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Calculus Latin, calculus, a small stone used for counting is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Cal broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
In American mathematics education, precalculus or Algebra 3 in some areas, an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry. Precalculus prepares students for calculus the same way as pre algebra prepares students for Algebra I. While pre algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topics that will be applied in calculus. Some precalculus courses might differ with others in terms of content. For example, an honors level course might spend more time on topics such as conic sections, vectors, and other topics needed for calculus. A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices which are used in business.
The field of discrete calculus, also known as "discrete exterior calculus", focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate calculus, discrete calculus establishes a separate, equivalent calculus that operates purely in the discrete space without any reference to an underlying continuous process. This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Although there have been a few intersections in the literature between these disciplines, they have developed largely independently of one another, yet researchers working in any one of these three areas can strongly benefit from the tools and techniques being used in the others. Many example applications from several fields of computational science are provided to demonstrate the usefulness of this framework to a broad range of problems. Readers are assumed to be familiar with the basics of vector calculus, graph theory, and linear algebra.
I would definitely agree with that statement. After taking Calculus I in my junior year of high school, I wanted to brush up on my Calculus because, although I had gotten a 5 on the AP Exam, I left feeling pretty clueless as to what Calculus is and how it works. It became even more apparent when I tried to teach someone Calculus: I fumbled around with words like 'limit', 'integral', 'area', 'derivative', 'tangent', and 'continuity' all because I had a very vague grasp of how all those concepts relate to one another.
Calculus is advanced math for the high school student, but it's the starting point for math in the most selective colleges and universities. Thinkwell's Calculus course covers both Calculus I and Calculus II, each of which is a one-semester course in college. If you plan to take the AP Calculus AB or AP Calculus BC exam, you should consider our Calculus for AP courses, which have assessments targeted to the AP exam.
Thinkwell's award-winning math professor, Edward Burger, has a gift for explaining and demonstrating the underlying structure of calculus, so that your students will retain what they've learned. It's a great head start for the college-bound math, science, or engineering student.
This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182 in this same series, Translations of Mathematical Monographs, and shows the theory ""in action"". ...
Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams.
This book is a basic text in advanced calculus, providing a clear and well-motivated, yet precise and rigorous, treatment of the essential tools of mathematical analysis at a level immediately following that of a first course in calculus. It is designed to satisfy many needs; it fills gaps that almost always, and properly, occur in elementary calculus courses; it contains all of the material in the standard classical advanced calculus course; and it provides a solid foundation in the "deltas and epsilons" of a modern rigorous advanced calculus. It is well suited for courses of considerable diversity, ranging from "foundations of calculus" to "critical reasoning in mathematical analysis." There is even ample material for a course having a standard advanced course as prerequisite....
Applied Calculus for Business, Economics, and Finance is a combination of the authors' two previous texts Precalculus and Elements of Calculus and Applied Calculus. This single text may be used to cover the content of an applied calculus course for non-science majors. Continuing the approach used in its precursor texts, Applied Calculus for Business, Economics, and Finance features the integration of precalculus with the calculus as well as the integration of technology with both subjects.
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The student would be helped by having knowledge of basic trigonometry and vectors to better understand AC waveforms, phase shift, and work with Ohm's and Kirchhoff's Laws for AC circuits.
Note: Basic trigonometric functions and vector arithmetic are covered in the class as these are included as a chapter in the prescribed textbook.
Prerequisite MATH C050
The student needs basic algebra and mathematical concepts including solving linear equations, proportionality, fundamentals of exponential arithmetic, and graphing in Cartesian coordinates. This is necessary for them to work with Ohm's and Kirchhoff's Laws that are fundamental to circuit analysis.
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Introduction To College Algebra –
mat219
(3 credits)
This course introduces algebraic concepts providing a solid foundation for college algebra. Topics range from properties of real numbers, the order of operations, and algebraic expressions to solving equations and inequalities. Additional topics include polynomials, factoring methods, rational and radical expressions as well as graphing and functions
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engrossing, how-to book designed to pique students' interest in the process of modelling in order to acquire both critical and creative modelling skills and the confidence to apply them. The author uses exercises, case studies and models, based on scientific literature, that are freely adaptable and presented in a fresh perspective as interlocking fragments of a mosaic. Examples are chosen from population dynamics, heat flow, optimal harvesting, traffic management and other areas that use models. Includes material for model builders.
Editorial Reviews
Booknews
A textbook that teaches both critical and creative modeling skills, primarily for a senior-level course that gives equal weight to deterministic and probabilistic modeling. It emphasizes both the validation of mathematical models and the rationale behind improving them. The approach embodies the belief that the three most fundamental ideas in mathematical modeling are transience, permanence, and optimality. The minimal mathematical prerequisites are the standard calculus sequence and first courses in linear algebra, ordinary differential equations, and probability and statistics. Probability and statistics are reviewed in an appendix
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0471970 Mathematics
Mathematics is finding ever wider areas of application as we seek to understand more about the way in which the natural world and the man-made environment operate and interact. In addition to the traditional use of mathematical models as design tools and for the prediction of the behaviour of many phenomena, mathematics is increasingly being used to model situations in many other disciplines including finance, management, politics and geography. Foundation Mathematics begins with a concise summary of arithmetic, basic algebra and a discussion of quadratics and cubics, strongly emphasising geometric ideas. Then follow the principles of Euclidean and Cartesian geometry and the concept of proof. Next are trigonometry, further algebra, functions and their inverses. Finally, the concepts of differential and integral calculus are introduced. Each chapter starts with a list of learning objectives and ends with a summary of key points and results. A generous supply of worked examples incorporating motivating applications is designed to build knowledge and skill. The exercises provided range in difficulty to aid consolidation and facilitate revision. Answers to the exercises, some including helpful hints, are placed at the end of each chapter. Foundation Mathematics together with its sequel Mathematics in Engineering and Science take the reader forward, in both content and style, from a level close to UK GCSE mathematics and its international equivalents to first year university-level mathematics. The concise and focused approach will help the student build the necessary confidence to tackle the more advanced ideas of the authors related book Mathematics in Engineering and Science (Wiley, 1998). This no-nonsense textbook will enable students to gain a basic grounding in the foundations of mathematics and will enable them to approach further study
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Product Details:
fractions, decimals and terms including Pi in alternate forms, exploring more advanced topicsThe two line display scientific calculator combines statistics and advanced
scientific functions and is a durable and affordable calculator for the classroom. The two line display helps students explore math and science concepts in the classroom.
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MATH 55555: Graduate students
About this Guide
General Information for Your Research
Improving Your Proofs
There are a number of books on mathematical proofs. Here are two that may help:
Reading, Writing, and Proving: a Closer Look at Mathematics by Ulrich Daepp (2003) Print version QA 13 .D34 2003, O'Meara Mathematic Library "How can someone learn to prove mathematical results? There are many theories on this. We believe that learning mathematics is the same as learning to play an instrument or learning to succeed at a particular sport. Someone must provide the background: the tips, information on the basic skills, and the insider's 'know how.' Then the student has to practice" (Preface).
An Accompanimentto Higher Mathematics by George Exner (1996) QA 9.54 E96, O'Meara Mathematics Library "Like music and athletics, the main pleasure in mathematics is in the process of doing: exploring, inventing, and discovering. You are ... intrinsically good doers of mathematics, but you may be fighting with one hand (or two hands) tied behind your backs without knowing it. This book is all about some active tools to make your doing of mathematics more effective, and thus, possibly, more enjoyable" (Introduction).
Checking Encyclopedias
In the course of your research, you may encounter topics that are unfamiliar to you. Reading a little about these topics in an encyclopedia is a great way to get a good overview.
Here are two highly recommended general reference resources:
Wolfram MathWorld "MathWorldTM is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica. MathWorld has been assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors."
Encyclopaedia of Mathematics Print version QA 5 .M3713 1987, O'Meara Mathematics Library reference "The Encyclopaedia of Mathematics is the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. [It] comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics."
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Description: This is a modified Physics 30S course with emphasis on application of mathematics in real (Physics) situations. it will help prepare students for Applied Math 40S as well as Physics 40S. The math component will include algebra, equation solving, some graphing, vectors, and trigonometry. The Physics component will include motion (velocity, acceleration) or mechanics as well as gravity and friction.
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Textbooks
The most important objective of this course is to introduce students to mathematical thinking and reasoning through a hands-on exploration of interesting and challenging topics in geometry. The emphasis in this course is on conjecture, exploration of interesting geometric ideas, leading to the development of a robust proof or refutation. The goals of the course can be roughly divided into the broad areas of process goals (exploration, proof, and communication) and content goals (in synthetic, analytic, and transformational geometry.)
Process Goals
By the end of the course, the successful student will be able to
Explore
use The Geometer's Sketchpad with reasonable proficiency,
discuss ideas in geometry – and more generally, in mathematics – that contain unsolved questions and unresolved issues,
demonstrate an understanding of the need to justify or refute any conjecture,
conduct geometric experiments and form an opinion on the validity of a geometric statement—and if necessary, revise the statement based on these experiments,
Text: Students are required to purchase the textbook, College Geometry Using The Geometer's Sketchpad By Barbara E. Reynolds SDS William E. Fenton.
Software: It is recommended that students purchase the following software: The Geometer's Sketchpad, Version 5. Students can purchase a non-expiring license or a one year license by scrolling to the bottom of the page of the following website ( ). Students who choose not to purchase the software can use computers on campus to complete homework that requires the use of the above software.
Additional Note: Students will need a jump drive to store electronic work.
Grading Standards
Grades will be calculated using the following point scheme:
Exams: 35% of course grade
Final Exam: 25% of course grade
Other graded assessments of student work: 25% of course grade
Active participation in-class: 15% of course grade
The traditional 90–80–70–60 scale will be used to determine course letter grades at the end of the semester.
Final Exam
5/9/2010 5:45 - 7:45
Submission Format Policy
Homework is due at the beginning of class, and late homework will not be accepted. A student who is absent may turn his/her homework in by faxing it to the attention of the instructor at 940-397-4442, or by scanning it and sending it through email to dawn.slavens@mwsu.edu. Homework must be faxed or emailed by the beginning of class to avoid being lateHomework: Late assignments are not accepted.
Exams: No make-up exams will be given!!!Participation
Students are expected to attend and be punctual to every class meeting. Excessive late arrivals or early departures from class will count as unexcused absences. Since this course relies heavily on group participation, any student with n unexcused absences, where n >0, will lose (2n-1)% from his/her final course average. For extreme circumstances in which the instructor is convinced that an absence was unavoidable, the instructor may consider an absence to be excused. It is the responsibility of the student to discuss any such absence with the instructor, as well as, when requested by the instructor, provide documentation supporting the reason for the absence. Regularly, between class meetings, students will be assigned to complete investigation type activities and come to class prepared to share your discoveries and thoughts about the mathematics within these activities. In addition, at times you will be asked to work specific problems from the text and come to class ready to present your solutions, or at least share your thoughtful ideas about solving the assigned problem. For each class meeting in which you have not prepared sufficiently (i.e. unable to have an intellectual discussion around the assigned activities or problems), your grade will be reduced by 1%.
Other Policies
OTHER INFORMATION:
Major Focus of Course Text Content: Chapters 1 – 7, 9
Additional Text: We will make some use of the text Geometry A Guided Inquiry, by G.D. Chakerian, et al. The instructor will provide loaner copies of this text as needed.
Reading: It is expected that you read the textbook. The class is not going to be run in a lecture style format. You must read the textbook or you will miss important information.
Homework: Homework will be assigned regularly and some of the homework will be turned in to be graded. Students will also be expected to present to the class many of their solutions to assigned problems.
Exams: Dates of hourly exams will be announced at least one week prior to the exam. Expect at least one, possibly two, take-home exams, as well as two in-class exams.
Cell Phones and Pagers: Please turn these off during class.
Student rights: All students should refer to the MSU Student Handbook for information related to student responsibilities, rights and activities. Topics such as Student Affairs and Student Life, Academic Issues, Financial Issues, University Policies and Procedures, and Code of Student Conduct are included in this handbook.
Evidence of cheating: If there is evidence of cheating on an exam or plagiarism on any written assignments or take-home exams, or assisting a student in cheating or plagiarizing, you will receive a zero on the work and possibly a letter grade of F for the course. Further, university policy concerning reporting evidence of cheating to college deans, etc. will be followed
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Online encyclopedias contain a wealth of information, be it user-generated or professionally vetted. The hyperlinked nature of an online encyclopedia makes reading about related topics as simple as clicking a link.
Courseware is software or organized content that can be used in the preparation or teaching of a course. This section contains links to web-based courseware resources. Downloadable courseware is listed on our Software page.
WikiBooks is a free, collaborative online collection of textbooks, including a set of mathematics texts. As always with online content, these are under construction.
CCNYMath.net is a Flash-based set of instructional web pages written and designed by Stanley Ocken, Professor of Mathematics at City College, and the late Jack Schwartz, a former CCNY math graduate and Professor Emeritus of Mathematics and Computer Science at New York University. You may contact Professor Ocken with any questions or suggestions for the site. You will need to have a Flash plug-in installed in your web browser to use this site.
Baruch College's Student Academic Consulting Center links to sample handouts and exams for some of Baruch's math classes, as well as math tutorial videos in Baruch's Digital Media Library. Video tutorials include college algebra, precalculus, and calculus. You must have a web browser with a plugin capable of playing QuickTime movies to view these videos.
Calculus+ is a series of tutorials in precalculus, calculus, linear algebra, and differential equations, using Maple 8 or higher. These projects were developed by CUNY faculty and tested in CUNY classrooms from 1998-2004.
Wolfram|Alpha, the Wolfram "computational knowledge engine", calculates answers to various questions using Mathematica packages and data from multiple online sources.
Math Overflow is a "place for mathematicians to ask and answer questions." The primary criterion for determining whether a question is appropriate for Math Overflow is, "is this of interest to mathematicians?"
The Tricki, a "a repository of mathematical know-how," is a wiki which seeks to codify methods of mathematical technique and problem-solvingThe Mandelbrot set, arguably the most famous fractal, is the result of repeating the same function over and over again on its output.
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Mathematics for EveryDispelling some of the subject's alarming aspects, this book provides, in a witty and engaging style, the fundamentals of mathematical operations. Topics include system of tens and other number systems, symbols and commands, first steps in algebra and algebraic notation, common fractions and equations, irrational numbers, much more. 1958 edition.
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Manufacturer's product description
QCA permitted for use in key stage 3 and 4 and GCSE maths exams. 2 line display shows sum and answer. Calculations can be entered as they are written. 240 functions including 164 scientific functions. Multi-line replay and edit facility.
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The Official Guide to the GMAT, 13th Edition is the only guide on the market that contains official questions from the new Integrated Reasoning component being fully integrated into the test in June 2012
This book targets your study and helps you improve your quantitative skills by focusing on your ability to solve equations, interpret data, coordinate geometry, and determine probability with assurance and ease. Learn More
Geometry - the branch of mathematics which received the earliest attention in the history of mathematics - offers the most bewildering choice of where to start and how to approach the subject. Geometry holds a great deal of importance in science and engineering. This book offers all important topics of geometry covered in the syllabus of JEE (Main & Advanced). Learn More
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Promoting Algebra for All
In some countries by the end of eighth grade, all students have been studying algebra for several years, although not ordinarily in a separate course. "Algebra for all" is a worthwhile and attainable goal for middle school students. In the United States, however, some efforts to promote algebra for all have involved simply offering a standard first-year algebra course (algebra through quadratics) to everyone. We believe such efforts are virtually guaranteed to result in many students failing to develop proficiency in algebra, in part because the transition to algebra is so abrupt. Instead, a different curriculum is needed for algebra in middle school:
"Algebra for all" is a worthwhile and attainable goal for middle school students.
Teachers, researchers, and curriculum developers should exploreways to offer a middle school curriculum in which algebraic ideas are developed in a robust way and connected to the rest of mathematics.
A different curriculum is needed for algebra in middle school.
Using Technology to Learn Algebra
Research has shown that instruction that makes productive use of computer and calculator technology has beneficial effects on understanding and learning algebraic representation. It is not clear, however, what role the newer symbol manipulation technologies might play in developing proficiency with the transformational aspects of algebra. We recommend the following:
Research should be conducted on the effects on students' learning ofusing the symbol-manipulating capacities of calculators and computers tostudy algebraic concepts and to transform algebraic expressions and equations.
Solving Problems as a Context for Learning
An important part of our conception of mathematical proficiency involves the ability to formulate and solve problems coming from daily life or other domains, including mathematics itself. That ability is not being developed well in U.S. pre-K to grade 8 classrooms. Studies in almost every domain of mathematics have demonstrated that problem solving provides an important context in which students can learn about number and other mathematical topics.
Problem-solving ability is enhanced when students have opportunities to solve problems themselves and to see problems being solved. Further, problem solving can provide the site for learning new concepts and for prac-
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This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants' general "definitions" of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary teachers' conceptions of algebra as subject matter are rather narrow. Most preservice teachers equated algebra with the manipulation of symbols. Very few identified other forms of reasoning – in particular, relational thinking – with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional symbol manipulation might be valued more than those that demonstrate relational thinking, suggesting that what is viewed as algebra is what will be valued in the classroom. This possibility, along with implications for mathematics teacher education, will be discussed.
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comments:
Welcome!
My name is Reidar Mosvold, and I am Associate Professor in Mathematics Education at University of Stavanger, Norway. This blog is my attempt to follow my field: mathematics education research. I hope you might find this site interesting too!
If you want to send me an e-mail rather than making direct comment to articles, you can reach me at: reidar.mosvold@uis.no
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The highly-acclaimed MEI series of text books, supporting OCR's MEI Structured Mathematics specification, has been updated to match the requirements of the new specifications, for first teaching in 2004 more...
This book is centrally concerned with how mathematics education is represented and how we understand mathematical teaching and learning with view to changing them. It considers teachers, students and researchers. It explores their mathematical thinking and the concepts that this thought produces. But also how these concepts acquire cultural layers... more...
There have been many advancements in sports technology that help athletes perform to the best of their abilities in the Olympic Games. Some of these advancements include shoes and equipment, tools used to measure times, clothing, and the surfaces on which many events take place. Now, computers are used to track timed events, which makes scores even... more...
Get your game on as you discover angles and their significance in games of pool, basketball, baseball, and soccer. The Winning Angle explains how angles can improve skills as well as illustrates all of the important angles that shape the perfect playing field. more...
Take a behind-the-scenes look at how an aquarium functions and explore diverse marine life while discovering why measuring volume is an important part of an aquarium's success. At the Aquarium examines water volume required by various tanks as well as animal food requirements based on weight measurement. more...
Now students can bring home the classroom expertise of McGraw-Hill to help them sharpen their math skills!. McGraw-Hill's Math Grade 2 helps your elementary-school student learn and practice basic math skills he or she will need in the classroom and on standardized NCLB tests. Its attractive four-color page design creates a student-friendly learning... more...
Now students can bring home the classroom expertise of McGraw-Hill to help them sharpen their math skills!. McGraw-Hill's Math Grade 3 helps your elementary-school student learn and practice basic math skills he or she will need in the classroom and on standardized NCLB tests. Its attractive four-color page design creates a student-friendly learning... more...
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Online learning with math computer software is gaining in popularity among college students. Distance learning has become one of the most viable ways in which to get a college education. Many people have careers that require them to further their education. For instance, an employee in a company could be eligible for a promotion if he or she earns a graduate level degree. Most students who are taking online learning courses to advance their careers have to take complicated math courses. Math computer software is an innovative way to learn.
Many students who use math computer software demonstrate good problem solving skills, which is important in every career. Many students like to use math computer software because it stimulates their ability to recall what they have learned. Many students like to study with the help of math computer software. Math computer software is an effective tool for all students, whether they are young or old. Online learning software is more versatile and is less expensive than taking traditional classes.
Math computer software is designed to lead students from the beginning to the end of the math course. For instance, if you signed up for an online learning course, you would receive software to download into your computer. Some of the software may have some computer graphics and games. Learning software that employs the use of math games helps to reinforce your math skills. Many students take algebra, geometry, calculus, and many other math courses online with math computer software.
Distance learning makes it so much easier for working people to advance their careers through higher education. You save time and money by going to school online. There is individual help available for all courses, including math. Math computer software is a wonderful computer application, which helps with the students' time management. The time saved from commuting to classes can be used more efficiently for study and getting on with life, in general.
Most online learning classes have a forum where the students can chat about the issues they are having. They can talk about math problems they are having difficulty with on their math computer software program. The forum is a great support for all students who take college courses online.
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Math 113 Quiz Information
Fall 2013 Quizzes:
Quiz 1 - in class Thursday, 8/29/13
Quiz 2 - in class Thursday, 9/5/13
Quiz3 - take home, 9/4/13
Quiz 4 - take home 9/10/13
Quiz 5 - In class 9/10/13
Quiz 6 - take home - Graph Trig Fns
Quiz 7 - take home - Inverse Trig Fns
Quiz 8 - take home - Establish Identities
Quiz 9 - in class - Trig Equations
Quiz 10 - take home - Law Sines Law Cosines
Quiz 11 - in class 11/21/13 Vectors
If you cannot open these handouts, you might need to download Adobe Reader 7.0.7. This is a free program that allows your computer to read PDF files. There is a link on my homepage where you can download this program.
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0495011592
9780495011590
A First Course in Mathematical Modeling:Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.
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Rent A First Course in Mathematical Modeling 4th edition today, or search our site for Frank R. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning.
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Professional Commentary: In this two-lesson unit, students explore geometric sequences and their relationship to exponential functions by considering the placement of frets on stringed instruments. ORC reviewers approved the unit as a reference site, but not as an instructional unit, because of the difficulty in collecting the required equipment....
Professional Commentary: Students investigate the pattern determined by the areas of squares inscribed in squares formed by joining the midpoints of the sides of the previous square. The sequence generated is a simple geometric sequence....
Professional Commentary: Students must compute the first three terms of a sequence and then find the fourth term. This multiple-choice question is a sample item used in the 2004 Ohio Graduation Test (see Overview of Ohio's Assessment System)....
Professional Commentary: Students are asked to write a rule describing a given pattern and then use the rule to find the 50th term. This short-answer question is a sample item used in the 2005 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System)....
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Algebra I Unit 10 (Pace 1106)
In Algebra I Unit 10, students will learn solve word problems involving averages, percents, interest, perimeter, area and volume of geometric figures, monetary value, two-digit numerals, and bodies in motion. The character trait is temperance. This unit is one unit in a series of twelve colorful independent study mastery-based units of instruction and includes direct instruction to the student as well as all necessary quizzes and tests.
Throughout the twelve Algebra I Paces your student will:
Learn basic algebraic concepts (definitions, signs, and expressions), introduced in a carefully structured way to make the learning material understandable.
Learn principles for logically solving, transposing, and canceling algebraic equations.
Work with monomial and polynomial expressions.
Work with algebraic addition, subtraction, multiplication, and division.
Work with complex fractions: reducing, simplifying, and solving word problems.
Learn algebraic graphing-linear equations, consistent, inconsistent, and dependent in word problems.
Encounter quadratic equations, factoring, positive and negative numbers, averages, percents, interest, ratios, and proportions, and translate word problems to algebraic equations.
Learn and implement the Pythagorean theorem.
*Twelve DVDs reinforce this course.
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CMATH for Borland C++ (32-bit) 4.0 description
CMATH is a comprehensive library for complex-number arithmetics and mathematics, both in cartesian and polar format (float, double, and extended precision). The implementation in Assembly language ensures superior speed, accuracy, and safety, as compared to other available complex class libraries with their inline or compiled C++ code. All CMATH functions may be called either from C with type-specific function names (e.g., cf_sin, cd_exp, pf_sqrt) or from C++ with overloaded function names (sin, exp, sqrt, etc.). They are optimized for Pentium/PentiumXX, but will run on computers down to 386+387. This version is for Borland C/C++ 4.0+ or BC++ Builder.
CMATH for Borland C++ (32-bit) 4.0
Brings the power of vectorized programming to the PC. Replacing loops over data arrays by the hand-optimized, Assembler-written vector and matrix functions of OptiVec can speed up program execution by 2-3 times and enhances accuracy and safety. More than 3500 functions for math, statistics, analysis, signal processing, matrix operations, curve fitting, etc. For CodeGear / Borland C++4.0+ or BC++Builder. Free Download
CMATH for Delphi 2006/2007 makes fast complex-number math functions (cartesian and polar) available in three precisions. This comprehensive library was written in Assembler for superior speed and accuracy. Free Download
CMATH is a comprehensive library for complex-number arithmetics and mathematics, both in cartesian and polar format (float, double, and extended precision). The implementation in Assembler ensures superior speed, accuracy, and safety, as compared to other available complex class libraries. All CMATH functions may be called from C or C++. For MS Visual C++ 5, 6, 2003, 2005, or 2008. Free Download
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Math Tutorial Lab
Tutorial Lab is located in 106 Ewing Hall
The Tutorial Laboratory provides tutorial support for many introductory math courses at the University of Delaware. This includes tutorial assistance in Math 010, Math 114, Math115, Math 117, Math 221 and Math 241. The lab is staffed by qualified undergraduate students and math graduate students.. Resources include previously administered exams, answer textbooks and a variety of math textbooks focusing on algebra and precalculus. In addition, the site contains one multi-media computer system connected to the internet. This computers can be used to access the departmental on-line resources, programs used in the student's courses and the World Wide Web. There is a laser printer available for student use.
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Algebra 2 Tutor teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry. It contains essential material to help students do well in advanced mathematics. Many of the topics in this series are used in other Math courses, such as writing equations of lines, graphing equations and solving systems of equations. These skills are used time and time again in more advanced courses such as Physics and Calculus. The Algebra 2 Tutor is a complete 15 lesson series covering all of the core topics in detail. What sets this series apart from other teaching tools is that the If a student has a problem with coursework or homework, simply find a similar problem fully worked on in the series and review for the steps needed to solve the problem. Students will be able to work problems with ease, improve their problem-solving skills and understand the underlying concepts of Algebra 2. This lesson teaches students how to multiply and divide expressions that contain radicals. Students are taught to simplify each radical expression individually and perform the multiplication or division on the simplified forms according to the rules of algebra. Numerous examples are presented to reinforce this material.
This product is manufactured on demand using DVD-R recordable media. Amazon.com's standard return policy will apply.
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In our standard Algebra 2 classes we don't do much with matrices, but I wanted my kids to see the power of matrices and their calculators for solving systems. This is step by step instructions and practice problems for the kids to work on individually, with a partner, or whatever you want. Sumbitted by MathTeacher44
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Introductory Algebra - 2nd edition
ISBN13:978-0077281120 ISBN10: 0077281128 This edition has also been released as: ISBN13: 978-0073406091 ISBN10: 0073406090
Summary: Introductory Algebraoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Introductory Algebrafocuses on solving equations and inequalities, graphing, polynomials, factoring, rational expressions, and radicals. Other topics include quadratic equations and an introduction to functions and complex numbers. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of dev...show moreelopmental level students. ...show less
Buy with Confidence. Excellent Customer Support. We ship from multiple US locations. No CD, DVD or Access Code Included.
$2860.00 +$3.99 s/h
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KatherinePlourde Goleta, CA
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COMAP, the Consortium for Mathematics and Its Applications, is an award-winning non-profit organization whose mission
is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and
business people to create learning environments where mathematics is used to investigate and model real issues in our world.
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The new series features 32 10-minute videos showing people from all walks of life using statistics in their work, as well as interactive tools, and guides.
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Mathematical Modeling Handbook I & II
The Mathematical Modeling Handbook is intended to support the implementation
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Consortium, published twice
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Mathematics: Modeling Our World (MMOW)
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Based on feedback from users of the first edition, COMAP has completed a major revision of Courses 1-3, now available in both print and CD-ROM.
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This is a free course in financial mathematics for upper high school and undergraduate students, with emphasis on personal finance. Teachers can make their own selections. Some of the lessons are articles published in various journals. Some are unpublished. This collection contains over forty lessons. A teacher can simply download and print a PDF, make copies, distribute them to students, and teach the lesson. Learn More
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Summary: James meticulou...show mores accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills. ...show less
James meticulous accuracy, patient explanations, and carefully graded problems.
Other Editions of Calculus : Concepts and Contexts Single Variable -Text Only:
0534410014Goodwill Discount Books North Las Vegas, NV
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an activity that provides the student with the graph of the derivative of a function and asks the student to use the...
see more
This is an activity that provides the student with the graph of the derivative of a function and asks the student to use the mouse to sketch the graph of the original function that passes through the origin.
TREEFROG is a system in which the user can solve mathematics problems (equations, integrals, etc.) and be guided by an...
see more
TREEFROG is a system in which the user can solve mathematics problems (equations, integrals, etc.) and be guided by an "electronic tutor״. The program allows the input of intermediate steps towards the solution and will check each step for correctness and give hints. The freely available demo focuses on linear equations.
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Cliff Reiter, Lafayette College, Mathematics
J gives my students the computational and visual tools they need to explore linear algebra. They can create and observe the effects of transformations, use transformations to create fractals, implement error-correcting codes on real messages, and do curve fitting.
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Presenting worked examples and solutions leading to practice questions, this helps students to learn maths. It features sample past exam papers for exam preparation, and includes regular review sections. It includes a CD ROM which contains what students need to motivate and prepare themselves.
Synopsis:
Edexcel and A Level Modular Mathematics C4 features: *Student-friendly worked examples and solutions, leading up to a wealth of practice questions. *Sample exam papers for thorough exam preparation. *Regular review sections consolidate learning. *Opportunities for stretch and challenge presented throughout the course. *'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. *Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. *Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary
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Functions and Change: Model Approach to...
9780618858040
ISBN:
0618858040
Edition: 1 Publisher: Houghton Mifflin Company
Summary: Intended for precalculus courses requiring a graphing calculator, Functions and Change emphasizes the application of mathematics to real problems students encounter each day. Applications from a variety of disciplines, including Astronomy, Biology, and the Social Sciences, make concepts interesting for students who have difficulty with more theoretical coverage of mathematics. In addition to these meaningful applicat...ions, the authors' easy-to-read writing style allows students to see mathematics as a descriptive problem-solving tool. An extended version of the successful Functions and Change: A Modeling Approach to College Algebra, this text includes three chapters of trigonometry.
Crauder, Bruce is the author of Functions and Change: Model Approach to..., published under ISBN 9780618858040 and 0618858040. Seven hundred fifty nine Functions and Change: Model Approach to... textbooks are available for sale on ValoreBooks.com, one hundred fifty eight used from the cheapest price of $87.18, or buy new starting at $104.97The course was great at giving concrete, real world examples. Actual data was used so you could understand why you were learning the material, and that makes a big difference in your understanding. The many examples help students learn for themselves the material.
The section on logs and exponentials really needs some beefing up with more basic abstract work. Too little time was spend on those subjects.
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Mathematics: A Brief Course
In this book, the author explains the history of mathematics by concentrating on the mathematics that was done and what it means in relation to other ...Show synopsisIn this book, the author explains the history of mathematics by concentrating on the mathematics that was done and what it means in relation to other mathematics and other areas of human endeavor. At all stages the reader will understand why people were interested in the problems that mathematicians were solving, and what consequences their solutions had for the further development of mathematics and its applications
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Synopses & Reviews
Publisher Comments:
Topics covered in this detailed review of algebra include general rules for dealing with numbers, equations, negative numbers and integers, fractions and rational numbers, exponents, roots and real numbers, algebraic expressions, functions, graphs, systems of two equations, quadratic equations, circles, ellipses, parabolas, polynomials, numerical series, permutations, combinations, the binomial formula, proofs by mathematical induction, exponential functions and logarithms, simultaneous equations and matrices, and imaginary numbers. Exercises follow each chapter with answers at the end of the book. Barrons continues its ongoing project of updating, improving, and giving handsome new designs to its popular list of Easy Way titles, now re-named Barrons E-Z Series. The new cover designs reflect the books Barrons E-Z books are self-teaching manuals focused to improve students E-Z books review their subjects in detail, using both short quizzes and longer tests to help students gauge their learning progress. All exercises and tests come with answers. Subject heads and key phrases are set in a second color as an easy reference aid.
Synopsis:
ALL THE ESSENTIALS IN ONE CLEAR VOLUME
High school-level algebra in the form of a fantasy novel Solving practical problems with algebra Hundreds of problems solved and explained Diagrams and amusing line illustrations
Synopsis:
'". . . a fine review for all ages packed with illustrations, cartoons, formulas and detailed explanations applying algebra to everyday life: perfect for any student!'"
'--The Midwest Book Review
Synopsis:
"Synopsis"
by Netread,
'". . . a fine review for all ages packed with illustrations, cartoons, formulas and detailed explanations applying algebra to everyday life: perfect for any student!'"
'--The Midwest Book Review
"Synopsis"
by Netread,
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Download "Training Skills" by Eric Garner for FREE. Read/write reviews, email this book to a friend and more...
Training SkillsIntegration involves ideas, with associated techniques, that are familiar from school mathematics; mastering this branch of mathematics is an essential requirement before moving to more sophisticated concepts and applications. The material in this text (Part I) introduces and develops the standard techniques of elementary integration and, in some cases, takes the ideas a little further. In Part II...
This is an HTML version of the ebook and may not be properly formatted. Please view the PDF version for the original work.
An excerpt is a selected passage of a larger piece, hence this is not the complete book.
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Math Competition LinksAmerican Mathematics Contest 8 (Middle School) The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (middle school) mathematics designed to promote the development and enhancement of problem solving skills. The examination provides an opportunity to apply the concepts taught at the junior high level to problems that not only range from easy to difficult but also cover a wide range of applications.
American Mathematics Contest 10 (Secondary Grades) The AMC 10 is a 25-question, 75-minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed. The main purpose of the AMC 10 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult.
American Mathematics Contest 12 (Secondary Grades) The AMC 12 is a 25-question, 75-minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed. The main purpose of the AMC 12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiple-choice format. Because the AMC 12 covers such a broad spectrum of knowledge and ability there is a wide range of scores. The National Honor Roll cutoff score, 100 out of 150 possible points, is typically attained or surpassed by fewer than 3% of all participants. The AMC 12 is one in a series of examinations (followed in the United States by the American Invitational Examination and the USA Mathematical Olympiad) that culminate in participation in the International Mathematical Olympiad, the most prestigious and difficult secondary mathematics examination in the world.
The Mandelbrot Competition (Secondary Grades) In those ten years the contest has grown to two divisions encompassing students from across the United States as well as from several foreign countries. Nearly half of the competitors in the USA Math Olympiad in the last couple of years have been Mandelbrot competitors. The Mandelbrot Competition is split into two divisions: Division A for more advanced problem solvers and Division B for less experienced students.
Mathcounts (Grades 7-8) Each year, more than 500,000 students participate in MATHCOUNTS at the school level. Those who do tell us that their experience as a "mathlete" is often one of the most memorable and fun experiences of their middle school years.
Math Problems of the Week (Grades K-12) The Problem of the Week is an educational web site that originates at the University of Mississippi. All the prizes are generously donated by CASIO electronics. All contest winners are chosen randomly from the pool of contestants that successfully solve that week's problem.
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1 Algebra Readiness, Cycle 1 The Effective Mathematics Classroom The Effective Mathematics Classroom What does the research say about teaching and learning mathematics? white paper_NL_2-1-10.pdf
Year 10 Sample Questions Alternative Education Equivalency Scheme (AEES) Year 10 English The following sample items show the types of items in the test, but do not ...
Math Content Research #6 - History of Algebra Gayle Nixon ED 654 Fall 2006 The history of algebra? Why should we consider teaching about the history of algebra when ...
Algebraic Thinking Math Project You Make the Call Page 1 The opportunity to examine and understand linear functions is a key component to ...
Introducing Linear Systems from the 10-part series OPERATION: ALGEBRA Produced by Noodle Logic 2000 Teacheru0027s Guide by Pamela Briskman Published and Distributed by ...
2006 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Board ...
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eBooks
Master calculus from the comfort of home!
Want to "know it ALL" when it comes to calculus? This book gives
you the expert, one-on-one instruction you need, whether you're
new to calculus or you're looking to ramp up your skills.
Providing easy-to-understand concepts and thoroughly explained
exercises, math whiz Stan Gibilisco serves as your own private
tutor--without the expense! His clear, friendly guidance helps
you tackle the... more...
This self-contained work introduces the main ideas and fundamental
methods of analysis at the advanced undergraduate/graduate level.
It provides the historical context out of which these concepts
emerged, and aims to develop connections between analysis and other
mathematical disciplines (e.g., topology and geometry) as well as
physics and engineering. A rigorous exposition, numerous examples,
beautiful illustrations, good problems, comprehensive... more...
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops... more...
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The text covers enough material for an advanced undergraduate or first-year graduate course. Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Many fine illustrations illuminate the text, along with numerous problems and solutions. 1972 edition.
Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available – yet covers all relevant material needed by, and appropriate to, the study of calculus at this level. It's conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate,... more...
Contemporary engineering design is heavily based on computer
simulations. Accurate, high-fidelity simulations are used not
only for design verification but, even more importantly, to
adjust parameters of the system to have it meet given performance
requirements. Unfortunately, accurate simulations are often
computationally very expensive with evaluation times as long as
hours or even days per design, making design automation using... more...
This book covers topics appropriate for a first-year graduate
course preparing students for the doctorate degree. The first half
of the book presents the core of measure theory, including an
introduction to the Fourier transform. This material can easily be
covered in a semester. The second half of the book treats basic
functional analysis and can also be covered in a semester. After
the basics, it discusses linear transformations, duality, the... more...
A new approach that treats complex analysis in a broad context
This book presents a new approach to one of mathematics' oldest
fields. It departs from the tradition of teaching complex
analysis as a self-contained subject and, instead, treats the
subject as a natural development from calculus. It also shows how
complex analysis is used in other areas, exploring connections
with calculus, algebra, geometry, topology, and other parts of
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Syllabus
Algebra II
J. van Veen
jvanveen@csuchico.edu
(530) 345-2330
Resident Staff: Nathan Evaro and Javier Herrera
COURSE DESCRIPTION:
Based on an initial written algebra assessment, this course will begin with the student from where he/she is and then take him/her through the basic concepts of algebra. The student will solve applicable real world problems and create weekly projects and reports. Homework will be checked for completion at the beginning of each class period. There will be three major exams: July 1, July 15, and July 27.
The student will also be evaluated on the extent of his/her mastery of some of the rules of academic success.
COURSE OBJECTIVES/GOALS:
Students will be able to solve and graph equations and inequalities.
Students will be able to solve systems of linear equations.
Students will demonstrate their knowledge of the rules for exponents and polynomials. Students will be able to reduce rational expressions and solve equations that include rational expressions.
Students will add, subtract, divide and multiply radical expressions.
Students will be able to use the quadratic formula.
Students will demonstrate some knowledge of logarithms by calculating the relative strength of earthquakes.
Students will explore entomology through the lens of mathematics.
Students will understand why Maya-Aztec math is considered to be the first modern system of math.
Students will write a coherent technical report.
Students will demonstrate their understanding of some of the rules of academic success:
Language – formal register, casual register
Time – delayed gratification, decisions made for the moment
Social Emphasis – self governance and self sufficiency, social inclusion
Transition to new peer group – opportunity, pain
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Book summary
The Dugopolski Precalculus series for 1999 is technology optional. With this approach, teachers will be able to choose to offer either a strong technology-oriented course, or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility. College Algebra and Trigonometry is designed for students who are pursuing further study in mathematics, but is equally appropriate for those who are not. For those students who will study additional mathematics, this text will provide the skills, understanding, and insights necessary for success in future courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Additionally, the focus on problem solving that is a hallmark of this text provides numerous opportunities for students to reason and think their way through problem situations. The mathematics presented here is interesting, useful, and worth studying. One of the author's principal goals in writing this text was to get students to feel the same way. [via]
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including algebra 1, algebra 2 and geometry algebra 1, algebra 2 and calculus algebra 1, algebra 2 and geometry
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College Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Conics; Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more. For individuals... MORE with an interest in learning algebra as it applies to their everyday lives. This text is highly dependable, having been fine-tuned over many years. Hallmarks are accuracy, precision, depth, strong student support and abundant, thorough, varied exercise sets. This title is fairly traditional and has optional graphing calculator coverage throughout. Part of a four title series.
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Elementary Algebra - 8th edition
Algebra is accessible and engaging with this popular text from Charles ?Pat? McKeague! ELEMENTARY ALGEBRA is infused with McKeague?s passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague?s attention to detail and exceptionally clear writing style help yo...show moreu to move through each new concept with ease. Real-world applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book?s multimedia learning resources, including ThomsonNOW for ELEMENTARY ALGEBRA, a personalized online learning companion49 +$3.99 s/h
Acceptable
GWBooks Vancouver, WA
A readable copy. All pages and cover are intact. Dust jacket is torn or missing. The book has moderate to heavy wear. Edges and/or covers are dirty; Covers have some wear. The corners of the covers ar...show moree bent
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Middle School Mathematics
The middle school math curriculum is aligned to the Common Core Standards. Students learn and understand math skills and concepts through problem solving, communicating, collaborating, creativity, and analytical thinking. The middle school mathematics curriculum utilizes engaging interactive problems and motivating everyday situations to help students understand math concepts.
The Common Core Standards provide a listing of essential core content to be taught and learned. They are designed to guide the planning of instruction and to anchor the assessment of learning. The Alternate Content Standards for each area expand the developmental spectrum of the Common Core Standards for students with significant disabilities while guiding instruction and assure all students access to the general education curriculum.
An accelerated math curriculum, including high school Algebra I and Accelerated Geometry, is available to students who meet the enrollment criteria.
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Presents articles showing the math behind our daily lives. Explains how and why math works, and allows readers to better understand how disciplines such as algebra, geometry, calculus and others affect what we do every day.
New additions! Have complete access to the archives and current issues of the National Geographic Magazine and National Geographic Kids plus books, 500 downloadable images and videos. One search term yields results from all aspects of the National Geographic Virtual Library!
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Beginning Algebra
9780321784919
ISBN:
032178491X
Edition: 6th Revise Pub Date: 2011 Publisher: Pearson Education
Summary: Written by Elayn Martin-Gay, Beginning Algebra was released in 2011 in this 6th revised format. Complete with plenty of new material compared to earlier versions, you can find out more about getting to grips with algebra and learning how to start in the right way. Published by Pearson Education, this text book is available at the cheapest prices. Buy Beginning Algebra online now and take advantage of the lowest price...s on previously owned text books. Sell back your copy now if you already own it and make the most of a good deal. Try Valore Books for Beginning Algebra deals now.
Martin-Gay, Elayn is the author of Beginning Algebra, published 2011 under ISBN 9780321784919 and 032178491X. Seven hundred twenty Beginning Algebra textbooks are available for sale on ValoreBooks.com, two hundred five used from the cheapest price of $64.36, or buy new starting at $123.85ALTERNATE EDITION: New Hardback Annotated Instructors Edition, All text is same as student edition but may contain additional information or answers. In Stock, Based in Ohio. Ships SAME or NEXT [more]
ALTERNATE EDITION:
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Mathematics for Elementary Teachers: A Contemporary Approach
The "Essentials" version of Musser, Burger & Peterson's best-selling textbook it brings together the many facets of elementary and middle school ...Show synopsisThe "Essentials" version of Musser, Burger & Peterson's best-selling textbook it brings together the many facets of elementary and middle school mathematics in one concise volume. With a focus on providing a complete understanding of mathematics that translates immediately into the classroom, the authors use their proven formula to present all the core subjects, including: Introduction to Problem SolvingSetsWhole NumbersNumerationNumber TheoryFractionsDecimalsRatioProportionPercentIntegersRational NumbersReal NumbersAn introduction to AlgebraStatisticsProbabilityGeometric ShapesMeasurement Material presented is supported by eManipulative activities, on-line problem-solving tools, and an expanded resource-rich Web site
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Elementary Statistics : A Brief Version with MathZoneElementary Statistics: A Brief Version, 3rd edition is a shorter version of the popular text Elementary Statistics: A Step by Step Approach, 5th edition. This softcover edition includes all the features of the longer book, but is designed for a course in which the time available limits the number of topics covered. The book is written for general beginning statistics courses with a basic algebra prerequisite. The book use a non-theoretical approach, explaining concepts intuitively and teaching problem solving through worked examples step-by-step.
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Applied Calculus:The fourth edition gives readers the skills to apply calculus on the job. It highlights the applications' connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically. The applied exercises challenge them to apply the math they have learned in new ways. This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do.
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Rent Applied Calculus 4th edition today, or search our site for Deborah textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Wiley.
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The primary purpose of this fourth edition of Linear Algebra is to present a careful treatment of the principal topics of linear algebra and to illustrate the power of the subject through a variety of applications. Our major thrust emphasizes the symbiotic relationship between linear transformations and matrices. However, where appropriate, theorems are stated in the more general infinite-dimensional case. For example, this theory is applied to finding solutions to a homogeneous linear differential equation and the best approximation by a trigonometric polynomial to a continuous function.
Although the only formal prerequisite for this book is a one-year course in calculus, it requires the mathematical sophistication of typical junior and senior mathematics majors. This book is especially suited for a second course in linear algebra that emphasizes abstract vector spaces, although it can be used in a first course with a strong theoretical emphasis.
The book is organized to permit a number of different courses (ranging from three to eight semester hours in length) to be taught from it. The core material (vector spaces, linear transformations and matrices, systems of linear equations, determinants, diagonalization, and inner product spaces) is found in Chapters 1 through 5 and Sections 6.1 through 6.5. Chapters 6 and 7, on inner product spaces and canonical forms, are completely independent and may be studied in either order. In addition, throughout the book are applications to such areas as differential equations, economics, geometry, and physics. These applications are not central to the mathematical development, however, and may be excluded at the discretion of the instructor.
We have attempted to make it possible for many of the important topics of linear algebra to be covered in a one-semester course. This goal has led us to develop the major topics with fewer preliminaries than in a traditional approach. (Our treatment of the Jordan canonical form, for instance, does not require any theory of polynomials.) The resulting economy permits us to cover the core material of the book (omitting many of the optional sections and a detailed discussion of determinants) in a one-semester four-hour course for students who have had some prior exposure to linear algebra.
Chapter 1 of the book presents the basic theory of vector spaces: subspaces, linear combinations, linear dependence and independence, bases, and dimension. The chapter concludes with an optional section in which eve prove that every infinite-dimensional vector space has a basis.
Linear transformations and their relationship to matrices are the subject of Chapter 2. We discuss the null space and range of a linear transformation, matrix representations of a linear transformation, isomorphisms, and change of coordinates. Optional sections on dual spaces and homogeneous linear differential equations end the chapter.
The application of vector space theory and linear transformations to systems of linear equations is found in Chapter 3. We have chosen to defer this important subject so that it can be presented as a consequence of the preceding material. This approach allows the familiar topic of linear systems to illuminate the abstract theory and permits us to avoid messy matrix computations in the presentation of Chapters 1 and 2. There are occasional examples in these chapters, however, where we solve systems of linear equations. (Of course, these examples are not a part of the theoretical development.) The necessary background is contained in Section 1.4.
Determinants, the subject of Chapter 4, are of much less importance than they once were. In a short course (less than one year), we prefer to treat determinants lightly so that more time may be devoted to the material in Chapters 5 through 7. Consequently we have presented two alternatives in Chapter 4—a complete development of the theory (Sections 4.1 through 4.3) and a summary of important facts that are needed for the remaining chapters (Section 4.4). Optional Section 4.5 presents an axiomatic development of the determinant.
Chapter 5 discusses eigenvalues, eigenvectors, and diagonalization. One of the most important applications of this material occurs in computing matrix limits. We have therefore included an optional section on matrix limits and Markov chains in this chapter even though the most general statement of some of the results requires a knowledge of the Jordan canonical form. Section 5.4 contains material on invariant subspaces and the Cayley-Hamilton theorem.
There are five appendices. The first four, which discuss sets, functions, fields, and complex numbers, respectively, are intended to review basic ideas used throughout the book. Appendix E on polynomials is used primarily in Chapters 5 and 7, especially in Section 7.4. We prefer to cite particular results from the appendices as needed rather than to discuss the appendices independently.
DIFFERENCES BETWEEN THE THIRD AND FOURTH EDITIONS
The principal content change of this fourth edition is the inclusion of a new section (Section 6.7) discussing the singular value decomposition and the pseudoinverse of a matrix or a linear transformation between finite-dimensional inner product spaces. Our approach is to treat this material as a generalization of our characterization of normal and self-adjoint operators.
The organization of the text is essentially the same as in the third edition. Nevertheless, this edition contains many significant local changes that improve the book. Section 5.1 (Eigenvalues and Eigenvectors) has been streamlined, and some material previously in Section 5.1 has been moved to Section 2.5 (The Change of Coordinate Matrix). Further improvements include revised proofs of some theorems, additional examples, new exercises, and literally hundreds of minor editorial changes.
We are especially indebted to Jane M. Day (San Jose State University) for her extensive and detailed comments on the fourth edition manuscript. Additional comments were provided by the following reviewers of the fourth edition manuscript: Thomas Banchoff (Brown University), Christopher Heil (Georgia Institute of Technology), and Thomas Shemanske (Dartmouth College).Read more › operators itself
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For which grade level(s) and specific populations was the curriculum developed?
8th grade Math regular education.
Who developed the curriculum and what expertise did they have in the content area?
Glenda Lappan-Professor in the Department of Mathematics at Michigan State University
James T. Fey-Professor of Curriculum and Instruction and Mathematics at the University of Maryland William M. Fitzgerald-(deceased) was professor in the Department of Mathematics at Michigan State University Susan N. Friel-Professor of Mathematics Education School of Education at the University of North Carolina
Elizabeth Difanis Philips-Senior Academic Specialist in the Mathematics Department of Michigan State University
What materials or other resources did they use in the curriculum development?
Field tested by over 100 classroom teachers at 49 school sites in 12 states and the District of Columbia
Were teachers involved in the development? Did teachers have an opportunity to review or pilot the curriculum before its release? Is there any indication that there will be ongoing support for teachers using the curriculum?
Teachers were instrumental on helping review the textbook and suggest improvements. The University of Michigan runs a training session during the summer. Having spoken to some of the authors I know they are very passionate about quality math education and are continually working towards improvement of the series.
Is the relationship between and among the various sections of the document(s) clear and logical?
The curriculum is broken into 8 separate books. Each book focuses on specific goals. Often skills or strategies used when working on one skill will transfer or be used to discover new skills in another section of the book.
Is there a system that will allow users to add details and set objectives for instruction based on the document?
Lessons are suggested based on either a 40 minute math period or a block schedule. Lessons of course have objectives set, but not all lessons have to be taught (the book even suggests which lessons to skip if necessary)
Does the document have a wide range of content that could be used as a scope and sequence by a curriculum committee at the system or school level?
The series was designed specifically to meet curricular the needs of a school.
How would the document help a classroom teacher plan?
A teacher could just follow the books from cover to cover and teach a decent year of 8th grade math. The books also explain the math concept behind each lesson giving the teacher the opportunity to understand the lesson objective more fully.
If the teacher looks at each individual book as a unit and follows the pacing guide within the book the program plans itself. With the supplemental CD-ROM it will even create a lesson plan complete with alignment to state standards.
It has been my experience teaching this book that some of the lessons examples are kind of contrived, but that the teacher can substitute alternative stories and or situations that can involve the students more.
Why was the document developed? (Think about: Was there a problem to be solved or a need that had to be filled?)
The Connected Math text was developed specifically as a better method of teaching middle school math. It is completely student-centered, allowing the math students to "discover" math concepts on their own. Each lesson or "investigation" is a mini science lesson asking students to answer questions that will hopefully illuminate a skill. Each section, a group of 4 or 5 lessons, will have an overall theme and connect together to create one concept. Each book has 4 or 5 sections that are all connected with a common theme, such as quadratic relationships.
II:Content of the Curriculum Document
Questions
Analysis
Does the document describe a philosophical basis for the curriculum document? Does it appear to be connected to a specific learning theory? Is there a statement of vision for the curriculum? What definition of curriculum did the authors use?
"What to teacher" and "How to teach it" are inextricably linked. (p. 2 Implementing and teaching guide) The Connected math curriculum is based on research from cognitive sciences mathematics education and education policy and organization. Overall the curriculum is a problem based curriculum.
Their definition seems to be: what is taught, how it is taught, skills, conceptual understanding and assessments in the form of quizzes, tests, and projects.
Does the document describe in detail the scope and sequence of the curriculum? What content did the authors think was the most important? Does the document describe a time frame for implementing the curriculum?
There is a very detailed scope and sequence chart for all grades 6th – 8th. The 8th grade course of study is almost entirely review of previously learned material It does however have a very broad reach, covering almost every topic in the curriculum.
What skills are needed before the curriculum is taught?
Basic multiplication and division skills are expected before the 6th grade section of the curriculum is introduced. If students learn using the Connected Math curriculum by 8th grade they are expected to have the skills necessary to achieve the tasks.
Is there a clear alignment with national standards in the content area? Describe how they are aligned.
The Connected Math curriculum is standards based. The books I have are older than the Common Core Standards, but from what I have heard and seen they should already meet the new standards.
Is there an integration of appropriate technologies to maximize teaching and learning?
The original curriculum can be taught using only pen, paper, and an overhead projector.
How could the curriculum and learning environment be designed to meet ISTE's NETS Standards for Administrators and Teachers?
How is the content of the curriculum aligned with your state curriculum (such as the Maryland Voluntary State Curriculum)? Give examples.
Each lesson has been reviewed by experts and aligned to specific standards in the state curriculum. The curriculum does meet all of Illinois standards, some better than others.
Is there support for differentiated instruction?For what type of students, e.g. special needs, gifted?How is the curriculum differentiated?If there are no suggestions for differentiated instruction, what would you recommend? Are there recommendations for accommodations for students with special learning needs? Are there any suggestions for assistive technology resources?
The curriculum is based on cooperative groups and discovery based learning. Each unit usually begins with concrete hands on activity and builds towards a concept. There is an entire special needs book filled with alternative activities for students who have difficulty with the regular curriculum.
I also suggest suing some video taped lessons for students to watch online when they need or want it. Some teachers do this with Compass Learning and find it very helpful.
Is there a multicultural approach to the curriculum? Is the curriculum appropriate for your school and community? Can you "see" all students in the curriculum?
I don't know if it is intentionally multicultural, but it does work well with our population.
Is there evidence of interdisciplinary connections in the curriculum? Do students have opportunities to apply what they are learning in real world situations?
There is some interdisciplinary connections, but there could be more.
Does the curriculum provide sample lesson plans?
Yes. The curriculum has full lesson plans complete with alignment to the state standards.
Does the curriculum provide assessments (formative and summative) to measure mastery of curriculum?
Yes. The curriculum has full quizzes, tests, and projects for assessments.
Is there a suggested plan for implementing the curriculum?
Yes. The curriculum is separated into 8 books with each book roughly equivalent to a unit.
Is there a recommended textbook or other text resources?
Yes. The curriculum is designed to go with the Connected Mathematics textbooks.
Are additional materials needed so that the curriculum is effectively implemented?Are suggestions provided, e.g. visual, literature, manipulative, or technology resources?
The curriculum comes complete with blackline masters and overhead transparencies. I think the student-centered curriculum is difficult for most teachers and support in model teaching, suggested lessons, and outside resources might be helpful.
What professional development will be provided to teachers? Who will be responsible for the professional development? How could the professional development be provided to meet Maryland or National Staff Development Council (NSDC) Standards for Professional Development?
Currently our district has none. We can buy some from the publisher. More likely we will develop our own. We are in the midst of planning a Math Coach position. The person in the position would work in a non-evaluative role to observe and help individual math teachers. He/she would create professional development opportunities such as Lesson Studies, Looking At Student Work, and other teacher centric professional development opportunities.
Assignment #2
Curriculum Analysis
Written Report
This paper analyzes the Waukegan Public Schools math curriculum. Waukegan bases their math curriculum almost entirely on the Connected Mathematics curriculum.The Connected Math curriculum is a full curriculum developed by mathematicians and math educators. It was specifically designed to meet the National Council of Teachers of Mathematics (NCTM) standards for math.The Connected Math curriculum uses a problem-based approach to teaching mathematics. Students are not taught the procedures for solving math problems, but are instead presented with problem situations that require mathematics to solve. In this way students discover the main concepts fundamental to middle school mathematics.
Currently Connected Math is in its second edition. The problems and lessons found within the curriculum have been developed and refined through actual use in classrooms around the country. The philosophy of Connected Math begins with the understanding that "what to teach" and "how to teach it" are inextricably linked. (Fey, Fitzgerald, Friel, Lappan, Phillips, 2006, p. 2). The overarching Goal of Connected Math (Fey, et al, p. 6) is:
All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness, and technical proficiency.
Connected Math describes itself as a problem based curriculum (fey, et al. 2006, p. 3) however the program can be more accurately described as discovery centered or constructivist as it attempts to set up situations for students to discover basic concepts of mathematics. Used as designed Connected Math lessons ask students to work in small groups to explore problems in depth. The emphasis on depth should allow students to build understanding and the ability to transfer knowledge and skills across concepts.
The Connected Mathematics curriculum is designed to be as teacher friendly as possible. In practice however it is not very teacher friendly. The textbook for Connected Math is broken into eight units designed to last on average four weeks. Each unit is designed to cover one major concept in depth, and to develop related skills. Each unit has a student book and teacher book. Within the teacher copy are detailed goals of the unit, an overview of the mathematics in the unit, a background of the mathematics in the unit, and connections between prior learning and future learning.Each unit has a suggested pacing guide complete with formative and summative assessments, a unit project is suggested instead of the test, but both are provided. This holistic view of math education is radically different than most math textbooks and I think leads to the difficulties most teachers have with teaching Connected Math, at least in my experience.
Many math textbooks divide the math curriculum into discrete skills. Each skill is taught in isolation. The separation of skills makes it easier for the teacher to focus each lesson. On the other hand this seems to lead to a common complaint from math teachers that students just apply procedures to problems in an attempt to find a solution. Often by high school students have memorized so many procedures that they get confused and misapply them. Connected Math asks students to recognize patterns and create their own procedures for solving them. The teacher's job is more to help students discover and formalize the procedures. Teachers not taking the time to formalize procedures after discovery would seem to lead to the chief Connected Math complaint of students not knowing how to "do math".
Having worked in several schools that implement this program I can see many areas that are ready for improvement. In the one school I taught in which teachers were given a week long professional development training the implementation of the curriculum was very similar to what is suggested by the authors. In the schools where teachers were never trained on the implementation of Connected Math the implementation varies immensely.
With Connected Math being so radically different from the normal mathematics textbooks professional development and an understanding of the philosophy behind Connected Math is of paramount importance. I see many teachers give up on Connected Math before seeing results because "some students are not highly motivated and tend toward procrastination and socializing rather than doing schoolwork and homework" (Ray, 2011
In an effort to help teachers understand and implement Connected Math I would change the teacher's manual. The average student lesson might be one to two pages in length while the teacher's manual will have up to ten pages of dense writing and still leave teachers confused as to what they are actually teaching.
For each lesson the teacher's manual has a full explanation of the lesson complete with goals, suggested discussion questions, and illustrations of the multiple ways students may solve each problem. The authors then follow that up with, the lesson at a glace, which is the same information in more condensed form. I would do away with the second part entirely. Instead I would include an annotated version of the student text. The annotations would include suggestions for student prompts when they get stuck, what are some of the interesting student thoughts to listen for and share during summary, and information on why these particular questions were asked and how they lead to building knowledge.
One of the weaknesses of Connected Math is its complete lack of technology. I understand, if I remember correctly from my professional development many years ago, that the authors did this intentionally so that Connected Math could be implemented at any school, but times have changed. There are many ways that technology can be used to enhance the Connected Math curriculum without making it too expensive. One simple way would be the use of multimedia in the launch section of the lesson to create an engaging anticipatory set as described by Madiline Hunter
Dan Meyer explores in depth ways to use multimedia to get students to ask their own motivational questions. In a series of posts on his blog tagged What Can You Do With This?. Dan holds an ongoing conversation with math educators on specific problems that can be posed to students through multimedia to start a math conversation. I find this very similar to the design of the lessons in Connected Math.
The ongoing conversation with Dan Meyer and other math teachers and bloggers brings up another limitation of the Connected Math curriculum. Connected Math is very static. The books and lessons haven't changed much in the last five years. There is little supported feedback from educators about using the curriculum in the classroom today. It would be very helpful for teachers to be able to see and discuss the implementation of the Connected Math curriculum in today's classroom. What ways are teachers including technology? What lessons are more difficult for students to grasp? What discussion starters work? What summaries are most effective? An open and active online forum to share should be included in the purchase of the Connected Math curriculum.
This isn't to say that Connected Math is completely devoid of any modern technical support. The Connected Math Project at Michigan State University ( does contain many resources ranging from professional development for teachers to homework help for students. The connected math page at Pearson Hall also contains some web links for parents, students, and teachers (
These resources are very nice additions to the curriculum. However, they are additions to the curriculum and not a part of the curriculum. Few of the technologies are designed to be used in the classroom. Rather the technology is mostly designed to be a support for students who need extra help or for teachers who would like to know more about teaching using Connected Math. Some third parties have also created some interactive activities which can also be used in the classroom. If Connected Math were to be funded for a third major revision I would assume that this lack of interactive technology in the classroom would be a major focus of the program.
Many of the initial lessons in Connected Math are based around an exploration or experiment. These are prime areas for inclusion of technology. There is some evidence of technology inclusion by means of web codes in the student books. By visiting the Pearson web site and using the code students can find material extending the classroom learning. This seems to be more of an after thought or an addition in later printings. There is no mention of the web codes in the teacher's edition.
Much of the web content would be useful in the classroom. At the very least it would be an alternative method of introducing the concepts for students who struggle with hands on activities. Technology could also be used to allow students to share between classes, schools, or even districts. Lastly, the Connected Math curriculum asks students to do a lot of reflection writing. Technology such as wikis and blogs are perfect forums for students to share their mathematical learning.
The most important consideration when using Connected Mathematics, is the support of the teachers. Implementing the Connected Math curriculum requires long term consistency, especially for students that are used to working quietly alone at a desk. Learning how to work in a learner-centered curriculum is the most difficult aspect of the program for most students and teachers.
If I were to write my own mathematics curriculum I would start with Connected Math. I think they identify the important concepts necessary for middle school math and cover them well. I also appreciate the emphasis on depth of knowledge as opposed to a spiraling curriculum. I have always felt that using a spiraling curriculum, where a concept is introduced then revisited again and again in later years, was an effective way to teach mathematics. What I realized after studying this curriculum is that the spiraling model doesn't allow students to fully integrate the skills and concepts learned. When they spiral back it is necessary for the teacher to reteach basic skills.
This reteaching of procedures for solving problems, I think, is a major contributing factor to student emphasis on brute force attempts to solve problems.Students learn a procedure for solving a problem, but they don't fully understand why or how it works before moving on to the next skill. In subsequent years students are asked to recall the procedure for solving those types of problems. If the students don't remember how to solve the problem they are reminded of one of many possible procedures and expected to use that procedure to develop further knowledge.
As a math teacher I find the philosophy that is the basis of Connected Math to be an excellent match with my own and I would recommend its continued use in our district. I also reviewed the district created pacing guide, which is based on the Connected Math curriculum and also includes some extensions.
I think it would very useful for the district to review the pacing guide and develop a district curriculum team to finish the pacing guide. At the moment the pacing guide does a great job of laying out an outline of the units to be taught during the year. The pacing guide does suggest the schedule and order of the books to be taught, but after talking with the Director of School Improvement, who also headed the writing of the pacing guide, the scheduling and time frames dictated in the guide are not meant to be a strict schedule, but rather a general guideline. She has mentioned on several occasions that she has attempted to communicate to building principals the necessity of a fluid schedule for Connected Mathematics.
The Director of School Improvement, who is my mentor and my direct supervisor, and I have talked often about the math curriculum. During our informal discussions we have brought up the topic of math curriculum and the pacing guide many times.In general we feel that the guide is a great start, but it is unfinished. Funding has been difficult of find over the last couple of years, which has stalled to completion of the project.
Currently the pacing guide is a table linking the school calendar to the lesson focus, text and supplemental resources, alignment to Illinois State standards, instructional tips, and assessments.We would like to finish adding supplemental resources and include technological resources. We would like to include an interactive resource such as a wiki that would allow teachers to share what they are using in their own classrooms. Finally, we would also like to create an observation guide for administrators.
Too often we have administrators who look at the pacing guide as a rigid structure for teachers to follow. For example they would look at the pacing guide for day 35 of the school calendar and expect to see teachers teaching a specific lesson. This is not what was intended during the creation of the pacing guide. Instead on a specific day during the school year all math teachers should be near a specific lesson, but there should be variation depending on the strengths and weaknesses of the specific class.
Overall, the Waukegan school district has made a good choice in adopting the Connected Math curriculum. It is a strong student-centered math curriculum that does meet all of the current state standards and soon to be adopted Common Core standards. The district has made a great start in implementing the curriculum by creating a solid pacing guide. There are three areas of concern. The first area of concern is the integration of technology into the curriculum. The second area of concern would be a stronger more systematic implementation of professional development concerning the implementation of Connected Math in the classroom. The final area of concern would be to finish the pacing guide and add an in interactive resource for teachers to share what works in the classroom.
Wednesday, February 16, 2011
Would you like to learn more about common core and its effects on our school. Pearson (yes the people who publish our textbooks) are giving a series of free webinars. If you go to one please write up and add it to a page on our wiki. Here or here
Monday, February 14, 2011
· As a school administrator and instructional leader, what instructional technology would you expect to see in the written, taught, and tested curriculum of a school or school district striving to meet the needs of 21st century learners?
·Taught curriculum
oI would expect to see extensions and resources for the written curriculum online.
oI would expect that every teacher in my school to create at least one detailed unit complete with differentiations and share it online.
oI would expect to see a discussion forum for the teachers. A place where they can reflect on each others lessons, share what they learned, make suggestions for improvement, and more.
oI would expect to see teachers using laptops and projectors on a regular basis.
oI would expect that students would be given the opportunity to use web 2.0 tools to create, collaborate, and share.
oI would expect to see a computer based, or preferably game based program designed and used to give students individualized instruction at their own level.
·Tested curriculum
oI would expect to see a test generator.
oI would expect that students would be given the opportunity to use web 2.0 tools to create, collaborate, and share. Less emphasis on tests and more on authentic assessments
oI would expect to see digital portfolios
·Written curriculum
oI would expect to see the entire published curriculum also in electronic form, even e-book form for my students.
oI would expect to see curriculum mapping software used to unify the entire curriculum.
oI would expect to see a discussion forum for the teachers so they can log and suggest revisions to the curriculum
oI would expect there to be a way for my teachers to get just in time PD if and when they need it.
· What instructional technology would you promote to differentiate instruction for all learners?Consider some of the tools and strategies outlined in the Jacobs' text.
Different representation
·I would promote the use of universal access technology built into most modern computers. Text-to-speech speech-to-text, contrast, zoom, etc…
·I would promote the use of technology that allows teachers to present materials in a variety of ways such as podcasts, or video.
·I would promote the use of individual technologies such as tablets, laptops, or smart phones to allow students to receive instructions.
Different engagements
·I would promote a student centered programming such as Compass Learning or Read 180 that gives student instruction at their level.
·I would promote the use of individual technologies such as tablets, laptops, or smart phones to allow students to participate in class. Polleverywhere.com, voki, voicethread, etc….
Different action and expression
·I would promote the use of web 2.0 technologies that allow students to publish authentic work to the world. Blooging, schooltube. Etc..
·I would promote tools that allow students to share and discuss with other students outside their classroom and school. Wiki, google docs, etc….
·I would promote the use of tools that allow students to participate in authentic activities at times even experts, authors, or other interested parties. Skype, diigo groups etc…
I think most people have heard of these, but not everyone knows what they are and how to use them. I'm not really going to explain that here. I have however found a great power point that is very easy to explain. A direct link to the power point is here. The Alliance for the Improvement of Mathematics site is here
What I will do is explain how to make your own set of tiles.
Start with four different colors of paper. Card stock would probably be best. Red, blue and yellow green is suggested. The x tiles will be red and blue and the y tiles will be yellow and green. One color will be for positive and one color for negative. I would also laminate when done if you can.
When making the tiles the important part to remember is that the long side of the tile should be immeasurable. This is easily enough to figure out by simple using any sort of diagonal on graphing paper. Make the short side 1cm in length. Make two different size tiles. This is important because the immeasurable length means that the tile is an unknown. When introducing the tiles to the students for the first time let them measure all they want and eventually they should come to the determination that the length of one is x and the length of the other is y.
The next two tiles to make are squares that are x2 and y2. Finally you will want 1cm by 1cm squares of white. (You can substitute centimeter cubes for this) If you want you can also include 10cm long strips.
The tiles can be used for everything from adding and subtracting integers to multiplying and dividing polynomials.
Finally, I want to end with a great video from Dan Meyer. He is sharing his application video for Apple's Distinguished Educator Program. It's a fun watch and because he uses Vimeo it is visible on school computers.
Tuesday, February 1, 2011
Did you see this cool activity created by our own Mr. Foster? Of course not I haven't shown it to you yet.
A simple excel file Students are to label points on a number line. Then move numbers around to make the columns equal zero. Great for practice in adding integers, but also great for building the concept of finding zeros,
I'm also thinking it can help build the concept of equations, but putting the zero block in the center and asking students to add or subtract from the ends.
Feel free to play with it.
We were also talking about setting up a way for students to access these files and turn them in on their own. We are thinking a separate google doc for each student. You can access the document here. When you share the link (a setting in google docs) your students don't need an account to view the page.
There is also a company Zoho.com with many of the same features as google docs. I uploaded the document there also. I think the formatting looks a lot better than it did in google docs. In Zoho you can share the document with other Zoho users (free plan even) but you can't share outside of Zoho unless you buy the premium plan. They also have an option of sharing to a group.
One idea we did have is to differentiate the lessons and give some students more challenging spreadsheets. This of course would mean sending each one to individual students negating the advantage of a group.
One final thought is that sharing the documents will mean a link somewhere. Either a hyperlink in a class blog (try to find a blog that isn't blocked). The other option I can think of is a URL shortener.
A service like tinyurl.com will shorten the URL (the address of the web page) to something such as It is even possible to customize the last part of the link. Perhaps something like a name and a date. Then you can assign each student a different spreadsheet and they can remember the URL easily.
Enjoy your snowday, and share some of your favorite lessons.
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Authored by members of the SCC Math Department faculty, it's considered the very best of professional-grade OER. Intermediate Algebra, now in its third edition, is one of four open workbooks that are core teaching resources at Scottsdale Community College. Along with Basic Arithmetic, Introductory Algebra and College Algebra, it has been used by thousands of students, saving them upwards of $150,000 per semester.
The SCC Math faculty realized early on the need for resources to support the learning of hybrid students outside of class. They made a collective decision to adopt OER for the benefit of their students. Faculty members developed and maintain the workbooks at virtually no cost to students. The faculty has enhanced the workbook by adding a suite of ancillary materials that include online help sessions, quizzes, and instructors' guides. All four workbooks are available at
Dr. Donna Gaudet, Chair of the Mathematics Department at Scottsdale Community College said, "Intermediate Algebra consists of 12 lessons. Each lesson includes a MiniLesson―topic coverage via video examples and You Try problems for students―Practice Problems, and an end-of-lesson Assessment. The workbook can be used as a stand-alone resource or in conjunction with an online homework/assessment system called MathAS, also an open source system. This makes it a one-stop shop for Scottsdale Community College students to learn everything they want to know about Intermediate Algebra."
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About Open Doors Group – College Open Textbooks
Open Doors Group (ODG) is a collaborative of individuals and educational, non-profit, for-profit and government institutions. Its purpose is to prepare students for the future by promoting, producing and distributing Open Educational Resources (OER); supporting students and educators in adopting and using OER; expanding access to education for all learners; and researching and evaluating the impact of OER. ODG sponsors a number of projects aimed at achieving these goals. ODG can be found at College Open Textbooks, a project of ODG, seeks to drive the awareness, adoption, access, and affordability of open textbooks, primarily at the two-year college level. The COT website links to more than 700 open textbooks in twenty-four subject areas, many of which are peer-reviewed. COT also sponsors a number of Communities of Practice, self-supporting peer groups of educators who wish to support the adoption of OER in particular subject areas.
For more information about this book and others published by ODG-COT, contact :
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College Algebra: Concepts Through Functions - 2nd edition
Summary: College Algebra: Concepts through Functions, Second Edition embodies Sullivan/Sullivan's hallmarks-accuracy, precision, depth, strong student support, and abundant exercises-while exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals:preparing for class,practicing their homework, and reviewing the concepts. After using this book, students ...show morewill have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus. KEY TOPICS: Functions and Their Graphs; Linear and Quadratic Functions; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Conics; Systems of Equations and Inequalities; Sequences; Induction; the Binomial Theorem; Counting and Probability MARKET: For all readers interested in college41.00 +$3.99 s/h
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Critical Thinking and Mathematical Problem Solving
With Alan Schoenfeld and Richard Paul. Good for all levels of math and science instruction. Topics include: student attitudes toward mathematics, the importance of real-world math problems, the difference between "reasoning mathematically" and performing calculations, and teaching for discovery vs. lecturing. (PBS)
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Self-Check Quizzes randomly
generate a self-grading quiz
correlated to each lesson in your textbook. Hints are available
if you
need extra help. Immediate feedback that includes specific
page
references allows you to review lesson skills. Choose your
chapter and
lesson from the list below.
Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to generate a different representation given one representation of data such as a table, graph, equation, or verbal description.
8.14 Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
8.14.A
identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;
select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and
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MAT 308
Theory of Games
Course info & reviews
The mathematical concept of a game is an abstraction which encompasses conflict-cooperation situations in which strategy (not just chance) plays a role. Central topics of the theory and some of its applications will be discussed. Introductory aspects of algorithmic game theory will be covered, if time permits.
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McGraw-Hill's 500 College Linear Algebra Questions to Know by Test Day wealth of problem-solving practice in the format that you want! This book is the ideal way to sharpen skills and prepare for your exams Get the problem-solving practice you need with McGraw-Hill's 500 College Linear Algebra Questions to Know by Test Day. Organized for easy reference and intensive practice, the questions cover all essential college linear algebra topics and include detailed answer explanations. Inside you will find: 500 college linear algebra questions and answers organized by subject Step-by-step solutions to every problem Co... MOREntent that follows the current college course curriculum
500 Ways to Achieve Your Best Grades
We want you to succeed on your college linear algebra midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and get your best grades. These questions and answers are similar to the ones you'll findon a typical college exam, so you will know what to expect on test day. Each question includes explanations for right and wrong answers for your full understanding of the concepts. Whether you have been studying all year or are doing a last-minute review, McGraw-Hill's 500 Linear Algebra Questions will help you achieve the final grade you desire.
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Mathematics for New Speakers of English text is designed to help teachers work with beginning ESL students in grades 5 to 12. It provides lessons and activities that will develop the students' vocabulary, English usage, and mathematical understanding
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Exam duration:
Aid:
Evaluation:
Not applicable together with:
Mandatory Prerequisites:
Qualified Prerequisites:
General course objectives:
To provide the participants with tools, e.g., infinite series, to solve ordinary linear differential equations. By the mathematical approach the student will gain sufficient matureness to be able to deal with more advanced topics within mathematical analysis and its aplications.
Learning objectives:
A student who has met the objectives of the course will be able to:
Determine the solutions to nth order homogeneous differential equations
Determine the solutions to linear homogeneous systems of differential equations
Master the transfer function and apply it to solution of inhomogeneous differential equations
Distinguish between linear/nonlinear systems and test the behaviour of nonlinear systems
Determine and argue for the stability of linear systems of differential equations
Master central convergence issues
Estimate the number of terms which is needed in order to obtain a desired approximation of an infinite series
Find the Fourier series for simple periodic functions, clarify their convergence properties, and approximation-theoretic properties
Apply Maple to calculations and verification of results
Apply Fourier series and various other types of infinite series to solution of differential equations
Master central proofs within the theory for infinite series and differential equations
Construct proofs for simple claims within the theory for infinite series and differential equations
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Multiply your chances of success on the ACT Math Test The ACT Mathematics Test is a 60-question, 60-minute subtest designed to measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade, and is generally considered to be the most challenging section of the ACT. ACT Math For Dummies is an approachable,... more...
Accessible Mathematics is Steven Leinwand?s latest important book for math teachers. He focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts... more...
Science does not exist in a vacuum and, therefore, shouldn't be taught that way. In that spirit, Activities Linking Science With Math, 5-8, is a hands-on guide for preservice and inservice elementary and middle school teachers who want to connect science instruction with other areas of study—including visual arts, social sciences, language... more...
Science does not exist in a vacuum and, therefore, shouldn't be taught that way. In that spirit, Activities Linking Science With Math, K-4, is a hands-on guide for preservice and inservice elementary school teachers who want to connect science instruction with other areas of study—including visual arts, social sciences, language arts, and... more...
The advancement of a scientific discipline depends not only on the "big heroes" of a discipline, but also on a community?s ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on both. It celebrates the merits of Michael Otte as one of the most important founding fathers... more...
Numerical mathematics is a subtopic ofscientific computing. The focuslies on the efficiencyof algorithms, i.e. speed, reliability, and robustness.This leads to adaptive algorithms.The theoreticalderivation und analysesof algorithmsare kept as elementary as possible in this book; the neededsligtly advancedmathematical theory is summarized in the appendix.Numerous... more...
The crisis around teaching and learning of mathematics and its use in everyday life and work relate to a number of issues. These include: The doubtful transferability of school maths to real life contexts, the declining participation in A level and higher education maths courses, the apparent exclusion of some groups, such as women and the aversion... more...
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Elementary Statistics-Text - 8th edition
Summary: ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for introductory statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, along with increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing ...show moretechnologies91.76 +$3.99 s/h
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books.google.com - B... is for Googol
G is for Googol: A Math Alphabet Book
B or gift book for the budding young mathematician at home. Even the most reluctant math student will be drawn in by the author's trademark wit, Marissa Moss's quirky illustrations and funny captions, and the answers revealed in W is for " When are we ever gonna use this stuff, anyway?" Download the G is for Googol Teacher's Guide(300K)
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Review: G Is for Googol: A Math Alphabet Book
User Review - Emma - Goodreads
G Is For Googol is the quintessential reference book for STEM because it covers topics that are relevant to all of the STEM subjects. From abacus to zillion, this advanced ABC book conveys complex ...Read full review
Review: G Is for Googol: A Math Alphabet Book
User Review - ckodama152 - Goodreads
Great book to talk about different math concepts and vocabulary. There are some more complex math terms defined, so this book would be perfect for 5th graders and up. The pictures and examples used are also funny and help explain the concepts well.Read full review
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IS FOR OOGOL Based on the book G is for Googol: A Math Alphabet Book. by David M. Schwartz. Illustrated by Marissa Moss. 9. 781582 460567. 50295. ISBN 1-58246-056-6 ... tenspeedpress.com/ resources/ documents/ Googol_Guide.pdf
G is for Googol: A Math Alphabet Book G is for Googol: A Math Alphabet Book. $15.95 $10.95 Price reduced!! B is for Binary, F is for Fibonacci, P is for Probability... even a small sample begins ... evolvefish.com/ fish/ product1089.html
math-mom.com: G Is for Googol: A Math Alphabet Book G Is for Googol: A Math Alphabet Book. by Schwartz David and Moss Marissa. Here'sa math dictionary you may not want to put down once you begin to look at it ... book-review/ g-is-for-googol/
David M. Schwartz the book G is for Googol: A Math Alphabet Book, by David M Schwartz to teach. probability. ... Alphabet Book, by David M. Schwartz and turned to p. 32. I .. ... unjobs.org/ authors/ david-m.-schwartz
C is for COUNTDOWN C is for COUNTDOWN. a worksheet to complement. G is for Googol, by David Schwartz & Marissa Moss. Make your own ABC math book by drawing a picture in each ... countdown.luc.edu/ pdfs/ Numbers_And_Operations/ N0027_Googol.pdf
G is for Googol: a math alphabet book. David Schwartz. How Much Is A Million. David Schwartz. Grandfather Tang' Story. Ann Tompert. Counting on Frank ... parents/ TurnUrdu.pdf.pdf.pdf
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About the author (1998)
DAVID SCHWARTZ is the author of 50 children's books, including G IS FOR GOOGOL and Q IS FOR QUARK. He is a frequent guest speaker at schools in the US abroad. He lives with his wife-and co-author-YAEL SCHY in Oakland, California. Marissa Moss was an honors math student and the only girl on her school math team. She is the creator of the Amelia's Notebook Series, RACHEL'S JOURNAL, and REGINA'S BIG MISTAKE, among others. She lives in Berkeley, CA.
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Basic Geometry for College Students : An Overview of the Fundamental Concepts of Geometry - 03 edition
Summary: Intended to address the need for a concise overview of fundamental geometry topics. Sections 1-7 introduce such topics as angles, polygons, perimeter, area, and circles. In the second part of the text, Sections 8-11 cover congruent and similar triangles, special triangles, volume, and surface area.
Benefits:
A five-step problem-solving strategy throughout the book teaches students to an...show morealyze the problem, form an equation, solve the equation, state the conclusion, and check the result.
The greatest strength of the Tussy/Gustafson approach and the key to students' grasp of the language of mathematics is the STUDY SETS, found at the end of each section.
VOCABULARY, NOTATION and WRITING problems in the STUDY SETS are structured to improve students' ability to read, write, and communicate mathematical ideas.
CONCEPTS sections in the STUDY SETS reinforce major ideas and foster independent thinking.
PRACTICE sections in the STUDY SETS provide the drill and practice necessary for mastery of the mathematics.
APPLICATIONS in the STUDY SETS provide opportunities for students to apply what they've learned to real-life situations.
Many problems require students to present their solutions in the form of a chart, table, or graph. Students are also asked to read data displays to obtain information necessary to solve problems.
SELF CHECK problems, adjacent to worked examples, reinforce newly learned skills and help students build confidence by working a similar problem. Students can refer to the solution and Authors' Notes as they solve the Self Check. The answer to each Self Check is printed underneath the problem to give students instant feedbackDust Cover Missing. Free
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Super Review All You Need to Know! : Basic Math and Pre-Algebra
by RESEARCH+EDUC
No options of this product are available.
Description
Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Basic Math & Pre-Algebra Super Review includes coverage of fundamental math concepts, sets, decimals, fractions, and more! Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study!
DETAILS - From cover to cover, each in-depth topic review is easy-to-follow and easy-to-grasp - Perfect when preparing for homework, quizzes, and exams! - Review questions after each topic that highlight and reinforce key areas and concepts - Student-friendly language for easy reading and comprehension - Includes quizzes that test your understanding of the subject.
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A Course in Linear Algebra by David B. Damiano, John B. Little Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter features multiple examples, proofs, and exercises. Includes solutions to selected problems. 1988 edition.
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Vector Spaces and Matrices by Robert M. Thrall, Leonard Tornheim Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.
Introduction to Matrices and Linear Transformations: Third Edition by Daniel T. Finkbeiner, II This versatile undergraduate-level text contains enough material for a one-year course and serves as a support text and reference. It combines formal theory and related computational techniques. Solutions to selected exercises. 1978Linear Algebra and Geometry: A Second Course by Irving Kaplansky The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. This volume features examples, exercises, and proofs. 1974
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Math Models 101
Mathematical Models with Applications (One-Half to One Credit).
(a) General requirements. The provisions of this section shall be implemented beginning September 1, 1998. Students can be awarded one-half to one credit for successful completion of this course. Recommended prerequisite: Algebra I.
(b) Introduction.
(1) In Mathematical Models with Applications, students continue to build on the K-8 and Algebra I foundations as they expand their understanding through other mathematical experiences. Students use algebraic, graphical, and geometric reasoning to recognize patterns and structure, to model information, and to solve problems from various disciplines. Students use mathematical methods to model and solve real-life applied problems involving money, data, chance, patterns, music, design, and science. Students use mathematical models from algebra, geometry, probability, and statistics and connections among these to solve problems from a wide variety of advanced applications in both mathematical and nonmathematical situations. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to link modeling techniques and purely mathematical concepts and to solve applied problems.
(2) As students do mathematics, they continually use problem-solving, language and communication, connections within and outside mathematics, and reasoning (justification and proof). Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.
(c) Knowledge and skills.
(1) The student uses a variety of strategies and approaches to solve both routine and non-routine problems. The student is expected to:
(A) compare and analyze various methods for solving a real-life problem;
(B) use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; and
(C) select a method to solve a problem, defend the method, and justify the reasonableness of the results.
(2) The student uses graphical and numerical techniques to study patterns and analyze data. The student is expected to:
(A) interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;
(B) analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;
(C) analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments; and
(D) use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.
(3) The student develops and implements a plan for collecting and analyzing data (qualitative and quantitative) in order to make decisions. The student is expected to:
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Madeleine Chowdhury's MIL Project
Visualization in Calculus
Recent curricular efforts have placed increased emphases on establishing bridges between visual and analytic representations of fundamental calculus concepts. The role of visual thinking is so fundamental to the understanding of calculus that it is difficult to imagine a successful calculus course which does not emphasize the visual elements of the subject (Zimmerman, 1991). However, as outlined in Eisenberg & Dreyfus (1991) , there seem to be valid reasons as to why students have difficulty thinking in visual frameworks. Understanding these reasons should help in the development of suitable materials and learning strategies to promote visual thinking. This project will investigate several hypotheses, ambiguities, and needs generated by research on in mathematics, the relationships of visualization skills to specific concepts in calculus, and the potentials of spatial training in enhancing mathematical understanding. The specific research questions are as follows:
What is the role of visualization in understanding the fundamental calculus concepts?
What effects does spatial training have on college students' calculus achievement and spatial visualization ability?
Are there gender differences in calculus achievement and use of visualization?
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12, University Preparation (MCB4U) ... calculus. Students will investigate and
apply the properties of polynomial, exponential, and logarithmic .... communicate
the solutions with clarity and justification. 7.
Functions multiplied, or divided to form a new function. ... Find the first three
iterates of each function using the given initial vaiue. 12. Fitness ... Glencoe/
McGraw-Hill 5 Advanced Mathematical Concepts ...
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Linear
algebra is two things in one: a general methodology for solving linear
systems, and a beautiful abstract structure underlying much of
mathematics and the sciences. This course will try to strike a balance
between both. We will follow the book of our own Peter Lax, which does
a superb job in describing the mathematical structure of linear
algebra, and complement it with applications and computing. The most
advanced topics include spectral theory, convexity, duality, and
various matrix decompositions.
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Prentice Hall Connected Mathematics 2 (CMP2)
Professional Development
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The Connected Mathematics 2 program is fully integrated for more effective teaching.
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HiDigit is a new calculating software with extended capabilities. This is an essential application for math, algebra, calculus, geometry, physics and engineering students. The main advantage of the software is a simple input format even for the most complicated formulas. For example, you can enter 10pi instead of "10*pi". For complex numbers, you can use the following format - "1+2i". For percentages - "number + %". The other important feature of HiDigit is its high precision - up to 15 decimals. The program boasts an impressive number of built-in formulas, functions, constants and coefficients. Importantly, the users can customize all of them or add their own variables. Also, the history of all actions is kept, so the users can come back and undo/redo any action at any time. While HiDigit is a serious scientific software, it is extremely simple in use. No special skills or knowledge are required. The interface is straightforward and very easy to navigate through. The...
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Prealrealgebra, Second Edition, helps students not only learn but also retain, mathematical concepts - an important challenge that math instruction must meet in order to ensure the current and future success of mathematics students. A strong revision that includes a new design, a new art program, and key content enhancements, our text incorporates a careful development of mathematical concepts, a focus on the ""why"" behind the mathematics, and a problem-solving approach that can be applied in all math courses, as well as in everyday life. Refine p... MOREedagogy and an enhanced supplements package also provide maximum help and support for both instructors and students. Prealgebra, Third Edition, is a significant revision of the second edition, especially with respect to design, an all-new art program, pedagogy, and an enhanced supplements package. Its unique approach, which has been developed and refined over many years, is designed to help students both learn and retain mathematical skills. It is our belief that the third edition will continue to help today's students through pedagogical use of full color and updated applications. As part of MathMax: The Bittinger System of Instruction, a comprehensive and well-integrated supplements package provides maximum support for both instructor and student. MathMax: The Bittinger System of Instruction offers a completely integrated package of four-color text, multimedia CD-ROM, interactive tutorial software and videos that guide students successfully through developmental math. Key elements of the MathMax system include learning objectives keyed to the exposition, exercises, and examples; a hallmark five-step problem-solving process; and modern, interesting applications and problems.
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Elementary Algebra for College Students - 8th edition
Summary: Today's students are visual learners, and Angel/Runde offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. New Understanding Algebra boxes and an innovative color coding system for variables and notation keep students focused. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math. Real Numbers; Solving Linear Equations and Inequalities; ...show moreApplications of Algebra; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Graphing Linear Equations; Systems of Linear Equations; Roots and Radicals; Quadratic Equations For all readers interested in algebra
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ula One Maths: Pupil's Book Bk. A2
A Key Stage 3 Mathematics course designed to follow the principles of the direct and interactive approach of the National Numeracy Strategy. It also ...Show synopsisA Key Stage 3 Mathematics course designed to follow the principles of the direct and interactive approach of the National Numeracy Strategy. It also includes relevant task, activities and investigations; step by step explanations of new skills; graded questions for each topic; and review exercises for each chapter Formula One Maths..
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Math Problem? There's An App For That!
Math functional as a scientific, graphing, fraction and matrix calculator, and it also is very handy as a tool to help complete one's algebra homework. The application is available for tablets and phones through the Android Market.
California (I-Newswire) September 29, 2013 - Gone Additionally, there are thousands of educational apps available to help students with their studies.
The Verizon Foundation recently commissioned a study of 1,000 students to determine what they were using their phones for. The study found that 39 percent of the students had used their phones to help them with homework, and 26 percent of those same students used it on a weekly basis as a study aid. Students also frequently took advantage of various applications to help them master a subject or study it further.
Math is one subject where students often utilize an application to help them study, but whilst many math apps have been created, they weren't all created equally; however, the Graphing Calculator app by Mathlab is one app that exceeds the expectations of students, teachers and parents alike.
The Graphing Calculator app is capable of performing simple math operations, but where it really excels is with its advanced features. It is functional as a scientific, graphing, fraction and matrix calculator, and it also is very handy as a tool to help complete one's algebra homework. The application is available for tablets and phones through the Android Market or by visiting
Parents will appreciate that the application is free, although a PRO version is available for students who want to eliminate those pesky ads. More than 500,000 users have downloaded the App, primarily by appreciative students and teachers worldwide; the developers are anticipating more than 5 million downloads by 2014.
The app's developers carefully programmed the Graphing Calculator app and spent over two years improving it so that it would perform smoothly and seamlessly. It has been described as a "gift from the math gods" by one appreciative customer and has also been featured as a 'Click Pick' by an Alabama TV station and 'Tech Check: Back-to-school apps' show by Doug Evans.
Vadim Pelyushenko from Mathlab said, "Our brand new app has been developed to exceed the expectations of parents, students and teachers and can make math problems a thing of the past. It performs simple operations and complex functions with ease thanks to its scientific, graphing, fraction and matrix calculator. We're passionate about using technology to enhance classroom education and have spent more than two years developing and refining so every math student gets the help they need to learn, understand and excel. And best of all? It can be downloaded for free around the world so there are no barriers to getting ahead."
Whilst a number of educators are against using phones in the classroom, many others appreciate the benefits of modern technology. Valerie Thompson, head of the E-learning Foundation has said, "What technology allows teachers to do is give children an individual learning experience. . . The revolution is not the technology, it is the changing role of the teacher to make the most of the technology."
As mobile technology continues to grow and evolve, its practical application in the classroom will become more apparent, and just as the Internet has revolutionized the way people communicate, there's a very real chance that mobile applications will revolutionize the way students learn.
About Mathlab
Math functional as a scientific, graphing, fraction and matrix calculator, and it also is very handy More.. as a tool to help complete one's algebra homework. The application is available for tablets and phones through the Android Market
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The Pre-Algebra Tutor DVD series teaches the fundamentals of pre-algebra through step-by-step example problems that progress in difficulty. Emphasis is placed on giving students confidence in their skills by gradual repetition so that the skills learned are committed to long term memory. This program covers the important topic of teaching students the order of operations in algebra. This central topic teaches students the order in which to calculate expressions involving addition, subtraction, multiplication, division, parenthesis, exponents and more. Grades 9-College. 47 minutes on DVD.
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Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology... more...
The fundamental aim of this book is to communicate the knowledge necessary for a competent mathematical assessment of modern developments in the age of the Internet. Most crucially, this includes an understanding of very large graphs, calculating with large numbers, and calculating using prime number bases. more...
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Hi fellow students, I heard that there are certain software that can help with us doing our homework,like a teacher substitute. Is this really true? Is there a software that can aid me with algebra? I have never tried one before, but they shouldn't be hard to use I assume. If anyone tried such a software, I would really appreciate some more information about it. I'm in Remedial Algebra now, so I've been studying things like how to solve equations involving rational expressions and it's not easy at all.
I find these routine queries on almost every forum I visit. Please don't misunderstand me. It's just as we enter college, things change in a flash. Studies become challenging all of a sudden. As a result, students encounter problems in doing their homework. how to solve equations involving rational expressions in itself is a quite complex subject. There is a program named as Algebrator which can assist you in this situation.
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Recommendations..., Relativity and the Fourth Dimension by Rudolf Rucker Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.Products in Geometry
Advanced Euclidean Geometry by Roger A. Johnson This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
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Analytical Conics by Barry Spain This concise text introduces analytical geometry, covering basic ideas and methods. An invaluable preparation for more advanced treatments, it features solutions to many of its problems. 1957 edition.
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Analytical Geometry of Three Dimensions by William H. McCrea Geared toward advanced undergraduates and graduate students, this text covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations, quadric in Cartesian coordinates, and intersection of quadrics. 1947 edition.
Our Price:$11.95Convex Surfaces by Herbert Busemann This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.
A Course in the Geometry of n Dimensions by M. G. Kendall This text provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. 1961 edition.
Curvature in Mathematics and Physics by Shlomo Sternberg Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Our Price:$19.95Differential Geometry by Heinrich W. Guggenheimer This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
Our Price:$17.95The Elements of Non-Euclidean Geometry by D. M.Y. Sommerville Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
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Euclidean Geometry and Transformations by Clayton W. Dodge This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
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Mathematics
Ancient thinkers recognized that mathematics was the language of the natural world. Today we recognize that it is also the language of science and social science, of business, commerce and industry, even of art and design. Doing math can be as simple as executing a computer search and as momentous as planning a mass evacuation or tracing a disease epidemic, but it assumes ever-greater importance in our lives. At Hamilton, mathematics is both a popular major and a crucial part of the College's broader liberal arts curriculum.
The study of mathematics requires the ability to abstract and organize information, to grasp quantitative concepts, to reason and argue logically, to employ effective problem-solving strategies, and to communicate ideas clearly and efficiently. Mathematics students graduate from Hamilton with all these skills. Faculty members work closely with students in a variety of course formats ranging from formal lectures to intensive seminars. In each, the focus is on both developing students' abilities and providing skills useful in the wider arenas of the College as a whole.
Highlights
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Questions About This Book?
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
Summary
Welcome toSingapore Maththe leading math program in the world! This workbook features math practice and activities for first and second grade students based on theSingapore Mathmethod. An introduction at the front of the book explainsSingapore MathandSingapore Mathand for those who just need extra math practice.
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Mathematics for Elementary Teachers, Third Edition offers an inquiry-based approach, which helps students reach a deeper understanding. Sybilla Beckmann, known for her contributions in math education, writes a text that encourages future teachers to find answers through exploration and group work. Fully integrated activities are found in her accompanying Activities Manual, which comes with every new copy of the text. As a result, students engage, explore, discuss, and ultimately reach a true understanding of mathematics.
The new Active Teachers, Active Learners DVD helps instructors enrich their classroom by expanding their knowledge of teaching using an inquiry-based approach. The DVD shows Beckmann and her students discovering various concepts, along with voiceover commentary from Beckmann. Also included are students' testimonials about the course, footage from other instructors' classrooms, and instructor insights about making the switch to an inquiry-based approach. This DVD is the ideal resource for instructors who are teaching with an inquiry-based approach for the first time, and for instructors who seek new ideas to integrate into their course.
The table of contents is organized by operation rather than number type to foster a more unified understanding of the math concepts. Throughout the text, students learn why the math works, rather than just the mechanics of how it works. In this new edition the contents have been updated and rearranged for a more natural organization. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. Purchase of this text includes the Activity Manual files.
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Short Course in Mathematical Methods with Maple
This unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts ...Show synopsisThis unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts important from the application point of view. Part I of this book follows the ?paper and pencil? presentation of mathematical methods that emphasizes fundamental understanding and geometrical intuition. In addition to a complete list of standard subjects, it introduces important, contemporary topics like nonlinear differential equations, chaos and solitons. Part II employs the Maple software to cover the same topics as in Part I in a computer oriented approach to instruction. Using Maple liberates students from laborious tasks while helping them to concentrate entirely on concepts and on better visualizing the mathematical content. The focus of the text is on key ideas and basic technical and geometric insights presented in a way that closely reflects how physicists and engineers actually think about mathematics
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In many history texts, algebra is considered to have three stages in its historical development:
The rhetorical stage – the stage where are all statements and arguments are made in words and sentences
The syncopated stage – the stage where some abbreviations are used when dealing with algebraic expressions.
The symbolic stage – the stage where there is total symbolization – all numbers, operations, relationships are expressed through a set of easily recognized symbols, and manipulations on the symbols take place according to well-understood rules.
These stages are reflected in some textbooks and in our own lesson. For example in in pattern-searching activities that we ask our students to express the patterns and relationships observed using words initially. From the students' statements we can highlight the key words (the quantities and the mathematical relationships) which we shall later ask the students to represent sometimes in diagrams first and then in symbols. I have used this technique many times and it does seem to work. But I have also seen lessons which goes the other way around, starting from the symbolic stage!
Apart from the three stages, another way of looking at algebra is as proposed by Victor Katz in his paper Stages in the History of Algebra and some Implications for Teaching. Katz argued that besides these three stages of expressing algebraic ideas, there are four conceptual stages that have happened along side of these changes in expressions. These conceptual stages are
The geometric stage, where most of the concepts of algebra are geometric;
The static equation-solving stage, where the goal is to find numbers satisfying certain relationships;
The dynamic function stage, where motion seems to be an underlying idea; and finally
The abstract stage, where structure is the goal.
Katz made it clear that naturally, neither these stages nor the earlier three are disjoint from one another and that there is always some overlap. These four stages are of course about the evolution of algebra but I think it can also be used as framework for designing instruction. For example in Visual representations of the difference of two squares, I started with geometric representations. Using the stages as framework, the next lesson should be about giving numerical value to the area so that students can generate values for x and y. Depending on your topic you can stretch the lesson to teach about functional relationship between x and y and then focus on the structure of the expression of the difference of two squares.
I always like teaching algebra using geometry as context so geometric stage should be first indeed. But I think Katz stages 2 and 3 can be switched depending on the topic. The abstraction part of course should always be last
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Quadratic formula helps the user to learn in a more relaxed, without the pressure of a classroom and still encouraging to strive more to get a better grade on each attempt.
features:
* A clear and interactive Layout ; * Several formulas to solve; * Free mode that allows the player to enter a 2nd degree equation and get the answer; * Grade to each formulas solved and General Grade; * Count attempts in each equation;
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Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.
The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrences (now called "Divide-and-Conquer"). It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this edition.
Whether you're a security practitioner, developer, manager, or administrator, this book will give you the deep understanding necessary to meet today's security challenges--and anticipate tomorrow's. Unlike most books, The Craft of System Security doesn't just review the modern security practitioner's toolkit: It explains why each tool exists, and discusses how to use it to solve real problems.
Peter Winkler's at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own library.
This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all it's for those who think that the world of mathematics is orderly, logical, and intuitive – and are ready to learn otherwise!
Discrete Mathematics for Computer Science covers most of the mathematical topics needed by computer scientists: basic combinatorics and graph theory, probability, logic and proof techniques (including proof by induction), recurrence relationships and their solution, and the number theory needed to understand the RSA encryption scheme. The examples are drawn from Computer Science. Probability is used to analyze hashing and the average run times for algorithms. Recurrence relations arise from the analysis of recursive algorithms. Trees (including binary search trees) are a focus of the graph theory, and their properties are often proved using induction.
Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers
A non-technical account of the history of the Riemann Hypothesis, a 150 year-old unsolved math problem, whose solution gets to the heart of out understanding of the way in the which the prime numbers are distributed among the integers.
How can one trust computation taking place at a remote site, particularly if a party at that site might have motivation to subvert this trust? In recent years, industrial efforts have advanced the notion of a "trusted computing platform" as a building block. Through a conspiracy of hardware and software magic, these platforms attempt to solve this remote trust problem, to preserve various critical properties against various types of adversaries. However, these current efforts are just points on a larger continuum, which ranges from earlier work on secure coprocessor design and applications, through TCPA/TCG, to recent academic developments. Without wading through stacks of theses and research literature, the general computer science reader cannot see this big picture.
Trusted Computing Platforms: Design and Applications fills this gap. Starting with early prototypes and proposed applications, this book surveys the longer history of amplifying small amounts of hardware security into broader system security---and reports real case study experience with security architecture and applications on multiple types of platforms. The author examines the theory, design, implementation of the IBM 4758 secure coprocessor platform and discusses real case study applications that exploit the unique capabilities of this platform. The author discusses how these foundations grow into newer industrial designs, and discusses alternate architectures and case studies of applications that this newer hardware can enable. The author closes with an examination of more recent cutting-edge experimental work in this area.
Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.
This timely and state-of-the-art topic is covered comprehensively in this book. Providing a complete and in-depth mathematical coverage of the topic - linear, generalized linear, and nonlinear mixed models, along with diagnostics - the book has dual appeal as both a graduate-level text and a reference. Special attention is given to algorithms and their implementations and several appendices make the text self-contained.
This book constitues the refereed proceedings of the Second International Symposium on Agent Systems and Applications and the Fourth International Symposium on Mobile Agents, ASA/MA 2000 held in Zürich, Switzerland in September 2000. The 20 revised full papers presented were carefully reviewed and selected from 107 submissions. The papers are organized in topical sections on migration, security issues, systems and applications, mobile agent applications, applications of multi-agent systems, communication and mobility control, cooperation and interaction.
This book is part of COMAP's Geometry and its Applications series. Books in this series are designed to give high-school students a richer understanding of mathematical concepts at the heart of geometry and the ways that applications of geometry affect their lives. It introduces the Voronoi diagram and uses it to solve a series of proximity problems that arise in running a chain of pizza parlors (deciding which parlor is closest to the location where a pizza is to be delivered, deciding where to locate a new parlor that is farthest away from existing parlors, finding for each parlor which other parlor is nearest to it).
Have you ever wondered how your GPS can find the fastest way to your destination, selecting one route from seemingly countless possibilities in mere seconds? How your credit card account number is protected when you make a purchase over the Internet? The answer is algorithms. And how do these mathematical formulations translate themselves into your GPS, your laptop, or your smart phone? This book offers an engagingly written guide to the basics of computer algorithms. In Algorithms Unlocked, Thomas Cormen—coauthor of the leading college textbook on the subject—provides a general explanation, with limited mathematics, of how algorithms enable computers to solve problems.
Readers will learn what computer algorithms are, how to describe them, and how to evaluate them. They will discover simple ways to search for information in a computer; methods for rearranging information in a computer into a prescribed order ("sorting"); how to solve basic problems that can be modeled in a computer with a mathematical structure called a "graph" (useful for modeling road networks, dependencies among tasks, and financial relationships); how to solve problems that ask questions about strings of characters such as DNA structures; the basic principles behind cryptography; fundamentals of data compression; and even that there are some problems that no one has figured out how to solve on a computer in a reasonable amount of time.
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0131481894
9780131481893
Elementary Surveying: An Introduction to Geomatics:For freshman and sophomore courses in surveying. This is a highly readable best-selling text that presents basic concepts and practical material in each of the areas fundamental to modern surveying (geomatics) practice. Its depth and breadth are ideal for self-study. The Eleventh Edition includes more than 400 figures and illustrations to help clarify discussions, and numerous worked example problems to illustrate computational procedures.
Back to top
Rent Elementary Surveying: An Introduction to Geomatics 11th edition today, or search our site for Paul R. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson.
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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S. S. M. Precalculus
9780495382874
ISBN:
0495382876
Edition: 11 Pub Date: 2007 Publisher: Cengage Learning
Summary: Check your work-and your understanding-with this manual, which provides solutions for all of the odd-numbered exercises in the text. You will also find strategies for solving additional exercises and many helpful hints and warnings.
Cole, Matt is the author of S. S. M. Precalculus, published 2007 under ISBN 9780495382874 and 0495382876. One hundred sixty three S. S. M. Precalculus textbooks are available for... sale on ValoreBooks.com, twenty seven used from the cheapest price of $5.15, or buy new starting at $32
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Error Analysis of Mathematics (page 2)
The purposes of error analysis are to (1) identify the patterns of errors or mistakes that students make in their work, (2) understand why students make the errors, and (3) provide targeted instruction to correct the errors. When conducting an error analysis, the teacher checks the student's mathematics problems and categorizes the errors. The following is a list of errors that students commonly make in various mathematical areas (Ashlock, 1986; Tindal & Marston, 1990).
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The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations
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goals of senior secondary education and on other official documents related to
the curriculum and assessment reform .... (c) the ability to manipulate numbers,
symbols and other mathematical objects; ...
while providing the rigor and relevance needed in a high school senior math
course. AIM meets the ..... students to see the context of the detailed math
formulas. Contributing to their decision was their ...
The reference is made to Botswana senior secondary school syllabus where one
of the aims ... In this paper we consider mathematical problems involving linear
equations with two variables solved in a ...
in secondary schools for 22 years and was a head of faculty before taking up her
current post with MEI in 2006. ..... Mathematics, DE is Differential Equations, M is
Mechanics, S is Statistics, D is Decision ...
This book is based upon the original Free High School Science Text which was
entirely written by volunteer ..... The punctuation marks of mathematics are the
different signs and symbols that are used ...
Former Senior Advisor for Mathematics. Office of Elementary ... that 80% of the
1992 U.S. high school graduating class went on to college. Only about ... Terms,
operations, and symbols must be defined ...
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Synopses & Reviews
Publisher Comments:
The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation. Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.
Synopsis:
This book examines all aspects essential for a successful application of geometric algebra to engineering--the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data.
"Synopsis"
by Springer,
This book examines all aspects essential for a successful application of geometric algebra to engineering--the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain
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Trigonometry - 2nd edition
Summary: Engineers trying to learn Parallel Words and Math...show more examples are included that provide more detailed annotations using everyday language. Your Turn exercises reinforce concepts and allow readers to see the connection between the problems and examples. Catch the Mistake exercises also enable them to review answers and find errors in the given solutions. This approach gives them the skills to understand and apply63 +$3.99 s/h
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Mathematics for Health Professionals - B. Louise Whisler
9780867203721
ISBN:
0867203722
Edition: 2 Publisher: Jones & Bartlett Publishers, Incorporated
Summary: This book is constructed to perform two major services for those in the health science professions. The first is to review the arithmetic and algebra that students need for calculations of health-related occupations. The second is to provide a detailed discussion of the specfic types of problems performed by those in health related occupations.
Whisler, B. Louise is the author of Mathematics for Health Profe...ssionals - B. Louise Whisler, published under ISBN 9780867203721 and 0867203722. Ten Mathematics for Health Professionals - B. Louise Whisler textbooks are available for sale on ValoreBooks.com, seven used from the cheapest price of $0.01, or buy new starting at $28
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Beginning Algebra With Applications - 7 ...show moreproblem areas, and, overall, promoting student success.
New! Interactive Exercises appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles.
New! Think About It
New! Important Points have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently.
New! A Concepts of Geometry section has been added to Chapter 1.
New! Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction
New! A Complex Numbers section has been added to Chapter 11, "Quadratic Equations."
New Media! Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool0618803599Good
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Math Homework
This is a discussion on Math Homework within the General Off Topic+ forums, part of the QJ.net Forum Miscellaneous category; Math is awesome.
What's even more awesome is math homework....
If anyone has any math homework problems, let me know... ...
you sound like your a pretty smart guy
I can do my own math homework tho lol
althought you might be able to help some lazy guy that doenst wnat to do his homework.
.....
whats a calculus???
Calculus is split up into two branches:
Differential Calculus - Branch of Calculus where one studies the rate of change of functions...
Integral Calculus - Branch of Calculus where one studies areas and volumes of functions...
If you're in Pre-Calculus or Physics, chances are you've experienced some calculus but you probably have been doing stuff the hard way. (e.g. finding the minimum/maximum of a parabola; you have to go through the trouble of completing the square, or memorizing the -b/2a formula, while the traditional method is to use differential calculus and find out where on the curve the slope is 0..)
Calculus isn't just where someone studies rate of change of functions, however... there are many applications of it such as finding roots of a cubic, quartic or even a quintic (Not sure if I spelt it right :P) equation using differentials... (Newton's Method)
You could even find the sine value of any number without using your calculator's sine function... (Taylor Series)
As to your comment about me sounding like a smart guy... my only strength is math... all I do at school is ***** about math and pretty much do terribly in my other classes, so I enjoy doing math.. :P
here's a simple question...
How do you calculate sine,cosine, and tangent functions without using a calculater. I only ones I know how to do are ones that form 30-60-90 and 45-45-90 triangles.
That really depends...
When you mean calculating sine, cosine and tangents without a calculator, you can do it with one of two ways...
First, you can be precise, or second you can be approximately near the value..
For instance, if you know the value of sin or cos 45 (pi/4 rad) and sin or cos 30 (pi/6 rad) then you can use the sum of angles formula to find the value of sin or cos 75 (pi/6 + pi/4 = 4pi/24 + 6pi/24 = 10pi/24 = 5pi/12 rad) assuming you knew the formula..
However, if you're just too lazy to use that formula, then you can do it another way-- Taylor Series...
Taylor series is a good approximation for a function using its derivatives and such...
The more terms you use for a Taylor series, the more accurate your answer will become...
A taylor series is like the following:
f(a) + f'(a)(x - a) + f''(a)(x - a)^2 / 2! + f'''(a)(x-a)^3 / 3! + f''''(a)(x-a)^4 / 4! ...
Where a is a point near where you want to approximate the value of the function..
However, most people are too lazy to expand those brackets and so they use MacLaurin Series which is a Taylor Series with x = 0:
f(0) + f'(0)x + f''(0)x^2 / 2! + f'''(0)x^3 / 3! + f''''(0)x^4 / 4! ....
So, how does this relate to sine and cosine? Let's say you wanted the sine of an angle... let's say pi/9..... which is approximately 3.1416/9 = 0.35... (Just take a guess here... you can be as close as you want..)
Now, we know that f(x) = sin x, so let's find its derivatives and come up with a Taylor Series of degree 4. (Degree 4 meaning we're going up to the 4th degree of x and 4th order in terms of derivatives)
So:
f(x) = sin x
f'(x) = cos x
f''(x) = -sin x
f'''(x) = -cos x
f''''(x) = sin x
So, we know sin 0 is 0, cos 0 is 1, thus we have:
f(0) = 0
f'(0) = 1
f''(0) = 0
f'''(0) = -1
f''''(0) = 0
So now we have:
sin x =approx= x - x^3 / 3!
Plugging in for 0.35 would give us 0.207...
Checking a calculator, this is PRETTY close.... the calculator gives 0.343 (3 d.p.) for the actual value and we get 0.343 (To 3 d.p.) using just the Taylor Series! Awesome! (Yes, geeky.. I know :P)
To show how increasing the degree of our Taylor Series would make the answer more accurate, let's be daring and go up a few more degrees...
f'''''(0) = 1
f''''''(0) = 0
f'''''''(0) = -1
Hmm... starting to see a pattern? We now have:
sin x = x - x^3 / 3! + x^5 / 5! - x^7 / 7!.....
See the pattern in sine approximations?
If you were to plug in 0.35 into this series, you'd find it's even MORE accurate to more decimal places..... which shows how amazing simple calculus is! (How do you think your calculator calculates sines and cosines? :P)
Anyway, I hope that helped some...
"ok so whats 2+2x2?? if you get that then I think you are smarter than Einstein!!"
6? :P
It must be one of those trick questions.. like "What is 2+2?" and then I'd say "4.." and you'd say "No, it's 22! HAHAH...."Yeah, I did hear there was a way to do that but I never had a chance to do a Pre-Calc class... so my methods are weird.
Maybe the part you got lost with was the f(x), f'(x) part? (That's stuff from differential calc, if you haven't done the class yet..)
Albert Einstein has entered the building!
Go be a Math teacher :)
No thanks, don't think there are many chicks majoring in math.... or many chicks fancy math.
I haven't had calculus yet, Im only a junior. But it was something I always wondered since algebra I.
Well, calculus kicks ass.
I got bored with math when I was in Algebra 1 so I used to do a little research on Calculus online-- it doesn't really take much to get into the subject...
Everything you're taking in Pre-Cal is pretty much an alternative way to do stuff that you'd do in Calculus...
For example, minimums, maximums, points of inflection and intermediate value theorem stuff.. (What's the point of that theorem anyway?)
Let's say you had an arbitrary function, let's say... f(x) = x^3 + 2x^2 + x + 1
To find the minimums and maximums of this function in Pre-Calc, you'd either graph it on your calculator and use its features to find the mins/maxs..... or you'd look at a graph and look closely and approximate the point... (This is a pain... I know I screw up alot when it comes to reading co-ordinates off a graph, like I'd say (2,3) instead of (2,4)...)
An alternative way to do it, is to use the concept of differentiation from calculus..
So, let's analyze this graph... here's a pic of it I got from gnuplot: (pic not available for the moment; I'll upload it in a bit once gnuplot compiles)
As you should know, or notice, at a maximum point or minimum point (relative minima and maxima, or relative extrema, that is) the slope of a line tangent to that point would be equal to 0.
Let's get back to the topic of differential calculus...
Differential calculus is mainly concerned with the rates of changes of non-linear functions... but recall from Algebra, the slope is essentially the graphical/geometric representation of "rate of change", in a sense that since a straight line, as you should know, is linear such that it has a constant slope, that the next plotted points would always follow a specific, constant pattern.
For example, consider the graph y = 3x + 2...
At x = 0, y = 2; at x = 2, y = 8... and so on; the x value is always multiplied by a constant and a constant is then added to it.... this is an example of constant rate of change; the independent variable, x, is never multiplied by itself, nor is it ever logarithmized, trigonometrized (Like my wording? :P) or exponentiated, rather, its change is only brought about by constant numbers.
Now, with a graph of a polynomial function of degree higher than 1 (or any other non-linear function, for that matter) you'll notice the slope is non-constant; it seems the slope gets steeper and steeper, or perhaps even.... the opposite of steeper... this is where calculus comes into play... so here's where I'll define the derivative. (Probably not in a formal way, but enough for you to understand how they work and why you use them)
General definition: A derivative is the rate of change of a function, f(x), at any x value of that function. (In other words, the instantaneous slope)
Numerical method:
-----------------------
Let's go to the function f(x) = x^2, and let's say you wanted to find the slope at point, hmm, say.... x = 3, or (3, 9).
Let's go to the slope formula you should have learnt in Pre-Algebra/Algebra 1:
m = delta y / delta x = (y2 - y1)/(x2 - x1)
Where delta means "change in", that is, the difference between two y or x values.
So if you wanted the slope at this point, (3, 9), using numerical means, you have to pick a point sufficiently close to (3,9) that lies on the graph of f(x) = x^2.... let's pick the point x = 3.000001, or (3.000001, 9.000006).
Now, calculating the approximate slope: (9.000006 - 9)/(3.000001 -3) = (0.00006)/(0.000001) = 6
Using the point slope formula,
(y - 9)/(x - 3) = 6
y = 9 + 6x - 18 = 6x - 9
And that's the slope of the line tangent to the graph f(x) = x^2 at point (3,9)....
That should pretty much cover the numerical method for calculating derivatives...
This gets a little boring sometimes, so I'll introduce the analytical method.
Analytical method
---------------------
OK, here I'll make a very very brief definition of a limit before I explain the analytical method...
Let's say you had a function, f(x) = x - 2.... the limit of that function as x approaches 3 is 1; that is, for a simple linear function you can quite simply plug in the x value which the function approaches.
The limit as x approaches c is denoted as:
lim
x->c
Now, let's say you had the function f(x) = [x^2 - 1]/(x+1); what's the limit of that function as x approaches -1? You can't directly plug it in because then you'd end up with the result f(x) approaches infinity; so when you're dealing with limits, always simplify what you're dealing with as much as possible before tackling it head-on, or you'll get an undesired answer.
Why did I have to introduce limits? Because it's very important to the analytic definition of derivatives, and if I did clarify the simplifying part you would have gone "Whoah, wait... is a derivative defined?"
Anyway, let's go back to the slope formula, which we'll write as Sy/Sx for simplicity, where S denotes delta:
m = delta y / delta x = Sy/Sx
What I did, numerically, was I picked a point that was VERY close to x to approximate a slope with....
This value was so close, you could say it was pretty much the same as x itself, but NOT quite...
Thus, we could say that the difference between the close number I chose, and the x itself, is very close, or approaches, 0..
We can denote this with limits:
Let's remember what Sx means-- the difference between the two x values I chose; recall how x2 is x1 plus the difference between x2 and x1? We can now rewrite the limit as:
= lim [f(x1 + Sx) - f(x1)]/Sx
Sx -> 0
Or simply:
= lim [f(x + Sx) - f(x)]/Sx
Sx -> 0
And, from this formula, you can derive a formula from a function which allows you to determine the slope of that function at any point...
Let's go back to f(x) = x^2... and use this formula:
lim [(x+Sx)^2 - x^2]/Sx = [x^2 + 2xSx + Sx^2 - x^2]/Sx = (2xSx + Sx^2)/Sx = 2x + Sx
Sx -> 0
And now, since we've simplified, we can directly substitute 0 into Sx, giving:
2x
Now let's test it with the point x = 3 we used in the numerical method section...
2 times 3 is 6, isn't it? That's the exact answer we got with our numerical method!
Since this limit method is long and tedious, most people just use the differentiation rules, which are simple:
C & n are constant, x is the independent variable:
If f(x) is a function, f'(x) denotes its derivative which can be found by the following rules:
So anyway, I'm too lazy to elaborate on non-polynomials or whatever, so I'll just go back to our initial question-- how to find the relative minimum and maximum of f(x) = x^3 + 2x^2 + x + 1...
Let's use the above short hand rules to come up with a formula to find the slope:
f'(x) = 3x^2 + 4x + 1
Now, since we know that the slope would = 0 at the minimum and maximum, (since they are stationary points) we'll set f'(x) = 0:
3x^2 + 4x + 1 = 0
And now, we solve for x to get the minimum/maximum:
x = -4 +/- root(16 - 12) / 6 = -4 +/- 2 / 6 = -2 +/- 1 / 3 = -1 or -1/3
Now, which is the minimum and which is the maximum? To tell, we'll use the SECOND DERIVATIVE RULE, which just means you differentiate the function again and plug in these values, (we denote this f''(x)), so....
f''(x) = 6x + 4
Now, let's try -1..
f''(-1) = -2
Since it's negative, that means that that point is a MAXIMUM, that it's concave down....
f''(-1/3) = 2
Since it's positive, that means that that point is a MINIMUM, that it's concave up...
-1
how would if find tan (opposite/adjacent) if I only have tan() and atan().
I did the above, just so i could have superscript. ;:)but your teacher would probably like the answer "the square root of 2" because it's the most exact.
"15% percent of programing is creating a program, 85% percent is getting it to work like it should." - Me
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Errm, are you any good with Boolean Algebra, Binary, Logic & Proof, Truth Tables etc? cos my lecturers and teachers who i learn from ain't the best of explainers!!!
Sorry... those are my weak points..
well im in 9th grade and im in algegra 2 OOOOOOOO
and if ur so smart, whats the square root of two?How would you calculate exponents without a calculator or by multiplying x by itself y times?
"15% percent of programing is creating a program, 85% percent is getting it to work like it should." - Me
[URL=
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