high school level math there - geometry, probability, discrete math, and the list goes on. if you aim a bit higher, I would recommend Paul J. Nahin books. these require some higher calculus level and are less approachable than the Gardner books. They are however full with interesting mathematical detective-like investigations ('when least is best' would be a good start). Again, be warned the the Nahin books are packed with sometimes non trivial university level math. Logged quot;who is more foolish - the fool, or the fool who follows the fool?" Star Wars - A New Hope
For one- or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis. This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mecha...
The CCSS for Mathematical Practice reflect "how" students should interact with math content to master essential skills and their underlying concepts. Math Solutions Common Core courses are specifically designed to align what teachers already know with what they need to know about developing expertise in the "processes and proficiencies" outlined in the Standards for Mathematical Practice. Students with a strong start to their mathematics education—one that encourages conceptual understanding, procedural fluency, and computational automaticity—will be better prepared for academic success. Math Solutions helps teachers deepen content understanding, which will allow them to build a strong mathematical foundation for their students. Math Solutions helps teachers incorporate literature and communication to promote thinking and reasoning and increase their students' problem-solving ability. In addition, real-life scenarios and classroom discussion advance students' understanding and ability to use and apply mathematical concepts in a multitude of contexts. Within a mathematics class, students exhibit a wide variety of learning styles and instructional needs. Math Solutions helps teachers develop strategies for adapting lessons to facilitate understanding for the diversity of learners in their classroom. Some students need more support, more time, and specialized instruction to learn. Math Solutions helps teachers provide intervention instruction that meets the needs of these struggling students and helps them succeed. Math Solutions helps high school classroom teachers understand how students learn mathematics, explores ways to make math accessible for students, and focuses on problem solving in the strands of algebra and geometry. Math Solutions . . . Solve the ProblemTM Math Solutions professional development services and courses are customized to meet your needs. Please contact us online or toll free at 800.868.9092 for a proposal based on your goals and objectives. Let us help you solve the problem. "I want to provide more "Ah ha!" moments for my students by using more hands-on activities like we have done this week. This will involve more group work and a different approach to learning. I want to help my students think algebraically by making the same types of connections that I have been guided to make this week."
Week 1 (USC classes begin on Monday; Friday is the last day to drop without a grade of W) Jan 12 (Mon) Read page xv from the preface as well as sections 1.1 and 1.2. In 1.1 do #2, 4, 7, 9, 14, 17. In 1.2 do #3, 7, 11, 12, 14, 15, 16. Get a graphing calculator by Wednesday. If you don't already own one, I suggest any of the TI-83 or TI-84 calculators. If you need to take or retake the Algebra Placement Test, go to and select the third link Take Me To The Tests. You could also look at the first two links which include practice tests. Jan 14 (Wed) Finish the assigned homework from 1.1-1.2 and read section 1.3. Bring your calculator to class from now on. Jan 16 (Fri) Read section 1.5. In 1.3 do #5, 9, 10, 11, 12, 20, 25, 26, 31. In 1.5 do #11, 12, 17, 18. There will be a quiz Wednesday on sections 1.1-1.3. Today we spent a lot of time on calculator usage. We discussed how to use the Y=, 2nd-TBLSET, and 2nd-TABLE features of your calculator in order to get a table of values for a function. We also discussed how to use the GRAPH and 2nd-CALC features of your calculator in order to find the intersection of two graphs. The quiz will include testing your ability to use your calculator effectively. We did not spend much class time on section 1.3 today but it will still be included on the quiz so be sure to read the book carefully and do all of the homework. Read section 1.6 and do #2, 5, 10, 21, 22, 23, 24, 31, 36 from that section. For many of the problems in sections 1.5 and 1.6, I recommend that you try solving them 3 ways — (1) with a table of values on your calculator, (2) with a graph along with the intersect or trace features of your calculator, (3) by hand with rules of algebra including logarithm rules. Week 3 Jan 26 (Mon) Read section 1.7. For now do #1, 5, 8. If you want to get ahead then do #10, 11, 15, 16, 18, 19. There will be a quiz Friday on sections 1.5-1.6. Jan 28 (Wed) Finish the problems from 1.7. There will be a quiz Friday on sections 1.5-1.6. Jan 30 (Fri) If you missed today's quiz, download a copy and allow yourself around 20 minutes to complete it. For homework read section 2.1 and do #1, 3, 5, 6, 12, 13, 15 from that section. Week 4 Feb 2 (Mon) Read section 2.2 and do #13, 17, 20, 24, 26, 27 from that section. There will be a quiz Friday on sections 1.7, 2.1, 2.2. Monday's test will cover sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, and 2.3. You should also be able to use your calculator effectively. In particular you should be able to easily generate graphs and tables of values. You should also know how to use the 2nd-CALC features of your calculator to find intersections. For this test, in section 1.4 you may skip the part on "marginal cost", "marginal revenue", and "marginal profit" at the bottom of page 25. You may also skip the part on "supply and demand curves" from the middle of page 26 to the end of page 28. You should be able to solve any of this semester's assigned homework problems or quiz problems. I recommend that you look at past quizzes and tests with solutions from every semester I have taught this course. Remember to bring a student ID and a graphing calculator with fresh batteries. Read section 3.3 and do the odd problems from #1–33 for practice with the chain rule. Also do #35, 36, 37, 39, 42, 43, 44, 45. There will be a quiz Wednesday on sections 3.1-3.2 and another quiz Friday on section 3.3. Now is a great time to use the free services of the Math Tutoring Center as well as Supplemental Instruction. Feb 25 (Wed) If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. Read section 3.4 and do the odd problems #1–27 for practice with the product rule and quotient rule. Also do #34, 35, 36, 39, 41. There will be a quiz Friday on section 3.3 and a quiz Monday on section 3.4. Feb 27 (Fri) If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. There will be a quiz Monday on section 3.4. There is no new homework - just get caught up this weekend. Week 8 Mar 2 (Mon) If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. Read sections 4.1-4.2. Without using a calculator, graph the functions found in #8, 9, 10, 11, 12 in section 4.1. Don't be too concerned with the terminology just yet – we'll get to that next time. Mar 4 (Wed) Read section 4.3. Without using a calculator, graph the functions found in section 4.2 (#11, 12, 13, 14, 15, 16, 17, 18, 19, 20) and section 4.3 (#24, 25, 26). Now compare your results to graphs obtained with your calculator. Be able to state the intervals upon which the function is increasing, decreasing, concave up, or concave down. Be able to find any local max/min, global max/min, or inflection points. There will be a quiz Friday on this material. There will be a quiz Wednesday based on the homework from sections 4.3 and 4.4 assigned the Friday before Spring Break. Mar 18 (Wed) If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. Mar 20 (Fri) Monday's test will cover sections 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 4.4. No calculators are allowed for this test. You should be able to solve any assigned homework problem from these sections as well as any problem from quiz 4, quiz 5, quiz 6, quiz 7 or quiz 8. I also recommend that you look at past quizzes and tests with solutions from every semester I have taught this course. Remember to bring a student ID. Week 11 Mar 23 (Mon) Test 2 Mar 25 (Wed) Read sections 5.1-5.2. In section 5.1 do #6, 8, 9, 11, 14, 15, 17. In class we worked on the following problem. A population changes at a rate of 5e0.05t people per year where t is the number of years since 1980. If the population is 4000 in 1980 then estimate the population in 2000. First we approximate the total change in population between 1980 and 2000. Estimate 3 (average of the two estimates above): 172.7 people (do you know if this is an overestimate or underestimate?) This tells us that the population in 2000 is somewhere between 4151.2 and 4194.2 people. An estimate of 4172.7 is probably closer to the actual population but it is more difficult to say whether this is an underestimate or an overestimate. For homework get more refined estimates by choosing Δ t = 1. Be sure to make all 3 estimates and state when you know that your estimate is an overestimate or an underestimate. Mar 27 (Fri) No new homework. Week 12 Mar 30 (Mon) In section 5.2 do #3, 6, 10, 11, 12, 17. Apr 1 (Wed) Read section 5.3. No new homework. Apr 3 (Fri) Do #1-11 on the handout Old test and quiz problems — Chapter 5. There will be a quiz Monday on sections 5.1-5.2 and #1-6, 11 on the handout. There will be a quiz Wednesday on section 5.3 and #7-10 on the handout. Week 13 Apr 6 (Mon) If you missed today's quiz, download a copy and allow yourself around 10 minutes to complete it. Do #3, 4, 5, 6, 7, 8, 11, 19 from section 5.3. There will be a quiz Wednesday on section 5.3 and problems #7-10 on the recent handout Old test and quiz problems — Chapter 5. Monday's test will cover sections 5.1, 5.2, 5.3, 5.4, and 5.5. It will include a non-calculator part. Bring your student ID. Be sure to look carefully over quiz 9 (blank copy, solutions), quiz 10 (blank copy, solutions), the handout on old tests and quiz problems (blank copy, solutions), and the handout on the Fundamental Theorem of Calculus (blank copy, solutions). On the Fundamental Theorem of Calculus handout, problems #1 and #2 will definitely be on the test. I also strongly suggest looking at my tests and quizzes from past semesters.
Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on... The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the... more... A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics... more...
Mathematics 4.0 can help students understand mathematics, science, and tech-related concepts with powerful, easy-to use tools including a graphing calculator, unit converter, triangle solver, and equation solver. Step-by-step solutions are provided for each problem, so students can learn problem solving skills fast and easy. An improved Computer Algebra System (CAS) helps teachers share and solve more complex equations and functions. It's capable of handling many subjects, including pre-algebra, algebra, trigonometry, calculus, physics, and chemistry. Handwriting recognition is also included, so all students can write out problems by hand.
34 Matrices Matrices are an important tool in algebra. A matrix nicely represents a homomorphism between two vector spaces with respect to a choice of bases for the vector spaces. Also matrices represent systems of linear equations. In GAP matrices are represented by list of vectors (see Vectors). The vectors must all have the same length, and their elements must lie in a common field. The field may be the field of rationals (see Rationals), a cyclotomic field (see Cyclotomics), a finite field (see Finite Fields), or a library and/or user defined field (or ring) such as a polynomial ring (see Polynomials). Because matrices are just a special case of lists, all operations and functions for lists are applicable to matrices also (see chapter Lists). This especially includes accessing elements of a matrix (see List Elements), changing elements of a matrix (see List Assignment), and comparing matrices (see Comparisons of Lists).
5 2011Product Description Review . (Cut the Knot ) [. (Blake Mellor Journal of Mathematics and the Arts ) . (Choice ) From the Inside Flap "The book's emphasis on a workshop approach is good and the authors offer rich insights and teaching tips. The inclusion of work by contemporary artists--and the discussion of the mathematics related to their work--is excellent. This will be a useful addition to the sparse literature on mathematics and art that is currently available for classroom use."--Doris Schattschneider, author of M. C. Escher: Visions of Symmetry "Concentrating on perspective and fractal geometry's relationship to art, this well-organized book is distinct from others on the market. The mathematics is not sold to art students as an academic exercise, but as a practical solution to problems they encounter in their own artistic projects. I have no doubt there will be strong interest in this book."--Richard Taylor, University of Oregon 5.0 out of 5 starsExcellent textbook on the mathematics of PerspectiveSep 5 2011 By Ed Pegg - Published on Amazon.com Format:Hardcover At the start of the book, students are looking at normal hallways, rooms, and buildings through sheets of plexiglas, and tracing the outlines of what they see with drafting tape. From there, it's easy to see the concept of vanishing points. A few pages later, an image from Jurassic Park with a velociraptor walking towards Sam Neill is shown. As an exercise, the students must compare the position of a clawtip to the bottom of a doorframe. I've messed up this issue of image placement many times, so this simple exercise brought home a lesson for me. The core part of the book is 1, 2, and 3 point perspective, but with the idea that you'll be using a modern program of some sort. Then they introduce fractal geometry in a way I didn't expect, by taking a picture of a patch of grass and a small rock, and photopasting in a toy gnu and a climber. Small rocks look like big rocks look like mountains. I knew that, but I hadn't been tricked by it before, so I got the lesson better this time. Recommended. 4.0 out of 5 starschallengingFeb 13 2013 By Proteus - Published on Amazon.com Format:Kindle Edition|Amazon Verified Purchase I have to admit, this book is pretty challenging. There is a ton of geometry math that is used to describe the mathematical aspects of perspective. But it is a face, it increased my understanding of perspective. It is not an easy book to get through, and frankly I probably only understood about 20% of it, but that 20% was useful, and some day I will probably go back and actually try to do the exercises.
Student Solution Manual for Foundation Mathematics for the Physical Sciences Choose a format: eBook - PDF Overview Book Details Student Solution Manual for Foundation Mathematics for the Physical Sciences English ISBN: 0511911181 EAN: 9780511911187 Category: Mathematics / General Publisher: Cambridge University Press Release Date: 03/28/2011 Synopsis: This Student Solution Manual provides complete solutions to all the odd-numbered problems in Foundation Mathematics for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to arrive at the correct answer and improve their problem-solving skills. Student Solution Manual for Foundation Mathematics for the Physical Sciences
A Mathematically Sound Introduction to Relativity for Math, Physics and Astronomy Majors A Poster Presented at the 195th Meeting of the American Astronomical Society in Atlanta, GA, January 2000 (106.14) Click here for the AAS version of the abstract. ABSTRACT: It is often commented that the special theory of relativity can be understood with little more background than high school geometry. This may be debatable, but everyone would agree that the mathematical background needed to understand the general theory of relativity is quite extensive. A course will be outlined which has linear algebra and multivariable calculus prerequisites. The first third of the course covers curvature of curves and surfaces, geodesics, and manifolds. The middle third covers special relativity, simultaneity, Lorentz geometry, and spacetime diagrams. The final third covers general relativity, Einstein's field equations, the Schwarzschild solution, the precession of orbits and the bending of light. The course maintains a high level of mathematical integrity, while still avoiding such complicated topics as tensor calculus. Content and course strategy, along with ideas for offering the course as an internet class, will be presented.
Q: A: Q: A: Math-U-See covers core concepts found in standardized testing. Its focus on concept mastery gives students the tools to excel in a variety of different circumstances including testing. Q: How do I decide where to place my student? A: Placement is based on skill level, not grade level. Please call our customer support team for help with your individualized placement questions. Q: If I haven't previously used Math-U-See with my older student, can they start at their level or must they start in Alpha? A: Students may start at any level if they have mastered the mathematical skills taught in previous levels of Math-U-See. Placement is based on skill level, not grade level. Please call our customer support team for help with your individualized placement questions. Q: Can a student start Algebra 1 without having previously used Math-U-See? A: It is possible to use Algebra 1 without completing the earlier levels of Math-U-See. The prerequisites necessary to be successful in our Algebra 1 level are: a mastery of all basic operations, fractions, decimals, percents, integers, and basic understanding of exponents and roots; an understanding of standard, expanded, and exponential notation, and ability to convert between various notations; an ability to determine the least common multiple and greatest common factor for a set of numbers; an ability to manipulate, simplify, and solve basic algebraic equations; have completed our Pre-Algebra course or an equivalent course. Q: What levels are included in your high school math? A: Algebra 1, Geometry, Algebra 2, PreCalculus, Calculus, and Stewardship make up our Secondary Math courses. Pre-Algebra or an equivalent course is a prerequisite to Algebra 1. Q: Can an older student learn the lesson concept on their own by watching the lesson video? A: While Math-U-See encourages teacher/parent participation in our program, we recognize that some students can be successful in learning the Upper Levels of Math-U-See on their own. We suggest that there should be guidance from a committed parent or teacher, so that if the student struggles, the parent will be able to assist. Q: Can I buy the DVD or the student workbook separately? I don't use the Instruction Manual or the Tests booklet. A: No, these are sold in sets. The Instruction Pack includes the Instruction Manual and DVD. The Student Pack includes the Student Workbook and Tests booklet. Q: Do we really need to use manipulative blocks? A: The manipulative blocks are the key to Math-U-See. We have found that those who are most successful in mastering and understanding each concept are those consistently using the manipulatives as recommended through Algebra 1. Q: Do I really need two sets of blocks? A: Two sets will allow you to have ten pieces of each number. This is helpful when building the clock in the Primer through Beta levels. It is helpful to have the extra pieces when building larger problems in the Beta, Gamma and Delta level. If you have multiple students working at the same time in the same level, it is very helpful to have two sets. Each student would be able to build without having to wait on the other student. Q: What is the Classic curriculum? A: The Classic curriculum refers to an older series of math books entitled Foundations, Intermediate, and Advanced, which were replaced in 2004. Call our customer support team with questions. Q: What do the titles of the general math series books mean? A: They are the first six letters of the Greek alphabet. Using Greek letters expresses sequence without indicating grade level. Math is sequential. One of the distinct elements of Math-U-See is that we are based on developing sequential learning skills. Our sequence progresses according to skill level rather than grade level. Q: Are there special offers or discounts for large orders? A: Math-U-See offers an excellent value for a video/DVD based curriculum. We strive to keep our prices reasonable, but do not have any special offers. You can check our Clearance Cart for items that are available at a discounted rate. Q: Do you sell used Math-U-See books? A: No. Check our Clearance Cart to see if the items you need are available at a discounted rate. Q: What is the Math-U-See sequence for high school math courses? A: Math-U-See uses this sequence: Algebra I, Geometry, Algebra II, PreCalculus and Calculus.Algebra 1 is the first book to be done in the upper level sequence, as it is a prerequisite for both Geometry and Algebra 2. After you have completed Algebra 1, you can proceed to Geometry. Pre-Algebra or an equivalent course should be completed prior to Algebra 1. Q: What level of Math-U-See should my student finish before taking chemistry? A: The student should have finished Algebra 1 before starting chemistry. If your student is taking Algebra 2 at the same time as chemistry, contact us for a suggested alternate order of lessons that may be helpful. Q: What level of Math-U-See should my student finish before taking physics? A: At the minimum, a student should have finished Algebra 1 and Geometry before beginning physics. The basic trig functions, which are used in physics, are presented at the end of the Math-U-See Geometry course. Taking physics and Algebra 2 together should work for most students. Some students may already be in PreCalculus when they begin physics, which will be to their advantage, although not absolutely necessary. Q: When does Math-U-See allow the use of calculators? A: If you are confident that your student can do the basic operations easily, you may allow calculator use in Pre-Algebra and up for the more cumbersome problems, such as surface area. We encourage students to continue to do shorter problems without a calculator. A scientific calculator is needed for PreCalculus. Q: In which level is Trig included? Why is it not its own category? A: Traditionally, trigonometry was the course taught before calculus. Today, it is more customary to call the same course precalculus, perhaps because calculus is now offered in most high schools. By either name, the course is essentially the same — lots of trigonometry and some advanced algebra topics. Math-U-See combined the names and calls its course PreCalculus with Trigonometry. Q: What grading system does Math-U-See recommend? A: Math-U-See does not have a recommended grading system. The primary purpose of test taking is to confirm that the student has mastered each concept as you move along. If you want or need to give grades, you may use any system that makes sense to you, and that you feel fairly reflects your child's progress. Q: Does Math-U-See publish any international editions? A: Math-U-See publishes special editions for several English-speaking countries. For contact information go to our International Distributors page.
The final grade will be determined by weekly quizzez, one midterm exam and a final exam. The real numbers. Infinite sequences of real numbers. Real functions of one variable: limits, continuity, continuity on a closed interval, monotonic functions and inverse functions. Differentiability and the main theorem of the differential calculus. The Taylor theorem, the l'Hopital rule and study of the behavior of a function. The antiderivative and methods of integration. The definite integral and its properties. Integrable functions. The principle theorems of the integral calculus. Improper integrals. Series of numbers, sequences of functions, series of functions and power series. In the course there is a greater emphasis on theory and applications than in 104003.
Session 5: Mathematical and Nonalphabetical Signs Many more textbooks make use of non-literary signs, specifically mathematical and nonalphabetical signs such as arrows, check marks, abbreviations for units of measure, and the like. Care must be taken to know when the use of the signs described in this session can be used versus the use of a fully technical code, such as the Nemeth Code for mathematics. Some of the general provisions of Rule 5 are provided in a separate reading. One of the more important provisions is the computation rule, which provides reasonably clear guidance on the use of technical codes such as Nemeth. The rules for the use of the mathematical symbols in this session are pretty straight-forward: use the braille symbol only when the text does not provide identifications or explanations of the print text. include all signs in a transcribers note or on a special symbols page The specific mathematical symbols shown below in table form include: General mathematical signs Arrows Arrowheads Monetary signs Mathematical Signs These signs are generally preceded and followed by a blank space, although you generally will follow the print example for spacing. Some notable exceptions to the use of these signs: Use the letter "x" for magnification, such as "10x" to mean "ten times", for example in the power of a telescope lens. Use the word "by" in a dimension, such as "2 x 4", which would be brailled "2 by 4". + plus sign - minus sign ± plus or minus sign × multiplication, times sign division sign = equal sign negated equal sign > greater than sign < less than sign : ratio sign : : proportion sign because therefore % percent sign slashed zero, null or empty set Arrows Arrow signs are used with blank cells preceding and following: left arrow right arrow left and right arrow up arrow down arrow up and down arrow northeast arrow southeast arrow Arrowheads Arrowheads are used to indicate direction or "coming from", as in the example: "Area> Population>GNP." The statement is not saying that area is greater than the population which is greater than the gross national product (GNP); rather, it states that the GNP depends on the population, which in turn depends upon the amount of land available (area). In this case, the transcriber should use the arrowhead versus the greater than sign. < left arrowhead, derived from > right arrowhead, when is derived <? left arrowhead and question mark, source unknown Monetary Signs The only peculiarity about these signs is that the dollar sign and the pound sterling signs must be preceded by a dot 4 if they are used as stand-alones or if they are used in conjunction with a word or contraction.
Key to Geometry offers a non-intimidating way to prepare students for formal geometry as they do step-by-step constructions. Students begin by drawing lines, bisecting angles, and reproducing segments using only a pencil, compass, and straightedge. Later they do sophisticated constructions involving more than a dozen steps and are prompted to form their own generalizations. When they finish, students have been introduced to 134 geometric terms and are ready to tackle formal proofs Key To… When it comes to higher math, if either you (teaching) or your student (learning) lack confidence, then this curriculum may be your answer. These consumable work booklets are so well laid out and easy to understand, he'll finally be able to say, "I got it!" Work through each at your own pace. What you won't find: Lots of wordy explanations that leave you going, "Huh??" What you will find: Short, simple explanations with lots of examples, and a handful of well-designed problems on each page. The Key To Geometry Answers and Notes are available separately or purchased as a complete set.
Modern Algebra: A Historical Approach Presenting a dynamic new historical approach to the study of abstract algebra Much of modern algebra has its roots in the solvability of equations ...Show synopsisPresenting a dynamic new historical approach to the study of abstract algebra Much of modern algebra has its roots in the solvability of equations by radicals. Most introductory modern algebra texts, however, tend to employ an axiomatic strategy, beginning with abstract groups and ending with fields, while ignoring the issue of solvability. This book, by contrast, traces the historical development of modern algebra from the Renaissance solution of the cubic equation to Galois's expositions of his major ideas. Professor Saul Stahl gives readers a unique opportunity to view the evolution of modern algebra as a consistent movement from concrete problems to abstract principles. By including several pertinent excerpts from the writings of mathematicians whose works kept the movement going, he helps students experience the drama of discovery behind the formulation of pivotal ideas. Students also develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can tell us about multivariate functions and the 15-puzzle. To further this understanding, Dr. Stahl presents abstract groups as unifying principles rather than collections of "interesting" axioms. This fascinating, highly effective alternative to traditional survey-style expositions sets a new standard for undergraduate mathematics texts and supplies a firm foundation that will continue to support students' understanding of the subject long after the course work is completed. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.Hide synopsis Description:Good. Discoloration, Tanning or Foxing on cover and pages. -Dog...Good. Discoloration, Tanning or Foxing on cover and pages. -Dog Eared Pages
Search Course Communities: Course Communities Lesson 42: Conic Sections: Hyperbolas Course Topic(s): Developmental Math | Conic Sections This lesson begins with centralized hyperbolas and then moves into translated hyperbolas. A review of conic sections is presented before exercises in determining the type of conic section from its equation are given.
EduTubePlus mathAnnenberg Media develops workshops and courses that provide teachers with content and pedagogical learning. Workshop and course resources consist of video, print and Web components that can be used for self-study. "Patterns, Functions, and Algebra" explores the "big ideas" in algebraic thinking, such as finding, describing, and using patterns; using functions to make predictions; understanding linearity and proportional reasoning; understanding nonlinear functions; and understanding and exploring algebraic structure. The course consists of 10 two-and-a-half hour sessions that each include video programming and activities, provided online and in a print guide. The 10th session explores ways to apply the algebraic concepts you've learned in K-8 classrooms. You should complete the sessions sequentially
This quiz will review relationships, algebraic patterns, ratios, and percentages. This quiz will also test your ability to use tables and various information to create equations. There will also be a short review of the properties of volume. You will also be given problems that involve conversions from one unit to another.
This is the book I will use as a text if and when I teach linear algebra again. While it is a bit weak in the area of formal proofs, that deficiency is more than made up for by the strengths in demonstrating … more With the exception of material such as encoding that requires a computer for the most complex problems; the area called modern algebra has not changed in decades. In fact, this is an area where the inclusion … more The prime audience for this book is working professionals whose education required at least the first two years of the math major. To be more specific, I mean people that had to take at least a two-semester … more If you were once able to master the principles of algebra II and need a quick refresher, then this book may satisfy your needs. However, if you have never mastered them and need to learn them, then you … more This book is basically a review of all the mathematics the typical child learns from kindergarten through eighth grade. Each chapter begins with a list of the terms used in the chapter and this is followed … more "Encapsulated and compressed" is a better phrase to use in describing this 176-page book. It opens with the definition of a function and immediately proceeds to differentiation. The movement is so fast … more The talented and extremely dedicated person can use almost any reference for successful self-study; the differences between references are in the degree of difficulty. This book is touted as "A Self-teaching … more Unless you are preparing to take a calculus exam consisting of a series of basic differentiation and integration problems, then I really don't see any use for this book. The reviews of what differentiation … more While this book will be of little value if you need to learn or significantly re-learn basic algebra, it is an excellent resource if you simply need a refresher to prepare for a competency or placement … more The vast majority of problems that math students solve are based on equalities, a situation that is somewhat artificial when related to the real world. Many engineering problems are based on an inequality, … more For reasons I cannot really explain, when I was reading this book the metaphor of an altered "Whack-A-Mole" game came to mind. The scenario is that it has been decided that a sequence of mathematical … more The 157 problems in this book are certainly challenging and it is clear to see how they can be characterized as problems one mathematician would pose to another over coffee. Nontrivial with unusual points … more Although the Mathematical Olympiads are for high school students, the problems that appear on the exams are unusual and challenging enough to provide mathematical exercise for college students and professional … more Whatever their personal focus is in mathematics, all mathematicians have a reverent love for numbers. Many other people also possess a fascination with numbers; this manifests itself in the large number … more This book is a review/overview of first-year college calculus and given the bloated nature of the modern calculus textbook, the slim 128 pages of this book demonstrate how condensed the subject matter … more A study of topology is an integral part of the education of most graduate students and knowledge of topology is an essential skill for theoretical physics and the essential topology of a network is discussed … more If you read this book without doing a little bit of familiarizing yourself with the short story, "The Library of Babel" by Jorge Luis Borges, you will be starting the process from a weak position. The … more This is a book that should be kept on the reference shelf and regularly consulted by all teachers of K-12 mathematics. It contains a series of exercises illustrating concepts in geometry that explain … more The phrase "Moore Method" refers to the teaching tactics employed by the late R. L. Moore, where the students were given a set of basic axioms and definitions as a beginning and then were required to … more The title was properly selected, for the writers describe the development and evolution of the use of numbers as if they are an entity that began as an infant, had a lengthy childhood and now a permanent … more The history of mathematics consists of a sequence of discoveries, some of which enhance what has come before, others that clarify and still others completely revolutionize how mathematics is practiced. … more The subject matter of a first course in abstract algebra is almost universally the same to all people. It begins with some fundamental background in number theory, relations, functions and a survey of … more
With the goals, aspirations, and background experiences of today's students so diverse and eclectic, the secondary school mathematics curriculum must not only prepare students for formal advanced study in the subject, but must also develop students' problem solving and communication skills as well. Mathematical numeracy is formulated through a three-pronged approach which stresses the acquisition of fundamental skills, the application of these skills in sophisticated and realistic situations, and the exposition of the problem solving process and its results using concise and coherent language. Fundamental Skills Most strongly associated with the traditional study of mathematics, the mastery of fundamental skills is an essential aspect of mathematical and scientific literacy. Students must be familiar with the formal notation, operations, procedures, and rules of mathematics as with any other foreign language or logical system, and they will receive ample instruction and practice in the same. Applications and Problem Solving Just as a pile of bricks and a trowel full of mortar are nothing until they are assembled by a skilled and experienced craftsperson into a sturdy and beautiful structure, a student with a hodgepodge of formulas and theorems is not fully educated until he or she can use these skills to solve complex and non-trivial problems. Unlike basic skills, however, problem solving acumen cannot be acquired by dutifully aping the actions of the instructor, but requires a measure of creativity and intellectual risk-taking. Many aspects of the process, nevertheless, can be formalized, and with sustained practice and exposure to models of effective problem solving, students will have ample opportunities to develop their analytical reasoning abilities. Communication Albert Einstein and Steven Hawking would not be the household names that they are unless, in addition to their first-rate intellects, they possessed the ability to communicate their findings in language accessible to a wide and varied audience. Scientific and thechnological breakthroughs are useless unless they can be shared with others, and thus, the ability to communicate one's thought processes and results is as important as having the ability to obtain those results in the first place. Reading, writing, and speaking are not the sole responsibility of departments of English, and are, by necessity, integrated through the mathematics curriculum. Assessments and Evaluations An integral aspect of the instructional process, assessment and evaluation provide teachers with tangible evidence of student achievement, as well as feedback for future modification and adjustment. Most often associated with in-class individual tests and quizzes, assessments can also take the form of projects, individual, small-group, and whole-class discussions, teacher observations, journal responses, and oral presentations. Opportunities for students to demonstrate their knowledge and achievement are frequent and varied. Standards Alignment In order to ensure that all students have access to a challenging and rigorous course of mathematical study, standards and benchmarks for student achievement have been established at both the state and national levels. Instructional activities are geared towards the acquisition of these standards, and assessments are tailored towards the demonstration of attainment of these standards.
Ready for a simple, easy to use calculator for all those tough math problems? Solve This is unlike any normal calculator in that instead of pushing buttons, you type in the equation as it would appear on paper. The appearance resembles the actual equation on a piece of paper, which appears more realistic. This application knows scientific and trigonometry functions. Also, there is a parenthesis program that works with any equation containing parenthesis and provides an accurate answer. In a nutshell, Solve This is a math tutor that shows a breakdown of the steps used to solve your equation. Start using Solve This now to knock out any math problems you need answered!
Three Uses for Khan Academy Three Uses for Khan Academy If you don't know, Khan Academy is a free online educational website that consists of an amazing set of videos (over 3000) made by the amazing, Salman Khan. Khan uses a Wacom type of tablet and a headset to make videos to teach a variety of subjects. Khan Academy is mostly known for Khan's mathematics and science videos but he also covers economics, art, history and more. Khan has made hundreds of videos for math including ones covering about every subject imaginable in algebra. The best thing about Khan Academy is that not only are there thousands of videos on multiple topics, but they are taught extremely well; he is definitely the teacher you dream of having in college. Khan explains more than just how to do problems, but actually gives you the intuition behind them. Khan Academy can be very a handy reource, and here are three good reasons to use it. Review: If you finished your high school math requirements during your junior year of high school and then you decided to not take math your freshman year of college, then the chances are you have forgotten everything about math. So, before you go back into calculus after not thinking about math for three years it might be wise to review a bit. Once you watch a couple of videos you'll probably get a sense of how behind you are and can then go from there. Study: Khan Academy is also a good resource when you are currently enrolled in a class. Books in general can be annoying and difficult to learn from, especially with subjects like math and science. Khan has most likely made a video on the subject you are struggling with and can help you with that upcoming quiz. Test out of Classes: If you were not an amazing high school student and did not take calculus, but have decided you want to in college, you have a long and slow ladder to climb. You can only take one math class at a time, and if you only took algebra in high school, it's going to take you a while to catch up. However, there is a solution. Most colleges will allow you to "test out of" or actually test into a certain class instead of taking all the prerequisites. So, if you think you could test out of trigonometry or whatever class you're missing, you can use Khan Academy to do so. During the summer, you could watch all of the Khan Academy videos on that subject, and try to test out
Tuesday, May 15, 2012 Period 2 We revisited the quiz we took on Friday. We discussed what the problems meant and how we could better solve them. Students were then able to correct errors. Assignment: no homework tonight. Period 3 We began some work on evaluating expressions and powers. These are skills that we have used in previous units and concepts that will be needed in Algebra 1. We reviewed vocabulary terms and related them to things we already know. We will continue this discussion tomorrow. Assignment: wksheet 1.1A, #1 - 22 Period 4 We went over the concepts that were covered in Friday's quiz and then students were able to correct errors. We also discussed how we can solve quadratic equations that are in factored form. This is something that we will continue tomorrow. Assignment: no homework tonight. Period 5 We continued our work with the quadratic formula. This is just one way to solve quadratic equations but the method that works for all of them. Tomorrow we will discuss how to use the discriminant to determine the number of solutions. This builds directly on what we have been learning when using the quadratic formula. Assignment: p. 674, #7 - 12, 19 -26