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About Me
Wednesday, August 31, 2011
Most math text books have examples that are completely worked out with the solution given. Take a piece of paper and hide the textbook answer and work, but show the question. Redo the problem and then check your work with their work and solution.
2. Study for Tests and Quizzes.
It is easy to just do the review homework and feel like you are ready for the test. You need to do this and more. Study for the test or quiz by going back through problems that have been given and solved in class. Actually redo them and check your work. Studying for math is DOING the MATH.
3. Make sure your homework is correct.
Check your answers with those that are in the back of the book while you are doing your assignment.
4. Do math EVERYDAY.
Do your homework every day. Try not to skip any days of homework. If you are cramming all your work into a short single session you will find this usually ends up in frustration as well as poor long term memory with the topic.
5. Attempt the most difficult questions.
The most difficult questions will usually teach you the most about the material. Never skip them. Try to get the most exposure to these problems as you can. Try to solve them on your own. Revisit them. Go in for help. Ask a question on the problems in class.
6. Take a break.
Give yourself a break when working with math. If you are being efficient, then three fifteen minute sessions in a day are better than one 45 minute session. Stand up. Stretch. Go for a walk. Move your work to a new place. A break is needed when working with math.
7. Have a good attitude.
Never think "I'm terrible at math". You usually meet your own expectations. Believe that you can do it!
8. Go in for help with your teacher and bring a specific question.
When you bring in a specific question to your math teacher they can help you with where you are struggling. The teacher then can typically give you more examples that are similar to what you are struggling with.
9. 5 minutes.
Once your homework is done, then take an extra 5 minutes to look at these possible things: vocabulary, formulas, notes, projects, and book examples.
Wednesday, August 24, 2011
Yesterday I made a math problem so that it took up one whole page of typing paper. I cut it up into 6 equal pieces that were approximately 3 by 3 inches. I put it a random order and put a paper clip on it. I did this for 5 problems in all and 2 sets of each for a total of 10 questions. I have 20 students in my class. So I had my students work in pairs. It is real easy to cut these problems up with a paper cutter. See the above cut out lines that I took with the problem.
Then I put the 5 stations with 2 sets of the same problem around the room. Four people, or two pairs of partners would be at each station. I would then have them start on the problem and set the timer for ONE MINUTE. The partners together would have to unscramble the pieces and then solve the problem. They would write their answer down on their paper. Once they were done, they could check the answer that is provided at each station. After the minute was over and students had checked their answers, I told them to rotate. They went to the next station and we did the process all over again.
I was happy with the outcome because they seemed to enjoy trying to figure out the puzzle and do the math. It also helps the students to MOVE and LEARN. They are moving after each problem.
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overview about bob
bob is currently interested in general relativity and cosmology, differential
geometry, Lie groups, and various physics stuff, and is somewhat computer
knowledgeable in TeX and LaTeX typesetting (the default medium of physics and
mathematics), MAPLE V mathematics software (and some Mathematica), web
page creation, miscellaneous computer user stuff and a few other things (math
education of course!).
bob has strong feelings about mathematics education. Coherent mathematical
expression communicating the steps used in working problems will be encouraged
to help students gain control over the mathematics. [Active learning on the part
of the student is essential in mastering mathematics: one learns by doing.]
"Writing intensive" and "writing enriched" courses across the curriculum try to
develop communication skills in English language expression—in a similar way the
key to a better understanding of mathematics is the development of clear
organization in the communication of worked mathematical problems. Especially
when doing homework problems for yourself, it is important to present your steps
cleanly, and their relationship to each other, in such a way that each step
conveys as much information as possible about your mental activities which are
supporting the written expression, and allows less room for mistakes to occur in
passing from one step to the next. This also helps develop the skills necessary
to communicate your technical work with others when it is no longer academic
(the workplace).
If you expect to just sit in class and inhale enough to do the homework,
don't pick bob. In order to learn enough to have some understanding of what you
are doing, you need to read the book and think about its discussion to acquire
some ownership of its ideas. Parroting back examples from class does not help
you in the long run. I try to predigest the main ideas of each section of the
text for you, but without your followup, you won't get it.
bob is not a grade grinch
(humor page courtesy of cyrus). [does anyone have a better Excel grade
spreadsheet than
this one?]
Is our educational system the right way to learn? Not always. Students have
rights and responsibilities as they work through the system which can seem
arbitrary at times.
Think
about it.
Think you are special? Maybe you are. You can get a
first class education at this institution if you set your own standards. Living
proof of this is a former physics major
Sean Carroll, who
puts it well in his blog.
teaching: courses bob is interested in
bob has both of his degrees in theoretical physics, although he took nearly
as many math as physics courses as a student himself. He does research work in
mathematical general relativity, applying modern differential geometry and the
theory of Lie groups and related mathematical techniques to questions in the
dynamics of cosmological models with symmetry and in the interpretation of
spacetimes from the observer point of view.
bob is therefore interested in the kinds of applied mathematics courses that
are important in solving physical problems in scientific applications. Besides
teaching in the MAT 1500/1505/2500 engineering/science calculus sequence, he is
course coordinator for
MAT 2705 (Differential Equations With Linear Algebra: see bob's
2705 site) and has taught MAT 3400 (Linear
Algebra). bob has taught MAT4230 (Partial Differential Equations, no longer
explicitly listed in the catalog but can be offered as MAT5930, Topics in Pure
Mathematics) , MAT5920 (Topics in Applied
Mathematics) using MAPLE to explore topics in higher mathematics, and MAT 5600
(Differential Geometry).
a complete set of on-line PDF handouts that provide extra explanation or
examples to supplement the textbook discussion
a 56 day (= 14 weeks x 4 days per week) class and homework log detailing
exactly how the course progressed the last time he taught it, with Maple
worksheet links for key examples and problems
an on-line quiz and test archive with handwritten answer keys for all
quizzes, tests and final exams given in recent years, together with Maple
worksheet answer keys to show the technology side of working mathematics
a link to a summary Maple worksheet showing how to use Maple for all of
the key calculational aspects of each course
an Excel spreadsheet grade calculator with bob's current letter grade
cutoffs for students to calculate their own grades
The VU MAPLE archives on the web used to contain a "maple/misc"
subdirectory of some neat MAPLE stuff, including (truly) nonlinear regression
worksheets like fitting logistic curves and a fun worksheet on
updating
Apollonius on the geometry of the ellipse and the distance problem [which
led to investitating the
evolute
of the ellipsoid].
A good place to start to locate gr stuff (gr
= general relativity,
and related topics) on the web is
Hyperspace GR Hypertext (courtesy of Malcolm MacCallum's relativity group at
the Queen Mary and Westfield University in London). The US government sponsored
scientific preprint archives at
(Los Alamos National Laboratories) contain preprints in bob's field in the list
gr-qc, as well as in many other areas (see also
SPIRES at Stanford).
Another on-line service in bob's area of research is the Institute of Physics in the UK which
publishes Classical and Quantum Gravity . The
American Physical Society (APS: bob is a
member), which publishes
Physical Review D15 where gravitation articles
are published, also has a topical group on gravitation with home page: APS Gravitation.
The Marcel Grossmann Meetings
on General Relativity and Gravitation are organized by bob's friend Remo
Ruffini, who got bob involved in the planning of the Eighth Marcel Grossmann
Meeting (MG8: Jerusalem, June,
1997) as the chairperson of the International Coordinating Committee, while bob
co-edited the proceedings of the previous meeting MG7 at Stanford University in
1994. He continued as chair of this ICC for
MG9 which took place in Rome, July 2-8, 2000 [bob developed the MG
proceedings editor macros] and for MG10 (Rio,
July, 2003) and MG11 (Berlin, July, 2006).
bob gr stuff
bob's research is described in the next section, but the
link to his list of publications, with many recent ones available in PDF format
on-line, may get lost inside the paragraph, so here it is all by itself:
physics stuff
tex stuff
for many years bob and liz barnhart of TV Guide in nearby Radnor codirected
the activities of the Delaware Valley Tex Users Group which met more and more
infrequently (from every several months to twice a year to once a year to ...
never again) in a Mendel Hall classroom at 4:30pm on a Thursday afternoon.
for those who would like to upgrade their PLAIN TeX knowledge to
LaTeX, see the zip file of an example
explaining how to do this.
[the text file explains the story of bobmacro.tex and bobmacrola.tex, the first
an early macro package that made bob a minor celebrity in the Italian physics
community for a time last century.]
for presentations with math, you want to forget MS Powerpoint and use the
Latex beamer software.
An example of such a presentation is here.
for web pages with math instead you want MathJax to convert Latex to HTML
multiculturalism stuff
Bob's life is very much interconnected with an international web of people
and activities.
Multicultural relationships have and continue to have an important influence
on Bob.
One of the most important such influence is Ani, who is an Armenian
Lebanese (and US) citizen from Anjar (Mousaler,
MousalerUSA) whose mom Isghouhi is
a great Armenian/Middle
East cook who has enriched our culinary lives with a wonderful cooking
heritage. [Lebanese food: check out Bitar's Pita
Hut Best of Philly Grilled Falafel Sandwich on the northwest corner across
the field from Pat's/Geno's on 10th St 2 blocks
south of Washington St, or Bitar's Cedar's Meza dinner south of 2nd and South St
in Philly. (We're fans of Jim's Steaks at
4th and South.)] Musically, Armenia is famous for the wooden flute called a
"duduk", one of the oldest musical instruments in the world, and the foremost
living duduk virtuoso is Djivan Gasparyan, whose name has reached mass western
audiences through Peter Gabriel's soundtrack album Passion (The Last
Temptation of Christ) and whose music is available on CD from
Traditional Crossroads, which distributes a small number of titles of mostly
alternative Middle Eastern music, primarily Armenian and Turkish
(Beirut Nights♪).
(Bob and Ani first heard Gasparian on the radio in a friend's apartment in Rome,
and thanks to a WXPN announcement were able to hear him in person at the Painted
Bride during the famous Blizzard of '94—the ice storm one, now that every year
seems to be hyped with its own "Blizzard of".)
[Armenian music radio:
365.] More world music can be found at the syndicated public radio
show ECHOES website and sometimes on our own local Public Radio International show World Cafe at
WXPN♪. [Also AllMusic.Com.]
More recently we frustratingly search for
foreign films on NetFlix.
"bobrom"
Bob is also unofficially an honorary Italian, having spent years of time
(when summed together) in Italy [Roma =
Rome = Rom (German)]
through his continuing connection with the
Physics Department at the University of
Rome and the International Center for Relativistic Astrophysics (ICRA) within that department (group G9), directed by Remo Ruffini. This has
included spending many summers at the
Vatican Observatory in Castel Gandolfo, also the summer
home of a
well known celebrity, and now occasional home of the
80th anniversary Villanova
University Mendel Award winner and friend. bob is also a confirmed pedestrian in
Italy, moving with legs (compensating for pasta
loading), buses, trains and boats,
while reading the Italian newspaper La
Repubblica
daily (now too poor to guy this), often hanging from one arm on the bus. A side benefit of his regular time
in Italy is the opportunity to visit some terrific places (like
Ponza
for example) and renew relationships with special people.
Nowadays, dr bob is more "bobusa" than "bobrom" (forced to read the
Philadelphia Inquirer daily not hanging on
to a bus), but he compensates with
extra pasta and risotto at home with ms ani [oops. the
low
carb/complex carb revolution has dialed down that food group lately,
but whole grain pastas have come to the rescue! including
flax.].
"Why of course the people don't want war... That is
understood. But after all it is the leaders of the country who determine the
policy, and it is always a simple matter to drag the people along, whether
it is a democracy, or a fascist dictatorship, or a parliament, or a
communist dictatorship ...Voice or no voice, the people can always be
brought to the bidding of the leaders. That is easy. All you have to do is
to tell them they are being attacked, and denounce the pacifists for lack of
patriotism and exposing the country to danger."
—Hermann Goering
[another one: Wars will stop when men refuse to fight —Albert Einstein]
"If you assume that there's no hope, you guarantee that there will be no
hope. If you assume that there is an instinct for freedom, there are
opportunities to change things, there's a chance you may contribute to
making a better world. That's your choice."
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Mathematics Soft
Mathematics educational software package.
An computer game that teaches mathematics whilst being fun and rewarding
Pick numbers to complete the equation.
Mathematics, Physics and Chemistry Educational software for High school students
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.
Genius Maker contains 34 educational softwares covering the subjects Mathematics, Physics and Chemistry for High school students. Out of the 34 softwares, 9 softwares are provided as Free and the remaining are for Trial.
GEUP is an interactive, powerful and easy to use software for learning and
doing Geometry on the computer. It allows to verify geometric properties in
a precise way and to discover new properties through the exploration.
Learning mathematics can be a challenge for anyone. Math Flight can help you master it with three fun activities to choose from! With lots of graphics and sound effects, your interest in learning math should never decline.
37988 algebraic equations with solutions and test authoring options. Enables creation of math tests, homeworks, quizzes and exams of varied complexity in a minute. Generates three variant tests around a constructed example. Includes basic and advance
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TH410 Technology in Math Education
Course Description
Computer Technology in the Mathematics Classroom
An overview of the computer-based technology in
the mathematics classroom. Evaluates graphing calculators, and computer software such as Maple, Scientific Workplace, Geometer¿s Sketchpad, MiniTab, SPSS, and others to determine their value in illuminating concepts in the curriculum.
Learning Outcomes
Demonstrate a basic understanding of and an ability to use representative programs from each of the following categories:
A. Computer applications and tools such as word processing, data bases, graphics, spreadsheets, telecommunications, networking, and program languages.
B. Computer-based technology assisted instruction and learning, such as simulations, demonstrations, tutorials, and drill and practice; and
C. Teacher utility programs such as those for recordkeeping, generating instructional materials, and managing instruction.
Identify criteria for evaluating the contributions of computer-based assisted instruction to problem-solving and concept development.
Demonstrate the application and use of a computer-based technology as a tool to enhance the development of problem-solving skills, critical thinking skills, or creative processes. Examples of such skills and processes are: gathering and analyzing data, generating and testing hypotheses, classifying, comparing and contrasting, inferring, evaluating, composing and designing.
Demonstrate the integration of a computer-based application into instruction.
Identify issues relevant to the use of computers in schools and in society, such as: health, equitable access regardless of gender, class, race; ethical concerns and national need.
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Geometry Textbooks
Geometry textbooks address a unique strain of mathematics that requires students to develop hypotheses and logically prove them using devices such as rotations, translations, reflections and coordinates. In addition to their emphasis on logic and reasoning, college geometry textbooks are easily identified by their attention to shapes and their properties. Textbooks.com is happy to provide a slew of geometry textbooks to aid students from algebraic geometry to modern geometry
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This program is about every thing you want to know about real numbers. It discusses introduction to real numbers in a very simple understandable mathematical language because the aim of this program is to understand and not memorize mathematics. It also include fractions, addition and subtraction, multiplication and division of real numbers. Exponential and order of operations, algebraic expressions, properties of real numbers, and how to use these properties in algebra. All discussions are self-learning so that you have your own tutor at home, and you can study it at your own pace. All of these are present in one package
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Mathematics and Statistics
Teaching and Learning Standards
The mission of the Department of Mathematics and Statistics at Bowling Green State University is three-fold:
to sustain a curriculum and programs that meet the intellectual and vocational needs of our students,
to foster a sound teaching environment, and
to provide a setting for professional research in mathematics and in statistics.
To accomplish the teaching and learning aspects of its mission, the Department has set seven goals that, ideally, every student will meet at an appropriate level. These are lofty goals or standards that all faculty will help all students meet. We believe that much will be gained by aspiring to meet these standards:
Each student will become proficient at using the language of mathematics and statistics.
Each student will understand what mathematics and statistics are, how they are done, and how they relate to other disciplines.
Each student will be able to objectively and critically evaluate information and assess performance using mathematical ideas.
Each student will develop an appreciation for the beauty, utility, and impact of mathematics and statistics.
Each student will learn mathematical problem solving techniques and become adept at applying them in novel situations.
Each student will learn to use the appropriate technology to successfully attack a wide variety of mathematical tasks.
Each student will understand the basic ideas, techniques, and results of the areas of mathematics and statistics studied.
Further explanation of each goal:
1. Communication Skills
Each student will become proficient at using the language of mathematics and statistics.
There are two distinct roles to communication: (1) sharing information in oral and written form and (2) receiving information by list pages, etc.). In short, every student must be able to read, write, listen and speak effectively about mathematics and statistics.
2. The Nature of Mathematics
Each student will understand what mathematics and statistics are, how they are done, and how they relate to other disciplines.
To delineate what mathematics is is a question that has perplexed philosophers for centuries, but is a question worth thinking hard about. The field has a distinct nature that students should try to understand. Mathematics pages, etc.). In short, every student must be able to read, write, listen and speak effectively about mathematics and statistics.
3. Valuation of Ideas
Each student will be able to objectively and critically evaluate information and assess performance using mathematical ideas.
A great benefit of mathematics and statistics is that they enable us to understand the world around us. Anyone who has studied mathematics and statistics must realize that information is not all of equal value. What one hears and reads must be analyzed critically, evaluated carefully and judged competently, regardless of whether its source was an acquaintance, a newspaper article, a textbook, a professor, or even something you wrote yourself. On some issues -- but not all -- there is a standard of absolute truth and we must learn to recognize when it can occur and when it does occur.
4. Aesthetic Response
Each student will develop an appreciation for the beauty, utility, and impact of mathematics and statistics.
Society has consistently expected the well-educated individual to have a degree of aesthetic understanding and sensitivity. Professional mathematicians are attracted to the field primarily by its beauty and aesthetic appeal. Students need to understand that mathematics and statistics is often done for its own sake. Moreover it is important to understand that mathematics and statistics have had a significant impact on our society and how mathematics and statistics reflect and effect cultural, political, and human issues. Students should be aware of mathematics and statistics as a human endeavor with a rich and complex history that have done much to benefit mankind.
5. Problem Solving
Each student will learn mathematical problem solving techniques and become adept at applying them in novel situations.
The heart of the mathematical sciences is problems. Posing problems, attacking problems, solving problems -- all of these are crucial. Fortunately there are general guidelines that can be taught and learned about problem solving. It takes practice to master them, but once mastered they apply to many situations, including those outside the mathematical sciences. This skill makes individuals educated in the mathematics and statistics incredibly valuable in business, government and teaching -- as well as good citizens.
6. Technology
Each student will learn to use the appropriate technology to successfully attack a wide variety of mathematical tasks.
No task can be accomplished without using the proper tools. In mathematics and statistics there are a great number of tools which the successful practitioner must be able to use effectively. One must learn to use the available tools, be open to the use of new tools, and know when to use which tool. The entering undergraduate major should quickly learn to use the graphic calculator, a word processor, email, and a computer algebra system. The upper-level undergraduate should be proficient at the use of the library (including computer searches), the internet, mathematical manipulatives, the overhead, and an ever expanding variety of software packages and languages (Logo, Geometer's Sketchpad, spreadsheets, statistical packages, etc.). The graduate student should, in addition, be able to create web pages and to use TeX.
7. Content
Each student will understand the basic ideas, techniques, and results of the areas of mathematics and statistics studied.
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Everyday Math Book 1
Photocopy Master book. Includes problem solving strategies such as Guess and Check, Act It Out, Make A Model, Look for a Pattern, Construct a Table and so on. These strategies are applied to a range of interesting problem situations. Children will enjoy the variety of characters that provide an amusing element to the serious business of solving mathematical concepts.
Your dinner bill came to $78.35, plus tip, divided amongst you and two friends. So how did you end up paying $50? In life, there are plenty of instances where a quick calculation would come in handy. ...
Expert guidance on the SAT Subject Test Math Level 1. Many colleges and universities require you to take one or more SAT II Subject Tests to demonstrate your mastery of specific high school subjects. ...
Newly revised! The second edition of this world-famous method by Will Schmid and greg Koch is preferred by teachers because it makes them more effective while making their job easier. Students enjoy ...
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Math 5326: Structure of Patterns & Algebra
Offered Summer 2012, this course provides an advanced perspective on the concepts in school algebra. For more information, please read the Course Syllabus.
Algebraic reasoning incorporating the use of technology. This course includes investigations of patterns, relations, functions, and analysis, with a focus on representations and the relationships among them.
Note: This course section is specially designed to leverage connections to high school mathematics.
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Mathematics
Subjects
Tutored
What is Linear Algebra?
You are familiar with the equation of a line you learned when you first took Algebra: y=mx+b, where all (x,y) are the points on the line themselves, m is the slope, and b is the y-intercept. Geometrically, this equation does represent a straight line, but unless b=0, f(x)=mx+b is not a linear function, instead we call it an affine function.
When you think about polynomials of x, remember that we call x0 the constant term, x the linear term, x2 the quadratic term, etc. A linear function, or a linear map, as it is more commonly called, is a function that consists of the linear term only, and nothing else. We care about linear maps because they are the only functions of real numbers where for any a, b, and c, f(a+b)=f(a)+f(b) and f(c*a)=c*f(a).
That sounds boring, right? The additive and scalar multiplication properties of the function itself are nice, but all the function f(x)=mx does is take a number and multiply it by m, so there's not much to discuss. However, we've only been looking at functions of single variables, and in Linear Algebra we are much more interested in linear maps of vectors. In physics, a vector is a quantity that has magnitude and direction, but in math, a vector is simply a list of numbers. In a three-dimensional real vector space, (1,2,3) is one example of a vector.
You will spend the first few weeks in Linear Algebra talking about vectors and vector spaces (sets of vectors that satisfy certain properties), but then you will start talking about linear maps themselves. A linear map of vectors is commonly represented as an array of numbers called a matrix. This matrix, for example:
takes three-dimensional vectors and maps them to two-dimensional vectors.
You probably recognize matrices from using Cramer's Rule or reduced row echelon form to solve a system of equations in high school. These methods involve using square matrices (linear maps that map a vector space to itself), and they are interesting and useful enough to get a special term: linear operators or simply operators. There are several reasons that operators are more useful, for example it is possible for an operator to be inverted, and you will learn more about them when you take the class.
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Mathematics
At the start of year 10, students are set according to ability. Setting is based on Key Stage 3 results as well as teacher recommendations. Pupils are taught using the Edexcel Specification A Foundation GCSE syllabus (no coursework) or the Edexcel Specification A Higher GCSE syllabus (no coursework).
Lessons make up four hours, or six periods, per week. Students are formally tested twice per term in class. The results are recorded and used to track pupil progress. The department uses past GCSE exam questions of varying levels to set exam papers.
All students take two written papers at the end of Year 11 (externally set and marked).Those pupils who follow the Foundation syllabus take paper 1 (a 1¾ hours non-calculator paper) and paper 2 (a 1¾ hours calculator paper) and are eligible for the award of grades C to G only.
Those pupils who follow the higher syllabus take paper 3 (a 1¾ hours non-calculator paper) and paper 4 (a 1¾ hours calculator paper) and are eligible for the award of grades A* to D only.
In both cases the non-calculator paper has a weighting of 50% and the calculator paper has a weighting of 50%.
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Math Courses
Math 100 is an overview of some of the seminal achievements in mathematics from ancient to modern times. Topics include Problem Solving, Number Theory, Geometry, Fractals, Topology, Probability and Statistics, and applications to other fields.
This course will introduce students to the processes by which valid statistical inferences may be drawn from quantitative data. Topics include design of experiments; sample surveys; measurement; summary and presentation of data; regression and correlation; elementary probability; the law of averages; the central limit theorem; the normal, t and chi-square distributions; confidence intervals; and hypothesis testing. A computer laboratory component will introduce the student to spreadsheets and statistical applications. Offered every semester.
This course, required of biology majors, is a survey of statistical concepts and methods, with an emphasis on concepts critical to the life sciences. Topics include design of experiments; measurement; summary and presentation of data; regression and correlation; elementary probability; the normal, binomial, t-, and chi-square distributions; confidence intervals and standard error; and hypothesis testing. Offered every Spring. Prerequisite: MATH 104 or sufficiently high score on the Mathematics
placement exam (consult with the Mathematics Department for the exact
score needed).
A cohort-based introduction to elementary statistics for students in the BAIS program. Topics include design of experiments; summary and presentation of data; regression and correlation; elementary probability; the law of averages; the central limit theorem; the normal t and chi-square distributions; confidence intervals; and hypothesis testing.
This course covers mathematical theory and techniques fundamental to university level scholarship. Topics include: the real number system with number theory concepts (algorithms for computation); percentage; simple and compound interest; linear and exponential functions; systems of linear equations; descriptive statistics. Two hours lecture. Offered every semester.
This course provides a one semester introduction to the theory of differential and integral calculus with an emphasis on technical fundamentals. The curriculum is designed for non-science majors for whom advanced coursework in mathematics is not required. Prerequisite: MATH 104 or sufficiently high score on the Mathematics
placement exam (consult with the Mathematics Department for the exact
score needed).
Topics include polynomial functions; factor and remainder theorems; complex roots; exponential, logarithmic, and trigonometric functions; and coordinate geometry. May not be taken for credit after completion of 0206-109. Offered every semester. Prerequisites: Two years of high school algebra and sufficiently high
score on the Mathematics placement exam (contact the Mathematics
Department for the exact level needed), or MATH - 104.
Contemporary society is filled with political, economic and cultural issues that arise from mathematical ideas. This service-learning Core mathematics course will engage students in using mathematics as a tool for understanding their world with a focus on the connection between quantitative literacy and social justice.Topics covered will include financial mathematics, voting theory, data representation and statistics.
Topics include systems of linear equations, matrices and determinants; the geometry of vectors in Euclidean space; general properties of vector spaces, bases and dimension; linear transformations in two and three dimensions, eigenvalues and eigenvectors. Offered every Fall. Prerequisite: MATH - 109.
An informal, discussion-oriented class to develop skills for investigating and solving mathematical problems. Topics include elementary mathematics, combinatorics, geometry, number theory and calculus, as well as problems from contests such as the International Mathematical Olympiad and the Putnam Examination. Strongly recommended for students interested in teaching mathematics. Prerequisite: MATH - 110 or permission of instructor.
An introduction to the Eastern European Mathematical Circles culture. Students will learn mathematical folklore and problem-solving methods drawn from geometry and discrete mathematics, and will both observe and teach students in several mathematical circles in the Bay Area. In addition to the mathematics and pedagogy, students will explore issues of equity in educational opportunity. This is a service earning course designed for math, physics, or computer science majors who are interested in teaching.
The methodology of mathematical modeling will be explored in several case studies from fields as diverse as political science, biology, and operations research. Problems of data collection, model fitting, and model analysis will be explored. Case studies incorporate topics from: analysis of conflict (business, military, social), population dynamics, and production management. Prerequisites: MATH - 110 and MATH - 130.
This is a one-semester colloquium course. Students will be exposed to approximately seven talks over the course of the semester on various topics of interest in modern mathematics. This course is intended for mathematics majors and minors. A student can take up to two units of colloquium for credit, buth the units cannot be applied to count for required classes. Prerequisite: MATH 110.
This course offers selected upper division students an opportunity to work on a sponsored research project under the direction of a faculty member. May be repeated for credit. Offered as often as suitable projects can be found. Prerequisite: Permission of instructor.
Topics include sequences and series, topology of the real line, limits and continuity, the real number system, the derivative and Riemann integral. Prerequisites: MATH 211 and MATH 235 or permission of instructor.
Topics include classical differential geometry of curves and surfaces, curvature, the bending of surfaces, shortest paths in a surface, and tensors in geometry and physics. Prerequisite: MATH - 211 or permission of instructor.
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Student placement in a mathematics course is subject to ACT-MATH scores or the COMPASS placement test scores or Academic Services Center approval. Students with ACT-MATH scores of 20 or above may enroll in any math course with numbers up to and including MATH 146 or MATH 165. Students with an ACT-MATH score below 20, or no ACT-MATH score, are required to take the COMPASS placement test. Placement of students is based on the level of achievement on the test.
ASC 090 Math Prep (2 credits)
This course improves basic math computational skills: addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals. Includes a study of percents and application of percents. This course may be required due to Compass test results and the course placement policy. (F, S, Su)
ASC 091 Algebra Prep I (2)
This course is designed for students with little or no algebra background who need to prepare for further study in mathematics or who need to review basic algebra concepts. It includes topics such as real numbers, fundamental operations, variables, equations, inequalities and applications. (F, S, Su, O)
MATH 120 Basic Mathematics I (2)
A review of whole numbers, fractions and decimal numbers in conjunction with the fundamental application of ratios, rates, unit rates, proportions and percents in solving everyday problems. The application of business and consumer mathematics such as simple and compound interest, purchasing and checkbook reconciliation. (F, S, Su)
MATH 135 Applied Mathematics (2)
A review of mathematics including fractions, decimals, percentages and basic algebra which incorporates algebraic fractions and equations with variables. Emphasis is placed on the strategies of problem-solving using agricultural applications. (F)
MATH 136 Technical Trigonometry (2)
A study of the fundamentals of trigonometry. Right triangle trigonometry, the Law of Sines, the Law of Cosines and Vectors. Emphasis is placed on problem-solving for the technology fields. Prerequisite: MATH 132. (F, S, O)
MATH 138 Applied Trigonometry (3)
A theory/lab course studying the fundamentals and applications of trigonometry, including right and oblique triangles, the Law of Sines, the Law of Cosines, vectors, angular velocity, graphs and complex numbers.
MATH 146 Applied Calculus I (4)
Review of algebra, including linear, quadratic, exponential and logarithmic functions. Calculus topics for this course will be limits, continuity, rates of change, derivatives, extrema, anti-derivatives and integrals. Emphasis is placed on real-data application. Course is intended for those majoring in business, management, economics, or the life or social sciences. Prerequisite: MATH 103 or MATH 104 or placement exam. (F) ND:MATH
MATH 147 Applied Calculus II (4)
Integrals, multivariable calculus, introduction to differential equations, probability and calculus, sequences and series, introduction to trigonometric functions, derivatives and integrals of trigonometric functions. Emphasis is placed on real-data application. Course is intended for those majoring in business, management, economics or the life or social sciences. Prerequisite: MATH 146. (S) ND:MATH
MATH X92 Experimental Course (1-9)
A course designed to meet special departmental needs during new course development. It is used for one year after which time the course is assigned a different number.
MATH 299 Special Topics (1-5)
A special purpose class or activity to be used for a mathematics course in process of development, for classes occasionally scheduled to meet student needs or interests, or offered to utilize particular faculty resources. (F, S, Su)
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Algebra I am getting ready to start an Algebra class for the first time and I was wondering what challenges people have with learning and using algebra concepts. Also what are the best ways to over come math anxiety? The best way? Learn the language of algebra.
Tuesday, March 20, 2007 at 9:02am by jeff
SHAY THE MATH QUESTION IS IT ALGEBRA , PRE ALGEBRA' OR GEOMETRY? Quadriatic functions. so algebra i think.
Wednesday, January 17, 2007 at 7:09pm by ROSA
College Algebra is this really algebra, im doing this now in freshman year algebra 2
Monday, February 21, 2011 at 1:06am by BOSSAlgebra This site has excellent explanations of both terms.
Monday, September 14, 2009 at 1:53pm by Ms. Sue
Algebra 1A How is algebra a useful tool? what concepts investigated in algebra can be apply to personal and professional life? I need help answering this question. Please help?
Sunday, November 30, 2008 at 7:34pm by Julissa
algebra 2 thats part of algebra 2 thats easy were doing that now in pre algebra
Wednesday, April 29, 2009 at 1:14pm by Tanisha
what does pre-algebra mean?? pre algebra is like a bunch of math that comes before algebra in middle school.
Monday, August 25, 2008 at 9:11pm by Grace
Algebra (Intermediate) Tutors can better help you when they know they're working with the same student. You might try something like this: Algebra (1), Algebra (2), and so on. Also -- you are more likely to get assistance if you tell us what you know and what you don't understand about your ...
Monday, October 11, 2010 at 12:26pm by Ms. Sue
algebra Once again did you click on the "answer" part of examples #6 and #7 ?
Tuesday, December 1, 2009 at 10:30pm by Reiny
Algebra 2 In Kentucky, where i am from, we do algebra and algebra two before pre-cal and calculus. I didnt realize that the problem could be solved in multiple ways and i apologise. But the solution should be done without calculus.
Thursday, February 24, 2011 at 10:33pm by Anon
7th grade There are at least 5 more than twice as many students taking algebra 1 than taking algebra 2. If there are 44 students taking algebra 2, what is the least number of students who could be taking algebra 1. Show all work
Thursday, November 20, 2008 at 8:37pm by lee
algebra 1 at a certain high school,350 students are taking algebra. the ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys? - How can you write a system of equations to model the situation? - Which equation will you solve for a variable in ...
Sunday, January 27, 2013 at 3:24pm by lucy
Algebra-still need some help Homework Help Forum: Algebra Posted by Jena on Thursday, February 3, 2011 at 7:32pm. Find the domain of the function. f(x)=(sqrt x+6)/(-2x-5) Write your answer as an interval or union of intervals. Algebra - David, Thursday, February 3, 2011 at 7:42pm (-6,-5/2)and(-5/2,...
Thursday, February 3, 2011 at 8:43pm by Jena
Algebra Nor was I in my algebra class of 1943. This COULD be a case of changing the rules (as has been done with all the SI units). A micron isn't a micron anymore (:(]. In fact my algebra teachers said, "DON'T forget there is a negative root of the square root of 4."
Sunday, January 4, 2009 at 5:46pm by DrBob222
Algebra The average mark on a test in an algebra class is 80. If the two lowest scores of 34 and 48 are not counted, the remaining scores would average 83. How many students are in the algebra class?
Thursday, October 28, 2010 at 7:52pm by Rocky
algebra x = 4 is the answer, if you take the positive square roots. There may be other answers if you take the negative square root on one or both sides. I got that by trial and error, not by using algebra. The algebra got too messy.
Tuesday, July 22, 2008 at 11:00pm by drwlsCollege Algebra Thank you very much. I'm not doing very good understanding this algebra right now so I will definately have other questions tonight. I'm working on getting a tutor here in my town because right after this class is over Sunday, I go into Algebra two.
Wednesday, November 18, 2009 at 7:41pm by LeAnn/Please help me
algebra An algebra book weighs 6 oz less than twice as much as a grammar book. If 5 algebra books weigh the same as 8 grammar books, how much does an algebra book weigh?
Wednesday, October 19, 2011 at 12:00am by AnonymousAlgebra I am having a problem with solving a composite function in Algebra 1 How do I solve f(x) = -2x + 1 and g(x) = 4x? Don't I need more info? No, that is all you need. I it unclear what you want to do here. see
Wednesday, July 18, 2007 at 9:45pm by Alec
Algebra ello i need help factoring I haven't had factorin sense Algebra one and now am in Algebra two and our school is screwed up were they shove in a year of Euclidean Geometry and Basic Trig inbetween first two years of Algebra... so i need to factor X^2-12X+35 I can sit there ...
Sunday, December 7, 2008 at 8:34pm by Algebra
collage algebra 1 no need to throw a hissy-fit. I also wondered why somebody claims to have a "college Algebra" question and can't spell 'college' Besides, this is at most a grade 9 type algebra question. Anyway, why don't you substitute the value of x given in the ...
Monday, January 5, 2009 at 10:55pm by Reiny
algebra X=2 Is that right Ms. Sue? I will spell Algebra correctly from now on thanks for your help.
Tuesday, March 26, 2013 at 5:03pm by Eric
algebra You'll find out after you complete your algebra assignment.
Friday, February 8, 2013 at 11:57am by Ms. Sue
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Book Description: Ensure top marks and complete coverage with Collins' brand new IGCSE Maths course for the Cambridge International Examinations syllabus 0580. Provide rigour with thousands of tried and tested questions using international content and levels clearly labelled to aid transition from the Core to Extended curriculum. * Endorsed by University of Cambridge International Examinations * Ensure students are fully prepared for their exams with extensive differentiated practice exercises, detailed worked examples and IGCSE past paper questions. * Stretch and challenge students with supplementary content for extended level examinations and extension level questions highlighted on the page. * Emphasise the relevance of maths with features such as 'Why this chapter matters' which show its role in everyday life or historical development. * Develop problem solving with questions that require students to apply their skills, often in real life, international contexts. * Enable students to see what level they are working at and what they need to do to progress with Core and Extended levels signalled clearly throughout. * Encourage students to check their work with answers to all exercise questions at the back (answers to examination sections are available in the accompanying Teacher's Pack).
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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.
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TI-34 MultiView is ideal for middle school math, pre-Algebra, Algebra I and II, trigonometry, general science, geometry, and biology. MultiView display shows fractions as they are written on paper. View multiple calculations on a four line display and easily scroll through entries. Enter multiple calculations to compare results and explore patterns on the same screen. Simplify and convert fractions to decimals and back again. Integer division key expresses results as quotient and remainders. Toggle Key lets you quickly view fractions, decimals and terms including Pi in alternate forms. Functions include previous entry, power, roots, reciprocals, variable statistics and seven memories. Scientific calculator also features user friendly menus, automatic shutoff, hard plastic color coded keys, nonskid rubber feet, impact resistant cover with a quick reference card, and dual power with solar and battery operation.
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Sixth Form: Mathematics
Subject Overview
Mathematics A Level is a chance to extend you skils in Mathematical techniques and problem solving. It covers four modules of Pure Maths, using a lot of your previous knowledge of algebra to build on your previous work with topics such as trigonometry and vectors. As well as learning about new Mathematical concepts such as differentiation and integration, you will also do two applied modules, where you will have the choice of studying Mechanics or Statistics.
Syllabuses (Course Outline and Structure)
At Heart of England Sixth Form we follow the AQA Syllabus. Both the AS and A2 sections of the course are marked out of 300 UMS points. The two sets of marks together constitute the entire A level, out of a total of 600 UMS points. The course is split into AS and A2 Mathematics as follows:
AS Mathematics
Pure Core 1 - Algebra methods, extended from GCSE, adding, subtracting, multiplying, dividing, sketching and translating polynomials, some work with coordinate geometry extending GCSE methods to work with circles and an introduction to calculus both differentiation and integration.
Pure Core 2 - Transforming functions and their graphs, introducing the concept of series—summing sequences, extending your GCSE work on trigonometry and introducing the measure of radians, some work with indices, introduction to the topic of logarithms and an extension of the work with differentiation and integration.
Choice of:
Mechanics 1 - Mathematical modelling of real life situations, displacement, velocity and acceleration in one and two dimensions, forces—including friction and tension, momentum, Newton's laws of motion, problems involving connected particles and projectiles or
A2 Mathematics
Pure Core 3 - Work with functions including inverse, compositions and combinations of transformations, extension of trigonometry including inverse and reciprocal trig functions, exponentials and logarithms, differentiation using the product, quotient and chain rules, integration by substitution and by parts, use of integration to find the volume of a revolution, iterative methods for solving equations and numerical methods of integration.
Pure Core 4 - Rational functions, algebraic division, partial fractions, conversion between Cartesian and parametric equations, extension of work with binomial series, further work with trigonometry including use of harmonic form and double angle formulae, exponential growth and decay, solving differential equations, differentiating parametric equations, integrating partial fractions and work on vectors including vector equation of lines and scalar product.
Choice of:
Mechanics 2 - Moments, finding the centre of mass, further work with displacement, velocity and acceleration including in three dimensions, Newton's Laws in up to three dimensions, application of differential equations, uniform circular motion and vertical circular motion as well as looking at work and energy, including GPE, KE and Hooke's Law or
The official AQA specifcations for all of the Maths modules are available in pdf form at:
AQA Mathematics Specification 2013
Entry Requirements
To study A Level Mathematics you must have at least five GCSEs at grade C or above, and we would recommend at least a grade B in your GCSE Maths. Since the course is very algebra based you must also have good skills in manipulating algebra and you will be tested on this during the first week of the course.
The 'step up' from GCSE Maths to A Level is quite significant and for those students who would like to get a good start on it, particularly if their algebra skills need a little brushing up, we recommend the CGP text 'Head Start to AS Maths'
Activities and Trips
We have no mandatory trips or activities in Maths, although throughout the two years there may be the opportunity to take part in activities, such as revision days and team challenges, run by the 'Further Maths Network' based at Warwick University, with whom we have been cultivating links over the last few years.
This would incur a small cost, usually of between £10 and £30 dependant on the type of activity, and may involve students arranging their own transport to and from the University.
Expected Costs
Other than the cost of the activities that we may run with the 'Further Maths Network' there are no expected costs associated with the Maths A Level. All the text books are lent to students for the duration of the course and they will only need to pay for them if they fail to return or badly damage them. There are no mandatory excursions and the only equipment they are required to have (other than the usual contents of a pencil case) is a scientific calculator, which they should have anyway from GCSE. Complementary Subject Combinations and Enrichment Activities
The main links between other subjects and Maths come from the choice of applied topic:
Mechanics – fits well with Physics as there is a lot of overlap in the content of the courses
Statistics – fits well with Pyschology and Biology as they use statistical analysis in some of their coursework.
Subject Resources
Schemes of Work
In Maths the Scheme of Work is based on the text books. For each module we have a text book produced by AQA which covers all the topics needed for that course. Students will be loaned these text books for the duration of their study
Past Papers
Past papers are an essential part of the revision process for Mathematics, it is important to get plenty of practice of the type of questions you will be asked in exams. At the end of each chapter in the text book there is a revision exercise made up of past exam questions and we always leave plenty of time after completing the learning for the module to do past paper practice, both under exam conditions and as an open book revision tool.
The AQA Maths past papers (and several other useful documents) can be found at:
AQA A Level Maths Materials
Useful Links
The AQA link above is very useful and provides access to past papers, mark schemes, examiners reports, specifications, practice papers for new specifications, the formula booklet and many other useful documents.
Also the school has paid for access to the website My Maths which students may have used in Key Stage 3 and 4 but which also has a wealth of resources for A Level revision. This can be accessed by asking your teacher for the school's login and password information.
Other Information
Maths A Level will support students who go on to study a wide range of different subjects at University or in other forms of Higher Education, the more obvious ones being Maths, Science and Engineering. It's logical thinking and problem solving based structure make it a qualification that can pick students 'out of the crowd' in the eyes of many universities and employers, even in non-Maths based courses or industries.
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Buy a Calculator
The first step in buying a calculator is identifying your needs. If your teacher has recommended a certain model of calculator, do your best to comply. After all, he or she probably has a lot more experience with calculators than you do.
I have always been a fan of Texas Instruments' calculators, primarily because they are the most popular among students, ensuring compatibility with your classmates and teachers. These calculators can be purchased at most large electronics and office-supply stores, or you can buy one online from Amazon.com. In fact, you can help support FreeMathHelp.com by buying your calculators through these Amazon.com links:
You have probably been told what type of calculator, scientific or graphing, that you will need. If you need a graphing calculator, skip this paragraph and keep reading. For scientific calculators, you basically have a number of products that all do the same functions, but some easier than others. Right now I use the TI-30X for simple calculations at home, but of course it's a pretty powerful machine, great for Algebra 1 & 2. I like that this model has a two-line display which shows you what commands you have entered instead of just a number.
Graphing calculators are a little more difficult, and more expensive, to buy. A good calculator will probably cost you at least $100, but you may be able to rent, buy used, or even borrow from your school library. The TI-84+ is a good calculator for algebra and geometry, and is a newer version of the ever-popular TI-83+. For about $135 you can buy a TI-89 Titanium from Amazon.com (You might pay $199 to buy it from a store!) The 89 offers symbolic manipulation software to easily solve any equation automatically, and is a must for AP Calculus courses. I use the TI-89 all the time for more complicated math problems. It has far more power than the 84/83+, and has a great interface. The Voyage 200 is also out there, but watch out -- it is currently not allowed on most standardized tests, including the SAT. I recommend the 89 for all serious math students, but if cost or a teacher are prohibitive, go with an 83 or 84.
You may be leaning towards a calculator from one of the other brands, like Casio or HP, and some of those are even more powerful than a TI-89. They're great machines, and if your teachers recommend them, then by all means, go for it. The fact is, though, that most American students use TI's in the classroom, and they are the easiest to use in my experience. And I'll say it again -- check with your teachers, even those you won't have for 2-3 years, before you or your parents plunk down $100 for a "cool looking" calculator that your teachers don't like!
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More About
This Textbook
Editorial Reviews
Booknews
A text for a first course in structural analysis for the junior or senior year. Chapters on major concepts such as computation of reactions, analysis of plane trusses, bending theory and deformation analysis, and the slope-deflection method contain worked examples, problems, and chapter summaries discussing the limitations and underlying assumptions of material (particularly useful for engineers evaluating structural-analysis computer program results). Includes an appendix on determinants, matrices, and linear equations
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Math Websites:
CLN's "Ask an Expert" page has about 100 links to specialists in the field who can serve as a valuable source of curricular expertise for both students and teachers. Questions/answers on Mathematics may be found in our "All Subjects" section at the top of the page, the "Mathematics" section, as well as the general "Reference" section.
The Canadian Mathematical Society's (CMS) page provides a large number of links to other math sites of interest to educators. You'll also find career information in the mathematics field, resources for post-secondary students, and links to the 1995 International Olympiad and other math related sites.
The University of Wisconsin provides an extensive meta-list of mathematics sites and servers around the world. These are organized under types of mathematics (e.g., pure, applied, statistics) and under type of resource (e.g., gophers, newsgroups, software).
"Problem-Based Learning (PBL) is an educational model which involves students in self-directed learning as they solve complex, real-world problems." This set of materials (complete with student and tutor guides) challenges students to do the research (Internet-based) and problem solving necessary to determine if they can afford to buy a car.
Can't remember a mathematical formula or reference? You may find it here in this collection of mathematical reference tables, for example trig identities, geometric formulas, algebraic basic identities, and more.
The primary goals of the Mathematics Archives are to organize and provide you with access to most public domain and shareware software and many other materials which are contained on the Internet and which can used in the teaching of mathematics at the community college, college and university level. In addition, they provide links to various WWW, Gopher and anonymous FTP sites which are of interest to mathematicians.
The Math Forum is a centre for teachers, students, researchers, parents, and mathematicians at all levels. The Math Forum offers "Ask Dr. Math", as well as problem-solving activities, an annotated collection of Internet math sites and sections devoted to math education and key issues of interest to the mathematics community.
"The Mathwright Library is a collection of interactive, electronic mathematics learning aids referred to as "books". These books are documents created with a Windows mathematics authoring program called Mathwright. The books are only available for the Windows platform, but the Library is compatible with all versions of Windows above 3.0, including Windows 95. The Library (this website) provides a Windows program which is a "reader" for the books collected here. The Library is supported by the NSF and all materials availble here are free of charge."
These are excerpts from a collection of graphical demonstrations Douglas N. Arnold developed for first year calculus students. The site's author uses many such demonstrations to illustrate and enrich his classes in the McAllister Technology Classroom.
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Description
Mathematical Proofs: A Transition to Advanced Mathematics, Second Edition, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book about Writing
1. Sets
1.1 Describing a Set
1.2 Subsets
1.3 Set Operations
1.4 Indexed Collections of Sets
1.5 Partitions of Sets
1.6 Cartesian Products of Sets
Exercises for Chapter 1
2. Logic
2.1 Statements
2.2 The Negation of a Statement
2.3 The Disjunction and Conjunction of Statements
2.4 The Implication
2.5 More on Implications
2.6 The Biconditional
2.7 Tautologies and Contradictions
2.8 Logical Equivalence
2.9 Some Fundamental Properties of Logical Equivalence
2.10 Quantified Statements
2.11 Characterizations of Statements
Exercises for Chapter 2
3. Direct Proof and Proof by Contrapositive
3.1 Trivial and Vacuous Proofs
3.2 Direct Proofs
3.3 Proof by Contrapositive
3.4 Proof by Cases
3.5 Proof Evaluations
Exercises for Chapter 3
4. More on Direct Proof and Proof by Contrapositive
4.1 Proofs Involving Divisibility of Integers
4.2 Proofs Involving Congruence of Integers
4.3 Proofs Involving Real Numbers
4.4 Proofs Involving Sets
4.5 Fundamental Properties of Set Operations
4.6 Proofs Involving Cartesian Products of Sets
Exercises for Chapter 4
5. Existence and Proof by Contradiction
5.1 Counterexamples
5.2 Proof by Contradiction
5.3 A Review of Three Proof Techniques
5.4 Existence Proofs
5.5 by7.4 A Quiz of "Prove or Disprove" ProblemsAnswers and Hints to Selected Odd-Numbered
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* How can sprinter fast Usain Bolt break his world record without running any faster?
* Why do high-jumpers use the Fosbury Flop?
* What's the best strategy for taking football penalties?
* What statistical advantage do left-handed boxers have over their right-handed opponents?
* And... more...
As in the field of "Invariant Distances and Metrics in Complex Analysis" there was and is a continuous progress this is the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent... more...
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the... more...
An introduction to risk assessment that utilizes key theory and state-of-the-art applications With its balanced coverage of theory and applications along with standards and regulations, Risk Assessment: Theory, Methods, and Applications serves as a comprehensive introduction to the topic. The book serves as a practical guide to current risk analysis... more...
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process.... more... the average guy in this clever and unusual take on statistical risk, chance, and how these two factors...
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Elementary Linear Algebra with Applications - 3rd edition
This book is intended for the first course in linear algebra, taken by mathematics, science, engineering and economics majors. The new edition presents a stronger geometric intuition for the ensuing concepts of span and linear independence. Applications are integrated throughout to illustrate the mathematics and to motivate the student.Edition/Copyright: 3RD 96 Cover: Hardback Publisher: Saunders College Division Published: 09/08/1995 International: No
View Table of Contents
Preface. List of Applications.
1. Introduction to Linear Equations and Matrices.
Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises.
Giving great service since 2004: Buy from the Best! 4,000,000 items shipped to delighted customers. We have 1,000,000 unique items ready to ship! Find your Great Buy today!
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This classic Algebra textbook by G.A. Wentworth set the standard by which later textbooks in mathematics were judged. It became known within academic circles for its emphasis on problem solving and the development of practical mathematical thinking. The text takes students from simple equations to more complex arithmetical and geometrical progressions.
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books.google.co.uk - This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations.... Differential Equations in Several Complex Variables.
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Calculus: One and Several Variables, Ninth Edition
Wiley is proud to publish a new revision of this successful classic text known for its elegant writing style, precision and perfect balance of theory and applications. This Ninth Edition is refined to offer students an even clearer understanding of calculus and insight into mathematics. It includes a wealth of rich problem sets which give relevance to calculus for students. Salas/Hille/Etgen is recognized for its mathematical integrity, accuracy, and clarity.
Customer Reviews:
Great book for learning
By C. Waldorf - March 23, 2005
This is a superb textbook and it's easy to see why the book is in its ninth edition. What I really enjoyed (yes, I know this may sound a little incongruous in relation to calculus) was the step-by-step build-up of knowledge with good, clear examples. Also, for the problems at the end of each section, all the odd problems have solutions, so one can get some practice (something that is unfortunately rare for many textbooks).
Before going through this book, I had minimal exposure to calculus and what I had seen wasn't very favorable. This book was a key reason why I now really enjoy the subject and feel very comfortable in this area.
Not for the mediocre
By A Customer - February 5, 2004
This book is a stunning rebuke to all attempts to dumb down the math curriculum in high schools and colleges. This book, in my opinion, expects the student to have mastered precalculus at the level set forth in, say, David Cohen's Precalculus with unit-circle trigonometry (ISBN 0-534-35275-8). It introduces mathematical rigor in the Calculus 101 semester (of a three semester calculus program) and thereby begins preparing the math major for the hard analysis courses that comes later on. There are no cute stories featuring 'How I Use Math In The Workplace' to inspire you - your self esteem will be hard won as you master the concepts as presented here (especially the problems). The book's greatest strength is that it is basic and traditional in its approach to calculus - no problem or example requires obscure special tricks from mathematical journals or Isaac Newton level ingenuity. This book is a must get!
Start with it but don't end with it!
By Mohammad - June 30, 2000
I used this book in my first engineering calculus course. The professor was incredibly theoretical and did not teach from the book which made matters somewhat difficult. However, he was showing us the meaning of math which I found refreshing. This book serves its purpose as one which teaches the mechanics of solving problems but very little in developing an intuitive feeling for mathematics. I must admit that the multitude of exercises were very helpful in getting comfortable with difficult mechanical problems. For single variable calculus it is a standard book with good examples, excellent diagrams, and some applications. Getting into multivariables, the ideas are not connected well and seem segragated from the rest of material. I guess as a brief overview, it makes its point but should not be used as a text for multivariable calculus. If you are interested in theory I recommend Apostol's Calculus which covers a great range of material with rigorous foundation... read more
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Introduction to Technical Mathematics, Fifth Edition, has been thoroughly revised and modernized with up-to-date applications, an expanded art program, and new pedagogy to help today's students relate to the mathematics they are learning. The new edition continues to provide a thorough review...
This text addresses the need for a new mathematics text for careers using digital technology. The material is brought to life through several applications including the mathematics of screen and printer displays. The course, which covers binary arithmetic to Boolean algebra, is emerging throughout t...
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Math 238 Course Policies
Textbook
Graphing Calculator
A graphical calculating device is allowed for this course.
You are free to use a graphing calculator for this course on homework,
quizzes, and exams -- however they
are not required. The exams and quizzes will be designed so that
the only thing you need is a thorough understanding of the material
and a good pencil.
Grading
Homework
Most Tuesdays will be homework day. See the syllabus.
You are responsible for understanding how to do all of the assigned homework problems. Each week
I will randomly assign (in advance) students to present certain problems at the board.
Your homework
grade is determined by your presentation of your problem(s).
I grade each homework presentation out of 4 points on the following scale:
Fully Correct
4
Almost Correct
3
Wrong, but Good Effort
2
Completely Unprepared, but Present
1
Absent
0
In addition, I drop the lowest homework grade.
Quizzes
At the beginning of class on most Wednesdays (unless otherwise noted in the syllabus) there will be
a 15 minute quiz based on the HW that was due the Tuesday before.
The purpose of the quiz is to encourage everyone to work (and understand)
ALL of the homework problems, not just the homework problem
he or she has been assigned to present. In addition, I drop the lowest
quiz score.
Exams
There will be three exams given during the semester and a final exam.
The Final Exam is mandatory, and unless you have documentation of
extenuating circumstances, you cannot pass the class if you do not
take the final.
Course Grade
Your grade in the course will be determined by your performance on the
three exams, a final exam, and your lecture grade.
The lecture grade consists of your HW grade,
quizzes, and in-class groupwork.
Your entire grade is out of 600 points (see below):
Attendance
I do not take attendance. However, if you are absent on a homework or quiz
day, then you get a zero for the quiz and homework on that day. Also,
it has been my observation that grades are strongly correlated with
attendance. Simply put, if you skip most of the classes, then you
probably won't do as well as you could in the course (that's obvious
isn't it?). Furthermore any anncouncements or changes to the course
will be announced in class. You are responsible for the material
discussed in class.
Academic Integrity
Honesty with oneself and with others is of utmost importance in life.
The work you do in this course should reflect your honesty and integrity.
In practical terms, this means that you should be honest with yourself
about how much time you spend on homework, how well you understand the
material, and the level of reliance you have on others to complete the
assignments. For example, you are encouraged to work with others on
homework; merely copying someone else's work and turning it in as your
own does not enhance your understanding and is dishonest.
If there is clear evidence that a student has committed fraud to
advance his/her academic status (for example, cheating on an exam or quiz),
your instructor will be obliged to deal with the matter in accordance with
the James Madison University Honor Code.
If you are aware of such activity by another student in the course,
you should bring the matter to your instructor's attention immediately.
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in a... more...
Mathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.The book,...This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach... more...
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Calculus
Chapter 1 What Is Calculus? In This Chapter * You're only on page 1 and you've got a calc test already * Calculus — it's just souped-up regular math * Zooming in is the key * The world before and after calculus "My best day in Calc 101 at Southern Cal was the day I had to cut class to get a ...
0 1 2 1 2 3 4 We want the area underneath the stepped line, not the area underneath the smooth curve. It is ironic that we can easily determine the area underneath the smooth curve using the infinite calculus but have trouble determining the much more simple area under the stepped line.
Calculus The infinitesimal calculus, with its two branches, differential and integral calculus, has its roots in two special geometrical problems: (1) To find the tangent to a curve; (2) To find the area enclosed by a plane curve ("quadrature").
Curriculum Module: Calculus: Functions Defined by Integrals 1 AP Calculus Functions Defined by Integrals Scott Pass John H. Reagan High School Austin, TX Reasoning from the graph of the derivative function f in order to obtain information about the behavior of the function F defined by F ( x ...
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97805213566gebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory.
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Product Information
High school and post-secondary math students will appreciate this Casio 8-line graphing calculator. It features a zoom function so you can accurately plot X and Y coordinates and determine the points of curves and parabolas. Storage is a cinch with its sleek blue case.
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ractical Problems in Mathematics for Carpenters, 9th Edition
ISBN10: 1-111-31342-3
ISBN13: 978-1-111-31342-5
AUTHORS: Huth
Take command of any building and carpentry project with the robust, construction-specific math skills you will get from the 9th Edition of PRACTICAL PROBLEMS IN MATHEMATICS FOR CARPENTERS. Divided into short units, this combination book/workbook explains the math principles essential to carpentry and building construction in straightforward, concise language, and then reinforces each concept with samples of problems common in the trade. Step-by-step solutions to the problems, as well as detailed illustrations, help you easily understand the math, visualize its application in everyday carpentry work, and perform functions yourself
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Maths for competitive Exams
This class is for students preparing for various competitive exams and aptitude tests. In this class we will be discussing about various topics Trigonometry, Algebra,Geometry, Mensuration, Number systems and Fundamental Arithmetic operations . And we will do some simple problems.
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The Elementary
Algebra test measures your skills in three main categories
a. Operations with integers and rational numbers
This includes addition, subtraction, multiplication and division with integers
and negative rational numbers along with the use of absolute values and
ordering.
b. Operations with algebraic expressions.
This includes evaluations of simple formulas and expressions as well as adding
and subtracting monomials and polynomials. Also covered is evaluation of
positive rational roots and exponents, simplifying algebraic fractions and
factoring.
c. Equation solving, inequalities and word problems.
This includes solving verbal problems presented in algebraic context, geometric
reasoning, the translation of written phrases into algebraic expressions and
graphing.
Elementary Algebra Practice Test Materials
Print out the
Practice Exam linked below. Work through each problem and if you don't
understand a question, use the TEGRITY video solutions to watch a video
presentation of the worked out solution.
The following file is a
sample test made by the ARCC math department. Note: this test consists of 30
problems, but the actual exam is 20 problems. TEGRITY solutions are linked
below:
For
Video Presentation of
Solutions to each of
the questions on the Elementary Algebra Practice Exam, click
Accuplacer Elementary Algebra Practice Exam Solutions.
Each problem is explained in a short video-like presentation complete
with audio explanations. (Make sure your speakers are on!) Warning:
Disable pop-up blockersin order to view the video
solutions.
Two sample questions for the
Elementary Algebra test:
1.
A.
B.
C. D.
2. The width of a rectangle
is of the
length which is 10x. If the area of the rectangle is 100, what is the
value of x
A.
B.
C.
D.
The answer to sample question 1 is B and the answer to
sample question 2 is C.
You may wish to visit the following sites to refresh your arithmetic skills:
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Villanova University Computer Algebra Systems
A computer algebra system (CAS) is a mathematics software package which manipulates mathematical objects symbolically ("algebra"), as well as giving numerical and graphical computing capabilities, with typesetting options for making nice technical reports. There are two leading computer algebra systems: Maple from Maplesoft and Mathematica from Wolfram. These symbolic based computer algebra systems should not be confused with more specific purpose mathematical computation tools like MathCad or MatLab.
Mathematica
In the summer of 2008 we began a Mathematica site license experiment for 30 simultaneous users on campus to support the existing individual Mathematica users at Villanova and allow faculty members to explore the rich array of possibilities that Mathematica offers.
Mathematica offers amazing access to current data through remote servers in all kinds of fields not limited to more traditional mathematically based fields like mathematics, statistics, physics, astronomy, meteorology, chemistry, biology, engineering, etc., but also in the social and political sciences, economics, finance, geography, etc. AND in addition, this data may be fed into Mathematica for analysis or visualization without a great deal of expertise in using the product. For some demonstrations see:
Mathematica 7 has added genomic data, protein data, and current and historical weather data. The Learning Center is a good place to start nosing around Mathematica for the first time, after watching the short video
To access Mathematica, simply log in to the Villanova Citrix Server (which requires a quick client install if your computer image does not already have this software) and find Mathematica under Academic Applications, Math and Stat: you will see the Mathematica icon listed alphabetically right after Maple. If you do not, simply request that UNIT give you access by calling the Help Desk 9-7777. At present the Mathematica icon should be visible to all faculty and staff.
To get started actually using Mathematica if you are a new user, there is a 15 minute hands on introduction:
There are a few scattered Mathematica users on campus, some of whom may be willing to offer limited help in getting started using it. Email bob jantzen to try connecting with someone like this.
Maple
We adopted Maple for use in teaching mathematics at Villanova in the mid 1990s and it has evolved into a very user-friendly powerful tool for aiding learning in the college mathematics environment as well as for professional research and applications. In the summer of 2008 we upgraded out site license to an unlimited license which allows access to local copies of the Maple program to any faculty, staff or students in the Villanova community. For more information on Maple at Villanova, see:
Maple is also available through Citrix under Academic Applications, Math and Stat: choose the red Standard Maple icon. Simply log in to the Villanova Citrix Server (which requires a quick client install if your computer image does not already have this software) and find Maple under Academic Applications, Math and Stat: you will see the red Standard Maple icon listed alphabetically.
Mathematica videos
Mathematica is used in a variety of fields—from math, physics, and engineering to sociology, finance, and earth science. Two of the most popular Mathematica tutorials are the following
"Hands-on Start to Mathematica" is a free, two-part online screencast that introduces Mathematica basics to get you started with your first calculations, visualizations, and interactive examples. If you haven't already, be sure to check out Part 1 here:
Many students have asked for more in-depth training, so we now also offer "M10: A Student's First Course in Mathematica," a self-paced video training course providing step-by-step instructions on the basic features of Mathematica for students. Through the included videos and practice exercises, students learn how to navigate the user interface, build calculations, create graphics and dynamic models, work with data, and more—for under $30:
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2000 Solved Problems in Discrete Mathematics
9780070380318
ISBN:
0070380317
Pub Date: 1991 Publisher: McGraw-Hill
Summary: Master discrete mathematics with Schaum'sNthe high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! I...f you don't have a lot of time but want to excel in class, use this book to: Brush up before tests;Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, SchaumOs Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to rememberNfast! And SchaumOs are so complete, theyOre perfect for preparing for graduate or professional exams. Inside you will find: 2000 solved problems with complete solutionsNthe largest selection of solved problems yet published in discrete mathematics; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems. If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have!Chapters include: Set Theory; Relations; Functions; Vectors and Matrices; Graph Theory; Planar Graphs and Trees; Directed Graphs and Binary Trees; Combinatorial Analysis; Algebraic Systems; Languages, Grammars, Automata; Ordered Sets and Lattices; Propositional Calculus; Boolean Algebra; Logic Gates
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David Lay, author of the currently used Linear Algebra
textbook, has provided a convenient way for faculty and students to access the
data in homework problems. With the Lay Linear Algebra toolbox installed, at
the command line you type "c2s3" for chapter 2, section 3. MATLAB responds with
a list of homework problems with data and prompts for an exercise number. After
entering the number, MATLAB responds by defining a matrix or matrices
containing the data. In addition, the Lay toolbox has various tools which
manipulate matrices in a way parallel to the presentation in the book. For
example, there are commands for each of the elementary row operations. The
author has included boxed MATLAB subsections in the Study Guide which
demonstrate how to use these tools. To get a hard copy of the Study Guide, you
may contact the publisher. The electronic version is on the CD-ROM that comes
with the book. I can provide you with an electronic copy if you do not have the
CD. I have made use of the slides provided by the publisher. Depicting examples
in 3 dimensions is difficult and the author has done a reasonably good job.
In the MATLAB toolbox folder (e.g.,
C:\MATLAB7\toolbox), create a new folder "Lay"
Extract the files from the zipped file (about 50, all
ending with .m) and put into the "Lay" folder
Open up MATLAB. Go to Set Path under the File menu and
add the "Lay" folder.
Go to the command line window in MATLAB and enter
"c1s1". You should get the following response and prompt: "Exercise number
(1-4,7-18,29-32,34)?"
In addition to the author's tools,
there is an extensive set of material online for creating labs, illustrating
concepts or as places for students to explore. A good place to start is MAA's
Digital Library
[Thomas Hern was a coauthor of a seminal article that I handed out
to attendees a week after the seminar: "Viewing Some Concepts and
Applications in Linear Algebra" from Visualization in Teaching and
Learning Mathematics (1991) of the MAA Notes Series.]
Most tools on the MAA Digital
Library site are stand alone, meaning that they do not need costly software
such as MATLAB, Maple or Mathematica. However, since
we do have access to this software, we may explore what is available for any or
each of them. A good start is the ATLAST project:
The files can be downloaded here
and documentation is available. However, there is a lab manual and guide
published by Prentice Hall. Since Prentice Hall has merged with Addison-Wesley,
we may get them to bundle the guide with the Lay text. I have asked Pearson
(Fred Speers) to send us a review copy or 2.
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Mathematics
Book of the month
The Murderous Maths series are suitable for everyone, even those who have never read a book about maths before.
Do You Feel Lucky is a great introduction to probability – everything is explained in simple language.
Mathematics is an extremely popular subject with a very high uptake at A Level. Many students go on to take Mathematics-related subjects at university with some students going to Oxford and Cambridge to read Mathematics or related subjects.
Under the umbrella of Science specialism, the department is keen to build up links with local partner schools and shared enrichment courses are now a regular feature of the summer term. Sixth Form lectures are also organised on a joint basis; recent topics include chaos theory, fractals and code-breaking.
We are lucky to have six classrooms dedicated to the study of Mathematics at Parkstone, one of which is also a computer suite. All classrooms also contain brand new 'Smart' boards for whole-class teaching.
Key Stage 3
Mathematics is taught as part of the national curriculum in Years 8 and 9, working towards the KS3 SATS at the end of Year 9. In Year 8 students are taught in form groups and in Year 9 they are put into sets based on ability. Many students are also keen to enter the National Mathematics Challenge for which Bronze, Silver and Gold certificates are awarded for different levels of achievement.
GCSE Mathematics
Students need to be sufficiently numerate to manage their finances, and to have sufficient command of percentages and graphs to comprehend the information presented in media, however Mathematics is really about problem solving. It develops the ability to solve questions with the logic, precision, creativity and clarity of expression which society values. GCSE Mathematics provides transferable skills that will open many doors to future opportunities.
A Level Mathematics
Mathematics at A Level is a demanding and challenging course. As well as being a worthwhile subject in its own right, it supports the work of a wide range of other subjects, from the sciences to the arts. The aim of the course is to develop problem solving skills by stimulating thought and imagination and providing a social base of knowledge and understanding.
All students follow a course in Pure Mathematics, which provides a grounding in the basic concepts and algebraic methods that underpin all applications work. This is combined with two applied modules chosen from a choice of three: mechanics, statistics and decision mathematics.
Mechanics takes a look at the physical world, analysing the laws of nature and exploring how mathematical modelling enables us to quantify their effects. Statistics builds on the data handling and probability encountered at GCSE and provides the skill to analyse and interpret numerical information. Decision maths offers a radical departure from maths previously studied, and focuses on decision making situations that occur in business and commerce.
A Level Further Mathematics
Students who enjoy Mathematics and who intend to study mathematics, engineering or an allied scientific subject after A Level will gain enormous benefit from this two year course. It combines pure mathematics with probability, statistics, decision analysis and mechanics. Students therefore obtain the best possible grounding in advanced techniques across the whole of the mathematical spectrum. The aim in lessons is to stimulate the imagination and provide a thought provoking insight into some of the higher levels of the subject. The challenge posed by topics such as imaginary numbers and multi-dimensional geometry rarely disappoints.
Enrichment Events
World Maths Day 2010
On 3rd March all students throughout the school who study mathematics had the opportunity to see how many questions they could answer on World Maths Day. Throughout the World 1,133,246 students and 56,082 schools from 235 countries set a new world record by correctly answering 479,732,613 questions!
Interform Mathematics Challenge
On Friday 8 January, every student in Year 8 competed in the Year 8 Interform Maths Challenge. They took part in teams of 4 or 5 students in rounds which included a head to head competition and a relay race. The aim was to get the highest score by getting as many correct answers as possible to some very difficult Maths problems.In a very close contest the winning teams came from 8A and 8S although congratulations go to all who took part.
Maths Teams Challenge
On 9th March four pupils from Years 8 and 9 took part in the Maths Team Challenge at Corfe Hills School.
Edge Hill Mathematics Challenge 2009
Students making their presentation
Explaining the poster
Once again Year 9 students from Parkstone Grammar School entered the annual Edge Hill University's Mathematics Challenge. Hundreds of teams throughout the country entered the event and the Parkstone team made it through to the final round. This took place at the university where the pupils gave their professional presentations to a team of judges.
"On Tuesday 7th July we left school to begin the long drive up to Omskirk, Liverpool. We got this opportunity by completing two different posters on different mathematics problems. After getting through these initial stages we were invited to stay at Edge Hill University to take part in a final presentation. After a good night's sleep it was finally time to present. It was very nerve-wracking, but we got through it with just a few hiccups. The results were announced later that afternoon and out of 23 teams we weren't placed in the top three, but still managed to get our hands on a maths puzzle book and a certificate each. We were very happy to come in the top 10% of teams out of the 230 who entered and it was a great opportunity which will be remembered for a long time. Finally we would like to say thankyou to Mrs Dungate and Mrs Bassett who took us and to Miss Beattie for making all the arrangements."
Mathematics Challenge
The Senior Maths Challenge for Years 12 and 13 took place in November. Congratulations to all students who took part.
The Intermediate Challenge for Years 9, 10 and 11 was held on 3rd February. We have a student, Jess Olive in 9S, going through to the next round - the Cayley Competition - many congratulations to her. The Junior Mathematics Challenge will be held in May.
Specialist School Activities
Lectures
On Tuesday 9th February Martin Lavelle from Plymouth University gave a lecture at our school on 'Mathematical Detective Work: Dimension Analysis'. On 10th February Year 12 students studying Further Mathematics went to Canford School for the 'Take Maths to the Limit 2010' conference. Martin Lavelle spoke at the conference on 'Opening Doors: Careers with Mathematics and Statistics', and there were talks on the history of geometry, the mathematics of movement and 'Juggling Numbers'. The day was rounded off with a talk on 'Rumours of Other Worlds' - parallel universes with more dimensions than our familiar three and a close look at the beauty of the Mandelbröt set.
Activities with Middle Schools
Every Wednesday afternoon pupils from local middle schools come to Parkstone Grammar School for Science and Maths activities.
On 3rd July 2009 middle school pupils took part in a mathematics challenge.
On Monday mornings maths prefects go to St Joseph's RC Combined School as part of their Sixth Form Enrichment.
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This practical introduction to the techniques needed to produce mathematical illustrations of high quality is suitable for anyone with a modest acquaintance with coordinate geometry. The author combines a completely self-contained step-by-step introduction to the graphics programming language PostScript with advice on what goes into good mathematical illustrations, chapters showing how good graphics can be used to explain mathematics, and a treatment of all the mathematics needed to make such illustrations. The many small simple graphics projects can also be used in courses in geometry, graphics, or general mathematics. Code for many of the illustrations is included, and can be downloaded from the book's web site: Mathematicians, scientists, engineers, and even graphic designers seeking help in creating technical illustrations need look no further.
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Hi guys, It's been more than a week now and I still can't figure out how to solve a set of math problems on algebra tricks . I have to finish this work by the end of next week. Can someone help me to get started? I need some help with binomial formula and decimals. Any sort of guidance will be appreciated.
Sounds like your bases are not clear. Excelling in algebra tricks requires that your concepts be concrete. I know students who actually start teaching juniors in their first year. Why don't you try Algebra Buster? I am pretty sure, this program will aid you.
I have tried out several software. I would confidently say that Algebra Buster has assisted me to come to grips with my difficulties on quadratic inequalities, converting decimals and trinomials. All I did was to just key in the problem. The response appeared almost at once showing all the steps to the result. It was quite simple to follow. I have relied on this for my algebra classes to figure out College Algebra and Algebra 2. I would highly suggest you to try out Algebra Buster.
algebra formulas, trigonometric functions and binomials were a nightmare for me until I found Algebra Buster, which is really the best math program that I have ever come across. I have used it through many math classes – Basic Math, Basic Math and Remedial Algebra. Simply typing in the algebra problem and clicking on Solve, Algebra Buster generates step-by-step solution to the problem, and my algebra homework would be ready. I really recommend the program.
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Prerequisite: acceptable placement score (or ACT math score of at least 28), or at least 3 years of high school algebra and trigonometry with at least a B average, or a grade of C or better in MATH 180. General Education course: G9.
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
(a) Develops an appreciation for the intellectual honesty of deductive reasoning.
(b) Understands the need to do one's own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students understand their own and other cultural traditions and respect the diversity of the human experience.
(a) Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
(b) Learns to use the symbolic notation correctly and appropriately.
NCTM Goals: The NCTM (National Council of Teachers of Mathematics) gives the following set of overall goals for mathematics education in general, which are worth including here, since I think they are such fundamental reasons for studying mathematics.
1. Learn to value mathematics.
2. Learn to reason mathematically.
3. Learn to communicate mathematically.
4. Become confident in your mathematical ability.
5. Become problem solvers and posers.
Course Goals:
1. Students shall develop a solid foundation in the basic concepts and methods of Differential Calculus.
2. Students shall develop problem solving skills.
3. Students shall understand the appropriate use of technological tools in their mathematical work.
Outcomes: This is a list of more specific mathematical outcomes this course should provide. The student shall...
Content:
1. ... demonstrate the knowledge of the theory and methods of Differential Calculus, specifically, limits, derivatives by definition, differentiation formulas, and applications of the derivative.
Problem-Solving:
2. …demonstrate the ability to apply appropriate mathematical tools and methods of novel or non-routine problems.
3. …demonstrate the ability to use various approaches in problem solving situations, and to see connections between these varied mathematical areas.
Technology:
4. …demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer.
5. …demonstrate the ability to efficiently and accurately graph functions using a calculator or computer.
6. …demonstrate the knowledge of the limitations of technological tools.
7. …demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work.
Communication:
8. …use the language of mathematics accurately and appropriately.
9. …present mathematical content and argument in written form.
COURSE POLICIES AND PROCEDURES:
Probably the best single piece of wisdom I can pass on to you as you begin this course is: "Mathematics is not a spectator sport!" You need to view yourself as the LEARNER – and "learn" is an active verb, not a passive verb. I will do what I can to help structure things so that you have an appropriate sequence of topics and a useful collection of problems, but it is up to YOU to DO the problems and to READ the book and THINK ABOUT the topics.
You must develop a system that works for you, but let me suggest that it might include finding a study group or coming to me with your questions or going to tutoring sessions in the learning center. In any case you should expect to spend at least the traditional expectation of 2 hours outside of class for each hour in class – this is important! Class time is for exploring the topics and answering questions you might have, but you simply can't master the material without putting in the time alone to really engage in the mathematics.
We are in the process of phasing in a new textbook and more than ever it is important that you actually READ the BOOK! The authors attempt to force the reader to think about the material and to develop an intuitive sense of what is going on; there is much emphasis on solving problems and much reliance on graphing technology as well as on symbolic manipulation.
HOMEWORK: In a nutshell, working problems is one of the key ways you will learn Calculus. Attending class is important, of course, but without doing problems you will not develop a solid foundation in the material. I will give you daily assignments and will expect that you will do as many as time allows (which I take to be roughly 2 hours per class period). I will not generally collect these assignments but I do see them as testing your understanding and as raising questions for you to ask in class.
LABS: Throughout the course there will be an occasional "lab", a problem set you will work on
EXAMS: There will be exams after each of the 4 chapters we will cover – these will be in two parts, a group practice problem set worth 20 points and then an individual exam worth 80 points, 100 points in total. The final exam will be cumulative and worth 150 points (25 on the group part, 125 on the individual part). By the way, I do not expect you to memorize the various formulas – you are allowed a page of notes for each exam, and you can bring all four pages in for the final exam.
GRADING POLICY: In general I use the rather traditional 90% of possible points for an "A", 80% for a "B", 70% for a "C", and 60% for a "D". I will try to make enough points available in non-test situations that "test-anxiety" should not entirely kill your chances for success, but I am a very firm believer in putting students through the exam experience so that I can see whether you, not your study group, understand the material.
AMERICANS WITH DISABILITIES ACT
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Let's Review Integrated Algebra
Using many step-by-step demonstration examples, helpful diagrams, informative "Math Fact" summaries, and graphing calculator approaches, this book presents:A clearly organized chapter-by-chapter review of all New York State Regents Integrated Algebra topicsExercise sections within each chapter with a large sampling of Regents-type multiple-choice and extended-response questionsRecent New York State Regents Integrated Algebra ExamAnswers are provided for all questions in the exercise sections and all questions on the Regents exam.
show more show less
Preface
Sets, Operations, and Algebraic Language
Numbers, Variables, and Symbols
Classifying Real Numbers
Learning More About Sets
Operations with Signed Numbers
Properties of Real Numbers
Exponents and Scientific Notation
Order of Operations
Translating Between English and Algebra
Linear Equations and Inequalities
Solving One-Step Equations
Solving Multistep Equations
Solving Equations with Like Terms
Algebraic Modeling
Literal Equations and Formulas
One-Variable Linear Inequalities
Problem Solving and Technology
Problem Solving Strategies
Using a Graphing Calculator
Comparing Mathematical Models
Ratios, Rates, and Proportions
Ratios and Rates
Proportions
Solving Motion Problems
Solving Percent Problems
Probability Ratios
Polynomial Arithmetic and Factoring
Combining Polynomials
Multipying and Dividing Polynomials
Factoring Polynomials
Multiplying and Factoring Special Binomial Pairs
Factoring Quadratic Trinomials
Solving Quadratic Equations by Factoring
Solving Word Problems with Quadratic Equations
Rational Expressions and Equations
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Combining Rational Expressions
Rational Equations and Inequalities
Radicals and Right Triangles
Square and Cube Roots
Operations with Radicals
Combining Radicals
The Pythagorean Theorem
General Methods for Solving Quadratic Equations
Similar Triangles and Trigonometry
Trigonometric Ratios
Solving Problems Using Trigonometry
Area and Volume
Areas of Parallelograms and Triangles
Area of a Trapezoid
Circumference and Area of a Circle
Areas of Overlapping Figures
Surface Area and Volume
Graphing and Writing Equations of Lines
Slope of a Line
Slope-Intercept Form of a Linear Equation
Slopes of Parallel Lines
Graphing Linear Equations
Direct Variation
Point-Slope Form of a Linear Equation
Functions, Graphs, and Models
Function Concepts
Function Graphs as Models
The Absolute Value Function
Creating a Scatter Plot
Finding a Line of Best Fit
Systems of Linear Equations and Inequalities
Solving Linear Systems Graphically
Solving Linear Systems By Substitution
Solving Linear Systems By Combining Equations
Graphing Systems of Linear Inequalities
Quadratic and Exponential Functions
Graphing a Quadratic Function
Solving Quadratic Equations Graphically
Solving a Linear-Quadratic System
Exponential Growth and Decay
Statistics and Visual Representations of Data
Measures of Central Tendency
Box-and-Whisker Plots
Histograms
Cumulative Frequency Histograms
Counting and Probability of Compound Events
Counting Using Permutations
Probability of Compound Events
Probability Formulas for Compound Events
Answers and Solution Hints to Practice Exercises
Glossary of Integrated Algebra Terms
The Integrated Algebra Regents Examination
June 2011 Regents Examination
Answers
June 2012 Regents Examination
Answers
Index
List price:
$16.99
Edition:
2nd (Revised)
Publisher:
Barron's Educational Series, Incorporated
Binding:
Trade Paper
Pages:
544
Size:
6.00" wide x 9
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A course which ensures that the student has a mastery of the concepts, methods, and practical applications of quantitative reasoning, with emphasis on logical reasoning and problem solving skills. Included will be the study of sets and functions; the concept, function, and solutions of algebraic equations and inequalities; application and interpretation of graphs and statistical data;
principles of mortgage, investment, and personal finance; computer applications
in mathematics; and the application of mathematical principles in deriving solutions to non-routine, cross-disciplinary problems. Prerequisite: Qualifying math placement, a grade of C or better in MA 095, or consent of the instructor.
Functions and their graphs; limits; the derivative and some of its applications; the integral; the fundamental theorem of calculus; some applications of the integral. CSET subtest II ($72) must be attempted during this course in order to receive a grade for the course. Prerequisite: Placement or consent of instructor.
This course is a comprehensive approach to the mathematical knowledge necessary (i.e. number theory, integers, rational numbers, real numbers, etc.) for a California multiple subject teaching credential (K-8). Planning of content-specific instruction and the methods of delivery of that content consistent with California state-adopted K-8 mathematics standards and framework are the focus. Prerequisite: MA 115.
Continuation of MA303. An integrated approach to the concepts and methods of elementary school mathematics. Students mathematical thinking and learning. Multicultural and gender issues in mathematics education. Traditional and alternative assessment methods in mathematics. Manipulatives, calculators, computers and their role in elementary mathematics teaching and learning. Activities and field experiences. Problem solving strategies. Logical reasoning, exploration and conjecture-making. Connectedness of different mathematical topics, their representations, and the relationship of mathematics to other subject areas. Fractions and decimals. Ratios, proportions, and percents. Patterns and relationships. Elementary number theory, algebra, functions, and graphing. Geometry and measurement. Data analysis, statistics, and probability. Prerequisite: MA 303.
A study of methods, techniques and materials of instruction appropriate to mathematics teaching in high school. The secondary school mathematics in relation to the NCTM Standards, the California Framework and state-adopted textbooks. Topics also include the use of technology and manipulatives in teaching, designing lessons to allow learners to develop knowledge, comprehension and problem solving skills in mathematics; developing and interpreting tests and other assessment strategies. Employing group learning and discovery learning strategies
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Lesson 13 2 Practice Worksheet Algebra 2
You are here because you browse for Lesson 13 2 Practice Worksheet Algebra 2. We Try to providing the best Content For pdf, ebooks, Books, Journal or Papers in Chemistry, Physics, mathematics, Programming, Health and more category that you can browse for Free . Below is the result for Lesson 13 2 Practice Worksheet Algebra 2 query . Click On the title to download or to read online pdf & Book Manuals
Lesson Analysis and Adaptation Worksheet - Foliji
20120604014659Huneh.doc. Lesson Analysis and Adaptation Worksheet - Foliji. Jun 4, 2012. for key indicators and components of effective instructional design using the Lesson Lesson Analysis and Adaptation Worksheet (page 2 of this Lab). Students must actively search for answers to essential questions. or not their stand had a profit or loss, and it's fair because it's not just based on ability.ΗΤΤΡ://FΟLΙJΙ.CΟΜ/UΡLΟΑDS/20120604014659ΗUΝΕΗ.DΟC
ALGEBRA 2/TRIGONOMETRY
0112ExamA2.pdf. ALGEBRA 2/TRIGONOMETRY. Jan 25, 2012 the last page of this booklet, which is the answer sheet for Part I. (1). 4 . 7. (3). 7 . 2. (2). 2. (4) 4. Algebra 2/Trigonometry. and three are green. Your answers for Parts II, III, and IV should be written in the test booklet.ΗΤΤΡ://
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This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected
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Attendance is not required. Students are responsible for all
material discussed in class whether choosing to attend class or not.
In addition, handouts will be distributed only once. Students not
attending class will have to obtain copies of any handouts from
fellow classmates. The instructor will recycle any extra handouts
immediately after the class in which they were distributed.
Classroom Ettiquette:
To maintain a proper atmosphere for learning, the following standards of classroom behavior will be observed:
Students will be on time for class. The instructor considers latecomers disrespectful of those who manage to be on time.
Students will show courtesy to others in the classroom by not talking when the instructor or a fellow classmate is speaking.
If a student decides to attend class, he or she will not disrupt class by leaving before the period has ended. There will be a ten minute break during the class.
Summer Mathematics Classes:
The syllabus for Math 102 will be covered over the course of five weeks.
(Normally, the same topics are covered over a fifteen-week period
during the Fall or Spring semesters.)
Consequently, the material will be presented at a very rapid pace.
Taking Summer mathematics classes is like drinking from a fire hose. You
have to swallow fast!
Only the most committed students will be successful in this course.
In addition, during the Summer sessions, there is no tutoring services offered
by the Department of Mathematical and Computer Sciences. A list of private
tutors is maintained in Damen Hall, Room 149.
Grading:
Final grades will be computed according to the following
recipe. There will be a final examination worth 32%. The final examination
will be comprehensive. In addition, there will be five
tests each worth 17%. The lowest test grade will be dropped.
Therefore, the tests will be worth
68% of the total grade. Students cannot make up missed tests.
Each test will be one half hour in duration, and
will be taken at the end of class.
Homework problems
will be assigned from the textbook
and should be completed before the beginning of the next class.
The instructor will also pass out additional homework problems.
Problems from the text will be announced at the end of class and will also be posted
on the web.
Homework will not be collected or graded. However, students will
have some opportunity to discuss homework problems in class.
The final examination will be on
Wednesday August 6 from 6:00p.m.-9:00p.m. in Damen Hall, Room 339 best
tests 7,
Test 2.....July 14, Test 3.....July 21, Test 4.....July 28 and
Test 5.....August 4.
The goal of the course is to acquaint the student with those results and
techniques from discrete mathematics needed for advanced study in computer
science.
Important Dates:
Friday July 25 is the last day a student may withdraw
from a course with a non-penalty grade of W. Monday August 4 is the last day
of class.
Academic Dishonesty:
Prohibited activity includes cheating on a test or examination, using
forbidden materials on a test or examination and helping others on a test or examination.
A student who violates these rules for the first time will receive
a failing grade on the test or examination on which the cheating occurred.
A second violation will result in an F for the entire course.
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Resources
Welcome to the world of Maple! With the right tools, you too can do amazing things. Maple will help you reduce the time to do any math problems. Graphing, calculus, equation solving, matrices … anything you'll likely encounter in a math course can be made easier.
The Maple Student Help Center is made specifically for you, with the right information to help get you up to speed and fully command the power of Maple. Remember, Maple is a professional product, and with a little help, you can get all of that power working for you.
The Math Oracles are a great way to get quick answers to standard math problems, including Plotting, Integration and Differentiation, Limits, Matrices, and Linear System Solving. Perhaps you're at the library and you don't have a computer with Maple on it ... and your homework involves a question where the answer is not in the back of the book. The solution? Simply visit the Maplesoft Online Math Oracles, enter your problem, and the answer will be given to you courtesy of an amazing technology called MapleNET.
Don't like reading manuals or help pages? Relax … these videos will be the ideal way for you to learn how to solve the most common types of math problems. They're short and easy to understand. So go get that bowl of popcorn and a nice cold drink and get a head start in Maple.
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Product Description
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems.
In this episode, concrete examples and practical applications show how the mastery of fundamental algebraic concepts is the key to success in today's technologically advanced world. Students will also learn the development of algebraic symbolism as well as the geometric and numeric currents. Grades 5-9
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This edited volume addresses the importance of mathematics for industry and society by presenting highlights from contract research at the Department of Applied Mathematics at SINTEF, the largest independent research organization in Scandinavia. Examples range from computer-aided geometric design, via general purpose computing on graphics cards, to... more...
Based on a teach-yourself approach, the fundamentals of MATLAB are illustrated throughout with many examples from a number of different scientific and engineering areas, such as simulation, population modelling, and numerical methods, as well as from business and everyday life. Some of the examples draw on first-year university level maths, but these... more...
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate... more...
About the Book: Application of Numerical Analysis has become an integral part of the life of all the modern engineers and scientists. The contents of this book covers both the introductory topics and the more advanced topics such as partial differential equations. This book is different from many other books in a number of ways. Salient Features:... more...
Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently. more...
This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the FejÚr property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative... more...
The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known... more...
The present collection of four lecture notes.... more...
The eighth edition of this popular book provides a hands-on introduction to MATLAB[registered] that can be used at the undergraduate level. The new edition features the use of MATLAB 8.0, which will be introduced to the market in March 2010. It covers object-oriented programming in MATLAB and the improvements that have been made to the MATLAB desktop... more...
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For Elementary Mathematics Methods or Middle School Mathematics Methods Covers preK-8 Written by leaders in the field, this best-selling book will guide teachers as they help all PreK-8 learners make sense of math by supporting their own mathematical understanding and cultivating effec...
This best-selling writing guide by a prominent biologist teaches students to think as biologists and to express ideas clearly and concisely through their writing. Providing students with the tools they'll ...For courses in Business Statistics. A classic text for accuracy and statistical precision. Statistics for Business and Economics enables students to conduct serious analysis of applied problems rather than running simple "canned" applications. This text is also at a math...
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A video that focuses on the TI-Nspire graphing calculator in the context of teaching algebra. In this program the TI-Nspire is used to explore the nature of linear functions. Examples ranging from ...How do you get started at mathematical modeling? Here is an easy, quick, and engaging activity and a "just add data" interactive Excel spreadsheet to accomplish that first modeling task. The task ... More: lessons, discussions, ratings, reviews,...
This activity is perfect for grade 7 and 8 students who are just learning about slope. The tutorial applet allows students to drag collinear points on a plane. As they move the points, the students wi... More: lessons, discussions, ratings, reviews,...
Guided activities with the Graph Explorer applet, in which students explore how the graph of a linear function relates to its formula, and learn to graph and edit functions in the applet, including on... More: lessons, discussions, ratings, reviews,...
How does changing the slope of a line affect the equation of that line? How might changing a part of an equation cause the related line to move? Explore these challenges using the Linear Transformer t... More: lessons, discussions, ratings, reviews,...
The Marabyn problem requires students to recommend a distance for someone to travel on a bus and a walking time to complete the journey home. The complicating factor is that there is a given window of... More: lessons, discussions, ratings, reviews,...
In conjunction with the simulation, a graph is generated by the applet that illustrates the relationship between number of people and time. Students are asked to investigate how the shape of the graph... More: lessons, discussions, ratings, reviews,...
Compare different representations of motion: a story, a position graph, and the motion itself. Create a graph that matches a story, or write a story to match a graph, and check either by watching Mell... More: lessons, discussions, ratings, reviews,...
This is a computer activity using Sketchpad and specially selected pictures located online (SlopePix web page) to help students understand the concept of slope. Following the instructions, students... More: lessons, discussions, ratings, reviews,...
Students use a two-player game to develop and refine their sense of the slopes of lines. The link to the activity itself is to a zip file that contains both the activity in pdf format and the corrThis activity focuses on:
* graphing an ordered pair, (a, f(a)), for a function f
* the connection between a function, its table, and its graph
* the interpretation of the horizontal coordinate o
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The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.
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OUR STUDENTS ADVANCE
24/7
Access to study guides and course materials.
"The Grantsburg Virtual Charter School was a great school for me. The teachers were very supportive, and they all wanted to help you whenever they could. I was able to make a big improvement with my work."
-Lauren, Milwaukee
COURSES
Challenging core courses. A growing number of career cluster classes. And electives to spark all sorts of new interests. iForward's extensive course catalog is always changing to meet students' needs. So check back often. Who knows what you'll discover?
Special Program Courses:
Math
Core
Algebra I
HONORS|1.0 Credits
Description: Algebra I is the foundation! The skills you'll acquire in this course contain the basic knowledge you'll need for all your high school math courses. Relax! This stuff is important, but everyone can do it. Everyone can have a good time solving the hundreds of real-world problems that are answered with algebra. Each module in this course is presented in a step-by-step way right on your computer screen. You won't have to stare at the board from the back of a classroom. There are even hands-on labs to make the numbers, graphs and equations more real. It's all tied to real-world applications like sports, travel, business and health. This course is designed to give you the skills and strategies for solving all kinds of mathematical problems. It will also give you the confidence that you can handle everything that high school math has in store for you.
Algebra II
HONORS|1.0 Credits
Description: This course connects algebra to the real world. It also demystifies algebra, making it easier to understand and master. The goal is to create a foundation in math that will stay with you throughout high school.
Prerequisites: Geometry
Calculus
1.0 Credits
Description: Students in this course will walk in the footsteps of Newton and Leibnitz.
An interactive text and graphing software combine with the exciting on-line course delivery to make calculus an adventure. The course includes a study of limits, continuity, differentiation, and integration of algebraic, trigonometric, and transcendental functions, and the applications of derivatives and integrals.
Description: For those students needing a slower approach at learning Algebra. This course will be held in Acellus, a different website than Brain Honey. A recommendation from the teacher or guidance counselor is needed.
Geometry
HONORS|1.0 Credits
Description: One day in 2580 B.C., a very serious architect stood on a dusty desert with a set of plans. His plans called for creating a structure 480 feet, with a square base and triangular sides, using stone blocks weighing two tons each. The Pharaoh wanted the job done right. The better our architect understood geometry, the better were his chances for staying alive. Geometry is everywhere, not just in pyramids. Engineers use geometry to bank highways and build bridges. Artists use geometry to create perspective in their paintings, and mapmakers help travelers find things using the points located on a geometric grid. Throughout this course, we'll take you on a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem solving. This course is all about points, lines and planes. Just as importantly, this course is about acquiring a basic tool for understanding and manipulating the real world around you.
Prerequisites: Algebra I
Integrated Math
0.5 Credits
Description: This course will review some of the fundamental math skills you learned in middle school, and then get you up to speed on the basic concepts of algebra. This course will be taught as a "blended" course. Students from the Grantsburg High School will be attending simultaneously as the teacher works with both traditional and online learners. Pre-approval is necessary to take this course. Call Mr. Beesley, Mr. Bettendorf, or Mr. Mark Johnson for more information.
Liberal Arts Mathematics
1.0 Credits
Description: The total weight of two beluga whales and three orca whales is 36,000 pounds. As you'll see in this course, if given one additional fact, you can determine the weight of each whale. To answer this weighty question, we'll give you all the math tools you'll need. The setting for this course is an amusement park with animals, rides, and games. Your job will be to apply what you learn to dozens of real-world scenarios. Equations, geometric relationships, and statistical probabilities can sometimes be dull, but not in this class! Your park guide (teacher) will take you on a grand tour of problems and puzzles that show how things work and how mathematics provides valuable tools for everyday living. Come reinforce your existing algebra and geometry skills to learn solid skills with the algebraic and geometric concepts you'll need for further study of mathematics. We have an admission ticket with your name on it and we promise an exciting ride with no waiting!
Pre-Calculus
1.0 Credits
Description: Students, as mathematic analysts, will investigate how advanced mathematics concepts can solve problems encountered in operating national parks. The purpose of this course is to study functions and develop skills necessary for the study of calculus. The pre-calculus course includes analytical geometry and trigonometry.
Prerequisites: Advanced Algebra or Algebra 2
Elective
AP Calculus AB AB exam given each year in May. With continuous enrollment, students can start the course and begin working on Calculus as early as spring of the previous year.
AP Calculus BC BC exam given each year in May. With continuous enrollment, students can start the course and begin working on Calculus as early as spring of the previous year.
AP Statistics
ADVANCED PLACEMENT|1.0 Credits
Description: Statistics are used everywhere from fast food businesses ordering hamburger patties to insurance companies setting rates to predicting a student's future success by the results of a test. Students will become familiar with the vocabulary, method, and meaning in the statistics which exist in the world around them. This is an applied course in which students actively construct their own understanding of the methods, interpretation, communication, and application of statistics. Each unit is framed by enduring understandings and essential questions designed to allow students a deep understanding of the concepts at hand rather than memorization and emulation. Students will also complete several performance tasks throughout the year consisting of relevant, open-ended tasks requiring students to connect multiple statistical topics together.
iForward is Wisconsin's leading nonprofit online charter school, administered by the award-winning Grantsburg School District. With career-focused academics tailored to meet each student's unique learning style and personal goals, we give middle and high school students the individualized instruction they need to reach their own potential.
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This is an introductory course to number theory. Topics include divisibility, prime numbers and modular arithmetic, arithmetic functions, the sum of divisors and the number of divisors, rational approximation, linear Diophantine equations, congruences, the Chinese Remainder Theorem, quadratic residues, and continued fractions.
Prerequisites: MA 232
Course Web Site:
Course Objectives
The purpose of the course is to give a simple account of classical number theory, prepare students to graduate-level courses in number theory and algebra, and to demonstrate applications of number theory (such as public-key cryptography). Upon completion of the course, students will have a working knowledge of the fundamental definitions and theorems of elementary number theory, be able to work with congruences, solve congruence equations and systems of equations with one and more variables, and be literate in the language and notation of number theory.
Learning Outcomes
Divisibility. Understand the concept and properties of divisibility. Know the definitions and properties of gcd and lcm.
Euclid algorithm and Bezout's identity. Be able to compute the greatest common divisor and least common multpiples.
Linear Diophantine equations. Describe the set of all solutions to linear Diophantine equations.
Primes, distribution of primes, and prime power factorization. Determine if a number is prime. Compute the prime power factorization of a number.
Modular arithmetic, congruences. Understand the concept of a congruence. Be able to perform basic operations with congruences (addition, multiplication, subtraction).
Linear congruences, systems of linear congruences, and Chinese remainder theorem (CRT). Compute the set of all solutions to linear congruence. Be able to apply CRT and reduce general systems of linear congruences to systems studied by CRT.
Simultaneous non-linear congruences. Describe the set of solutions of non-linear congruence equations (with relatively small moduli) and be able to solve systems of such equations.
The arithmetic of Zp. Studentís must understand and be able to use the founding theorems: Lagrange theorem, Fermat's little theorem, Wilson's theorem.
Primality-testing, pseudoprimes, and Carmichael numbers. Understand the concept of a pseudoprime and be able to determine if a number is pseudoprime or Carmichael.
Units. Euler's function phi. Understand the definition of a unit, know characterization of units, be able to compute a group of units directly. Compute Eulerís function phi, be able to use a formula for phi to study relations between numbers n and phi(n). Understand Euler's generalization of Fermat's little theorem.
The group of units Un. Understand the concepts of the order of an element, primitive root, generating set for a group, Cayley graph for a group. Be able to determine if a group Un has a primitive root and find it. Be able to find a generating set for Un and draw the Cayley graph relative to the chosen set.
The group of quadratic residues Qn. Construct the group Qn directly. Determine the size of Qn. Compute Legendre symbol, know the properties of Legendre symbol. Know and be able to use the law of quadratic reciprocity.
Arithmetic functions. Mobius inversion formula and its properties.
RSA cryptography. Understand the basics of RSA security and be able to break the simplest instances.
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Extra Examples shows
you additional worked-out examples that mimic the ones in
your book. These requirements include the benchmarks from
the Sunshine State Standards that are most relevant to this
course. The benchmarks printed in regular type are required
for this course. The portions printed in italic type
are not required for this course.
Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.
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In this section
Lifeskills Mathematics
New National Qualifications
Lifeskills Mathematics sits within the Mathematics curriculum area.
Finalised Course and Unit documents are now available for all the new qualifications, from National 2 to Advanced Higher. These documents contain both mandatory information (in the Specifications) and advice and guidance (in the Support Notes). You can download all of these documents for this subject from our download page, using the button below, or use our check-box facility to download a selection of documents.
Assessment support materials are also now available for all the new National 2, National 3, National 4 and National 5 qualifications. Information on Course assessment support material (such as Specimen Question Papers and coursework information) is available on the National 5 subject page and, for all National 2 to National 5 qualifications, information on how to access Unit assessment support materials can be found on each subject page.
Following the development of these support materials, some documents with mandatory information (Course Assessment Specifications, in particular) have been updated with further information and clarifications. In line with our standard practice, these documents contain version information and, if necessary, a note of changes. This ensures you can recognise the most up-to-date documents.
Development process
The final documents have been published following a lengthy engagement process. Find out how we got here. Considerable work has been carried out by the Curriculum Area Review Groups (CARGs), the Qualifications Design Teams (QDTs) and Subject Working Groups (SWGs) to develop the final documents.
At each stage of the qualification development process, we publish draft documents outlining our proposals and plans.
Visit our timeline to find out when the next documents for each qualification will be published.
Key points
National 3 to National 5
develops confidence and independence in being able to handle information and mathematical tasks in both personal life and in the workplace
motivates and challenges learners by enabling them to think through real-life situations involving mathematics
has mathematical skills underpinned by numeracy and is designed to develop learners' mathematical reasoning skills relevant to learning, life and work
provides opportunities in Units for combined assessment
has a hierarchical Unit structure that provides progression from National 2 to National 5
has a test as the added value assessment at National 4, and question papers at National 5
National 2 Lifeskills Mathematics
offers opportunities for flexible delivery through the use of Units which can be delivered sequentially, in parallel or in a combined way
offers increased opportunities for personalisation, choice and flexibility in Unit assessment, with opportunities for integrated assessment
provides increased opportunities for interdisciplinary and cross-curriculum working
includes both mathematical operational and reasoning skills in the Units
provides an opportunity to use mathematical skills in real-life contexts
The Unit titles have been changed to better reflect the Unit content, which has been reorganised. Units, including the National 4 Added Value Unit Outcomes, Assessment Standards and Evidence Requirement statements, have all been revised to increase flexibility. Additional information is provided in the Evidence Requirements for all Units.
At National 2, there has been a change of Unit title from Personal Mathematics to Shape, Space and Data to better reflect content. There is now a range of small optional Units, which aims to improve accessibility for learners at this level.
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Welcome to Math 126. This is the third quarter of an introductory course in calculus.
What makes this course interesting?
The use of calculus and its consequences cuts across many disciplines,
ranging from biology to business to engineering to the social sciences.
At the risk of oversimplifying, calculus provides powerful tools to study
"the rate of change." For example, we might want to study how fast a disease
is spreading through a population, by studying the "number of diagnosed cases per day".
We hope that seeing how calculus can be used to solve real world problems will be interesting.
This course first expands upon the idea of linear approximations
learned in math 124. You will learn how to make better approximations
and to estimate how good these approximations are.
Many practical applications of calculus involve functions that depend
on more than one variable. You will learn about the geometry of curves
and surfaces and get an introduction to differentiation
and integration of functions two variables.
What makes this course difficult?
The hardest thing about calculus is precalculus. The hardest
thing about precalculus is algebra.
You all know from previous math classes how one course will build upon
the next, and calculus is no exception. Math 126 will not only use
material from precalculus and algebra, but it will use material you
learned in Math 124 and Math 125.
Very few of you will go on to major in mathematics or computer
science, but most of you will eventually see how calculus is applied
in your chosen field of study. For this reason, we aim for ability to
solve application problems using calculus. Some of the homework
problems are quite lengthy and building up your "mathematical problem
solving stamina" is just one of the aims of this course. If you have
taken the Math 120 at UW, you know what this all
means. If you have not, it means that a large number of "word
problems" ("story problems") or "multi-step problems" are encountered
in the course. This is one key place Math 126 will differ from a
typical high school course. In addition, it is important to note that
the ability to apply calculus requires more than computational skill;
it requires conceptual understanding. As you work through the
homework, you will find two general types of problems:
calculation/skill problems and multi-step/word problems. A good rule
of thumb is to work enough of the skill problems to become proficient,
then spend the bulk of your time working on the longer multi-step
problems.
Five common misconceptions
Misconception #1: Theory is irrelevant and the lectures should be
aimed just at showing you how to do the problems.
The issue here is that we want you to be able to do ALL problems
– not just particular kinds of problems – to which the
methods of the course apply. For that level of command, the student
must attain some conceptual understanding and develop judgment. Thus,
a certain amount of theory is very relevant, indeed essential. A
student who has been trained only to do certain kinds of problems has
acquired very limited expertise.
Misconception #2: The purpose of the classes and assignments is to
prepare the student for the exams.
The real purpose of the classes and homework is to guide you in
achieving the aspiration of the course: command of the material. If
you have command of the material, you should do well on the
exams.
Misconception #3: It is the teacher's job to cover the material.
As covering the material is the role of the textbook, and the textbook
is to be read by the student, the instructor should be doing something
else, something that helps the student grasp the material. The
instructor's role is to guide the students in their learning: to
reinforce the essential conceptual points of the subject, and to show
their relation to the solving of problems.
Misconception #4: Since you are supposed to be learning from
the book, there's no need to go to the lectures.
The lectures, the reading, and the homework should combine to produce
true comprehension of the material. For most students, reading a math
text won't be easy. The lectures should serve to orient the student in
learning the material.
Misconception #5: Since I did well in math, even calculus, in a good
high school, I'll have no trouble with math at UW.
There is a different standard at the college level. Students will
have to put in more effort in order to get a good grade than in high
school (or equivalently, to learn the material sufficiently well by
college standards).
How do I succeed?
Most people learn mathematics by doing mathematics. That is, you learn
it by active participation; it is very unusual for someone to learn
calculus by simply watching the instructor and TA perform. For this
reason, the homework is THE heart of the course and more than anything
else, study time is the key to success in Math 126. We advise an
average of 15 hours of study per week, OUTSIDE class. Also, during the
first week, the number of study hours will probably be even higher as
you adjust to the viewpoint of the course and brush up on
precalculus/algebra skills. In effect, this means that Math 126 will
be roughly a 20 hour per week effort; the equivalent of a half-time
job! This time commitment is in line with the University Handbook
guidelines. In addition, it is much better to spread your studying
evenly as possible across the week; cramming 15 hours of homework into
the day before an assignment is due does not work. Pacing yourself,
using a time schedule throughout the week, is a good way to insure
success; this applies to any course at the UW, not just math.
What is the course format?
On Monday, Wednesday and Friday, you will meet with the Instructor
for the course in a class of size approximately 160; these classes are
each 50 minutes long. On Tuesday and Thursday
you will have a 50 minute section of
about 40 students run by a TA. During these sections, you will take quizzes and
exams, work in small groups
on worksheets, and participate in question and answer sessions. The
worksheets are
designed to lead you through particular ideas related to
this course.
The TA for the course will circulate around the
individual groups to insure everyone is progressing.
What resources are available to help me succeed?
Calculus is a challenging course and the math department would like
to see every one of you pass through with a positive experience. To
help, a number of resources are available.
Your instructor and TA will be accessible to help you during
office hours, which will be announced early the first week of the
term. If you are new to the university, you might have the false
impression that professors are aloof and hard to approach. Our faculty
and TA's make themselves very accessible to help their students and
you should not be afraid to ask for advice or help.
The math department operates a Math Study Center (MSC), located in
B-14 of Communications. This facility is devoted to help students in
our freshman math courses only. The center has extensive hours of
operation that will be announced the first week of class. The MSC is
staffed by advanced undergraduate and graduate students who can help
you with difficulties as you work through the course. In addition,
many faculty hold office hours there as well. One useful piece of
advice: The MSC is often overcrowded the day before homework is due;
this is another good reason to spread your study time out over the week.
Some students use the MSC as a place to meet a small group of
fellow students in the course and work through problems
together. Explaining solutions to one another is often the best way to
learn.
A large amount of material is available on line (including old
quizzes, midterms, finals and worksheets) at
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Welcome to my page.
Open Algebra Textbooks
Writing these textbooks was quite the effort! It is nice to be done... Elementary and Intermediate Algebra both have been published by Flat World Knowledge
Elementary Algebra is an open textbook designed to be used in the first part of a two part algebra course. It is written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.
Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. In addition to the creative commons license and FWK features, this textbook offers a true pedagogical improvement over the current very expensive options.
Latest Activity Blogger ports to mobile quite well automatically. So it looks OK on the phone too!See More
John Redden's Blog
Instead of waiting for the option to "share" my Elementary Algebra blackboard course, I just copied and pasted the content over to blogger. Google docs makes for easy sharing of course pdf material. I am not quite finished yet but here is my first attempt:
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KEY MESSAGE: Elayn Martin-Gay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Mart ... more »in-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful. Martin-Gay also strives to provide the highest level of instructor and adjunct support. KEY TOPICS: Real Numbers And Algebraic Expressions; Equations, Inequalities, And Problem Solving; Graphs and Functions; Systems of Linear Equations and Inequalities; Exponents, Polynomials, and Polynomial Functions; Rational Expressions; Rational Exponents, Radicals, and Complex Numbers; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem MARKET: For all readers interested in intermediate algebra, and for all readers learning or revisiting essential skills in intermediate algebra through the use of lively and up-to-date applications36007295/9780136007296 (0-136-00729-5/978-0-136-00729 LOOK AT A BOOK Bookstore Rating: 4(of 5) Book Location: Miamisburg, OH, U.S.A. Quantity: 1 --but the notes can not obscure the text. Pages might be wavy from humidity. Please don't buy as a gift, this is a personal reader copy. Satisfaction Guaranteed!Book Seller: LOOK AT A BOOK OH Bookstore Rating: 4.66 of 5.00 (5613 votes) Book Location: Miamisburg, OH Textbook Description: 2008 Hardcover Fair 48 New from $24.99 and 308 Used from $3.73 BookHolders Book Availability: Usually ships in 2-3 days TextbooksRus.com Book Location: USA Textbook Description: Very Good9.97 45 days - $10.42 60 days - $11.20 90 days - $11.86 125 days - $12.65 0 days - $ 0 days - $
Book Seller: TextbooksRus Bookstore Rating: 4.6(of 5) Book Location: Ohio Quantity: 3 Textbook Description: book
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much the problem with Calculus is the way it is taught. I took 2 terms of it in college, and both teachers explained the concept and never explained how to solve the problems. They had a mathematics lab on campus where students who had taken the class would explain how to do the problems, and when they explained it, it was usually pretty easy.
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I am 30+ graduate in Arts from India. I'm very poor in math. I can do basic math calculations, i.e. addition, subtraction, multiplication, and division of simple numbers in writing (on paper only) - I can't do it orally. I want to learn math from scratch, but can't join a local course or institute. My aim is to effectively learn math of 1st class to 10th class "For Teaching Purpose". Please suggest some of the following:
From which very 1st book, video tutorial or online resource, I should start with?
I've edited your post to remove the unnecessary bold formatting, and to improve the grammar in some places. You will need to explain what "1st to 10th standard" means - is it some teaching standard in India? – Zev Chonoles♦Jun 18 '12 at 13:34
Please note that lots of bold text is harder to read - bold formatting should be used sparingly if at all. Also, your use of capital letters in words in the middle of a sentence is incorrect. – Zev Chonoles♦Jun 19 '12 at 4:28
1 Answer
is probably your best bet if you want to start out with basic calculations. The practice problem sections on there should especially help, since they're structured so that you can't get to certain questions unless you've done the needed math already.
not a video series, but a question archive with all kinds of math in it. You can also email professors with whatever questions you may have. As long as you explain yourself properly (what you've tried, where you have trouble) they'll answer questions on any level.
Also youtube. If you have trouble with a concept, someone on youtube has almost definitely made a video explaining it. It's not just the scary part of the internet anymore.
As for steps of learning, I guess that depends on where you're at right now:
If you have standard arithmetic (including exponents, which you didn't mention), then I'd start off after that with some geometry: formulas for area, perimeter, and that sort of thing for various shapes (circles, triangles, rectangles/parallelograms, trapezoids for 2D, spheres, cylinders, various prisms and pyramids for 3D). Pythagorean formula and the distance between two points. Working with angles, especially in triangles.
Then go for integers, if you haven't already: negative numbers are an absolute must for pretty much everything.
After that I'm going to suggest what my high school did, though I'm sure there are many other ways:
cartesian coordinates and graphs. Plotting points in the plane. What a function is, on a basic level. Start out with equations of lines, which get all the main concepts but are easy to work with.
more graphs, this time of parabolas. understanding the more complicated algebra involved in completing the square, factoring, and the derivation of the quadratic formula.
trigonometric functions and identities. Working with sine, cosine, and tangent. Understanding the pythagorean identity and the angle addition laws. Introducing the sine law and cosine law and proving more complicated identities.
--Grade 10 ends here where I'm from, but the rest is worth knowing if you're interested when you get there--
Higher order polynomials, especially drawing graphs and finding roots. Factoring and the remainder theorem. Graphs of sine, cosine, and tangent, as well as their reciprocal and inverse functions. Properties of exponents (if you haven't already), exponential functions and logarithmic functions. Shifts and stretches of graphs. Working with rational functions and understanding asymptotes.
introductory calculus: slopes and rates of change. The definition of the derivative, and higher order derivatives. The use of these to find maxima and minima, and how to use these practically in optimization problems.
basic vector math. What vectors are in the first place. How to add them, graphically and symbolically. Understanding the value/difference between cartesian and polar forms. How to calculate the length of a vector. Basis vectors of space. Dot product and cross product. Projections. Using these to work with distances in 3D, as well as the equations of lines in 3D and the equations/intersections of planes.
This might not be thorough, but it's a rough outline of the 'order of ideas'. keep in mind that this isn't strict: for example, trigonometry could have been moved up in the list without much of a problem. But it's a start, and if something isn't clear then it'll at least give you a sense of what you should be looking for. Also as you learn you'll find more and more resources that deal with the more difficult topics that you're learning, so keep in mind that you'll probably end up with far more reliable resources than you started out with. You're also more than welcome to ask us for any help, as long as you show what you've tried (no free handouts). Best of luck to you!
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Based on his two successful textbooks [Lineare Algebra. Eine Einführung für Studienanfänger. 16th revised and enlarged ed. Wiesbaden: Vieweg (2008; Zbl 1234.15001) see also ME 2001a.00676 and ME 2007f.00322] and [Analytische Geometrie. Eine Einführung für Studienanfänger. 7., durchgesehene Aufl. Wiesbaden: Vieweg (2001; Zbl 0980.51018)], the author presents another introduction for beginners. It is called a "Lernbuch" rather than a "Lehrbuch", which would be the usual term in German. (Reviewer's remark for those, who do not know German: "Buch" means "book", "lernen" means "to learn", but "lehren" means "to teach".) Indeed, the goal of the book is twofold: On the one hand it is to be a book which presents the most important parts of linear algebra and geometry. On the other hand it aims at assisting the first year student by providing very extensive explanations and a great number of examples. Both task are accomplished without any doubt. The text is very well written and accompanied by a big number of illustrations, thus emphasising the geometric nature of linear algebra. In order to sketch the contents of the book, here are the titles of its six chapters: 0.~Linear geometry in $n$-dimensions (over the real numbers); 1.~Basic notions; 2.~Vector spaces and linear mappings; 3.~Determinants; 4.~Eigenvalues; 5.~Bilinear algebra and geometry.
Reviewer:
Hans Havlicek (Wien)
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Search Mathematical Communication:
Mathematical Communication
MathDL Mathematical Communication is a collection of instructional strategies, materials, and references for having students write and speak about mathematics, whether for the purpose of learning mathematics or learning to communicate as mathematicians.
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Saint Davids, PA Precalculus...Combinatorics studies the way in which discrete structures can be combined or arranged. Graph theory deals with the study of graphs and networks and involves terms such as edges and vertices. This is often considered a very specific branch of combinatorics
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Can low achieving mathematics students succeed in the study of linear inequalities and linear programming through real world problem based instruction? This study sought to answer this question by comparing two groups of low achieving mathematics
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Catalog Description: This course is intended to be a one-semester survey of Calculus topics specifically for Biology majors. Topics include limits, derivatives, integration, and their applications, particularly to problems related to the life sciences. The emphasis throughout is more on practical applications and less on theory. Pre-requisite: grade of C in Math 180, or suitable placement score. This course qualifies as a General Education course, G9.
Text:Calculus with Applications for the Life Sciences, by Greenwell, Ritchey, and Lial (Addison-Wesley, 2003).
General Education Core Skill Objectives
1. Thinking Skills: Students engage in the process of inquiry and problem solving, which involves both critical and creative thinking.
(a) The student understands the "big problems" in the development of differential calculus, the tangent problem and the area under the curve problem.
(b) The student understands the mathematical concept of Limit.
(c) The student explores differentiation and works with differentiation formulas for a variety of functions, including exponential and logarithmic functions, and the applications of these methods, especially to problems from the realm of life sciences
(d) The student explores integration and a variety of integration techniques, and applications of these techniques to a variety of problems, especially those related to the life sciences in the computer labs - to solve problems and to be able to communicate solutions and explore options.
(c) The student will use the language of mathematics accurately and appropriately.
(d) The student will present mathematical content and argument in written form.
3. Life Values: Students analyze, evaluate, and respond to ethical issues from informed personal, professional, and social value systems.
(a) The student develops an appreciation for the intellectual honesty of deductive calculus and the role it has played in mathematics and in other disciplines.
(b) The student learns to use the language of mathematics - symbolic notation - correctly and appropriately.
5. Technology:
(a) The student will demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer.
(b) The student will demonstrate the ability to efficiently and accurately graph functions using a calculator or computer.
(c) The student will demonstrate the knowledge of the limitations of technological tools.
(d) The student will demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work.
Course Outline
1. Functions
a. Linear functions
b. Least squares line
c. Properties of functions
d. Quadratic functions
e. Polynomial and rational functions
2. Exponential and Logarithmic Functions
a. Exponential functions
b. Logarithmic functions
c. Applications: growth and decay
3. The Derivative
a. Limits
b. Continuity
c. Rates of change
d. Definition of the derivative
e. Derivatives and graphs
4. Calculating the Derivative
a. Techniques for finding derivatives
b. Derivatives of products and quotients
c. The chain rule
d. Derivatives of exponential functions
e. Derivatives of logarithmic functions
5. Graphs and the Derivatives
a. Increasing and decreasing functions
b. Relative extrema
c. Higher derivatives, concavity, the 2nd derivative test
d. Curve sketching
6. Applications of the Derivative
a. Absolute extrema
b. Applications of extrema
c. Implicit differentiation
d. Related rates
e. Differentials and linear approximation
7. Integration
a. Antiderivatives
b. Substitution technique
c. Area and the definite integral
d. The Fundamental Theorem of Calculus
e. Area between curves
8. Further Techniques and Applications of Integration
a. Numerical integration
b. Integration by parts
c. Volume and average value
Required Course Work
Your basic work in this course is to learn the material and develop your problem-solving kills so that you can apply the concepts and methods of the calculus to problems you will encounter along the way. It is important that you attend class regularly and especially that you do the homework. The homework may seem "hidden" to you since it will not be graded, but it precisely in that outside of class practice that you learn the material. There is a rule of thumb that says college courses require roughly 2 hours outside of class for every hour in class and I think this is not at all an overstatement. It takes discipline to leave class on a Wednesday or Thursday, knowing that you have class again the very next day, and still find a couple hours to practice your calculus, but it is exactly that sort of discipline that is required for success in the course. In short: DO YOUR HOMEWORK!
Your grade will be based on two primary factors: (1) Exams; and (2) Group work. There will be an exam following chapters 1 and 2, chapters 3 and 4, chapters 5 and 6, and then a final cumulative exam at the end of the course, following chapters 7 and 8. These exams will be done in class subject to the 50 minute time limit, but you can use a set of notes you prepare for the exam and you may use a graphing calculator as well. I see exams as a way to see if you as an individual can actually do what the course asks of you.
Secondly, there will be two types of groupassignments: (a) Labs; and (b) practice exams. Every so often, roughly once a chapter, I will take a day and have you work in small groups of 3 or 4 students on a set of problems. I will refer to these problem sets as "labs", in the sense that you will be exploring the concepts and trying to apply them to the problems. I like the idea of asking you to occasionally work in groups – I think the opportunity to discuss the mathematical ideas is extremely valuable. After all, mathematics is a language as well as a way of thinking about things. After each of these labs I will ask you to write up a brief reflection paper about the lab you just did. These will be due the next class period and should comment on the basic idea you were supposed to learn from the lab problems.
I will also have you take a "practice exam" during the class period just prior to each individual exam. These practice exams will be done in groups like the labs, and must be turned in by the end of the period, as do the labs. This is an attempt on my part to give you an idea of what to expect on the exam.
It is also worth mentioning here that because one of our goals is to develop some skills with technological tools, I will be asking you to use DERIVE on a few problems along the way. DERIVE is a computer program created by Texas Instrument, the calculator people, to perform a very wide variety of mathematical procedures. It is a CSA (Computer Algebra System), which means it can perform algebraic manipulations like solving equations or factoring polynomials, as well as graphing functions in 2 or 3 dimensions. It can also perform calculus procedures and we will have a chance to see some of this power.
Instructional Methods
My general "lecture" style is more of a give-and-take discussion than simply a rote presentation of material. I like to try to see that the class is following what I am doing and so I want feedback along the way. I often will ask a leading question to see that you are ready for what is about to come.
One specific strategy I will use is called Think-Pair-Share. In this case I will ask a question and have each of you think about it for a bit, then pair up with a "neighbor" and finally share the answer with the rest of the class. Not every pair will share with the class each time, but I hope as we do this on a regular basis most of you will have an opportunity to speak.
I have already mentioned the "Labs" we will do on occasion. I will randomly assign you to a group and give each of you rotating roles within the process; I'll explain the details when we do that first lab on Wednesday, 7 September. I will try to keep the labs reasonably short so that the group can turn in the work at the end of the period – this is required. I am also requiring each of you to write up a brief reflection paper on each of the labs, due the next class meeting, in which you reflect on what you learned from the lab, or what you think you were supposed to have learned – this will be more or less a "journal".
Assessment Strategies
The main outcomes I want to see in each of you can basically be listed briefly as: (1) thinking, or problem solving; (2) communicating your mathematical ideas and solutions; and (3) using technology to do some of the work. I will be assessing your ability to do these things throughout the course by grading the labs, the technology assignments, and the exams. I will also be noting your participation in the class room, both in your group work and in general class discussion.
Grading System
Because this is the first time this course has been taught we are all serving as guinea pigs, and there may very well need to be some adjustments made along the way. But I need to put something down on paper at the start, so here it is.
I will then assign letter grades as follows: 90% of possible points for "A", 80% for a "B", 70% for a "C", and 60% for a "D". By the way, I am aware that the biology program requires a grade of at least a "C" in its support courses, so you needn't tell me that if the going gets "close" later on in the course. I wish this wasn't the case, since it is sometimes stressful on me as well as on you, and I don't like "losing" the possibility of giving a "D" grade – sometimes people pass a course but "just barely".
Disability Statement
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 335Attendance Policy
I think that regular attendance in of paramount importance in any course, but perhaps a mathematics course more than most. There may be the occasional exception, a student who is so mathematically talented that she or he can get the material by just reading the text and doing some problems, but for most students it is important to be in class every day. To encourage this I am going to include attendance in the grading scheme in a simple way: 1 point for each day you are there. I'm not going to engage in whether absence is "excused" – too many subtleties and degrees there - just a point a day when you are there.
One other note about the labs: because I want to collect them all at the end of class and grade them for the next class meeting, there will be no opportunity to "make them up". You either do it or you don't. But I am making a bit of an allowance here; the total value of the labs is 140, but it is possible to earn 160 points in total – basically I have one lab as a "freebie".
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The Everything Guide to Calculus I
A step-by-step guide to the basics of calculus—in plain English!
By Greg Hill, National Council of Teachers of Mathema
Format:
SKU# Z9326
Details
Calculus is the basis of all advanced science and math. But it can be very intimidating, especially if you're learning it for the first time! If finding derivatives or understanding integrals has you stumped, this book can guide you through it. This indispensable resource offers hundreds of practice exercises and covers all the key concepts of calculus, including:
Greg Hill has more than twenty-five years of experience teaching AP Calculus and other advanced math classes. He is a two-time Illinois state finalist for the Presidential Award for Excellence in Mathematics and Science Teaching, and is a member of the Illinois and National Councils of Teachers of Mathematics. Hill has been a College Board consultant and AP Calculus exam grader for the past ten years. He currently teaches at Hinsdale Central High School, and also conducts day- and week-long professional development seminars for AP Calculus teachers. He is the author of CLEP Calculus, a test prep book for the College Board's College Level Entrance Exam.
Additional Information
SKU
Z9326
Author/Speaker/Editor
Greg Hill, National Council of Teachers of Mathema
File/Trim Size
9 x 9-1/4
Format
No
ISBN 13
9781440506291
Number Of Pages
320
Retail:
$16.95
Your price:
$11.53
You save: $5.42
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Elementary MathematicsIn secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary schoolstudents, is usually considered college level mathematicsIn the United States, there has been considerable concern about the low level of elementary mathematics skills on the part of many students, as compared to students in other developed countries. The No Child Left Behind program was one attempt to address this deficiency, requiring that all American students be tested in elementary mathematics.
"A school is not a factory. Its raison d'être is to provide opportunity for experience." —J.L. (James Lloyd)
"Cloud-clown, blue painter, sun as horn, Hill-scholar, man that never is, The bad-bespoken lacker, Ancestor of Narcissus, prince Of the secondary men. There are no rocks And stones, only this imager." —Wallace Stevens (1879–1955)
"The longer we live the more we must endure the elementary existence of men and women; and every brave heart must treat society as a child, and never allow it to dictate." —Ralph Waldo Emerson (1803–1882)
"He taught me the mathematics of anatomy, but he couldn't teach me the poetry of medicine.... I feel that MacFarland had me on the wrong road, a road that led to knowledge, but not to healing." —Philip MacDonald, and Robert Wise. Fettes (Russell Wade)
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Introduction
Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science
Mathematical science is the science in which mathematical and statistical models are constructed, developed mathematically and diagnosed empirically in order to understand practical phenomena which occur in the fields of natural science, social science, technology, biology and so forth. For the purpose, one needs to utilize computers with advanced levels to make computer simulations, computer graphics and to develop algorithms, among others. This area consists of two large groups. One is a group of applied mathematics and the other a group of statistical science, each having two smaller subgroups. In this area, emphasis is placed on research and education of differential equations, mathematical physics, statistical analysis and data science.
Laboratories
Area of Mathematical Modelling
The Area of Mathematical Modelling comprised of the following two research groups is concerned with research and education of mathematical theory and applications on modelling phenomena occurred in several fields of natural science, social science and engineering.
An important purpose of multivariate analysis is to identify any relations among many variables based on statistical data. The recent topics in this field are new modeling and statistical causal inference. In this research group, we apply mathematics and computers extensively to study structural equation modeling,graphical modeling,and independent component analysis as well as survival analysis in biostatistics. Our research includes methodological and application aspects.
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Master the fundamentals of discrete mathematics and proof-writing with MATHEMATICS: A DISCRETE INTRODUCTION! With a clear presentation, the mathematics text teaches you not only how to write proofs, but how to think clearly and present cases logically beyond this course. Though it is presented from a mathematician's perspective, you will learn the importance of discrete mathematics in the fields of computer science, engineering, probability, statistics, operations research, and other areas of applied mathematics. Tools such hints and proof templates prepare you to succeed in this courseA First Course in Differential Equations with Modeling Applications, 9th Edition
A First Course in Differential Equations with Modeling Applications, 9
Introduction to MultiplicationThis book is designed to help children aged 5 to 8 years old in order to understand the basic concepts of multiplication. As multiplication is more complex than addition and subtraction, guidance from parents or a teacher is required to understand the concepts of multiplicative problems in this workbook. It covers multiplication from 1 x 1 to 5 x 5.
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Elementary Number Theory latest edition of Kenneth Rosen's widely used Elementary Number Theory and Its Applications enhances the flexibility and depth of previous editions while preserving their strengths. Rosen effortlessly blends classic theory with contemporary applications. New examples, additional applications and increased cryptology coverage are also included. The book has also been accuracy-checked to ensure the quality of the content. A diverse group of exercises are presented to help develop skills. Also included are computer projects. T... MOREhe book contains updated and increased coverage of Cryptography and new sections on Mvbius Inversion and solving Polynomial Congruences. Historical content has also been enhanced to show the history for the modern material. For those interested in number theory. The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage. The blending of classical theory with modern applications is a hallmark feature of the text. the Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included. Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.
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Simple Sets
Simple Sets
In this Algebra video, we introduce a few of the most fundamental aspects of mathematics and set theory. This lesson covers some of the terminology and concepts about sets that we will use in future algebra lessons. Below, we show some of the common ways we will represent sets.
The first set is the set of letters G, D, and Q and is given by the pictorial diagram and is more concrete than our other representations. The second shows the five integers 3, 56, 34, 6, and 38 inside of braces. Notice that these elements are not in order, even though we often order our lists for clarity. Like the second set, the third set is given in braces, but is more descriptive; this set is just {1,2,3,4}. The fourth and final set is read as "the set of elements x such that x is an integer and x is between 3 and 8." This set is just {4,5,6,7}, but it is given in formal notation that we will commonly use.
Although our first sets above are all finite, we will often use infinite sets like the set of integers. Also, we will refer to the set with no elements in it: this set is called the empty set and is denoted by a circle with a line through it. Sets with a single element like this, {2} are called singleton sets. Below, we show the infinite set integers, the empty set and a singleton set containing 7, respectively.
There is some additional notation that we will use. First, we will typically assign sets a letter name so that we can refer to them more succinctly. Second, we will use the character that looks like a strange "e" to specify that something "is an element of" a given set. We will use the same symbol with a strike through to denote the something "is not an element of" a given set.
Above, we have assigned the set {1,2,4} the name A. The second statement reads "1 is an element of A." The third statement reads "3 is not an element of A."
Furthermore, we define three set-wise operations that we will apply to pairs of sets: Intersection, Union, and Difference. Examples of these are given below.
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Over the 2 year course students will use a textbook for classwork and another for use at home. Most students will use the Higher Plus textbook which covers grades B to A* at GCSE, with a few students using the Higher textbook which covers grades D to B.
Additional Mathematics
This is only open to those students who are in the top set because of the content of the syllabus, which mainly draws work in from the A Level specification. There are elements of C1, C2, M1, S1 and D1 which allows an insight into the workings of A Level Mathematics. It enables the top set to be challenged at the same time as having their mathematical horizons broadened. It is a Free Standing Mathematics Qualification with UCAS points attached to the award if students perform to certain standards.
Each of these is used to support a topic from a recognised branch of Applied Mathematics.
The assessment is by a single 2 hour examination in the Summer of each year, with grades A, B, C, D, E or U available. There is no coursework.
We anticipate that most students studying Additional Mathematics will go on to study A Level Mathematics, with a possibilty of taking Further Mathematics. Below are a series of powerpoints that provide worked examples and some extra questions for students to tackle.
Due to a change in the syllabus, students will be sitting the Higher Tier or Foundation Tier paper. This is because the exam board have gone to 2 tiers, so that every child who sits their Mathematics exam as a chance of obtaining a grade C.
Tier
Grades Available
Foundation
G to C
HIgher
D to A*
It is our aim to ensure that our students are entered for the tier that is most suitable for them. Our setting from year 9 upwards allows us to ensure that all pupils are placed in the correct set for their ability. Pupils are assessed on a regular basis and these assessments, along with their teacher's judgement, ensure that they are placed appropriately.
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Product Description
This series combines a variety of new perspectives on teaching and learning algebra to produce a rewarding learning experience for both students and teachers. Uses concrete examples and practical applications so students understand the true importance of mastering fundamental algebraic concepts. Each program comes with a worksheet with follow-up questions. Set of 10 includes The Language of Algebra, Exploring Functions with the Aid of a Graphing Calculator, Exploring Linear Functions - Introductory Explorations, Linear Functions and Geometry, Exploring Quadratic Functions - Introductory Explorations 1, Exploring Quadratic Functions - Introductory Explorations 2, Multiple Representations of Linear Functions, The Geometry of Linear Function Graphs, Problem Solving with Linear Equations, and Polynomial Explorations (Degree Greater than Two). Each program is 30 minutes for a total running time of 5 hours. Grade 7 and up.
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges.
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Course Description: This course is an integrated sequence of advanced topics in algebra and trigonometry. Students will further develop equation-solving and graphing skills. It is designed for those students with above average mathematical ability and who wish to take calculus in high school or intend to pursue a career in a mathematics or science related major in college.
COURSE OBJECTIVES
CONTENT OUTLINE
Sketch and analyze graphs
Identify parent graphs and their transformations (multiple)
Sketch step functions and other piecewise-defined functions
Identify odd and even functions graphically
Use zeros of a function as a sketching aid
Sketch inverse functions
Use the Leading Coefficient Test to determine end behaviors
Use the Intermediate Value Theorem to help locate zeros of polynomial functions
Identify domains and ranges of functions
Find horizontal, vertical, and slant asymptotes
Sketch six trigonometric parent graphs
Sketch transformations of sine and cosine graphs
Manipulate and analyze algebraic representations
Find and interpret zeros algebraically
Find compositions of functions
Find inverse functions algebraically
Use polynomial division
Work with complex numbers
Use the Fundamental Theorem of Algebra to determine the numbers of zeros of polynomial functions
Use Descartes' Rule of Signs and the Upper and Lower Bound Rules to find zeros of polynomials
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The standards below outline the content for a one-year course in
Algebra II. This course is designed for students who have successfully
completed the standards for Algebra I and Geometry. All students preparing
for postsecondary and advanced technical studies are expected to achieve
the Algebra II standards. A thorough treatment of advanced algebraic
concepts will be provided through the study of functions, "families of
functions," equations, inequalities, systems of equations and
inequalities, polynomials, rational and radical equations, complex
numbers, and sequences and series. Emphasis will be placed on practical
applications and modeling throughout the course of study. Oral and written
communication concerning the language of algebra, logic of procedures, and
interpretation of results should also permeate the course.
These standards include a transformational approach to graphing
functions. Transformational graphing uses translation, reflection,
dilation, and rotation to generate a "family of graphs" from a given graph
and builds a strong connection between algebraic and graphic
representations of functions. Students will vary the coefficients and
constants of an equation, observe the changes in the graph of the
equation, and make generalizations that can be applied to many graphs.
Graphing utilities (graphing calculators or computer graphing
simulators), computers, spreadsheets, and other appropriate technology
tools will be used to assist in teaching and learning. Graphing utilities
enhance the understanding of realistic applications through mathematical
modeling and aid in the investigation and study of functions. They also
provide an effective tool for solving and verifying solutions to equations
and inequalities.
The student, given rational, radical, or polynomial expressions,
will write radical expressions as expressions containing rational
exponents and vice versa.
Indicator 1.c.1
Convert
from radical notation to exponential notation
Convert from radical notation to exponential
notation.
Indicator 1.c.2
Convert
from exponential notation to radical notation
Convert from exponential notation to radical
notation.
Benchmark 1.d
Factor
Polynomials Completely
The student, given rational, radical, or polynomial expressions,
will factor polynomials completely.
Indicator 1.d.1
Factor
polynomials by applying general patterns
Factor polynomials by applying general patterns including
difference of squares, sum and difference of cubes, and
perfect square trinomials.
Indicator 1.d.2
Factor
polynomials completely over the integers
Factor polynomials completely over the
integers.
Indicator 1.d.3
Verify
polynomial identities
Verify polynomial identities including the difference of
squares, sum and difference of cubes, and perfect square
trinomials.
Benchmark 1.e
Expand and
condense logarithmic expressions.
Expand and condense logarithmic expressions.
Indicator 1.e.1
Condense
& expand logarithmic expressions using log properties
Use properties of logarithms to condense and expand
logarithmic expressions.
MTH.ALG2
Standard 2
INVESTIGATE/APPLY PROPERTIES OF
ARITHMETIC/GEOMETRIC SEQUENCES/SERIES
The student will investigate and apply the properties of arithmetic and
geometric sequences and series to solve real-world problems, including
writing the first n terms, finding the nth
term, and evaluating summation formulas. Notation will include Σ and
an.
FCPS Notes:
An arithmetic sequence is a linear function.
A geometric sequence is an exponential function.
The graphs of sequences are discrete.
Essential Understandings:
Sequences and series arise from real-world situations.
The study of sequences and series is an application of
the investigation of patterns.
A sequence is a function whose domain is the set of natural
numbers.
Sequences can be defined explicitly and recursively.
Benchmark 2.a
Investigate/Apply Properties of Arithmetic/Geometric
Sequences/Series
The student will investigate and apply the properties of
arithmetic and geometric sequences and series to solve real-world
problems, including writing the first n terms, finding the
nth term, and evaluating summation formulas.
Notation will include Σ and
an.
Indicator 2.a.1
Distinguish between a sequence and a series
Distinguish between a sequence and a
series.
Indicator 2.a.2
Generalize
patterns in a sequence using explicit and recursive formula
Generalize patterns in a sequence using explicit and
recursive formulas.
Indicator 2.a.3
Use and
interpret notations
Use and interpret the notations Σ,
n, nth term, and
an.
Indicator 2.a.4
Find the
nth term for an arithmetic or a geometric sequence
Given the formula, find an (the
nth term) for an arithmetic or a geometric
sequence.
Indicator 2.a.5
Find the
sum of the first n terms of an arithmetic or geometric series
Given formulas, write the first n terms and find
the sum, Sn, of the first
n terms of an arithmetic or geometric
series.
Indicator 2.a.6
Given the
formula, find the sum of a convergent infinite series
Given the formula, find the sum of a convergent infinite
series.
Indicator 2.a.7
Model
real-world situations using sequences and series
Model real-world situations using sequences and
series.
Indicator 2.a.8
Write an
explicit formula for an arithmetic or geometric sequence
Write an explicit formula for an arithmetic or
geometric sequence.
Indicator 2.a.9
Use sigma
notation to express an arithmetic or geometric series
Express an arithmetic or geometric series in
abbreviated form using sigma
notation.
Indicator 2.a.10
Find the
position of a term in an arithmetic sequence
Find the position of a term in an arithmetic sequence,
given its value.
Indicator 2.a.11
Represent
sequences and series using a table or graph
Represent sequences and series using a table or
graph.
Indicator 2.a.12
Use the
arithmetic or the geometric mean to find a missing term
Use the arithmetic mean or the geometric mean to find a
missing term in an arithmetic or geometric
sequence.
MTH.ALG2
Standard 3
PERFORM OPERATIONS ON COMPLEX
NUMBERS
The student will perform operations on complex numbers, express the
results in simplest form using patterns of the powers of i, and
identify field properties that are valid for the complex
numbers.
Essential Understandings:
Complex numbers are organized into a hierarchy of subsets.
A complex number multiplied by its conjugate is a real number.
Equations having no real number solutions may have solutions
in the set of complex numbers.
Field properties apply to complex numbers as well as real
numbers.
All complex numbers can be written in the form a+bi
where a and b are real numbers and i is
−1.
Benchmark 3.a
Perform
Operations on Complex Numbers
The student will perform operations on complex numbers, express
the results in simplest form using patterns of the powers of
i, and identify field properties that are valid for the
complex numbers.
Place the following sets of numbers in a hierarchy of
subsets: complex, pure imaginary, real, rational, irrational,
integers, whole, and natural.
Indicator 3.a.7
Write a
real number in a+bi form
Write a real number in a+bi
form.
Indicator 3.a.8
Write a
pure imaginary number in a+bi form
Write a pure imaginary number in a+bi
form.
Indicator 3.a.9
Divide
complex numbers using complex conjugates
Divide complex numbers using complex
conjugates.
MTH.ALG2
Standard 4
SOLVE A VARIETY OF EQUATIONS,
ALGEBRAICALLY AND GRAPHICALLY
The student will solve, algebraically and
graphically, a) absolute value equations and
inequalities; b) quadratic equations over the set of
complex numbers; c) equations
containing rational algebraic expressions; and d) equations
containing radical expressions. Graphing calculators will be used for
solving and for confirming the algebraic solutions.
Essential Understandings:
A quadratic function whose graph does not intersect the
x-axis has roots with imaginary components.
The quadratic formula can be used to solve any quadratic
equation.
The value of the discriminant of a quadratic equation can be
used to describe the number of real and complex solutions.
The definition of absolute value (for any real numbers a and
b, where b≥0, if |a|=b, then a = b or a = - b)
is used in solving absolute value equations and inequalities.
Absolute value inequalities can be solved graphically or by
using a compound statement.
Real-world problems can be interpreted, represented, and
solved using equations and inequalities.
The process of solving radical or rational equations can lead
to extraneous solutions.
Equations can be solved in a variety of ways.
Set builder notation may be used to represent solution sets of
equations and inequalities.
Benchmark 4.a
Solve Absolute
Value Equations and Inequalities
The student will solve, algebraically and graphically, absolute
value equations and inequalities. Graphing calculators will be
used for solving and for confirming the algebraic
solutions.
Indicator 4.a.1
Solve
absolute value equations algebraically and graphically
Solve absolute value equations algebraically and
graphically.
Indicator 4.a.2
Solve
absolute value inequalities algebraically and graphically
Solve absolute value inequalities algebraically and
graphically.
Indicator 4.a.3
Apply an
appropriate equation to solve a real-world problem
Apply an appropriate equation to solve a real-world
problem.
Indicator 4.a.4
Verify
possible solutions to absolute value equations
Verify possible solutions to absolute value
equations.
Indicator 4.a.5
Verify
possible solutions to absolute value inequalities
Verify possible solutions to absolute value
inequalities.
Indicator 4.a.6
Recognize
absolute value equations/inequalities with no solution
Recognize absolute value equations and inequalities
that have no solution.
Indicator 4.a.7
Express
solutions to abs. val. ineq. in set and interval notation
Express solutions to absolute value inequalities in
both set and interval
notation.
Indicator 4.a.8
Given the
equation, graph a piecewise or step function
Given the equation, graph a piecewise or step
function.
Indicator 4.a.9
Given a
graph, write an equation for a piecewise or step function
Given a graph, write an equation for a piecewise or
step function.
Benchmark 4.b
Solve a
Quadratic Equation Over the Set of Complex Numbers
The student will solve, algebraically and graphically, quadratic
equations over the set of complex numbers. Graphing
calculators will be used for solving and for confirming the
algebraic solutions.
Indicator 4.b.1
Solve a
quadratic equation over the set of complex numbers
Solve a quadratic equation over the set of complex numbers
using an appropriate strategy.
Indicator 4.b.2
Use the
discriminant to determine the number and type of solutions
Calculate the discriminant of a quadratic equation to
determine the number of real and complex
solutions.
Indicator 4.b.3
Apply an
appropriate equation to solve a real-world problem
Apply an appropriate equation to solve a real-world
problem.
Indicator 4.b.4
Recognize
that the quad form can be derived from completing the square
Recognize that the quadratic formula can be derived by
applying the completion of squares to any quadratic equation
in standard form.
Benchmark 4.c
Solve Equations
Containing Rational Algebraic Expressions
The student will solve, algebraically and graphically, equations
containing rational algebraic expressions. Graphing
calculators will be used for solving and for confirming the
algebraic solutions.
Solve exponential and logarithmic equations using
properties of logarithms.
MTH.ALG2
Standard 5
SOLVE NONLINEAR SYSTEMS OF
EQUATIONS
The student will solve nonlinear systems of equations, including
linear-quadratic and quadratic-quadratic, algebraically and graphically.
Graphing calculators will be used as a tool to visualize graphs and
predict the number of solutions.
Essential Understandings:
Solutions of a nonlinear system of equations are numerical
values that satisfy every equation in the system.
The coordinates of points of intersection in any system of
equations are solutions to the system.
Real-world problems can be interpreted, represented, and
solved using systems of equations.
Benchmark 5.a
Solve Nonlinear
Systems of Equations
The student will solve nonlinear systems of equations, including
linear-quadratic and quadratic-quadratic, algebraically and
graphically. Graphing calculators will be used as a tool to
visualize graphs and predict the number of solutions.
Indicator 5.a.1
Predict
number of solutions to a nonlinear system of two equations
Predict the number of solutions to a nonlinear system of
two equations.
Indicator 5.a.2
Solve a
linear-quadratic system of two equations
Solve a linear-quadratic system of two equations
algebraically and graphically.
Indicator 5.a.3
Solve a
quadratic-quadratic system of two equations
Solve a quadratic-quadratic system of two equations
algebraically and graphically.
Indicator 5.a.4
Solve a
circle-linear system of two equations graphically
Solve a circle-linear system of two equations
graphically.
Indicator 5.a.5
Solve a
circle-quadratic system of two equations graphically
Solve a circle-quadratic system of two equations
graphically.
Indicator 5.a.6
Solve a
circle-linear system of two equations algebraically
Solve a circle-linear system of two equations
algebraically.
Indicator 5.a.7
Solve a
circle-quadratic system of two equations algebraically
Solve a circle-quadratic system of two equations
algebraically.
Indicator 5.a.8
Sketch
graph of a conic section (parabola or hyperbola) in (h, k)
form
Sketch the graph of a conic section (parabola or
hyperbola) in (h, k) form.
Indicator 5.a.9
Write the
equation of a conic section in (h, k) form from a graph
Write the equation of a conic section (parabola or
hyperbola) in (h, k) form from
a graph.
Indicator 5.a.10
Use conic
sections to model practical problems
Use conic sections to model practical
problems.
MTH.ALG2
Standard 6
RECOGNIZE MULTIPLE
REPRESENTATIONS OF FUNCTIONS
The student will recognize the general shape of function (absolute
value, square root, cube root, rational, polynomial, exponential, and
logarithmic) families and will convert between graphic and symbolic forms
of functions. A transformational approach to graphing will be employed.
Graphing calculators will be used as a tool to investigate the shapes and
behaviors of these functions.
FCPS Notes:
(Honors) Parametric equations are used to express two
dependent variables, x and y, in terms of an
independent variable (parameter), t.
Essential Understandings:
The graphs/equations for a family of functions can be
determined using a transformational approach.
Transformations of graphs include translations, reflections,
and dilations.
A parent graph is an anchor graph from which other graphs are
derived with transformations.
Benchmark 6.a
Recognize
Multiple Representations of Functions
The student will recognize the general shape of function
(absolute value, square root, cube root, rational, polynomial,
exponential, and logarithmic) families and will convert between
graphic and symbolic forms of functions. A transformational approach
to graphing will be employed. Graphing calculators will be used as a
tool to investigate the shapes and behaviors of these
functions.
Indicator 6.a.1
Recognize
graphs of parent functions
Recognize graphs of parent
functions.
Indicator 6.a.2
Identify
the graph of the transformed function
Given a transformation of a parent function, identify the
graph of the transformed
function.
Indicator 6.a.3
Given
equation & using a transformational approach, graph a
function
Given the equation and using a transformational approach,
graph a function.
Indicator 6.a.4
Given the
graph of a function, identify the parent function
Given the graph of a function, identify the parent
function.
Indicator 6.a.5
Identify
the transformations of a function to determine the equation
Given the graph of a function, identify the transformations
that map the preimage to the image in order to determine the
equation of the image.
Indicator 6.a.6
Given the
graph, write the equation of the function
Using a transformational approach, write the equation of a
function given its graph.
Indicator 6.a.7
Write the
equation of a linear function in point-slope form
Write the equation of a linear function in point-slope
form.
Indicator 6.a.8
Use
parametric equations to represent a linear or quadratic
function
Use parametric equations to represent a linear or
quadratic function.
MTH.ALG2
Standard 7
INVESTIGATE AND ANALYZE
FUNCTIONS, ALGEBRAICALLY & GRAPHICALLY
The student will investigate and analyze functions algebraically and
graphically. Key concepts include a) domain and range,
including limited and discontinuous domains and ranges; b)
zeros; c) x- and
y-intercepts; d) intervals in which a function is
increasing or decreasing; e) asymptotes; f)
end behavior; g) inverse of a function;
and h) composition of multiple functions. Graphing
calculators will be used as a tool to assist in investigation of
functions.
Essential Understandings:
Functions may be used to model real-world situations.
The domain and range of a function may be restricted
algebraically or by the real-world situation modeled by the
function.
A function can be described on an interval as increasing,
decreasing, or constant.
Asymptotes may describe both local and global behavior of
functions.
End behavior describes a function as x approaches
positive and negative infinity.
A zero of a function is a value of x that makes f(x) equal zero.
If (a, b) is an element of a function, then
(b, a) is an element of the inverse of the
function.
Exponential (y=ax) and logarithmic
(y=logax)
functions are inverses of each other.
Functions can be combined using composition of functions.
Benchmark 7.a
Determine the
Domain and Range of Functions
The student will investigate and analyze functions algebraically
and graphically. Key concepts include domain and range, including
limited and discontinuous domains and ranges. Graphing
calculators will be used as a tool to assist in investigation of
functions.
Indicator 7.a.1
Identify
the domain and range of a function
Identify the domain and range of a function presented
algebraically or graphically.
Indicator 7.a.2
Describe
restricted/discontinuous domains and ranges
Describe restricted/discontinuous domains and
ranges.
Indicator 7.a.3
Write
domain and range of a function using interval notation
Write domain and range of a function using interval
notation.
Benchmark 7.b
Determine the
Zeros of Functions
The student will investigate and analyze functions algebraically
and graphically. Key concepts include zeros. Graphing
calculators will be used as a tool to assist in investigation of
functions.
Indicator 7.b.1
Identify
the zeros of a function
Identify the zeros of a function presented algebraically or
graphically.
Indicator 7.b.2
Use long
division to find all zeroes of a polynomial
Use long division to find all zeroes of a
polynomial.
Indicator 7.b.3
Use
synthetic division/substitution to find all zeros
Use synthetic division/substitution to find all
zeros.
Benchmark 7.c
Determine the X-
and Y-Intercepts of Functions
The student will investigate and analyze functions algebraically
and graphically. Key concepts include x- and
y-intercepts. Graphing calculators will be used as a
tool to assist in investigation of functions.
Indicator 7.c.1
Identify
the intercepts of a function
Identify the intercepts of a function presented
algebraically or graphically.
Benchmark 7.d
Determine
Intervals in Which a Function is Increasing or Decreasing
The student will investigate and analyze functions algebraically
and graphically. Key concepts include intervals in which a function
is increasing or decreasing. Graphing calculators will be used
as a tool to assist in investigation of functions.
Indicator 7.d.1
Identify
intervals on which the function is increasing and decreasing
Given the graph of a function, identify intervals on which
the function is increasing and
decreasing.
Benchmark 7.e
Determine the
Asymptotes of Functions
The student will investigate and analyze functions algebraically
and graphically. Key concepts include asymptotes. Graphing
calculators will be used as a tool to assist in investigation of
functions.
Indicator 7.e.1
Find the
equations of vertical and horizontal asymptotes of functions
Find the equations of vertical and horizontal asymptotes of
functions.
The student will investigate and analyze functions algebraically
and graphically. Key concepts include end behavior. Graphing
calculators will be used as a tool to assist in investigation of
functions.
Indicator 7.f.1
Describe
the end behavior of a function
Describe the end behavior of a
function.
Indicator 7.f.2
Describe
end behavior of a function as x approaches pos & neg
infinity
Describe the end behavior of a function as x approaches
positive and negative
infinity.
Benchmark 7.g
Determine the
Inverse of a Function
The student will investigate and analyze functions algebraically
and graphically. Key concepts include the inverse of a function.
Graphing calculators will be used as a tool to assist in
investigation of functions.
Indicator 7.g.1
Find the
inverse of a function
Find the inverse of a
function.
Indicator 7.g.2
Graph the
inverse of a function as a reflection across the line, y = x
Graph the inverse of a function as a reflection across the
line, y = x.
Indicator 7.g.3
Investigate exponential and logarithmic functions
Investigate exponential and logarithmic functions, using
the graphing calculator.
Indicator 7.g.4
Convert
between logarithmic and exponential forms of an equation
Convert between logarithmic and exponential forms of an
equation with bases consisting of natural
numbers.
Benchmark 7.h
Determine the
Composition of Multiple Functions
The student will investigate and analyze functions algebraically
and graphically. Key concepts include composition of multiple
functions. Graphing calculators will be used as a tool to
assist in investigation of functions.
Indicator 7.h.1
Find the
composition of two functions
Find the composition of two
functions.
Indicator 7.h.2
Use
composition of functions to verify two functions are inverses
Use composition of functions to verify two functions are
inverses.
Indicator 7.h.3
Find the
composition of multiple functions
Find the composition of multiple
functions.
Indicator 7.h.4
Find the
value of a composition of multiple functions
Find the value of a composition of multiple functions
for a given element from the
domain.
Indicator 7.h.5
Find the
domain and range of a piecewise function
Find the domain and range of a piecewise
function.
MTH.ALG2
Standard 8
INVESTIGATE AND DESCRIBE
RELATIONSHIPS
The student will investigate and describe the relationships among
solutions of an equation, zeros of a function, x-intercepts of a
graph, and factors of a polynomial expression.
FCPS Notes:
Imaginary roots are complex conjugates and come in pairs.
Essential Understandings:
The Fundamental Theorem of Algebra states that,
including complex and repeated solutions, an nth degree
polynomial equation has exactly n roots (solutions.)
The following statements are equivalent: - k is a
zero of the polynomial function f; - (x -
k) is a factor of f(x); - k
is a solution of the polynomial equation f(x) =
0; and - k is an x-intercept for the graph of
y = f(x).
Benchmark 8.a
Investigate and
Describe Relationships
The student will investigate and describe the relationships among
solutions of an equation, zeros of a function, x-intercepts
of a graph, and factors of a polynomial expression.
Indicator 8.a.1
Describe
relationships among solutions/zeros/intercepts/factors
Describe the relationships among solutions of an equation,
zeros of a function, x-intercepts of a graph, and
factors of a polynomial
expression.
Indicator 8.a.2
Define a
polynomial function, given its zeros
Define a polynomial function, given its
zeros.
Indicator 8.a.3
Determine
a factored form of a polynomial expression
Determine a factored form of a polynomial expression from
the x-intercepts of the graph of its corresponding
function.
Indicator 8.a.4
Identify
zeros of multiplicity greater than 1
For a function, identify zeros of multiplicity greater than
1 and describe the effect of those zeros on the graph of the
function.
Indicator 8.a.5
Determine
the number of real solutions and nonreal solutions
Given a polynomial equation, determine the number of real
solutions and nonreal solutions.
Indicator 8.a.6
Use long
division to find all zeroes of a polynomial function
Use long division to find all zeroes of a polynomial
function.
Indicator 8.a.7
Use
synthetic division/substitution to find all zeros
Use synthetic division/substitution to find all
zeros.
MTH.ALG2
Standard 9
COLLECT/ANALYZE DATA TO MAKE
PREDICTIONS & SOLVE PRACTICAL PROBLEMS
The student will collect and analyze data, determine the equation of
the curve of best fit, make predictions, and solve real-world problems,
using mathematical models. Mathematical models will include polynomial,
exponential, and logarithmic functions.
FCPS Notes:
For the r-value to appear on the graphing calculator after
calculating a regression, the diagnostics feature must be turned
on.
Essential Understandings:
Data and scatterplots may indicate patterns that can be
modeled with an algebraic equation.
Graphing calculators can be used to collect, organize,
picture, and create an algebraic model of the data.
Data that fit polynomial (f(x)=anxn+an−1xn−1+...+a1x+a0 where n is a nonnegative integer, and the
coefficients are real numbers), exponential (y=bx), and logarithmic
(y=logbx) models
arise from real-world situations.
Benchmark 9.a
Collect &
Analyze Data to Make Predictions & Solve Practical Problems
The student will collect and analyze data, determine the equation
of the curve of best fit, make predictions, and solve real-world
problems, using mathematical models. Mathematical models will
include polynomial, exponential, and logarithmic
functions.
Indicator 9.a.1
Collect
and analyze data
Collect and analyze
data.
Indicator 9.a.2
Investigate scatterplots to determine if patterns
exist
Investigate scatterplots to determine if patterns exist,
and then identify the patterns.
Indicator 9.a.3
Find an
equation for the curve of best fit for data
Find an equation for the curve of best fit for data, using
a graphing calculator. Models will include polynomial,
exponential, and logarithmic
functions.
Indicator 9.a.4
Make
predictions, using data, scatterplots, or curve of best fit
Make predictions, using data, scatterplots, or the equation
of the curve of best fit.
Indicator 9.a.5
Determine
the model that would best describe the data
Given a set of data, determine the model that would best
describe the data.
Indicator 9.a.6
Determine
how well a regression curve approximates data points
Use the correlation coefficient, r, from the graphing
calculator to determine how well a regression curve
approximates data points.
MTH.ALG2
Standard 10
SOLVE PROBLEMS INVOLVING DIRECT,
JOINT, & INVERSE VARIATIONS
The student will identify, create, and solve real-world problems
involving inverse variation, joint variation, and a combination of direct
and inverse variations.
FCPS Notes:
A direct variation graphs as a linear function that passes
through the origin.
An inverse variation graphs as a rational function.
Essential Understandings:
Real-world problems can be modeled and solved by using inverse
variation, joint variation, and a combination of direct and
inverse variations.
Joint variation is a combination of direct variations.
Benchmark 10.a
Solve Problems
Involving Direct, Joint, and Inverse Variations
The student will identify, create, and solve real-world problems
involving inverse variation, joint variation, and a combination of
direct and inverse variations.
Indicator 10.a.1
Translate
"y varies jointly as x and z" as y=kxz
Translate "y varies jointly as x and
z" as y=kxz.
Indicator 10.a.2
Translate
"y is directly proportional to x" as y=kx
Translate "y is directly proportional to
x" as y=kx.
Indicator 10.a.3
Translate
"y is inversely proportional to x" as y=k/x
Translate "y is inversely proportional to
x" as y=kx.
Indicator 10.a.4
Determine
the value of the constant of proportionality
Given a situation, determine the value of the constant of
proportionality.
Indicator 10.a.5
Use
combinations of direct/joint/inverse variation to solve
problems
Set up and solve problems, including real-world problems,
involving inverse variation, joint variation, and a
combination of direct and inverse
variations.
Indicator 10.a.6
Identify
inverse or direct variation
Identify inverse or direct variation given a graph,
equation, table, or real-world
application.
MTH.ALG2
Standard 11
IDENTIFY AND APPLY PROPERTIES OF
A NORMAL DISTRIBUTION
The student will identify properties of a normal distribution and apply
those properties to determine probabilities associated with areas under
the standard normal curve.
Essential Understandings:
A normal distribution curve is a symmetrical, bell-shaped
curve defined by the mean and the standard deviation of a data
set. The mean is located on the line of symmetry of the
curve.
Areas under the curve represent probabilities associated with
continuous distributions.
The normal curve is a probability distribution and the total
area under the curve is 1.
For a normal distribution, approximately 68 percent of the
data fall within one standard deviation of the mean, approximately
95 percent of the data fall within two standard deviations of the
mean, and approximately 99.7 percent of the data fall within three
standard deviations of the mean.
The mean of the data in a standard normal distribution is 0
and the standard deviation is 1.
The standard normal curve allows for the comparison of data
from different normal distributions.
A z-score is a measure of position derived from the mean and
standard deviation of data.
A z-score expresses, in standard deviation units, how far an
element falls from the mean of the data set.
A z-score is a derived score from a given normal distribution.
A standard normal distribution is the set of all z-scores.
Benchmark 11.a
Identify and
Apply Properties of a Normal Distribution
The student will identify properties of a normal distribution and
apply those properties to determine probabilities associated with
areas under the standard normal curve.
Indicator 11.a.1
Identify
the properties of a normal probability distribution
Identify the properties of a normal probability
distribution.
Indicator 11.a.2
Describe
impact of standard deviation & mean on normal distribution
Describe how the standard deviation and the mean affect the
graph of the normal
distribution.
Indicator 11.a.3
Use
standard normal distribution and z-scores to compare data sets
Compare two sets of normally distributed data using a
standard normal distribution and
z-scores.
Indicator 11.a.4
Represent
probability as area under the curve
Represent probability as area under the curve of a standard
normal probability distribution.
Indicator 11.a.5
Determine
probabilities or percentiles based on z-scores.
Use the graphing calculator or a standard normal
probability table to determine probabilities or percentiles
based on z-scores.
MTH.ALG2
Standard 12
Compute and distinguish between
permutations and combinations
The student will compute and distinguish between permutations and
combinations and use technology for applications.
Essential Understandings:
The Fundamental Counting Principle states that if one
decision can be made n ways and another can be made m
ways, then the two decisions can be made nm ways.
Permutations are used to calculate the number
of possible arrangements of objects.
Combinations are used to calculate the number of
possible selections of objects without regard to the order
selected.
Benchmark 12.a
Compute and
distinguish between permutations and combinations
The student will compute and distinguish between permutations and
combinations and use technology for applications.
Indicator 12.a.1
Compare
and contrast permutations and combinations
Compare and contrast permutations and
combinations.
Indicator 12.a.2
Calculate
the number of combinations of n objects taken r at a time
Calculate the number of combinations of n objects
taken r at a time.
Indicator 12.a.3
Calculate
the number of permutations of n objects taken r at a time
Calculate the number of permutations of n objects
taken r at a time.
Indicator 12.a.4
Use
permutations and combinations to solve real-world problems
Use permutations and combinations as counting techniques to
solve real-world problems.
MTH.ALG2
Standard 13
USE MATRIX MULTIPLICATION TO
SOLVE PRACTICAL PROBLEMS
The student will use matrix operations to solve practical problems
including systems of equations.
FCPS Notes:
When an n x n matrix is multiplied by its
inverse, the product is an n x n identity
matrix.
Essential Understandings:
Matrices can be used to model and solve practical problems.
Matrices are a convenient shorthand for solving systems of
equations.
Matrices can model a variety of linear systems.
Solutions of a linear system are values that satisfy every
equation in the system.
Benchmark 13.a
Use Matrix
Multiplication to Solve Practical Problems
The student will use matrix multiplication to solve practical
problems including systems of equations.
Indicator 13.a.1
Find the
product of two 2 x 2 matrices by hand
Find the product of two 2 x 2 matrices by
hand.
Indicator 13.a.2
Find the
product of 2 matrices greater than 2 x 2 w/a graphing calc
Find the product of two matrices greater than 2 x 2
using a graphing
calculator.
Indicator 13.a.3
Use matrix
multiplication to solve practical problems
Use matrix multiplication to solve practical
problems.
Indicator 13.a.4
Represent
and solve a system of linear equations in matrix form
Represent and solve a system of no more than three
linear equations in matrix
form.
Indicator 13.a.5
Find the
inverse of a matrix with a graphing calculator
Find the inverse of a matrix with a graphing
calculator.
Indicator 13.a.6
Find the
determinant of a matrix with a graphing calculator
Find the determinant of a matrix with a graphing
calculator.
Indicator 13.a.7
Identify
the identity matrix and its properties
Identify the identity matrix and its
properties
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AIM teaches math used in jobs that employ graduates with 2- and 4-year degrees.
Real = Relevant
AIM is real to students because they can see how the math applies as they build robots to meet challenges, designing those robots using CAD and process design software. AIM is real because the math can lead to high-tech jobs.
Real = Rigorous
Too often, "relevant" means "not as hard." AIM is specifically designed with the rigor associated with pre-calculus or statistics classes. Exploratory learning is combined with Accuplacer-like weekly tests that demand mastery of the content.
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Content/concepts goals for this activity
Higher order thinking skills goals for this activity
Using algebra to derive the needed equation from other given equations. Analyzing a large data set using equations in the spreadsheet.
Other skills goals for this activity
Learning how to document a mathematical derivation of an equation and to document units and their consistency in the equations. Learning how to produce a correctly annotated graph with the spreadsheet software.
Description of the activity/assignment
Students download a comma-delimited data set that is a time series of stream discharge measurements and the concentration of a trace element in the stream. Given the concentration of this element in the precipitation and in the groundwater, the students analyze the data using spreadsheet software to separate the hydrograph into baseflow and quickflow components. Students produce a graph of their results. To do the analysis, students must derive an appropriate equation based on other equations presented in the text (Eqs. 1.2 and 1.3).
Determining whether students have met the goals
They are asked to derive and annotate the correct equation to use in the spreadsheet, and then must submit a graph showing their resulting hydrograph separation.
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Understanding Probability and Odds DVD Facing the odds goes far beyond gambling and games of chance. Why is it that people are afraid to get on a plane but are not fazed by the drive to the airport?
6 - 12
DVD
$59.95
Discovering Math: Advanced Probability DVD This program introduces and develops concepts of probability, such as discrete and continuous variables, and dependent and independent events. It also discusses various methods of determining probabilities, as well as their applications.
9 - 12
DVD
$59.95
What are the Odds? DVD Professor Jeff Rosenthal breaks down the probability of twenty-five fantastic events in an entertaining blend of mathematics, science, and popular culture.
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Algebra
Introduction to Linear Bialgebra
The algebraic structure, linear algebra happens to be one of
the subjects which yields itself to applications to several
fields like coding or communication theory, Markov chains,
representation of groups and graphs, Leontief economic
models and so on. This book has for the first time,
introduced a new algebraic structure called linear bialgebra,
which is also a very powerful algebraic tool that can yield
itself to applications.
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#1
#2
#3
#4
#5
Guide to Essential Math, Second Edition: A Review for Physics, Chemistry and Engineering Students
This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly), which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. Detailed Illustrations and links to reference material online help further comprehension.
By combining algebraic and graphical approaches with practical business and personal finance applications, South-Western's FINANCIAL ALGEBRA, motivates high school students to explore algebraic thinking patterns and functions in a financial context. FINANCIAL ALGEBRA will help your students achieve success by offering an applications based learning approach incorporating Algebra I, Algebra II, and Geometry topics.
Suzanne thinks it would be fun if the whole class did a community service project together. This way, they can all share the same satisfied feeling they get from helping others. Mrs. Miyamoto agrees and tells the class that they can start planning the project today!
Toward the end of the afternoon on Tuesday, Mr. Griffin asks the students in his class to think about circles again. That morning they reviewed circumference and diameter of circles. Now Mr. Griffin wants to talk about the ratio pi. ....
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Engineering mathematics 4ed. - Solution manual
Engineering mathematics 4ed. - Solution manual
Engineering Mathematics is a comprehensive textbook for vocational courses and foundation modules at degree level. John Bird's approach, based on numerous worked examples supported by problems, is ideal for students of a wide range of abilities, and can be worked through at the student's own pace. Theory is kept to a minimum, placing a firm emphasis on problem-solving skills, and making this a thoroughly practical introduction to the core mathematics needed for engineering studies and practice.
The book presents a logical topic progression, rather than following the structure of a particular syllabus. However, coverage has been carefully matched to the two mathematics units within the new BTEC National specifications, and AVCE specifications. New sections on Boolean algebra, logic circuits matrices and determinants have been added to ensure full syllabus match.
Includes: 900 worked examples, 1700 further problems, 234 multiple choice questions (answers provided), and 16 assessment papers - ideal for use as tests or homework. These are the only problems where answers are not provided in the book. Full worked solutions are available to lecturers only as a free download from
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Role in Curriculum
The course will prepare students to take 100-level math courses needed for their majors.
Learning Goals and Assessment Plans
Learning Goal
Assessment
Solving a system of linear equations in two variables. (using algebra or graphing)
When the class is being assessed, the common final exams will include embedded questions to assess whether the students have sufficiently mastered the topic-specific learning goals. Instructors will be responsible for tallying their students performance on these questions, and the developmental math coordinator will provide an overall summary.
Solving quadratic equations using Completing the Square and the Quadratic formula
same
Complex numbers, operations and as solutions in the quadratic formula
same
When assessment activities are done, the results will be summarized in memorandum form and filed with the department chairperson for record keeping purposes.
Information obtained from assessment will be used to assess and self-reflect on the success of the course and to make any necessary changes to improve teaching and learning effectiveness.
Last updated Mon May 24 14:48:07 2010
Department of Mathematics
College of Staten Island
City University of New York 1S-215, 2800 Victory Boulevard, Staten Island, NY 10314 (718) 982-3600
This website was created using
Twitter Bootstrap,
Blosxom, and
Glyphicons Free.
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TANIMATE
Visual Representation of Rates of Change
Dirk A. DeLo and Gregory R. Somers
Abstract
The greatest potential for the TI-82 program TANIMATE, which is the focus of this module, may lie in its ability to help students visualize patterns in the rate of change of a function before they are formally introduced to the derivative of that function. We hope this tool will deepen students' understanding of the concept of a derivative and help them make some connections between the skills needed to find the derivative and what the derivative actually represents. We have included some suggestions for activities which use TANIMATE. We also encourage teachers to create new ways of using this tool to fit their needs and the needs of their students.
Directions for Using TANIMATE
TANIMATE (see attached program listing) is a collection of tools for the exploration and analysis of rates of change of functions. The program operates on a function which has been entered into Y1 and graphed on the function window. With this program, the user can display a single tangent line at a point on the curve, choose many points along the curve and display a tangent at each point, or create an animation sequence which will dynamically display the tangent lines to the curve along a predetermined interval. Once this has been done, TANIMATE stores the x-values that were sampled and the slope of the tangent lines at these points and will display the information graphically; which in effect gives a visual approximation of the derivative of a function. This "derivative" can be viewed by itself, or along with the original function.
In order to start the program, call the program after the function has been graphed in an appropriate window by accessing the program [PRGM] menu and executing [EXEC] the program TANIMATE. The first menu the user encounters is the MODE? menu:
MODE?
1:STATIC
2:DYNAMIC
3:PLOT CHANGE
4:PLOT CHNG W/Y1
5:GRAPH OPTIONS
6:QUIT
1:STATIC
This option will enable the user to draw tangent lines to the curve at selected x-values. The user will be prompted to enter the number of x-values desired. Valid x-values include the interval from 1 to 99 draws tangent lines at the selected x-values.
2:TANGENT/POINTS
This option draws the tangent line and plots the coordinate (x-value, slope at x-value) in the same graphing window.
3:POINTS ONLY
This option displays the coordinate (x-value, slope at x-value) in the same graphing window.
After selecting one of these options, the function will appear in the graphing window with the flashing cursor on the curve. Using the right or left arrow keys, the user selects a point at which to draw the tangent and presses [ENTER]. The slope will appear in the upper left hand corner. Repeat this process until all points and/or tangents have been plotted. Pressing [ENTER] at the conclusion will return to the MODE? menu.
2:DYNAMIC
This option will enable the user to animate tangent lines to the curve along a predetermined interval of x-values. The user will encounter the SAMPLING RATE? menu:
SAMPLING RATE?
1:LOW (plot tangent every 5 pixels)
2:MEDIUM (plot tangent every 2 pixels)
3:HIGH (plot tangent every pixel)
The lower the SAMPLING RATE?, the faster the animation of the tangent lines will execute animates tangent lines at the selected interval of x-values.
2:TANGENT/POINTS
This option animates the tangent line and plots3:POINTS ONLY
This option displaysAfter selecting one of these options, the function will appear in the graphing window with the flashing cursor on the curve. Using the right or left arrow keys, the user will be prompted to select the left endpoint for the x-values and press [ENTER]. Then the user will be prompted to select the right endpoint and press [ENTER]. The program will animate tangent lines along the curve between the end values at the interval specified in the SAMPLING RATE? menu. When the animation is complete, pressing [ENTER] at this point will return to the MODE? menu.
3:PLOT CHANGE
This option displays the coordinates (x-value, slope at x-value). However, this differs from the previous displays because it uses values which have been stored in the calculator as lists. This allows the user to view only the rate of change data without viewing the original function, and it displays the coordinates in a scatter plot using boxes instead of dots. The left and right arrow keys enable the user to identify coordinates of the rate of change points. Since the rate of change data is now in list form (L1 and L2,) it is possible to fit a curve to this data using the built in statistical data analysis of the TI-82. When PLOT CHANGE has been selected, the user will encounter the WINDOW? menu:
WINDOW?
1:SAME AS Y1
2:RESCALE
1:SAME AS Y1
This option preserves the windows setting used for the original function Y1 and plots the rate of change data as a scatter plot. Pressing [ENTER] returns the user to the MODE? menu.
2:RESCALE
This option sets new windows setting for optimum visibility of the rate of change data and plots these data points as a scatter plot. These windows settings are temporary and will be restored to the previous settings after you leave this option. Pressing [ENTER] returns the user to the MODE? menu.
4:PLOT CHNG W/Y1
This option displays the coordinates (x-value, slope at x-value) in addition to the original function. This option also differs from the previous displays because it uses values which have been stored in the calculator as lists. This allows the user to view only the rate of change data while viewing the original function. The arrow keys enable the user to identify coordinates of the rate of change points and points on the original curve. Pressing [ENTER] returns the user to the MODE? menu.
5:GRAPH OPTIONS
This option allows the user to change Y1, window settings, and access zooming options. The menu will display the current graph in its window settings and then present the user with the following GRAPH OPTIONS? menu:
GRAPH OPTIONS?
1:NEW Y1
2:NEW WINDOW
3:ZBox
4:Zoom In
5:Zoom Out
6:MODE MENU
1:NEW Y1
This option will prompt the user for a new function, Y1. The function must be entered between quotations, for example, "sin 3x" would be a valid entry. If the quotations are missing, the program will break and needs to be started again.
2:NEW WINDOW
This option allows the user to set the window settings manually. The user will be prompted to specify Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl. The function will then be displayed with these new window settings. Pressing [ENTER] will return the user to the GRAPH OPTIONS? menu.
3:ZBox
This option allows the user to zoom to a specific region using the arrow keys. When the user has reached the upper left corner of the box, he/she should press [ENTER] and continue to outline to the lower right hand corner of the zoom box and press [ENTER]. The function will be displayed with its new window settings. Pressing [ENTER] will return the user to the GRAPH OPTIONS? menu.
4:Zoom In
This option zooms in on the currently displayed graph using the TI-82 default zoom settings. The function will be displayed with its new window settings. Pressing [ENTER] will return the user to the GRAPH OPTIONS? menu.
5:Zoom Out
This option zooms out on the currently displayed graph using the TI-82 default zoom settings. The function will be displayed with its new windows settings. Pressing [ENTER] will return the user to the GRAPH OPTIONS? menu.
6:MODE MENU
This option returns the user to the MODE? menu and exits the GRAPH OPTIONS menu.
6:QUIT
Quits the program. We highly recommend using this option to quit the program. Exiting the program by other means may cause complications the next time you use the program.
Sample Activities for TANIMATE
The following are examples of activities which would incorporate TANIMATE into courses ranging from Algebra II to calculus. They introduce some of the concepts of calculus before students encounter then in a more formal sense. These are not meant to be student-ready worksheets (with the exception of the exploration summary sheet), but rather a discussion of possible ways to introduce a TANIMATE exploration or to prepare student explorations and teacher demonstrations.
When and why should students use TANIMATE?
As soon as students have been introduced to the concept of drawing a tangent line to a curve (representing the instantaneous rate of change) they are ready to use the TANIMATE program for the TI-82. The calculator has a built-in function which allows the user to draw a tangent line to a curve. TANIMATE, however, enables the student to draw many tangents without having to repeatedly access this function and it also computes the slopes of these tangent lines and stores those values for later use.
Sample activity:
Rates of Change of Polynomial Functions
Student instructions could take the following form:
1. Enter a quadratic function into Y1 and graph it.
2. Run TANIMATE several times in STATIC mode, drawing tangent lines at various x-values.
3. Based on the slope of the tangent line at each x-value, try to envision what the rate of change plot will look like.
4. Proceed to the DYNAMIC mode and look at the rate of change plot which has been generated in this mode. Does it look like you thought it would?
5. View the rate of change plot together with the original function. Sketch this picture on the exploration summary sheet. Try to understand the connection between them.
6. Repeat this process using several other quadratic functions.
7. Look for patterns and make conjectures.
8. Now proceed to cubics, quartics, etc. Continue to look for patterns and make conjectures about the observations.
Here are examples of quadratics that the students might explore:
f(x) = x2 f(x) = 3x2 f(x) = x2 + x - 4
f(x) = x2 + 4 f(x) = .5x2 f(x) = x2 - 3x + 2
f(x) = x2 - 3 f(x) = -2x2 f(x) = 2x2 + 6x - 7
f(x) = -x2 f(x) = -.125x2 f(x) = .5x2 - 2x
f(x) = -x2 + 2 f(x) = -3.5x2 f(x) = .5x2 - 2x + 3
Student conjectures from this activity might take the following form:
• The rate of change of a quadratic function is linear.
• The rate of change of a cubic function is a quadratic.
• Etc. ...
It is now possible to use the definition of the derivative to justify the results that the students have already discovered. By presenting the definition of the derivative in this way, students may connect it to the visual representation which they have already encountered.
Note: When TANIMATE computes the slopes of the tangent lines it stores the x-values in list 1 (L1) and the corresponding slopes in list 2 (L2). This enables the user to fit a function to this data after exiting the program.If students use the data analysis capabilities of the TI-82 to fit functions to the rate of change data, more specific conjectures may be obtained.
Similar types of explorations can be used when introducing the derivatives of other types of functions. For example:
Before introducing the derivative of other functions, students could explore groups of functions like these using TANIMATE:
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COURSE DESCRIPTIONS
This course is offered for students that have NOT yet
met the criteria for entering Algebra 1. Topics include
simple equations and inequalities, exponent rules,
linear graphing, radicals, and algebraic evaluations. The
course counts towards elective credit and does not meet
the Math requirements for high school graduation.
This course covers the same concepts as the first
semester of Algebra 1 course, with the only difference
being the pace. It takes 2 semesters to complete this
algebra series. Topics covered are integers, properties, order
of operations, solving equations and inequalities, word
problems, proportions, percents, trigonometry, plotting
points, relations, functions, graphing and writing line
equations.
ALGEBRA CD
Course Code: 2125 (9-12)
2 Credits
2 Semesters
Materials: A scientific calculator is required
This course is a continuance of Algebra AB. Concepts
covered are the same as 2nd semester Algebra 1, with
the only difference being the pace. It takes 2 semesters
to complete this algebra series. Topics covered are
solving systems, solving linear inequalities and systems
of inequalities, word problems, exploring polynomials,
factoring, solving quadratic equations, exploring rational
expressions and equations, exploring radicals, and solving
radical equations.
APPLIED MATH
Course Code: 2210 (11-12)
2 Credits
2 Semesters
Materials: A scientific calculator is required; A graphing calculator is recommended
This is a class for juniors or seniors who have only
passed Algebra I and Geometry, or Algebra AB, CD, and
Discovery Geometry. (Not for students who have passed
Algebra II) This course explores practical applications in
real life scenarios of algebraic and geometric concepts.
The student will examine the complete real number
system and its structure through the development of
algebraic language and skills. Major skills covered
are graphing, writing, and solving linear equations and
solving quadratic equations.
In the first semester, students will be able to explore
expressions, equations and functions and rational
numbers, solve multi-step linear equations, apply
proportions and percents, graph relations and functions
and analyze / solve linear equations.
In the second semester, students will solve systems
of linear equations and inequalities, explore polynomials
using the rules of exponents, factor polynomials, explore
rational and radical expressions and equations and solve
quadratic equations using the quadratic formula, use
scientific notation and use the Pythagorean Theorem to
find the distance and the midpoint formulas.
Major skills covered are a study of higher degree
polynomials, logarithms and exponents, conics, and
sequences and series. Some concepts presented in
Geometry will be most helpful to the student of Algebra
2.
First semester includes these topics: analyze
equations and inequalities, graph linear relations and
functions, solve systems of linear equations, solve
inequalities and quadratic equations, investigate
polynomial functions, perform arithmetic operations with
complex and irrational numbers, solve radical equations
and work with rational exponents.
Second semester, students will solve and graph
exponential and logarithmic functions, graph and solve
rational functions, analyze the four conic sections,
investigate sequences and series and investigate
probability.
This course is designed for the highly motivated
student who is looking to move on to Accelerated Pre-
Calculus. Major skills covered are a study of higher degree
polynomials, logarithms and exponents, conics, sequences
and series, periodic functions, and trigonometry. Some
concepts presented in Geometry will be most helpful to
the students of Algebra 2.
First semester includes these topics: analyze equations
and inequalities, graph linear relations and functions,
solve systems of linear equations, solve inequalities and
quadratic equations, investigate polynomial functions,
perform arithmetic operations with complex and irrational
numbers, solve radical equations, work with rational
exponents, solve and graph exponential and logarithmic
functions.
Second semester, students will graph rational
functions, solve rational functions, investigate sequences
and series, investigate probability, analyze periodic
functions, graph and write equations for trigonometric
functions, apply trigonometric laws to real world problems.
Sets, functions, complex numbers, graphing,
exponential and logarithmic functions, are expanded
from Algebra 2. New topics introduced will include
trigonometry, analytic geometry, sequence and series.
In semester 1, students will perfect their use of linear
relations and functions, linear irregularities, graphs of
polynomial and rational functions, derivative and critical
points of graphs, quadratics and radical equations,
remainder and factor theories, graphs of inverses,
definition of trig functions, right-triangle trigonometry, and
the law of sines and cosines.
In semester 2, students will learn how to graph
trigonometric functions and their inverses, use
trigonometry identities and solve trig equations,
graph using polar coordinates and complex numbers,
sequences and series, and logarithmic and exponential
functions.
Some of the concepts studied in elementary
Algebra will be helpful to the student's understanding
of Geometry. Geometry is valuable because of its
wide variety of applications to other subjects such as
astronomy, art and chemistry. Through the use of logic
and imagination, the student will examine and apply the
postulated structure of EuclIn the second semester, students will be able to
connect proportion and similarity, apply right triangles
and trigonometry, analyze circles, explore polygons and
area, investigate surface area and volume and continue
coordinate geometry.
Accelerated Pre-Calculus is for the highly motivated student
who knows he or she will take AP Calculus. Sets, functions, complex
numbers, graphing, exponential and logarithmic functions, are
expanded from Algebra 2. New topics introduced will include
trigonometry, analytic geometry, mathematical induction,
sequence and series.
In semester 1, students will perfect their use of linear relations
and functions, linear irregularities, graphs of polynomial and
rational functions, derivative and critical points of graphs,
quadratics and radical equations, remainder and factor theories,
graphs of inverses, definition of tri functions, law of sines and
cosines, right-triangle trigonometry, and graphs of rigonometry
functions and equations for inverses.
In semester 2, students will use trigonometry identities and
solve trig equations, polar coordinates and complex numbers,
conics, sequences series, limits, statistics and data analyses.
MATH 143 AT CHS (NIC CREDIT)
Course Code: (11-12)
2 Credits
2 Semesters
MATH 143 begins by taking a deeper look at the definition of
functions, their properties and notation in both an algebraic and
graphical context. The course then focuses on the study of equations
and graphs of polynomial, rational, exponential, and logarithmic
functions. Additional topics include conic sections and sequences.
This course prepares students for MATH 160. The combination of
MATH 143 followed by MATH 144 may be used in place of MATH
147 as the prerequisite for MATH 170. MATH 143 satisfies the math
requirement for the A.A., A.S., and A.A.S. degrees. Note: MATH 143
carries no credit if taken after successful completion of any higher
numbered Math course with the exception of MATH 148.
This course includes a study of functions, limits, differentiation,
integration, transcendent functions and applications of each. It
is equivalent to the first semester and about half of the second
semester of Calculus at the college level.
The first semester contains the following core topics: the
Cartesian plane and functions, limits and their properties,
differentiation, and applications of differentiation.
In the 2nd semester, students will practice integration, logarithmic,
exponential and other transcendental functions, applications of
integration, integration techniques, L'Hopital's Rule and improper
integrals.
This course may be offered online through the Idaho Digital
Learning Academy if unable to be offered on campus. Please note
that students will need to purchase their own textbooks and materials
for this course.
CALCULUS 1 - MATH 170 AT CHS (NIC CREDIT)
Course Code: 2610 (10-12)
2 Credits
2 Semesters
Prerequisite: Successful passage of AP Calculus
MATH-170 is an introduction to calculus as the mathematics of
change and motion. It emphasizes limits, the derivative, techniques
of differentiation, and the integral. This course builds a foundation for
all further study in mathematics and science that is typically required
in mathematics, engineering, computer science, physics, chemistry,
and other transfer degrees.Note: MATH-170 carries no credit if taken
after successful completion of a higher numbered math course with
the exception of MATH-187, MATH-253, and MATH-257.
CALCULUS 2 - MATH 175 AT CHS (NIC CREDIT)
Course Code: 2612 (10-12)
2 Credits
2 Semesters
Prerequisite: Successful passage of Calculus 1 (Math 170)
MATH-175 is a continuation of the calculus sequence
emphasizing techniques of integration, applications of
integration, polar coordinates, parametric equations,
sequences, and series. It is required for most transfer degrees
in mathematics and science. Note: MATH-175 carries no credit
if taken after successful completionof a higher numbered
math course with the exception of MATH-187, MATH-253,
MATH-257, and MATH-335.
SENIOR MATH
Course Code: (12)
2 Credits
2 Semesters
Prerequisite: A scientific calculator is required
1st Semester: This class is an introduction to mathematical
concepts dealing with signed numbers, variables,
polynomials, exponents, factoring, solving and graphing
first degree equations, and inequalities. The course also
introduces solving factorable second-degree equations. It
emphasizes the practical applications of these concepts.
2nd Semester: This is a continuation of the 1st
semester. It continues development of mathematical
concepts. It includes linear and quadratic equations,
algebraic fractions, radicals, circles and parabolas,
complex numbers, functions, and logarithms.
This course is designed to help seniors prepare for
entry into college-level math courses. It is designed for a
student who may need further understanding of algebra
and algebra 2 skills.
Accelerated Geometry is for the highly motivated
student who knows he or she will take Advanced Algebra
2, Advanced Pre-Calculus and AP Calculus. Some of the
concepts studied in elementary Algebra will be helpful
to the student's understanding of Advanced Geometry.
Geometry is valuable because of its wide variety of
applications to other subjects such as astronomy, art and
chemistry. Through the use of logic and imagination, the
student will examine and apply the postulated structure of
EuclStudents will also learn how to do constructions using
a straight edge and compass and geometry software.
Proof writing will be emphasized throughout the course.
In the second semester, students will be able to
connect proportion and similarity, apply right triangles
and trigonometry, apply the Law of Sines, derive
formulas, analyze circles, explore polygons and area,
investigate surface area and volume and continue
coordinate geometry. Students will also explore vector
geometry through transformations on the Cartesian
plane.
Many concepts learned in algebra, geometry and
advanced algebra will be studied through a graphical
approach. Other applications of mathematics are finance,
matrices, and trigonometry. The class is not theory-based,
and the concepts can be managed quite well by most
students, even those who struggled with advanced algebra,
proving they have a good work ethic and desire to learn. The
class also offers the student a chance to use a graphic display
calculator in order to calculate, display, and graphically
present data. Regular attendance is essential for success.
This course will introduce students to the major concepts
and tools for collecting, analyzing, and drawing conclusions
from data.
Students are exposed to four broad conceptual
themes:
Exploring Data: Describing patterns and departures
from patterns
Sampling and Experimentation: Planning and
conducting a study
Anticipating Patterns: Exploring random phenomena
using probability and simulation
Statistical Inference: Estimating population parameters
and testing hypotheses
This course draws connections between all
aspects of the statistical process, including design,
analysis, and conclusions. Additionally, using the
vocabulary of statistics this course will teach students
how to communicate statistical methods, results and
interpretations. Students will learn how to use graphing
calculators and read computer output in an effort to
enhance the development of statistical understanding.
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COURSE DESCRIPTIONS Math
The Foundations of Mathematics (A New Course) Section Code: MTHX9301 Nothing hurts a student more in the area mathematics than not having a strong foundation. Different students have different math challenges. The Internet can help customize and improve understanding of these critical basic building blocks for higher levels of math. You will explore a number of these resources as you develop an understanding of the scope of resources. Then, using these and other resources of your choice, you will develop a Web quest as a course project to use with your students. By using Web quests, students can conduct research, analyze the information, and draw their own conclusions. The critical thinking skills they develop will lead them to resources that meet their particular learning needs.
Math With Calculus, Trigonometry, and Fractals (A New Course) Section Code: MTHX9302 The Internet is rich with mathematics resources. This course explores just three math areas, calculus, trigonometry, and fractals. It is a sampling of the resources in these areas of math but each site leads to dozens of other resources. You can find lesson plans, interactive sites where students can insert numbers and watch fractal form. There are illustrations of simple and complex math functions. You can even find videos that will present the solution to a problem from different perspectives so every student has something to meet his/her learning style. Even see how the mathematical foundations of fractals has evolved into beautiful art and learn how students can create their own. By the end of your research, you will a wealth of information and Internet resources to use in the development of one web quest project for this course.
Statistics and Other Measurement Techniques (A New Course) Section Code: MTHX9303 Mathematical measurement techniques are probably one of the most common forms of math used in everyday life. Every time you talk about how many inches that piece of wood is, how many miles to travel, how much time it will take to do something, how many square feet are in a room, or what percentage of a population has some specific characteristic, you are using one form of measurement or another. Statistics, geometry and other measurement techniques are part of everyday life and this course will provide you with many great resources you can use to help your students grasp these concepts. When you explore the assignments in this course, you will find a wealth learning tools to help your students understand and remember them. For the course you will develop a web quest style lesson plan that will be something you can use with your students.
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It covers all core subjects, including American, English and World Literature, U.S. History, Art, Science, and Math, including Pre-Algebra, Algebra I and II, Geometry, Calculus, and Trigonometry. It also includes valuable extras, such as the Rapid Calculation Method that teaches how to solve math problems without pencil and paper.
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This is a free, online textbook. According to the author, "This text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text."
Primary Audience:
College Lower Division,
College Upper Division
Mobile Compatibility:
Not specified at this time
Technical Requirements: According to the site, As part of these terms, we offer this text free of charge to students using it for self-study, and to lecturers evaluating it as a required or recommended text for a course. All other uses of this text are subject to a charge of $10US for individual use and $300US for use by all individuals at a single site of a college or university."
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Mathematics can be viewed as a language for describing the world around us. Indeed, this is largely how mathematics developed. For instance, Calculus was invented by Newton in order to describe how a cannon ball falls to the ground or to describe how the moon orbits the Earth.
This course will be very much in this tradition. We will consider problems or objects that we might observe or encounter every day, for instance: "Why (in terms of the reproductive function of a pine cone) is a pine cone shaped as it is?" Or "Can California water shortages be alleviated by towing icebergs from Antarctica?" Such systems as the human body, the stock market, and sports games are amenable to description, called models, via the mathematics that we encounter early in our college years (and of course, more advanced mathematics can provide more detailed models!).
The goal of this course will be to increase the mathematical literacy of the students taking it. We will provide a set of tools and frameworks with which students can use familiar mathematics to predict and analyze real world problems. The mathematics required will be a "just in time production:" that is, it will be taught when it is needed.
The principal text for this course is Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics by R.B. Banks. On occasion we will use Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics also by R.B. Banks, as well as Topics in Mathematical Modeling by K.K. Tung.
Each class will feature a focus problem or focus problems for which we will develop a mathematical model that attempts to describe and predict the system in question. These in-class projects will typically be tackled in teams, and thus attendance for each class is required. In addition to these in-class projects, there will be at least two large modeling problems given to teams for which 5 to 6 page research reports will be required. Some homework- as preparation for the coming discussion- will be required weekly.
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Do the Math: Secrets, Lies, and Algebra
In the eighth grade, 1 math whiz < 1 popular boy, according to Tess's calculations. That is, until she has to factor in a few more variables, like:
1 stolen test (x),
3 cheaters (y),
and 2 best friends (z) who can't keep a secret.
Oh, and she can't forget the winter dance (d)!
Then there's the suspicious guy Tess's parents know, but that's a whole different problem.—
Allie (Forest Hill, MD)
This was a very interesting book. It had a new way of looking at life: through math. As the main character discovers, math is so logical that it can often help to solve problems in real life--and she has some big ones. Any math lover would instantly love this book, and anyone else would love it also for its unique perspective on life. I would highly recommend it to anyone, even those who think math is useless (maybe this will change their minds).
—
Molly (Agua Dulce, CA)
This wonderful, witty book puts things in a refreshingly new perspective, relating everyday things to math in a way that will have you thinking. This book evokes an interest in math without being a textbook and also allows us to enter the world of a typical teenage girl. This book combines typical teenage life and math in a way that will make you excited for math class.
—
Darcy (Hudson, WI)
Do the Math: Secrets, Lies, and Algebra is a light-hearted read, perfect for a breezy summer day and a cold glass of pink lemonade. Tess, a self-proclaimed "math lover" finds ways to relate her real-life eighth grade situations to (what else?) algebra. For once, Tess must question everything- even math. She soon learns the true value of friends, family, and algebra.
Do the Math #2: The Writing on the Wall
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From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
DescriptionFeatures & benefits
Key features
Contents address the syllabus topics studied at year 10.
A theme-based exercise at the end of each chapter, called Application, provides a set of exercises to show the practical application of the maths learned in the chapter.
Written in straightforward language to ensure ease of comprehension.
Each chapter opens with a problem to illustrate the relevance of the maths to be learned. This problem is reviewed at the end of the chapter.
The chapter-opening page also includes a list of the key concepts to be covered in the chapter plus a clear reference to the relevant syllabus outcome so that students know exactly what they will be studying.
A background quiz, Before you start, to test that students have the skills to complete the chapter, immediately follows the chapter-opening page.
Plenty of clear worked examples and well-graded exercises - each question is coded to indicate the level of difficulty.
Did you know? boxes in the margin provide interesting snippets of information to stimulate students' interest.
Language references in the margin explain key terms and other language features to address maths literacy.
Hints remind students of key points to remember when tackling specific questions; Error Alerts! remind students of common mistakes.
Many practical and group activities are included throughout the text.
Visually appealing design with not too much material on each page, enlivened by frequent use of cartoon-style illustrations.
Each chapter concludes with Test Yourself! which reviews the work of the chapter.
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This course is a review of elementary algebra. Topics include real numbers, exponents, polynomials, equation solving and factoring.
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MATH 0099: Intermediate Algebra
4-0-4. Prerequisite: Satisfactory placement scores/MATH 0097
This course is a review of intermediate algebra. Topics include numbers, linear equations and inequalities, quadratic equations, polynomials and rational expressions and roots. Students must pass the class with a C or better and pass the statewide exit examination.
This course places quantitative skills and reasoning in the context of experiences that students will be likely to encounter. It emphasizes processing information in context from a variety of representations, understanding of both the information and the processing and understanding which conclusions can be reasonably determined. Topics covered include sets and set operations, logic, basic probability, data analysis, linear models, quadratic models and exponential and logarithmic models. This course is an alternative in area A of the core curriculum and is not intended to 1071: Mathematics I
3-0-3. Prerequisite: Satisfactory placement scores/MATH 0097
This course in practical mathematics is suitable for students in many career and certificate programs. Topics covered include a review of basic algebra, ratio and proportion, percent, graphing, consumer mathematics and the metric system.
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MATH 1111: College Algebra
3-0-3. Prerequisite: Satisfactory placement scores/MATH 0099
This course is a functional approach to algebra that incorporates the use of appropriate technology. Emphasis will be placed on the study of functions and their graphs, inequalities, and linear, quadratic, piece-wise defined, rational, polynomial, exponential and logarithmic functions. Appropriate applications will be included. This course is an alternative in Area A of the core curriculum and does 1113: Precalculus
3-0-3. Prerequisite: MATH 1111 with a grade of C or better
This course is designed to prepare students for calculus, physics and related technical subjects. Topics include an intensive study of algebraic and trigonometric functions accompanied by analytic geometry as well as DeMoivreís theorem, polar coordinates and conic sections. Appropriate technology is utilized in the instructional process.
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MATH 2008: Foundations of Numbers and Operations
3-0-3. Prerequisite: Math 1001, Math 1101, Math 1111, or Math 1113
This course is an Area F introductory mathematics course for early childhood education majors. This course will emphasize the understanding and use of the major concepts of number and operations. As a general theme, strategies of problem solving will be used and discussed in the context of various topics.
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MATH 2200: Elementary Statistics
3-0-3. Prerequisites: MATH 1001/MATH 1111
This is a basic course in statistics at a level that does not require knowledge of calculus. Statistical techniques needed for research in many different fields are presented. Course content includes descriptive statistics, probability theory, hypothesis testing, ANOVA, Chi-square, regression and correlation.
Conic sections, translation and rotation of axes, polar coordinates, parametric equations, vectors in the plane and in three-space, the cross product, cylindrical and spherical coordinates, surfaces in three-space, vector fields, line and surface integrals, Stokeís theorem, Greenís theorem and differential equations are studied in this course.
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MATH 2280: Discrete Mathematics
3-0-3. Prerequisite: MATH 1113 with a grade of C or better or permission of the instructor or permission of the academic dean.
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Understanding linear algebra?
Understanding linear algebra?
It's almost the end of the semester for my first linear algebra course. The course has been taught from a pure mathematics standpoint and I can safely say I have no intuition for the subject. There have no been no physical interpretations or even geometric extensions given in my textbook or lectures.
Am I alone in being clueless and unsatisfied? Is it always like this for the average student?
I think this is normal. Just like geometrical and physics intuition, an intuitive grasp of abstract mathematical objects is something that needs to be developed with lots of work. The unfortunate part is that most people are never given an opportunity to develop this intuition until they are thrown into their first pure math course, which could be overwhelming and turn them away. Stick with it. You may never be able to relate some things in mathematics to familiar physical or geometric concepts (although in some cases you will), but you can develop a taste for the math itself.
Some linear algebra books are written to give the student a "gentle" introduction to the subject and they concentrate on systems of linear equations, determinants and similar topics that look familiar to students of secondary school algebra. If you have such a text, it isn't unusual to have no intuition about the purpose and nature of eigenvalues, characteristic polynomials, cannonical forms. Even if you understand vectors as used in elementary physics, those topics may be inscrutable.
Linear Algebra is sometimes the first place students encounter the systematic use of mathematical logic and rigorous proofs. Part of the sensation that you feel might be a reaction to that material, which would happen in any course where "real" mathematical reasoning is introduced.
Understanding linear algebra?
My comment may not be helpful at all, but I absolutely LOVED linear algebra. If I could have majored in linear algebra as an undergrad, I would have.
I think, as with most anything, it depends on the student. I'm a very visual person with strong spatial skills...I can see the basis vectors, rotations, etc., floating around me. I'm even more comfortable with geometry than linear algebra.
But there are so many other things that just don't come as naturally to me. So, I'm good at linear algebra, but poor in other areas. You might struggle with linear algebra, but you'd surpass me in other subjects.
I find it interesting that you can kind of develop an "intuition" for linear algebra by really understanding the notion and symbols, and then the "picture" you have in your head might not be a geometric one.. but a "symbolic" one.
well, Russell did once say that the essence of a good notation is the notations ability to convey its meaning/concept (something along these lines, and it's definitely true)It appears the author has concerns about students becoming attached to their intution from two and three dimensions. He wants the students to be as comfortable in high dimensions as they are in low ones. Linear algebra is very general, which is where its power comes from. He wants to demonstrate that.
I can say, however, that I never felt hindered by my attachment to three dimensions. Whenever I tutor a student in linear algebra, I'm constantly throwing my arms around in the air pointing wildly to try and help them visualize what span, independence, etc. mean. It helps, I think.
Abstraction and generality should come later, when you can appreciate it and have a use for it. Having sat through an introductory linear algebra course (and being bored out of my mind), it was a revelation being introduced to operator theory and Hilbert space theory. That's when the theory "clicked" for me, and linear algebra suddenly became the most gorgeous branch of math.
I second the other recommendations for a different text book. One with a heavier emphasis on the geometry. Are you a math major or science major?
I did not understand much of linear algebra the first time I took it but I have since taken a few classes that uses concepts like eigenvalues and linear transformations and these concepts have more meaning when you learn how they are applied.
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MSP:MiddleSchoolPortal/Math Focal Points: Grade 8
From Middle School Portal
Math Focal Points - Grade 8 - Introduction
With the goal of highlighting "the mathematical content that a student needs to understand deeply and thoroughly for future mathematics learning," the National Council of Teachers of Mathematics has developed Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics. A "focal point" is an area of emphasis within a complete curriculum, a "cluster of related knowledge, skills, and concepts."
This is the fourth and last in a Middle School Portal series of publications that highlight the focal points by grade level. Others in the series are Math Focal Points: Grade 5, Math Focal Points: Grade 6, and Math Focal Points: Grade 7. This publication offers resources that directly support the teaching of the three areas highlighted for eighth grade: (For a complete statement of the NCTM Curriculum Focal Points for grade 8, please see below.)
NCTM recommends that students in grade 8 analyze linear functions, translating among their verbal, tabular, graphical, and algebraic representations. They should also solve linear equations and systems of linear equations in two variables as they apply them to analyze mathematical situations and solve problems. In our section titled Linear Functions and Equations, we offer tutorials, games, carefully crafted lessons, and online simulations that provide varied approaches to these algebraic concepts. You will also find opportunity for the practice needed for understanding.
Eighth-graders are expected to use fundamental facts of distance and angle to analyze two- and three-dimensional space and figures. NCTM recommends that they develop their reasoning about such concepts as parallel lines, similar triangles, and the Pythagorean theorem, both explaining the concepts and applying them to solve problems. In the section titled Geometry: Plane Figures and Solids, we feature visual, interactive experiences in which your students can work with concepts of angle, parallel lines, similar triangles, the Pythagorean theorem, and solids. You will find games as well as lessons and challenging problems.
In grade 8, the emphasis is on understanding descriptive statistics; in particular, mean, median, and range. Students organize, compare, and display data as a way to answer significant questions. In the Analyzing Data Sets section, you will find tutorials, lesson ideas, problems, and applets for teaching these topics, and even full projects that involve worldwide data collection and analysis.
In Background Information for Teachers, we identify professional resources to support you in teaching the materials targeted in the focal points for grade 8. In NCTM Standards, we relate the curriculum focal points to Principles and Standards for School Mathematics.
NCTM Curriculum Focal Points for Grade 8
Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations..
Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle..
Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets..
Background Information for Teachers
If looking to refresh your mathematical content knowledge, or simply to find a new approach to teaching the material targeted in the Grade 8 Focal Points, you will find these professional resources valuable.
Learning Math: Patterns, functions, and algebra
In this online course designed for elementary and middle school teachers, each of ten sessions centers on a topic, such as understanding linearity and proportional reasoning or exploring algebraic structure. The teacher-friendly design includes video, problem-solving activities, and case studies that show you how to apply what you have learned in your own classroom.
Linear functions and slope
In one session from the online workshop described above, teachers gather to explore linear relationships--as expressed in patterns, tables, equations, and graphs. Video segments, interactive practice, problem sets, and discussion questions guide participants they consider such concepts as slope and function.
Similarity
Explore scale drawing, similar triangles, and trigonometry in terms of ratios and proportion in this series of lessons developed for teachers. Besides explanations and real-world problems, the unit includes video segments that show teachers investigating problems of similarity. To understand the ratios that underlie trigonometry, you can use an interactive activity provided online.
Indirect Measurement and Trigonometry
For practical experience in the use of trigonometry, look at these examples of measuring impossible distances and inaccessible heights. These lessons show proportional reasoning in action!
Pythagorean Theorem
A collection of 76 proofs of the theorem! From the diverse approaches used by Euclid, Da Vinci, President Garfield, and many others, these proofs are clearly and colorfully illustrated, often accompanied by an interactive Java illustration to further clarify the brief explanations. Incredible as it sounds, this page is far from boring.
Variation about the mean
Just what do we mean by "the mean"? This workshop session, developed for K-8 teachers, explores this statistic in depth. Participants work together to investigate the mean as the "balancing point" of a data set and come to understand how to measure variation from the mean.
Gallery of Data Visualization: The Best and Worst of Statistical Graphics
This site offers graphical images that represent data from a range of sources (historical events, spread of disease, distribution of resources). The author contrasts the differences between the best and worst graphics by showing how some images communicate data clearly and truthfully, while others misrepresent, lie, or totally fail to "say something." If you are looking for innovative representations of data or examples of misrepresentation, you will find this resource helpful.
Linear Functions and Equations
(NCTM, 2006, p. 20).
These resources offer a variety of ways to learn the material targeted in this Focal Point: tutorials, games, carefully crafted lessons, and online simulations. Your middle school students will also find plenty of opportunity for practice in real-world as well as imaginative scenarios.
Lines and Slope
At this site, students learn to draw a line and find its slope. Joan, a cartoon chameleon, is used throughout the tutorial to demonstrate the idea of slope visually. Background information on solving equations and graphing points is laid out clearly, followed by a step-by-step explanation of how to calculate slope using the formula. Finally, the slope-intercept form (y = mx + b) is carefully set out.
Walk the Plank
Students place one end of a wooden board on a bathroom scale and the other end on a textbook, then "walk the plank." They record the weight measurement as their distance from the scale changes and encounter unexpected results: a linear relationship between the weight and distance. Possibly most important, the investigation leads to a real-world example of negative slope. An activity sheet, discussion questions, and extensions of the lesson are included.
Writing Equations of Lines
This lesson uses interactive graphs to help students deepen their understanding of slope and extend the definition of slope to writing the equation of lines. Online worksheets with immediate feedback are provided to help students learn to read, graph, and write equations using the slope intercept formula.
Linear Function Machine
The functions produced by this machine are special because they all graph as straight lines and can be expressed in the form y = mx + b. In this activity, students input numbers into the machine and try to determine the slope and y-intercept of the line.
Algebra: Linear Relationships
Seven activities focus on generalizing from patterns to linear functions. Designed for use by mentors in after-school programs or other informal settings, these instructional materials have students work with number patterns, the function machine, graphs, and variables in realistic situations. Excellent handouts included.
Explorelearning.com
The following three resources come from this subscription site; a free 30-day trial is available. Experiment with the online simulations, particularly selected for their use in teaching equations of a line. Subscriptions include inquiry-based lessons, assessment, and reporting tools.
Examine the graph of two points in the plane. Find the slope of the line that passes through the two points. Drag the points and investigate the changes to the slope and to the coordinates of the points.
Compare the slope-intercept form of a linear equation to its graph. Find the slope of the line using a right triangle on the graph. Vary the coefficients and explore how the graph changes in response.
Slope slider
What difference does it make to the graph of a function if you change the slope or the y-intercept? Students can see the changes in the equation itself and in its graph as they vary both slope and y-intercept. Excellent visual! The activity could be used for class or small group work, depending on computer access.
Grapher : algebra (grades 6-8)
Using this online manipulative, students can graph one to three functions on the same window, trace the function paths to see coordinates, and zoom in on a region of the graph. Function parameters can be varied as can the domain and range of the display. Tabs allow the student to incorporate fractions, powers, and roots into their functions.
Planet hop
In this interactive game, students find the coordinates of four planets shown on the grid or locate the planets when given the coordinates. Finally, they must find the slope and y-intercept of the line connecting the planets in order to write its equation. Players select one of three levels of difficulty. Tips for students are available as well as a full explanation of the key instructional ideas underlying the game.
Constant dimensions
This complete lesson plan requires students to measure the length and width of a rectangle using both standard and nonstandard units of measure, such as pennies and beads. As students graph the ordered pairs, they discover that the ratio of length to width of a rectangle is constant, in spite of the units. This hands-on experience leads to the definition of a linear function and to the rule that relates the dimensions of this rectangle.
Barbie bungee
Looking for a real-world example of a linear function? In this lesson, students model a bungee jump using a doll and rubber bands. They measure the distance the doll falls and find that it is directly proportional to the number of rubber bands. Since the mathematical scenario describes a direct proportion, it can be used to examine linear functions.
Exploring linear data
This lesson connects statistics and linear functions. Students construct scatterplots, examine trends, and consider a line of best fit as they graph real-world data. They also investigate the concept of slope as they model linear data in a variety of settings that range from car repair costs to sports to medicine. Handouts for four activities, spread out over three class periods, are provided.
Supply and Demand
Your company wants to sell a cartoon-character doll. At what price should you sell the doll in order to satisfy demand and maintain your supply? The lesson builds from graphing data to writing linear equations to creating and solving a system of equations in a real-world setting. Discussion points, handouts, and solutions are given.
Printing Books
Presented with the pricing schedules from three printing companies, students must determine the least expensive way to have their algebra books printed. They compile data in tables, spreadsheets, and a graph showing three equations. Throughout the lesson, students explore the relationships among lines, slopes, and y-intercepts in a real-world setting.
Purplemath - Your Algebra Resource
Algebra modules provide free tutorials in every topic of algebra, from beginning to advanced. Lessons concentrate on "practicalities rather than the technicalities" and include worked examples as well as explanations. Of particular interest are the modules on Systems of Linear Equations and Systems-of-Equations Word Problems. A site worth visiting!
Geometry: Plane Figures and Solids
(NCTM, 2006, p. 20).
These activities offer your eighth graders visual, interactive experiences with geometry. Through games as well as lessons and problems, they work with concepts of angle, parallel lines, the Pythagorean theorem, and solids.
Angles
This Java applet enables students to investigate acute, obtuse, and right angles. The student decides to work with one or two transversals and a pair of parallel lines. Angle measure is given for one angle. The student answers a short series of questions about the size of other angles, identifying relationships such as vertical and adjacent angles and alternate interior and alternate exterior angles.
Triangle Geometry: Angles
This site directly addresses students as it leads them to explore angles and their measurement. Most important, it offers applets to introduce the Pythagorean theorem by collecting data from right triangles online and provides an animated picture proof of the theorem.
Manipula math with Java : the sum of outer angles of a polygon
This interactive applet allows users to see a visual demonstration of how the sum of exterior angles of any polygon sums to 360 degrees. Students can draw a polygon of any number of sides and have the applet show the exterior angles. They then decrease the scale of the image, gradually shrinking the polygon, while the display of the exterior angles remains and shows how the angles merge together to cover the whole 360 degrees surrounding the polygon.
Parallel Lines and Ratio
Three parallel lines are intersected by two straight lines. The classic problem is: If we know the ratio of the segments created by one of the straight lines, what can we know about the ratio of the segments along the other line? An applet allows students to clearly see the geometric reasoning involved.
Area triangles
This applet shows triangle ABC, with a line through B parallel to base AC. Students can change the shape of the triangle by moving B along the parallel line or by changing the length of base AC. What happens to the length of the base, the height, and the area of the triangle as students make these moves? Why?
Understanding the Pythagorean Relationship Using Interactive Figures
The activity in this example presents a visual and dynamic demonstration of this relationship. The interactive figure gives students experience with transformations that preserve area but not shape. The final goal is to determine how the interactive figure demonstrates the Pythagorean theorem.
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation.
Measuring by Shadows
A student asks: How can I measure a tree using its shadow and mine? This letter from Dr. Math carefully explains the mathematics underlying this standard classroom exercise.
Finding the Height of a Lamp Pole
Without using trigonometry, how can you find the height of a lamp pole or other tall object? Two methods, both depending on similar triangles, are outlined and illustrated. A rich problem.
Polygon Capture
In this lesson, students classify polygons according to more than one property at a time. In the context of a game, students move from a simple description of shapes to an analysis of how properties are related.
Sorting Polygons
In this companion to the above game, students identify and classify polygons according to various attributes. They then sort the polygons in Venn diagrams according to these attributes.
Fire hydrant : what shape is at the very top of a fire hydrant?
This activity begins an exploration of geometric shapes by asking students why the five-sided (pentagonal) water control valve of a fire hydrant cannot be opened by a common household wrench. The activity explains how geometric shape contributes to the usefulness of many objects. A hint calls students' attention to the shape of a normal household wrench, which has two parallel sides. Answers to questions and links to resources are included.
Diagonals to Quadrilaterals
Instead of considering the diagonals within a quadrilateral, this lesson provides a unique opportunity: Students start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore characteristics of diagonals and the quadrilaterals that are associated with them.
Image:Geometric Solids and their Properties
A five-part lesson plan has students investigate several polyhedra through an applet. Students can revolve each shape, color each face, and mark each edge or vertex. They can even see the figure without the faces colored in — a skeletal view of the "bones" forming the shape. The lesson leads to Euler's formula connecting the number of edges, vertices, and faces, and ends with creating nets to form polyhedra. An excellent introduction to three-dimensional figures!
Slicing solids (grades 6-8)
So what happens when a plane intersects a Platonic solid? This virtual manipulative opens two windows on the same screen: one showing exactly where the intersection occurred and the other showing the cross-section of the solid created in the collision. Students decide which solid to view, and where the plane will slice it.
Studying Polyhedra
What is a polyhedron? This lesson defines the word. Students explore online the five regular polyhedra, called the Platonic solids, to find how many faces and vertices each has, and what polygons make up the faces. An excellent applet! From this page, click on Polyhedra in the Classroom. Here you have classroom activities to pursue with a computer. Developed by a teacher; the lessons use interactive applets and other activities to investigate polyhedra.
Analyzing Data Sets
(NCTM, 2006, p.20).
As reflected in this set of resources, the emphasis here is on understanding descriptive statistics; in particular, measures of center. You will find tutorials, lesson ideas, problems, and applets for teaching these topics, and even full projects that can involve your middle school students in worldwide data collection.
Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how these statistics change (or, in some cases, how they don't change).
Understanding Averages
Written for the student, this tutorial on mean, median, and mode includes fact sheets on the most basic concepts, plus practice sheets and a quiz. Key ideas are clearly defined at the student level through graphics as well as text.
Plop It!
Users click to easily and quickly build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. An efficient tool for viewing these statistics visually.
Working hours : how much time do teens spend on the job?
This activity challenges students to interpret a bar graph, showing only percentages, to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance! A hint suggests that students assume that 100 students participated in the survey; a full solution sets out the math in detail. Related questions ask students to calculate averages for additional data sets.
Stem-and-Leaf Plotter
Can your students find the mean, median, and mode from a stem-and-leaf plot? They can use this applet to explore the measures of center in relation to the stem-and-leaf presentation of data. Students use the online plotter to enter as much data as they choose; then they determine measures of center and have the program check and correct their values. Ideas for class practice and discussion are provided in a lesson outline.
Train race
In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Players extend their basic understanding of these statistics as they try to find the most reliable train for the trip. Students can select one of three levels of difficulty. There are tips for students as well as a full explanation of the key instructional ideas underlying the game.
Comparing Properties of the Mean and the Median Through the Use of Technology
This interactive tool allows students to compare measures of central tendency. As students change one or more of the seven data points, the effects on the mean and median are immediately displayed. Questions challenge students to explore further the use of these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other extreme?
The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students can participate in the project each spring, April-June. Students learn to collect, organize, and interpret data. You will find project information, lesson plans, and implementation assistance at the site Students must develop a hypothesis, conduct an experiment, and present their results.
Data analysis : as real world as it gets
Resources that firmly place data analysis in context! The lessons and interdisciplinary projects were selected to promote student interest by focusing on real-world situations and developing skills for using the power of mathematics to form important conclusions relevant to life. Students learn that working with data offers insights into society's problems and issues.
SMARTR: Virtual Learning Experiences for Students
Visit our student site SMARTR to find related math math-related careers (click on the Math link at the bottom of the home page).
NCTM Standards
You may be asking yourself, "What do the curriculum focal points have to do with the Principles and Standards for School Mathematics (PSSM)?" NCTM answers that identifying areas of emphasis at each grade level is the next step in implementing those principles and standards. Curriculum Focal Points for Prekindergarten Through Grade 8: A Quest for Coherence "provides one possible response to the question of how to organize curriculum standards within a coherent, focused curriculum, by showing how to build on important mathematical content and connections identified for each grade level, pre-K–8" (NCTM, 2006, p. 12).
The curriculum focal points draw on the content standards described in PSSM, at times clustering several topics in one focal point. Also, the process standards are pivotal to well-grounded instruction, for "it is essential that these focal points be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations" (p.20).
This Middle School Portal publication offers resources intended to support you in teaching the key mathematical areas identified for grade 8: linear functions and simple systems of linear equations, parallel lines and angles in polygons, the Pythagorean theorem, polyhedra, and descriptive statistics. The selected resources are grounded in the Algebra, Geometry, and Data Analysis standards, and particularly in the process standards of Problem Solving and Representation.
A variety of formats (tutorials, lesson plans, games, problems, and projects) are provided for your use in teaching these focal points. We believe you will find here resources that engage your eighth graders in probing the deeper and increasingly abstract concepts of middle school mathematics.
Reprinted with permission from Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, copyright 2006 by the National Council of Teachers of Mathematics. All rights reserved.
Connect with colleagues at our social network for middle school math and science teachers at
Copyright May 2008 - The Ohio State University
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Computational Introduction To Number Theory And Algebra - 05 edition
Summary: Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus...show more is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students
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Service Teaching for Foundation Studies
Course Units
Course Information
Course Coordinator
Course Description
Mathematics forms a substantial part of the Foundation Year. Students take 2
mathematics modules in semester 1 and up to 4 maths modules in semester 2. Each
module consists of two lectures and a tutorial per week.
Semester 1
The ability to carry out calculations in calculus and algebra is extremely important
in all the disciplines into which the foundation year feeds. Students take a module in
semester 1 and most take another module in semester 2.
There are two pathways available i.e. the B-pathway and the C-pathway.
The B-pathway (0B1 in semester 1) is taken by the majority of students and takes up
the subject at around AS level or equivalent. However, some students may benefit
more from the C-pathway (0C1 in semester 1) which starts from a point a little further back.
This module is in two parts ; The first deals with vectors i.e. the line from
one point to another and how this can be of use in many practical situations.
The second part deals with probability i.e. the chances of
particular events happening and what can be inferred.
The ability to understand moving and stationary objects is of paramount
importance to students moving forwards to schools such as MACE, Physics, Materials etc.
and is useful for students moving forward to other schools.
This unit considers statics (the study of stationary objects) and dynamics
(the study of moving objects).
This module takes the ideas of 0B1/2 and 0C1/2 further and also includes a section on
basic numerical methods. Success in this module will be a great bonus to take forward
to Year 1.
Tutorials
For most modules the tutorials normally are based around example sheets i.e. sheets of questions. These are handed out in the lectures and students will be expected to attempt the questions in their own time. The tutorial session is led by a lecturer or postgraduate student (the tutor) and will involve these questions; it is found that students who have attempted the questions in advance will gain more understanding in the tutorial than those who have not. The tutorial will be a place to ask questions about any of the examples causing difficulty. It is also a place to ask any more general questions about the module (although detailed questions on the notes are best dealt with by the lecturer). For 0C1, the tutorial session will involve an element of work with a
Computerised Virtual Learning Environment.
Assessment and Coursework
For each course, there will be a two hour examination in January. This will count 80 % of the assessment
for the course (75 % for 0C1, 60% for 0N1 ). The remaining 20% (or 25% or 40%) will come from coursework i.e. assignments to be
handed in or tests or assignments done during class time.
NOTE: Action will be taken against any student
submitting coursework which is not totally their own work. This can
include resetting a mark to zero. It is recognised that a constructive
discussion between students on questions is a good thing. However, if a
group of students drafts out a solution to a question, it is up to each
student to show that they understand the solution by writing the
solution independently.
No credit will be given for coursework handed in late unless the student's personal tutor contacts Dr Steele to request otherwise (e.g. in case of illness etc).
Questions on the subject matter of the course should be directed to the lecturer or the tutor or to the director of Service Teaching / Course Coordinator (Dr Steele, details above) who can also deal with any questions about the maths courses in general).
Each lecturer or tutor has an office in the school of Mathematics (Alan Turing Building) and a phone number and e-mail address which can be found from
the university staff directory pages ( staff
or postgraduate). Students using e-mail to contact staff are reminded to use their university e-mail accounts and to make the subject line meaningful.
Course Assignment
The set of maths course units taken by particular students is determined by the choice
of destination school for year 1 and also, in some cases, by selection of options.
Note that Mathematics 0B1 acts as a pre-requisite for 0B2 ; 0C1 acts as pre-requisite for
0C2 ; 0B2 or 0C2 acts as co-requisite for 0F2, 0J2 and 0D2 ; 0F2 acts as pre-requisite for
0J2.
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This learn node points to the page here at MIT Open Courseware for digital tools like the one illustrated above called Curves in Two Dimensions. There are more than two dozen tools for topics ranging such as precalculus, algebra and vectors, curves, surfaces and differential equations. In the MIT course with tools like the one shown are chapter outlines like this one called Curves about, as the Introduction explains:
"The tools of calculus developed so far allow us to describe most of the important properties of a smooth curve: which are its direction at any point, and how much it deviates from straightness there. This is measured by its curvature. How its path differs from planarity is measured by its torsion, also easily calculated."
This learn node cluster math help available online virtually from an amazing array of open sources. The picture here of Wolfgang Pauli and Niels Bohr as they "stare in wonder at a spinning top" is from lectures by David Tong of Cambridge University on Classical Dynamics. The picture is included in the third Tong lecture titled The Motion of Rigid Bodies. Pauli and Bohr � great mathematicians of the early 20th century � would surely turn the full intensity of their wonder on how a click of a 21st century mouse sends students to math help, math problems and math mentors
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Algebra is the symbolic language of thought. When we mentally manipulate words and ideas, we use logical reasoning to process information and make decisions. Whether we substitute 'x' and 'y' with ideas to form beliefs, or with numbers to solve equations, our brains use Algebra to sort through these ideas. We are all capable of using Algebraic reasoning--it's our foundation for knowledge!
_______________________
Contact Information
Email: victoria.argeroplos@springbranchisd.com
Phone: 713-251-3400 Ext. 3511
About Me
This is my first year at Stratford, teaching Algebra I. I have recently graduated from the University of Washington in Seattle with Bachelor of Arts degrees in Mathematics and Philosophy, and a minor in Education.
The students have a project that uses the ShowMe app for iPad. They will create a video showing the class how to apply a skill we learned in class, and will sign up for a chapter of the book. Only one student will be assigned to a chapter, and this is an individual project. The due date depends on when I teach the material in class; the student will have four class days after I teach the material to complete their video. This means, for students who have me on A days, the video will be due by 3:00 pm on the fourth A day after I teach the material.
Tutorials
Tutorials in my room:
Mondays 3:00 - 3:45
Wednesdays 3:00 - 3:45
or by appointment
Test make-ups Mondays at 3:00 in room 204
My Classes
Period 1 Algebra I Grade level
Period 2 Conference
Period 3 Algebra I Grade level
Period 4 Algebra I Grade level
Period 5 Conference
Period 6 Algebra I Grade level
Period 7 Algebra I Grade level
Period 8 Algebra I Grade level
Resources
Khan Academy has tons and tons of free video tutorials to help you learn literally any math concept. Just type "Algebra I ________" for any topic we cover in class.
Wolfram Alpha is like a giant graphing calculator database. You can input any equation on and it will graph the solutions for you.
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