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It comes with a 106-page answer key and a test bank that includes 14 tests.
Multimedia Explanations Available Separately
The set of computer DVD-ROMs (available separately, or purchase the complete set and save!) adds an audio-visual presentation of the 95 lectures, step-by-step multimedia explanations to all the practice problems as well as for the text's more than 2,600 problems, plus an additional DVD-ROM with complete, step-by-step solutions for every test problem.
About Teaching Textbooks
Designed for Homeschoolers
A number of years ago we did the unthinkable and took a poke at a sacred cow when we said that we didn't like the conventional big-name homeschool math programs. Though some families were steadfast in their defense, there has since been an increasing number of families who have come to realize that math programs originally designed to be used in government schools are wholly inadequate to meet the needs of home educators.
You Don't Have to Be a Math Teacher!
What is wrong with adapting a school-based text for home use? There are a couple of significant issues with doing that. First, because a typical school text assumes a knowledgeable math teacher, the explanations are often meager and brief. If you double as a math teacher, this will present no problem to you. However, many parents either did not take upper level math as a teen, or if they did, the process is just a distant, unpleasant memory. So sparse explanations in typical texts can be frustrating to both child and parent. Second, government schools' math texts often contain excessive use of terminology, making simple ideas seem complex.
Combines a Teacher and a Textbook into One!
The Teaching Textbooks series is written with home educators in mind so it tackles those issues head-on in a rather innovative way, by combining a teacher and a textbook into one. Firstly, their textbooks, since they were designed specifically for independent learners, contain far more explanation than any others on the market, and the tone is friendly and conversational. Because the Teaching Textbooks series was designed for homeschoolers studying independently, it uses far less irrelevant jargon than other textbooks, while still retaining all the terms that students need to know for those important standardized tests. The textbook also comes with an answer key and a test bank.
Step-by-Step Multimedia Explanations
Secondly, and what ultimately sold me on this program, are their computer CDs with down-to-earth, step-by-step multimedia solutions for every problem in the book, plus an additional CD-ROM with complete step-by-step solutions for every test problem. The lectures - one for each lesson in the textbook - provide hours of instruction. They cover the same material as the written lessons in the textbook, but many students prefer to listen to (and watch) an explanation for each lesson rather than read it out of a book. (Note that you'll still need the textbook, because it has all the homework assignments and the answer key.) This is a brilliant idea, long overdue and skillfully done, with many hours of instruction.
Review Method
The Teaching Textbooks series has been field-tested with outstanding results. Like other quality math programs, Teaching Textbooks uses the review method because it is a proven method for ensuring children are able to master difficult subjects such as algebra and geometry. Students using Teaching Textbooks are fully prepared for College Board examinations and college courses. Enjoyable, efficient, and effective, what more could you want from a math program?
Delivered within time frame and in excellent condition. Will use your service again.
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0 of 0 people found the following review helpful:
94 Lessons
November 15, 2010
Reviewer:
Tawn B from Shelton, WA United States
My family has loved the Teaching Textbook series so it wasn't a question as to what brand we would buy when my oldest reached the pre-calculus level. It is a similar format to the lower levels of other Teaching Textbooks. However, some of the explanations in the book are not as detailed as in lower levels. There are also only 94 lessons -- hardly enough to count as a school year. I do appreciate the practice problems scattered throughout the book that prepare the student for the SAT though, and my daughter likes the way it walks her through the buttons to push on the recommended graphing calculator.
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0 of 0 people found the following review helpful:
Helpful to my whole family
October 20, 2008
Reviewer:
Susan D. from Milwaukie OR
This product is easy to use and does a great job in explaining the lesson to the student. The student can work independently. That is helpful to my whole family. I will definitely purchase more for my other children. My only suggestion would be to ofter more of the same product for younger children!
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0 of 0 people found the following review helpful:
A great program that frees up more of my time
October 20, 2008
Reviewer:
Joyce E. from Redmond, WA
We have enjoyed the teaching textbooks. I do sit in on the class with my sons every few lessons to make sure they are understanding what they are learning. Sometimes they need more explanation. Over all it's a great program that frees up more of my time.
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0 of 0 people found the following review helpful:
Makes math relevant
October 20, 2008
Reviewer:
Cathy from Buffalo, NY
The Teaching Textbooks are done in a conversational format that my children preferred over the "most" popular other curriculum (S***n). It also weaves in interesting historical and scientific facts that illuminate math's relevance to the rest of life. | 677.169 | 1 |
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus. This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application... more...
Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm,... power series rings and rings of invariants of finite linear groups to the convolution algebra... Weierstrass models and endomorphism algebras of abelian varieties to the generic Torelli... more...
Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the... more...
Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work... more...
Welcome to The Amazing 7-Day, Super-Simple, Scripted Guide to Teaching or Learning Percents. I have attempted to do just what the title says: make learning percents super simple. I have also attempted to make it fun and even ear-catching. The reason for this is not that I am a frustrated stand-up comic, but because in my fourteen years of teaching... more...
Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitous?they have... more...
Here is a comprehensive exposition of the key results and ideas connected to the Poncelet theorem, focusing on the mathematics and including the dynamics of integrable billiards and the algebraic geometry of hyperelliptic Jacobians, among other material. more... | 677.169 | 1 |
In addition to the general recommendations for majors,
programs for students preparing to enter the nonacademic workforce
should include
A programming course, at least one data-oriented
statistics course past the introductory level, and coursework in an
appropriate cognate area; and
A project involving contemporary applications of
mathematics or an internship in a related work area.
At most colleges and universities, most mathematics majors are
heading neither into teaching nor toward a graduate degree in
mathematics. After graduation, they will be looking for a job. While mathematician
is not a common job title in the nonacademic workforce, there are a lot
of jobs for mathematics majors. The mathematical societies have put
together resources to show students what can be done with a Bachelor's
degree in Mathematics. Links to the various sites can be found at
and The
Mathematical
Science Career Information website, a joint project of AMS,
MAA, and SIAM with support from the Alfred P. Sloan Foundation, is a
particularly rich source of information. The Illustrative
Resources provides links to programs at several colleges and
universities that inform students about both the opportunities and
requirements for employment in government and industry.
One of our greatest difficulties in communicating the usefulness
of a degree in mathematics comes from the fact that there is a sharp
disconnect between the skills we appear to assess in our courses and
the skills our students will need in their future careers. Few of our
students will have any occasion to differentiate or integrate a
function, to find an exact solution to a differential equation, to
invert a matrix or find its eigenvalues, or to prove a theorem. Our
students know this, and they often wonder what they are equipped to do
with the skills they think they are learning in our classes.
What employers value in mathematics majors are problem-solving and
communication skills. In spite of ourselves, we often do a good job of
nurturing these abilities. We could be much more effective if we were
conscious of these goals as we think about what and how we teach, and
if we communicated these goals to our students.
Problem-solving is not easy to teach. It rests on a bed of
competency with many different types of mathematics and is more likely
to draw on discrete mathematics than continuous, areas such as
combinatorics, linear algebra, statistics, and number theory. It relies
on knowing when and how to draw on available tools, especially
computers, and so requires familiarity with a variety of computing
tools and the ability to come quickly up to speed with new software.
And it requires practice.
Students learn techniques of problem-solving by solving problems.
Every course needs to include challenging problems for which the
methods and techniques are not prescribed. A problem that occurs in the
section on the product rule probably has a solution that employs the
product rule. That is the kind of big hint that is not available
outside the classroom. Students need to tackle problems for which it is
not immediately clear what knowledge is applicable. Students need to
progress through increasingly challenging and open-ended problems
during their four years, culminating in a project or internship that
requires them to experience the complexity and ambiguity of true
problem-solving.
Communication skills provide the other requirement for successful
employment. While aspects of these skills are taught in other
departments, mathematics faculty have a particular responsibility to
help students learn the effective communication of technical
information, especially mathematical information with its requirements
of logical reasoning and precision. Again, this takes time and is
something that should be woven into every mathematics course. It is not
enough to be able to find a solution to a difficult problem. Students
need practice explaining how they came to their solution, how they
justify it, what it means, and how it can be applied. Proof plays a
particularly important role here. To dissect a proof is to explore and
come to understand how someone else solved a problem. To construct a
proof is to communicate one's own understanding of how a particular
result relates to the rest of mathematical knowledge. Our students need
to develop confidence in giving these explanations both in writing and
orally, both formally and informally.
At Macalester College, all senior mathematics majors are required
to write a senior thesis and then explain it to an audience of
undergraduates ranging across the full four years. We have found that
employers focus in on this experience. Students who can give a clear
and succinct account of how they solved a particular problem and why
this solution is both interesting and useful find themselves at a great
advantage as they compete for employment. Even those who are not
heading into the nonacademic workplace benefit from these skills.
It is also important to help our students build the networks that
will enable them to meet and learn from mathematicians who are out in
the general workforce. Internships, if well designed and supervised,
can do this. The Harvey Mudd Mathematics Clinic is a model for
combining both problem-solving and networking.
The nonacademic workforce is often so far from what we do as
mathematicians that it can be hard for us to connect to its particular
requirements. But we do our students a great disservice if we do not
make the effort.
Do you know of programs, projects, or ideas
that should be included in the CUPM Illustrative Resources?
We would appreciate more examples that document experiences with the
use of technology as well as examples of interdisciplinary cooperation.
David Bressoud is DeWitt Wallace Professor of
Mathematics at Macalester College in St. Paul, Minnesota, he was one of
the writers for the Curriculum Guide, and he currently serves as Chair
of the CUPM. He wrote this column with help from his colleagues in
CUPM, but it does not reflect an official position of the committee.
You can reach him at bressoud@macalester.edu. | 677.169 | 1 |
ninth edition of Mathematics for Elementary Teachers: A Conceptual Approachcontinues the innovative time-tested approach of the previous editions: an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation. Features of the text focus on ensuring that prospective teachers will gain not only a deeper understanding of the mathematical concepts, but also a better sense of the connections between their college math courses and their future teaching experiences, along with helpful ideas for presenting math to their students in a way that will generate interest and enthusiasm. The text draws heavily on NCTM Standards and contains many pedagogical elements designed to foster reasoning, problem-solving and communication skills. The ninth edition represents a significant step forward in terms of online course management as roughly half of all problems in the text will be assignable through our new online homework platform, Connect Mathematics. In addition, Connect Mathematics will be fully integrated with Blackboard, providing the deepest integration of an online homework and course management system in the market today. Additionally, this text contains an activity set that corresponds to each section of the companion text, Mathematics for Elementary Teachers: An Activity Approach,also by the Bennett, Burton, and Nelson team. Mathematics for Elementary Teachers: An Activity Approachcan be used independently or along with its companion, Mathematics for Elementary Teachers: A Conceptual Approach. | 677.169 | 1 |
Additional Product Information
Features and Benefits
An Innovative Critical-Thinking Feature: Concept Investigations. The directed-discovery activities called Concept Investigations are ideal as group work during class, incorporated as part of a lecture, or as individual assignments to investigate concepts further. Inserted at key points within the chapter, each Concept Investigation helps students explore patterns and relationships such as the graphical and algebraic representations of the functions being studied.
Worked Examples with In-Text Practice Problems. This text offers a comprehensive range of examples from basic techniques (solving by hand, exponent rules, graphing) to realistic applications with manageable data sets to intriguing applications that call for critical thinking about phenomena (population growth) and daily activities (interest rates in action, the cost of a truck rental). Worked examples are labeled so students can make the connection between the example and the concept being studied. The accompanying in-text practice problems help students to gain a sense of a concept through an example and then to practice what has been taught in the preceding discussion. In addition, examples of hand-drawn graphs help students visualize what their own work should look like.
Practical Help for Instructors. Practical tips are provided in the Annotated Instructor's Edition on how to approach and pace chapters as well asIntegrated "Student" Work. Clearly identifiable examples of "student" work appear throughout the text in Examples and Exercises. These boxes ask students to find and correct common errors in "student" work.
An Eyeball Best-Fit Approach. Linear, quadratic, and exponential functions are analyzed through modeling data using an eyeball best-fit approach. These models investigate questions in the context of real-life situations. Creating models by hand leads students to analyze more carefully the parts of each function reinforcing solving techniques and making a better connection to the real-life data and how they affect the attributes of the function's graph. Graphing calculators are used to plot data and check the fit of each model.
Margin Notes. The margin contains four kinds of notes written to help the student with specific types of information: Skill Connections provide a just-in-time review of core mathematical concepts, reinforcing student skill sets; Connecting the Concepts reinforce a concept by showing relationships across sections; Specific vocabulary of mathematics and the applications are helpfully defined and reinforced through margin notes called "What's That Mean?"; and Using Your TI-Graphing Calculator offers just-in-time calculator tips for students. Additional material is available in the Using the Graphing Calculator Appendix.
Exercise Sets. The exercise sets include a balance of both applications and skill-based problems developed with a clear level of progression in terms of difficulty level. Most exercise sets begin with a few warm-up problems before focusing on applications. Exercise sets typically end with additional skill practice to help students master the concepts when needed. A balance of graphical, numerical, and algebraic skill problems is included throughout the book to help students see mathematics from several different views. End-of-book answers are written in full sentences to underscore the emphasis on student communication skills.
Enhanced WebAssign, used by over one million students at more than 1,100 institutions, allows you to assign, collect, grade, and record homework assignments via the Web. This proven and reliable homework system includes thousands of algorithmically generated homework problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more. New Assignable Stand Alone Master It questions are unique to INTERMEDIATE ALGEBRA, and reinforce student understanding and develop conceptual knowledge. These modeling type problems contain real-life data, break the question into multiple parts, and reflect the step-by-step process that is taught in the text. These problems support the conceptual and applied approach of the textbook and force students to confirm their understanding as they work through each step of the problem.
Appropriate Use of the Calculator. Graphing calculators are used in this text to help students understand mathematical concepts and to work with real-world data. Graphing calculators are used to create scatterplots of real data and to check the reasonableness of algebraic models for the data. Linear, quadratic, and exponential models are created by hand, using an eyeball best-fit approach and algebraic techniques. The calculator is also used to check solutions both graphically and numerically and to do some numerical calculations. However, students are also required to solve problems, graph, and do other algebraic skills by hand.
Extensive End-of-Chapter Material. Includes Chapter Summaries, Review Exercises, Chapter Tests, Chapter Projects, Equation Solving Toolbox, and Cumulative Reviews. Chapter Summaries revisit the big ideas of the chapter and reinforce them with new worked-out examples. Students can also review and practice what they have learned with the Chapter Review exercises before taking the Chapter Test.
Chapter Projects. To enhance critical thinking, end-of-chapter projects can be assigned either individually or as group work. Instructors can choose which projects best suit the focus of their class and give their students the chance to show how well they can tie together the concepts they have learned in that chapter. Some of these projects include online research or activities that students must perform to analyze data and make conclusions.
Equation Solving Toolbox. This feature appears after every two chapters and revisits and summarizes skills students have used to solve equations in preceding chapters and processes for finding models.
Cumulative Reviews. Cumulative reviews appear after every two chapters, and group together the major topics across chapters. Answers to all the exercises are available to students in the answer appendix.
InstructorEach section of the main text is discussed in uniquely designed Teaching Guides containing instruction tips, examples, activities, worksheets, overheads, assessments, and solutions to all worksheets and activities.
Solutions Builder
(ISBN-10: 0840054122 | ISBN-13: 9780840054128)
This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. Visit
The Complete Solutions Manual provides worked-out solutions to all of the problems in the text.
Text-Specific DVD
(ISBN-10: 0534496431 | ISBN-13: 9780534496432)
Honored with two Tellys, a Communicator Award, and an international Aurora Award, these ten- to twenty-minute problem-solving lessons cover almost every learning objective from each chapter. Rena Petrello--recipient of the "Mark Dever Award for Excellence in Teaching"--presents each lesson using her experience teaching online mathematics courses. It was through this online teaching experience that Petrello discovered the lack of suitable content for online instructors, prompting her to develop her own video lessons and ultimately create this video project. Students will love the additional guidance and support when they miss a class or when they are preparing for an upcoming quiz or exam(or DVD).
Student Workbook
(ISBN-10: 1111568898 | ISBN-13: 9781111568894)
Providing the perfect head start, the Student Workbook contains all of the assessments, activities, and worksheets from the Instructor's Resource Binder for classroom discussions, in-class activities, and group work.
: Contains fully worked-out solutions to all of the odd-numbered end-of section exercises as well as the complete worked-out solutions to all of the exercises included at the end of each chapter in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answerOffering practical help for instructors, the Annotated Instructor's Edition provides the complete student text with answers next to each respective exercise as well as tips on how to approach and pace chapters andStudentGo beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text as well as the complete worked-out solutions to all of the exercises included at the end of each chapter in the text. This gives you the information you need to truly understand how these problems are solved youMark ClarkCynthia Anfinson | 677.169 | 1 |
An Introduction to Wavelets Through Linear Algebra
This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context…
Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see non-trivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory. | 677.169 | 1 |
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Student responses to an algebraic task bring
teachers insight into students' approach, their interpretation and what
knowledge they drew on in answering the question.Learn how to plan better instruction to develop
students' understanding of mathematical proofs. | 677.169 | 1 |
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The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems. Every section ending in the text begins with six simple writing exercises. These exercises are designed to get students to review the definitions and rules of the section before doing more traditional exercises | 677.169 | 1 |
MathWorld is possibly the most extensive math reference site on the web, and is geared toward the very advanced student. The algebra index is no exception, offering reference material on mainly upper level topics. Information is also available on more basic skills such as the quadratic equation, general identities, and algebraic properties. This resource is part of the Teaching Quantitative Skills in the Geosciences collection.
Intended for grade levels:
High (9-12)
College (13-14)
College (15-16)
Graduate / Professional
Type of resource:
Text:
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Subject:
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These pages may not be copied, mirrored, or reproduced in bulk without permission of the author. Reproduction for commercial purposes is not permitted, nor is use of robots to create archival copies. Copyright 1999-2002 Wolfram Research, Inc. | 677.169 | 1 |
Visual Calculus is a collection of notes, primarily for the instructor, that give some ideas for how technology - in particular computers - can be used in the teaching of calculus.
TOPICS include:
Pre-Calculus Limits and Continuity Derivatives Applications of Differentiation Integration Applications of Integration Sequences and Series
You'll find all your favorite equations with graphs and tables that illustrate their solutions, and detailed instructions for using a variety of public domain, shareware, and commercial software packages. An appendix provides a series of tables showing the software programs used with each topic.
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FROM THE EMAILBAG - MINORITIES AND MATH
I'm an initially certified teacher of High School Mathematics. I have been trying to find some information on minority contributions to mathematics and came across your page. I think it is a very good resource; however, I believe that it is important for us (as public school teachers) to have the resources and knowledge to be able to give our students examples of people like themselves who have succeeded and made relevant contributions to fields like math, science, and engineering. For that reason, I have been searching for information on minority contributions to math. I would be pleased if you could add some biographical histories of minority mathematicians... - Tracy Poche'
Thanks for your question, Tracy. We've just made a start in this area, looking for what's on the Web and collecting some of the best resources at
Kristin Lockwood has put together an annotated bibliography of resources for mathematics teachers and others interested in how language may affect the thought, achievement and assessment of students of limited English proficiency, as well as these students' access to knowledge and education.
WE'D LIKE YOUR HELP in finding more information to add to our materials on minorities and mathematics. Maybe we can give you hand with putting something you've written on the Web. Send your website suggestions or other materials to | 677.169 | 1 |
Edgenuity Adds Algebra I for Blended Classrooms
"The full-year course focuses on the key areas of the Common Core model pathway for Algebra I and builds on the foundation established in middle grades by deepening students' understanding of linear and exponential functions, and developing fluency in writing and solving one-variable equations and inequalities," according to a news release.
Features include:
On-screen teachers thinking aloud to model problem solving;
Guiding questions for each lesson to promote inquiry and a focus on bigger ideas;
Performance tasks, designed to allow students to show understanding with real-world applications.
"Algebra is critical to student success in college and career because it sharpens essential reasoning skills," said Sari Factor, CEO of Edgenuity, in a prepared statement. "Our new Algebra I course raises the bar for accessibility, using multimedia and interactives to develop analytical problem-solving skills and to ensure mastery for students with a variety of learning styles | 677.169 | 1 |
Details about Math for Civil Service Tests:
All civil service exams have a required math section. Many candidates havenAEt taken math in years and are nervous about being tested in this area. They receive targeted help with this book that emphasizes the math skills needed to score higher on their exam. A supplement to the civil service test prep book for the career of choice, this book helps candidates improve their chances of a higher overall score on the exam. Fast, focused practice helps test takers remember, build, and improve math skills."
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Rent Math for Civil Service Tests 1st edition today, or search our site for other textbooks by Jessika Sobanski. Every textbook comes with a 21-day "Any Reason" guarantee. Published by LearningExpress, LLC.
Need help ASAP? We have you covered with 24/7 instant online tutoring. Connect with one of our History tutors now. | 677.169 | 1 |
Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators.
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Challenging but rewardingMarch 31, 2011
by Steve
This textbook has a thorough coverage of AP Calculus AB/BC. I used this textbook for the multiple-choice section and CollegeBoard's own materials for the free-response section. Most of my students scored 5. I also used some of its chapters for my IB Mathematics SL and HL students. Most US high-school students feel calculus is too challenging for them since they did not have enough practice in algebra, geometry, and pre-calculus. The following is my suggestion: if you got at least an A in pre-calculus/trigonometry, you may want to learn calculus in high school; otherwise, wait until you get into the college.
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What are the technology issues involved in making math accessible?
Learning Points:
By using universally designed math technologies like MathML to create
accessible math equations, the resulting content will also
provide for alternative access
to meet a student's special access needs.
Most math equations currently used in digital environments like the
Web are simply static bitmaps (digital drawings) of equation images, and are
inherently inaccessible.
Using MathML provides a number of
accessibility benefits and produces math equations that can be both
rendered visually on the screen and also available through alternative
access means.
Turning math expressions
into audio form can be a very effective form of alternative access for
people who have visual or learning disabilities. Images of equations do not
by themselves supply information to support any form of audio rendering, but
coherent and consistent audio rendering of math expressions is available
when using MathML.
Since there are many users who can see but who have some form of
visual impairment, the need to enlarge
mathematical equations on a computer screen is very common. Using MathML
provides for user flexibility to change visual aspects such as the size and
color of the font as well as the background of the display.
Synchronous highlighting of math equations with audio can be beneficial
for students with learning disabilities or attention deficit disorders, as
well as for students with low vision. Math equations which have been encoded
in MathML can permit a range of highlighting reinforcement options.
The ability to better comprehend longer or more complex mathematical
equations in audio form is aided by
user navigation within a math
equation. This is not feasible with prerecorded audio files or text
equivalents, but can be made possible when using math content encoded in
MathML.
In the past, it is sad to say that math accessibility was not considered a
viable concern among many educators. It was not unusual to hear people express
the opinion that math was not a primary subject needing much focus, that
providing access to math content was too difficult, or that most students with
disabilities would simply find math too complex anyway and therefore not worth
the trouble. At Design Science, we reject these notions as regressive and
insulting to people with disabilities. Such old attitudes are now changing, and
greater levels of effective access to mathematical information has been made
available thanks to continuing improvements in math accessibility. Although there are many technical
issues involved in making math accessible, Design Science wants you to know
that we have found solutions for many of these issues, and are actively involved
in research projects with an aim to design even better math accessibility
technologies in the near future.
For users with special needs, having access to math
information in something other than just ink on paper is essential. In
educational settings many students with
print disabilities
must rely upon alternative format materials in place of standard print in order
to access textbooks, tests, classroom hand-outs or other types of instructional
content. Having math displayed on a computer screen begins to remedy some
accessibility issues by providing an environment where the content can be
enlarged for people with low vision, or by allowing someone with no use of their
hands to virtually "turn pages." But the common current practice of using graphical images to represent mathematical
equations in computer applications, such as using GIF or JPG image files to
display math in Web pages, does nothing to make those equations accessible to many people
with disabilities who depend upon assistive technologies like synthetic speech
or refreshable braille displays.
By using MathML to create universally designed accessible math equations, the resulting content
can be translated into any other imaginable output format needed, which ensures
that alternative formats that meet a student's access needs will be available
for use with their assistive technology. Math with accessible equations can be
rendered with synthetic speech, can be utilized with synchronized highlighting,
and can be also converted into braille math code for blind students.
Synchronized highlighting of math equations on a computer screen with synthetic
speech helps those with low vision, and can be a significant aid to students
with learning disabilities.
Accessible equations, unlike images, will format and
display correctly on PDAs and on high-resolution output devices not yet
invented. They can use larger fonts and match a user's preferred color schemes.
Accessible equations will form the basis of universally designed math
instructional content, as well as fully accessible math assessments for use by
all students. By having accessible math content available in instructional
software, e-books, and assessments, all students will have equal access to the
same content and the same learning supports, regardless of whether or not they
have a disability. This eliminates the need to have a totally separate process
to create an alternative format at a later date, and virtually guarantees that
students with disabilities will be able to access the same content at the same
time as students without disabilities.
Most of the math equations one currently finds in digital environments like
the Web are simply static bitmaps (digital drawings) of equation images in GIF, PNG,
or JPEG formats. These images can be seen with the human eye, but they are
devoid of non-visual information that can be utilized by assistive technologies.
Such image formats are, by themselves, inherently inaccessible. They do not
provide for alternative output modalities, such as braille or synthetic speech
and cannot be easily altered for people with low vision (for example, font
enlargement or color and contrast changes). Furthermore, such image formats are
plagued by other usability and aesthetic problems such as ease of alignment,
sizing, and color conformity with the text, require the author to spend much
more editing time to make visually appealing web content, and require authors to
keep a large inventory of static equation images which are not easily editable, requiring the author to
redraw images when even small changes are made. Finally, images take up
relatively large amounts of bandwidth, which is a hindrance for low-speed
Internet connections.
Alt tags are limited to a narrative description of math
equations, and must be laboriously hand coded by someone who can fully
understand the context of the expression and unambiguously describe it with
complete consistency. Even if this could be guaranteed, there would still be no
way to intelligently navigate though a math equation, and still doesn't fix some
of the previously mentioned issues like support for brailled math output. So
although the use of properly authored alt tags may supply minimum access to math
content, it is still a far cry from the maxim that individuals with disabilities
should "have access to and use of information and data that is comparable to
that provided to the public who are not individuals with disabilities" as
mandated by the provisions of the
1998
Amendment to Section 508 of the Rehabilitation Act.
As we just discussed, math images (with or without a text equivalent) cannot provide a
level of access that is comparable to, or as effective as, the level of access
that individuals without disabilities are being provided. Instead, the preferred
(and vastly more effective) technique is to use a
standardized markup language that can be accessed by the assistive technologies
that people with disabilities use. Using such a technique means that the author
has to encode information only once because there is no need to go back through
a second time and add an alternative (alt tag) description. The same coding
supplies, at the same time, the needs of both those who use and those who do not
use assistive technologies, and hence is a much more effective authoring method.
MathML (Mathematical Markup Language)
has been adopted by the W3C as the standard way of expressing math on the Web,
and provides the basis for math equations that can be both rendered visually on
the screen and also available through alternative access means. MathML contains
sufficient information and structure to provide support for both visual display
and alternative access means such as synthetic speech and braille. Equations
which are encoded in MathML will increase in size as users change font size to
increase readability, unlike images. When using synthetic speech, MathML will
allow the user to set different verbosity levels and can automatically adjust
for the user's native language. For braille users, using MathML will allow for
the choice of various braille math formats, depending upon braille translation
software support.
Turning math expressions into audio form can be a very effective form of
alternative access for people who have visual or learning disabilities. Images
of equations do not by themselves supply information to support any form of
audio rendering, although text equivalents can be audibly rendered by synthetic
speech applications as mentioned previously. Producers of alternative format
materials can also provide previously recorded audio files (either from human
readers or synthetic speech used at the producer end) that can supply an audio
rendering of math equations in digital environments even without the presence of
a screen or text reader on the end user system, as is commonly done in currently
available Digital Talking Books. This approach does provide access for users
with visual or learning disabilities, but would be of no benefit for deaf-blind
users. Just as in the case of text equivalents, this type of audio rendering can
only supply a very limited level of accessibility and only for the most simple
equations.
However, much more coherent and consistent audio rendering of math
expressions is available when using MathML. Synthetic speech engines used by
students who are blind, such as JAWS, Window-Eyes, HAL, Supernova, MAGic, and Serotek
System Access, and text readers
used by students who have learning disabilities, like TextHelp's Read & Write Gold
and BrowseAloud, can
already seamlessly interface the reading of MathML math expressions by using
MathPlayer. Further development of math speech technologies will allow user customization of speech
generation rules and control of prosodic cues such as the pitch and rhythm of
the math speech, which will help to increase the
comprehension rate of users for both the structure the content of
the expression.
Since, in comparison to the number of people who are blind, there are many
more users who can see but who have some form of visual impairment (commonly
referred to as having "low vision") the need to enlarge mathematical equations
on a computer screen is much more common. Such users may also need to change
the color of the font as well as the background of the display. Math images
(graphical formats) do not enlarge well, and cannot be enlarged by simply
changing browser settings. There is also no simple user defined method available
to change image colors. When math equations are encoded in MathML, however,
visual definition does not degrade with size increase, and users have control
over the size, color, and contrast of math font display just as they do for
literary text. MathML also provides for consistent linebreaking when math
equations are enlarged, which
is important for all users but particularly important for people
with low vision.
Most of the text reader applications currently on the market make use of
synchronized highlighting
of literary text as the words are being spoken. This technique is also available
with Digital Talking Books when they are used with visual display environments.
Synchronous highlighting is beneficial for students with learning disabilities
or attention deficit disorders, as well as for students with low vision.
Although significant research has been conducted demonstrating the value of
synchronous highlighting toward increasing reading comprehension of literary
materials, the fact that synchronous highlighting of math has only recently
become possible has limited the availability of research supporting increased
comprehension of math expressions through synchronous highlighting to this
point. However, the implication that synchronous highlighting of math
expressions as they are spoken increases comprehension seems very likely.
Math equations which have been encoded in MathML can permit a range of
highlighting reinforcement options. Equations can be broken down into various
subcomponent sections as they are being spoken depending upon the flexibility
provided within the reading application. The degree of highlighting granularity
desired will likely depend upon the individual student's instructional need or
user preference.
The ability to provide math access through refreshable braille
displays and hard copy braille output is important for both blind and deaf-blind
users. Most good braille readers
find audio-only access to
mathematics considerably inferior to braille or combined braille and audio
access. Math images cannot be accessed by braille, but braille access to math
encoded in MathML can be provided. However, there are a number of competing math
braille codes in use around the world, which complicates the ability to support
braille output for MathML. A relatively new type of two dimensional math braille
called
DotsPlus is simple to produce with MathML content. Support for other
commonly used math braille, like Nemeth code, is dependent upon MathML support
by makers of braille translation software.
The ability to better comprehend longer or more complex mathematical
equations in audio form is aided by user navigation within the equation to hear
different expression elements separately. This is not feasible with prerecorded
audio files or text equivalents, but can be made possible when using math
content encoded in MathML.
Allowing navigation of math expressions using keyboard commands will allow
the user to explore the structure of an equation at the user's own pace.
Although it may be difficult to comprehend especially long equations through
audio access only, the ability to audibly walk through an unambiguous vocalization of the
expression and subdivide lengthy equations at natural "chunking" spots greatly
enhances intelligibility of accessible math expressions. | 677.169 | 1 |
The Texas Instruments TI-Nspire is a graphing calculator that is designed exclusively for students of any math class. Its technology allows students to see and make connections with up to four problems at a time on one screen.
Bonus: Get the best graphing calculator from Calcustar.com, if you are not interested in Ti-Nspire. The CAS version is better and newer.
These four representations of a problem include algebraic, numeric, graphical and written formats. All these can be viewed and studied in real time. This is an ideal choice for students struggling in math class.
They can learn different types of equations and expressions by watching the practice problems being produced. They can also get an idea about how various concepts are linked. These functions help students sharpen their critical thinking skills because they will be able to actually see mathematical patterns and relationships.
The TI-NSpire graphing calculator contains functionality similar to that of a computer. Students can even create, save, and edit documents. This means that if a user runs out of time when inputting an equation, he/she can save the progress and resume later. For instance, students can study the relationships of rise, run and slopes by using a graph on the TI-NSpire.
This handheld device can be used on all the important high school exams, such as the ACT, PSAT and SAT. Corresponding software can be attained online, along with other applications and packages.
Studies show that the use of apps makes students feel more excited and interested in math! Even students who normally claim to hate math class find that learning can be easy with the TI-NSpire graphing calculator.
What's more, this hand held device can be used for scientific purposes as well as mathematical! Here are some details about the TI-NSpire:
PROS
Dynamic, instant linking from one representation to another in real time.
Multiple representations of the same problem or representations on different problems, all at once.
Computer interface and cursor controls.
Easy navigation between various functions and screens.
Rechargeable battery
Snap-in, TI-84 keypad.
Can be hooked up to the PC for downloading programs and even games!
Can be used to solve any type of math problem for any math class.
CONS
As with all graphing calculators, there are unfortunately a few cons of the TI-NSpire, including:
The high cost.
Lack of speed.
Large, bulky size.
The snap-in keyboard may be a con for some rather than a pro.
Those who always seem to lose or drop everything need to be extra careful.
CONCLUSION
Obviously, the pros outweigh the cons, making the TI-NSpire a great Texas Instruments calculator. New TI-NSpires can be ordered on the internet for $129.99 or so, depending on the store. The average price for a used one is about $85. Usually, a warranty is provided for new purchases.
Pregnant women always need to feel comfortable and should always give a perfect relaxation to their body. A body pillow for pregnant is a pillow that provides a comfortable feel to the women while they sleep or lay down. A woman gets a complete support and this is good for her and also for the baby inside her.
At the time of pregnancy a woman should be taken proper care of as a new life is growing inside her body. If a pregnant woman is to get a pillow for herself, then she should select the pillow that has some unique qualities that make the difference between a normal pillow and a pregnancy body pillow. Read this top pregnancy pillow guide from Pillowfiesta.
The materials used are polyester and cotton, which gives a nice feel and comfort to the body. The pillows don't contain any kind of toxic materials. Hence, these are safe for the pregnant woman in every aspect. Some pregnancy pillows are hypoallergenic too! The body pillow has the thickness of 19 inches and length of 64 inches on each side that gives complete comfort. The night's sleep is much convenient and gives a great relief.
What are the features of Body pillow for pregnant women?
The features of the Body pillow for pregnant women are as follows:
Comfortable for the whole body
Whether a pregnant woman wants to give support to her belly or her back, this body pillow will be comfortable for her entire body, which is very good to relax.
Perfect Ventilation
The most important feature is the necessary ventilation that a pregnant woman gets through this pillow. The rise and fall of temperature affect a pregnant woman more than a normal body. This pillow is completely comfortable to give a cool as well as warmth at that time.
Safe fabrics
The fabrics used in this pillow are safe as cotton is used on the outer portion and polyester is used in the inner portion. It's very much convenient for her at the time of resting.
Adjustment band
The band can easily be adjusted and the woman and her child feel comfortable.
Easy to clean and store
This is very easy to clean and can easily be stored at room. A woman can easily wash it after use.
To sum it up
Pregnancy pillows are really useful for pregnant mothers. It will offer a lot of comfort and it will greatly lessen the pains of pregnancy. It comes from different sizes, shapes and prices. My recommendation is, do not hesitate to get one. It will surely help you throughout your pregnancy. | 677.169 | 1 |
Course Content and Outcome Guide for MCH 130 Effective Fall 2016
Course Description
Introduces the rules, methods and procedures for using trigonometry formulas that deal with both the sides and the angles of the right triangle and oblique triangle to solve for the unknown parts. Prerequisites: MCH 100. Audit available.
Addendum to Course Description
Text:
Mathematics for Machine Technology by Smith, published by Delmar, 6e Edition, ISBN: 1-428-33656-7
Intended Outcomes for the course
Upon successful completion of this course students will be able to: 1. Use sine, cosine, and tangent and functions to determine coordinates of a part to be machined.
Course Activities and Design
MCH 130 will be presented by means of audio-visual presentations, demonstrations, lab experiences, and research activities. The course activities and design emphasize the development of skills and knowledge outcomes prescribed by established industry standards. The identified outcomes will be achieved by means of individual and team activities.
Outcome Assessment Strategies
The final grade will be calculated from the average of a mid-term and a final exam. The two exams present questions based on the exercises assigned in the class.
Course Content (Themes, Concepts, Issues and Skills)
Machine Shop Math / Trigonometry consists of the following modules: Module 1 €" Fundamentals of Plane Geometry €" Plane Geometry is the branch of mathematics that deals with points, lines, and various figures that are made of combinations of points and lines.
Module 2 €" Applying Shop Trigonometry - Most of the trigonometric relationships used by machinists are based on the right triangle. The right triangle formulas we used previously dealt with the length of the sides only. Trigonometry formulas deal with both the sides and the angles.
Related Instruction
Computation
Hours: 65
Use sine, cosine, and tangent and functions to determine coordinates of a part to be machined. | 677.169 | 1 |
Plantation, FL StatisticsBruce CJenn SHongjun C.
...Precalculus includes algebra, coordinate geometry, trigonometry, and most of all, functions---the general concept as well as specific functions. Students come to this course familiar with basic algebra and geometry. A precalculus course builds on all of their previous mathematical knowledge and experience to understand calculus that is essential to succeed in a college. | 677.169 | 1 |
ok. I'm going to be pretty slow replying to vms because I don't have a working laptop right now. Been using phone, tablet, and my mom's and brother's computers when I can. But hey, that's pretty cool that you're part of some exchange programme! And yes, let's continue. c:
Ah ok I see it's just a term for more advanced math. All of the terms like logarithms and integration and factor theorem kind of went over my head cause I'm far from being a math whiz. XD I almost failed the basic math and algebra in high school. XD
That's definitely a good thing though to be able to pass a complex class like that so good job! | 677.169 | 1 |
High School Algebra II course Outline
This course begins with a review of Algebra I topics and introduces the following new topics: matrices, complex numbers, exponential and logarithmic functions, conic sections, higher degree polynomial functions, sequences and series, and trigonometry. This course is required for students who are planning to attend most post-secondary institutions.
20- Equations that are Quadratic in Form
1- Solving Equations in Quadratic Form
2- Quadratic Equation Example
3- Quadratic Equation Examples(cont)
4- Quadratic Equations Example 3
Handout: Equations that are Quadratic in Form
Assignment: Equations that are Quadratic in Form
29- Circles
1- Equation of a Circle
2- Equation of Circles (examples)
3- General Form of an Equation of a Circle
4- General Form of Equation(examples)
5- General Form of Equations Examples(Cont)
Handout: Circles
Assignment: Circles | 677.169 | 1 |
What every College Bound Math Student Should Know
(a guide to help students transition between high school and college)
Below is a list of general guidelines for what to expect in college-preparatory mathematics courses. It is far from comprehensive but is intended to help the student understand the difference between core mathematical requirements (through Algebra II) and those beyond (Pre-Calculus and Calculus).
1) The goal of college bound math students is more than just being able to reproduce what was told to you in the classroom. Expect to be able to apply what you have learned in new situations.
2)Expect material to be covered at what seems to be an increased pace. Retention of previous material is essential to further development of the concepts and success. It is expected that students have mastered the concepts of the pre-requisite courses and having to relearn these concepts while expanding and applying them will cause additional stress.
3)Classroom time is at a premium so it must be used efficiently. Do not expect to be able to get your homework done in class as well as learn new material simultaneously. Also, do not expect to do homework for another class and be successful in this one.
4)Take notes in class! Since learning the material is your responsibility, having the information written by your own hand will increase your opportunity to learn and retain the information.
5)You cannot be "taught" everything inside the classroom as experience working the problems and combining the theory takes time and practice. Therefore it is essential that you do your homework to give you this needed time to process the material.
6)The instructor's job is to provide a solid framework with some particulars to guide the student into learning the concepts and methods which comprise the material of the course. It is NOT to "program" you with isolated facts and problem types that you can simply regurgitate.
7)You must use your textbook to guide you through the class. There are two different approaches:
a.Read for the first time the appropriate section(s) of the book before the material is presented in the classroom. As the material is taught, you can then process and sort the specific content into what you have generally learned. Being prepared for class makes the accelerated pace more manageable (recommended for most students).
b.Try to pick up what you can from the lecture by absorbing the general idea or through taking notes. Then read through the appropriate section(s) of the book to sort through the learned material properly (not recommended for most students as this tends to cause "information overload").
8)Ask questions in class. Though it may appear most people are "getting it," chances are more people will appreciate your question rather than resent your asking it (provided that your question shows that you have been fully engaged in the classroom discussion).
9)Study with other students in the class. This will greatly decrease your chances of "learning the material wrong." More importantly, it will give you the opportunity to engage others in the discussion of the material which will help clarify everyone's knowledge. | 677.169 | 1 |
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Essential MATLAB for Engineers and Scientists/i>
Overview design and algorithm development are presented clearly and intuitively, along with many examples from a wide range of familiar scientific and engineering areas.
This is an ideal book for a first course on MATLAB or for an engineering problem-solving course using MATLAB, as well as a self-learning tutorial for professionals and students expected to learn and apply MATLAB.
Updated with the features of MATLAB R2012b
Expanded discussion of writing functions and scripts
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Editorial Reviews
From the Publisher
"This book provides an excellent initiation into programming in MATLAB while serving as a teaser for more advanced topics. It provides a structured entry into MATLAB programming through well designed exercises." - Carl H. Sondergeld, Professor and Curtis Mewbourne Chair, Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma
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"For a while I have been searching for a good MATLAB text for a graduate course on methods in environmental sciences. I finally settled on Hahn and Valentine because it provides the balance I need regarding ease of use and relevance of material and examples." - Professor Wayne M. Getz, Department Environmental Science Policy & Management, University of California at Berkeley
"This book is an outstanding introductory text for teaching mathematics, engineering, and science students how MATLAB can be used to solve mathematical problems. Its intuitive and well-chosen examples nicely bridge the gap between prototypical mathematical models and how MATLAB can be used to evaluate these models. The author does a superior job of examining and explaining the MATLAB code used to solve the problems presented." - Professor Mark E. Cawood, Department of Mathematical Sciences, Clemson University
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Product Details
Related Subjects
Meet the Author
Daniel Valentine is a Professor of Mechanical and Aeronautical Engineering at Clarkson University and Affiliate Director of the Clarkson Space Grant Program which is part of the New York NASA Space Grant Consortium. This program has provided support for undergraduate research appointments, and for graduate students. He is currently investigating the nonlinear dynamics of two-dimensional, Navier-Stokes flows as part of his work on the development of computational methods to solve fluid dynamics problems. He is also working on the flow-structure interaction of long-span bridges, unsteady hydrodynamics and offshore renewable energy. Other activities include investigations to develop a computational method to predict the effect of a marine propulsor on wave resistance of ships, to examine the effect of density stratification on rotating flows, to develop computational tools to predict the time-averaged properties of high-Reynolds number flows among other fluid mechanics problems. | 677.169 | 1 |
Modify Your Results
Beecher, Penna, and Bittinger's College Algebra is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively. Mid-chapter Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Summaries provide built-in tools to help them prepare for tests. The MyMathLab course (access kit required) has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Review exercises from the text as well as example-based videos created by the authors.
The Bittinger series changed the face of developmental education with the introduction of objective-based work texts that presented math one concept at a time. This approach allowed readers to understand the rationale behind each concept before practicing the associated skills and then moving on to the next topic. With this revision, Marv Bittinger continues to focus on building success through conceptual understanding, while also supporting readers with quality applications, exercises, and new review and study materials to help students apply and retain their knowledge.
Drawing examples from business, chemistry, and physics, this textbook walks through graphical and algebraic methods for solving linear equations, inequalities, and polynomials, as well as rational, radical, quadratic, exponential, and logarithmic equations. The second edition moves the conic sections material to an appendix and adds a section on factoring the sums and differences of cubes.
There are many features built into the daily lessons of this text that will help you learn the important concepts and skills you will need to be successful in this course. There are numerous Exercises in each lesson to give you the practice you need to learn. Practice Multiple Choice exercises are included in the lesson to help you prepare for success on your state test. The text also contains Error Analysis, Test Prep exercises, Critical Thinking exercises, Challenge exercises | 677.169 | 1 |
Consumer Mathematics presents basic math skills used in everyday situations—paying taxes, buying food, banking and investing, and managing a household. The full-color text helps students and young adults become wiser, more informed consumers.
Lexile Level
850
Reading Level
3-4
Interest Level
6-12 | 677.169 | 1 |
topic scientific here
"what a nice Calculator, more of a tool for Students Smile But still it has lots of shortcuts, a math book etc, VERY Nice! " Could we disagree ? | 677.169 | 1 |
Operations With Integers
Course
Course Title
Class
Lab/ Shop
Clinical/ Co-op
Credit
DMA 010
Operations With Integers
.75
.50
0
1
Prerequisites: None
Corequisites: None
Effective Term: Spring 2012
This course provides a conceptual study of integers and integer operations. Topics include integers, absolute value, exponents, square roots, perimeter and area of basic geometric figures, Pythagorean theorem, and use of the correct order of operations. Upon completion, students should be able to demonstrate an understanding of pertinent concepts and principles and apply this knowledge in the evaluation of expressions.
Legend
: Comprehensive Articulation Agreement - This course is recommended for students transferring to a four-year university. | 677.169 | 1 |
Description
Monash Science supports current students studying VCE Specialist Maths Units 3 and 4 by inviting you to attend free VCE revision. These sessions are tailor made to reinforce key mathematical concepts in the curriculum and will be delivered by a qualified VCE teacher boasting extensive experience this area.
Please click here for the campus map and location of the revision session.
Science precinct tour
While you're here, take a closer look and visit our new science facilities and learning spaces. The Monash Science Precinct is a vibrant space which will form the perfect setting for further studies in science. The tour will take place during the break between Units 3 and 4 and you're welcome to eat lunch along the way. If you'd like to register, please click here.
9.30am - 12.00pm Unit 3
12.00pm - 1.00pm Break
1.00pm - 3.00pm Unit 4
The revision will be presented by;
Dr Tod Nestor studied Mathematics and Physics at Monash University and subsequently completed a PhD in Theoretical Geophysics at the Australian National University. He has been teaching Units 3 & 4 Mathematical Methods and Specialist Mathematics for the last 20 years. He has written for the VCAA, publishers of textbooks and vendors of School Assessed Coursework tasks. He has assessed VCAA examinations in Specialist Mathematics. He is currently the Head of Mathematics at the Berwick Campus of Beaconhills College. | 677.169 | 1 |
Find a SunolNot being ready, students can't study calculus successfully. Therefore, in Precalculus, students will be introduced to the important and basic mathematical concepts inquired before in algebra with deeper and higher details. They comprise, but not limited in, inequalities, equations, absolute values, and graphs of lines and circles | 677.169 | 1 |
Details about Algebra DeMYSTiFieD, Second Edition:
Your SOLUTION to mastering ALGEBRA!Trying to tackle algebra but nothing's adding up? No problem! Factor in Algebra Demystified, Second Edition and multiply your chances of learning this important branch of mathematics.Written in a step-by-step format, this practical guide covers fractions, variables, decimals, negative numbers, exponents, roots, and factoring. Techniques for solving linear and quadratic equations and applications are discussed in detail. Clear examples, concise explanations, and worked problems with complete solutions make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.It's a no-brainer! You'll learn how to:Translate English sentences into mathematical symbolsWrite the negative of numbers and variablesFactor expressionsUse the distributive property to expand expressionsSolve applied problemsSimple enough for a beginner, but challenging enough for an advanced student, Algebra Demystified, Second Edition helps you master this essential math subject. It's also the perfect resource for preparing you for higher level math classes and college placement tests.
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Rent Algebra DeMYSTiFieD, Second Edition 2nd edition today, or search our site for other textbooks by Rhonda Huettenmueller. Every textbook comes with a 21-day "Any Reason" guarantee. Published by McGraw-Hill Education.
Need help ASAP? We have you covered with 24/7 instant online tutoring. Connect with one of our Algebra tutors now. | 677.169 | 1 |
The Barnett, Ziegler, Byleen "College Algebra" series is designed to be user friendly and to maximize student comprehension. The goal of this series is to emphasize computational skills, ideas, and problem solving rather than mathematical theory. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, the students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematically concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful.
Book Description McGraw-Hill Science/Engineering/Math. Hardcover. Book Condition: New. 0073312622 New Condition *** Right Off the Shelf | Ships within 2 Business Days ~~~ Customer Service Is Our Top Priority! - Thank you for LOOKING :-). Bookseller Inventory # 1BOOK4P398077 | 677.169 | 1 |
Description: Calculus isn't just a required math class to weed out would-be science majors-it's a useful way to understand the patterns in physics, economics, and the natural world. With its distinctive mix of serious educational content and Japanese-style comics, The Manga Guide to Calculus will entertain you while it helps you understand the key concepts of calculus (and ace those exams).
Our story begins as Noriko, a recent liberal arts grad, arrives at a branch office of the Asagake Newspaper to start her career as a journalist. With the help of her overbearing and math-minded boss Kakeru, she's finally able to do some real reporting. But Noriko soon discovers the mathematical functions behind all the stories she struggles to cover.
How to integrate and differentiate trigonometric and other complicated functions
Multivariate calculus and partial differentiation
Taylor expansions
Reluctant calculus students of all abilities will enjoy following along with Noriko as she learns calculus from Kakeru's quirky stories and examples. This charming and easy-to-read guide also includes an appendix with answers to the book's many useful exercises.
This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of | 677.169 | 1 |
You still have you matrices and can use reduced row echelon form to solve a system. NYSED doesn't want the integrity of the exam to be compromised with a model that does everything for the student on an exam.
Please just check with NYSED if you have concerns on a specific model or functionalty. | 677.169 | 1 |
Mathematics is said to be an abstract form of science that deals with numbers, quantity, structure and space. Modern day mathematics encapsulates a range of topics such as arithmetic, algebra, geometry and analysis. These broad categories are further subdivided into logical reasoning, set theory and applied mathematics. Whether you\'re a pro at mathematics or just starting your study into the basics, it always helps to go through a range of mathematical books that offers simple to complex mathematical problems with detailed explanations and clear solutions.
Students preparing for their board exams or engineering exams can definitely look into these books to get a better perspective of mathematics as a subject. Moreover, most jobs these days require candidates to have proficiency in logical reasoning and quantitative aptitude that are possible only if your mathematical skills are good. Furthermore, mathematical books brush up your knowledge on various formulae, theorems and much more.
Flipkart is definitely an online shopping website that offers you a huge range of mathematical books. The books are aimed at all age groups such as primary school students, high school students, college students and for professional courses. Simply place the order online and the product will be delivered to your doorstep. Avail easy payment options such as cash on delivery and net banking. | 677.169 | 1 |
Pre-algebra skills come easy with plenty of practice! If you are looking for extra pre-algebra help for your child, this invaluable resource has it all. Featuring hundreds of exercises, Practice Makes Perfect: Pre-Algebra offers plenty of opportunities for practice, practice, practice on the math found in sixth, seventh, eighth, and ninth grade... more...
The Literature Workbook is a practical introductory textbook for literary studies, which can be used either for independent study or as part of a taught class. Laying the ground for further study, The Literature Workbook introduces the beginning student to the essential analytic and interpretative skills that are needed for literary appreciation... more...
Improve your efficiency -- and bring in big profits! Need help implementing or understanding Six Sigma? Want to take this powerful problem-solving methodology and apply it to your business? Six Sigma isn't just for Fortune 500 companies anymore; it's for every business, even yours, no matter how big or small. This hands-on workbook provides the... more...
Gruber's Complete SAT Reading Workbook includes shortcuts and tips, strategies and practice tests. It also features the exclusive Gruber system that has raised actual SAT scores by more than 600 points! more...
Gruber's Complete SAT Writing Workbook includes shortcuts and tips, strategies and practice tests. It also features the exclusive Gruber system that has raised actual SAT scores by more than 600 points! more...
If you are one of the millions of people who have already discovered the power of NLP, Neuro-linguistic Programming Workbook For Dummies will allow you to perfect its lessons on how to think more positively and communicate more effectively with others. This workbook is packed with hands-on exercises and practical techniques to help you make the... more...
Fully updated for a UK audience Bookkeeping Workbook For Dummies is the easiest way to get up to speed in all the basics of bookkeeping: from setting up a bookkeeping system and recording transactions to managing payroll, preparing profit and loss statements, tackling tax and filing month and year end reports finances. Expert author Jane Kelly guides... more...
Internationally renowned marketing expert Jay Conrad Levinson and co-author Al Lautenslager offer a hands-on workbook in the famed Guerrilla Marketing series. Designed for use either as a stand-alone tool or as a supplement to Guerilla Marketing in 30 Days, this interactive workbook provides practical exercises that deliver a customized, action-oriented | 677.169 | 1 |
Presented by HippoCampus, a project of the Monterey Institute for Technology and Education, this free online course "is a study of the basic skills and concepts of elementary algebra, including language and operations...
Presented by HippoCampus, a project of the Monterey Institute for Technology and Education, this free online course follows up on a previous course, Algebra 1A, which "develops algebraic fluency by providing students... | 677.169 | 1 |
pack contains a question book full of test-style practice questions for students studying KS3 Maths. It covers all the topics from the current National Curriculum with a range of exercises that test what you know and how well you can apply your knowledge. The questions are written in a clear, straightforward style aimed at levels 3-6 to give practice on each topic. The separate answer book is included. Matching study notes are available in CGP's Revision Guide (9781841460406). | 677.169 | 1 |
At what point did I say you don't need math at all? I clearly understand the need for math, but what I understand is the need for practical math, not stuff like what's being shown in the content, long problems that take up half a page and consist of more letters then numbers.
Long equations like the one on the content actually exist in "practice". If you don't believe me look in wikipedia "Navier-Stokes equations" which are used in fluid motion.
For the 99% of the people basic math are enough for living. But if you wanna build a bridge, a nuclear plant or a water distribution system somebody will have to deal with equations like those. I know this shit cause I am an electrical engineer | 677.169 | 1 |
Algebra 1
Algebra success for allProduct Descriptions
The Student Center is a suite of learning tools on CD-ROM to help students study, learn, and succeed in class. The Student Center includes the entire program in interactive format, including powerful tools such as:
Complete Interactive Student Edition
Built-In Assessments
Activities
Discoveries Channel Videos
Chapter Vocabulary Flashcards
Active Math Explorations
Step-by-Step Examples
Homework Video Tutors
Lesson Quizzes
Student Worksheets
Product Details
Product Name: Student Center 6-year Online Access
System Title: ALGEBRA 1 STUDENT CENTER 6-YR ONLINE
Type: Teacher Resources
Medium: Online
ISBN-10: 0133659631
ISBN-13: 9780133659634
These essential teaching resources are real teacher time-savers and provide a wealth of resources to help you reach all your students.
Vocabulary & Study Skills—Focus on key mathematical vocabulary and specific support on study skills so every student can be successful.
Product Details
Product Name: All-in-One Student Workbook
System Title: ALGEBRA I STUDENT WORKBOOK SSG 2007
Type: Student Resources
Medium: Print
ISBN-10: 0131657186
ISBN-13: 9780131657182
Also available is a unique adapted version of the Student Workbook with resources developed specifically for your struggling and special needs students.
Product Details
Product Name: All-in-One Student Workbook, Adapted Version
System Title: ALGEBRA 1 WORKBOOK (ADAPTED) SSG 07C
Type: Student Resources
Medium: Print
ISBN-10: 0131657224
ISBN-13: 9780131657229
Contains a wealth of activities that allow you to present mathematical concepts concretely using manipulatives or everyday items.
Product Details
Product Name: Hands-on Activities
System Title: ALGEBRA I ALG 1&2 HANDS-ON ACT BLM 2007C
Type: Teacher Resources
Medium: Print
ISBN-10: 0131657518
ISBN-13: 9780131657519
A wide variety of technology-related activities extends the mathematical ideas in a practical and engaging way.
Product Details
Product Name: Technology Activities
System Title: ALGEBRA I HS MATH TECHNOLOGY ACT BLM 07C
Type: Teacher Resources
Medium: Print
ISBN-10: 0131657526
ISBN-13: 9780131657526
Provides a comprehensive review of data analysis and probability topics covered in middle grades. This allows you to provide, if necessary, a critical review of these topics before high-stakes tests.
Product Details
Product Name: Data Analysis and Probability Workbook
System Title: ALGEBRA 1 DATA ANALYSIS & PROB SSG 07C
Type: Student Resources
Medium: Print
ISBN-10: 0131657259
ISBN-13: 9780131657250
These innovative components allow you to use the regular texts in classes that need special help and pacing so you can truly reach all students with one program.
Product Details
Product Name: Basic Algebra Planning Guide
System Title: ALGEBRA I BASIC ALG PLANNING GD TMK 07C
Type: Teacher Resources
Medium: Print
ISBN-10: 0131657437
ISBN-13: 9780131657434
Designed for use with overhead projectors, this kit helps you demonstrate concepts in a using probability tools, including algebra tiles, tangrams, a geoboard with rubber bands, a spinner, and pattern blocks.
Product Details
Product Name: Overhead Manipulatives Kit
System Title: PH MATH OVERHEAD MANIP KIT MAN N/A 2004
Type: Student Resources, Ancillary
Medium: Other
ISBN-10: 0131158465
ISBN-13: 9780131158467
A complete Spanish translation of the Student Edition's core instruction, providing support for every lesson.
Product Details
Product Name: Spanish Study Guide
System Title: ALGEBRA 1 SPANISH STUDY GUIDE
Type: Ancillary
Medium: Print
ISBN-10: 0133644839
ISBN-13: 9780133644838
Provides extra practice for every lesson.
Product Details
Product Name: Spanish Practice Workbook
System Title: ALGEBRA 1 SPANISH WORKBOOK SSG 07C
Type: Student Resources
Medium: Print
ISBN-10: 0131658360
ISBN-13: 9780131658363
Focus on key mathematical vocabulary and specific support on study skills so every student can be successful.
Product Details
Product Name: Spanish Vocabulary and Study Skills Workbook
System Title: ALGEBRA 1 SPANISH VOCAB WKBK SSG 2007C
Type: Student Resources
Medium: Print
ISBN-10: 0131658387
ISBN-13: 9780131658387
Spanish translations of all the Checkpoint Quizzes, Chapter Tests, and Cumulative Assessments. Also includes Alternative Assessment in Spanish.
Product Details
Product Name: Spanish Assessment Resources
System Title: ALGEBRA I SPAN ASSESSMENT RES BLM 2007
Type: Teacher Resources
Medium: Print
ISBN-10: 0131658875
ISBN-13: 9780131658875
A comprehensive, easy-to-use resource for providing remediation, one skill at a time, for students needing another opportunity for review and practice.
Product Details
Product Name: High School Math Skills Review and Practice
System Title: ALGEBRA I HS SKILLS&CONCEPTS REV BLM 07C
Type: Ancillary
Medium: Print
ISBN-10: 0131657496
ISBN-13: 9780131657496
Prepare your students for high-stakes with complete practice tests and test-taking strategies for national, ACT, and SAT tests.
Product Details
Product Name: Test Prep Workbook
System Title: ALGEBRA 1 TEST PREP SSG 2007C
Type: Student Resources
Medium: Print
ISBN-10: 0132503417
ISBN-13: 9780132503419
Your Prentice Hall Teacher Center is the one resource you need for complete support for planning your instruction with TeacherEXPRESS™ Powered by LessonView® planning software, to digital presentations of your lessons found on the PresentationEXPRESS™ CD ROM, to a fun way to assess and review with MindPoint™ Quiz Show. Only Prentice Hall provides all this support in one convenient location.
Product Details
Product Name: Algebra 1 Teacher Center (2009)
System Title: ALGEBRA 1 TEACHER CENTER CD-PACK
Type: Teacher Resources
Medium: CD
ISBN-10: 0133659771
ISBN-13: 9780133659771
The most powerful test generator available with the most comprehensive test banks.
Quick Test Wizard to build assessments in seconds
All test item translated into Spanish
Support for modifying tests quickly and easily
Math Art Gallery to import images into your assessments
New Worksheet Banks allow you to edit and modify existing worksheets
Product Details
Product Name: ExamView® 6.1 (2007/2009)
System Title: ALGEBRA 1 EXAMVIEW CD
Type: Teacher Resources
Medium: CD
ISBN-10: 0133659917
ISBN-13: 9780133659917
Personalized intervention for each student
Assess—Students take Diagnostic Tests or Benchmark Tests online.
Diagnose—Based on assessment results, each student automatically receives an assignment for any skills that have not been mastered.
Product Details
Product Name: Teaching with TI Technology Booklet with CD-ROM
System Title: ALGEBRA I TI83/84PLUS ACTIVITIES BLM 07C
Type: Student Resources
Medium: CD
ISBN-10: 0131657534
ISBN-13: 9780131657533
This product was developed for use with the TI-Navigator System. The CD conatins built-in assessment from your Prentice Hall textbook are provided in a format that can be used with the Navigator System.
Product Details
Product Name: Instant Check System for TI-Navigator CD-ROM
System Title: ALG1/GEOM/ALG2 INSTANT CK SYS FOR TI-NAV
Type: Teacher Resources
Medium: CD
ISBN-10: 013250460X
ISBN-13: 9780132504607
This resource provides all the support your students need—in one convenient workbook! The following resources are included:
Daily Notetaking Guide—Provides the structure your students need to take effective notes as you teach. Student notes make a great study guide for quizzes and tests.
Practice—Provides additional practice for every lesson.
Guided Problem Solving—Helps students master word problems by providing step-by-step guidance for a selected problem from every lesson.
Vocabulary & Study Skills—Focus on key mathematical vocabulary and specific support on study skills so every student can be successful.
Product Details
Product Name: With text purchase, add All-in-One Student Workbook
System Title: ALGEBRA 1 STUDENT WKBK WITH SE PURCHASE
Type: Teacher Resources
Medium: Print
ISBN-10: 0133660087
ISBN-13: 9780133660081
Also available is a unique adapted version of the Student Workbook with resources developed specifically for your struggling and special needs students. The following resources are included: | 677.169 | 1 |
Find a Washington, DCAlgebra 2 is the springboard for the more advanced mathematics that a student will encounter in college. Having a firm grasp of polynomial operations, graphs, systems of equations and inequalities, matrix operations, logs and exponents, conic sections, and complex numbers is essential for succee... | 677.169 | 1 |
Find an AlamedaPrecalculus (or Algebra 3) is an advanced form of secondary school algebra and is a foundation mathematical discipline. Precalculus prepares students for calculus and explores topics which will be applied in calculus. The topics that are studied in precalculus are real and complex numbers; solv | 677.169 | 1 |
Product Description
Created for the independent, homeschooling student, Teaching Textbooks has helped thousands of high school students gain a solid foundation in upper-level math without constant parental or teacher involvement. Teaching Textbooks Algebra 2 covers fractional equations, powers and exponents, second-degree equations, equations with variables, inequalities, absolute value, and other important Algebra 2 topics.
Extraordinarily clear illustrations, examples, and graphs have a non-threatening, hand-drawn look, and engaging real-life questions make learning Algebra 2 practical and applicable. Textbook examples are clear while the audiovisual support includes full lectures (reading the textbook), practice and solution CDs for every chapter problem, homework problem, and test problem. The review-method structure helps students build problem solving skills as they practice core concepts and rote techniques.
Teaching Textbooks' new Algebra 2 Version 2.0 edition now includes automated grading! Students watch the lesson on the computer, work a problem in the consumable workbook, and type their answer into the computer; the computer will then grade the problem. If students choose to view the solution, they can see a step-by-step audiovisual solution. Version 2.0 also includes a digital gradebook for multiple students, parent and multiple student accounts, interactive lectures, and second chance options. In addition, twenty new lessons on more advanced topics with 150 extra problems and solutions have been added! These new features mean that this 2.0 version is not compatible with the 1.0 edition.
Teaching Textbooks Algebra 2 2.0 includes the following new features:
Automated grading
A digital gradebook that can manage multiple student accounts and be easily edited by a parent.
Twenty new lessons on more advanced topics and over 150 extra problems and solutions
Interactive lectures
Hints and second chance options for many problems
Animated buddies to cheer the student on
Reference numbers for each problem so students and parents can see where a problem was first introduced
My daughter has never liked math though she is good at it. Teaching textbooks has helped her better understand the concepts and helps her feel more accomplished. She loves the teaching buddies, which she missed in the older versions of Algebra 1 and Geometry. I also appreciate the computer version with automated grading. It's a great help for her to see immediately what she did wrong and what the answers should be. This curriculum is great!
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9780486680354Linear Differential Operators
This graduate-level, self-contained text addresses the basic and characteristic properties of linear differential operators, examining ideas and concepts and their interrelations rather than mere manipulation of formulae. Written at an advanced level, the text requires no specific knowledge beyond the usual introductory courses, and some 350 problems and their solutions | 677.169 | 1 |
Other topics taught will include conversions within
and between the metric and standard systems.
Topics in geometry and algebra will be introduced.
Learning
Objectives:
To successfully complete
this course, the student (without the aid of a calculator) is expected to:
1.
Estimate the result of an addition, subtraction, multiplication or division
problem.
2. Evaluate the expression containing integers: perform order of operations.
3. Evaluate the expression containing negative and positive fractions or mixed
numbers.
4. Evaluate the expression containing negative and positive decimals.
5. Solve applications utilizing proportions, including those involving percent,
base and amount.
6. Convert measurements in both the U.S. Customary and Metric Systems within
each system and from one system to the other.
7. Convert between percentages, fractions and decimals and solve related
applications.
8. Evaluate algebraic expressions.
9. Solve algebraic equations that contain one variable and up to two
operations.
10. Choose the appropriate basic geometric formulae and laws, including finding
the area and perimeter of polygons, the area and circumference of a
circle.
Class Learning Outcomes:
The student should demonstrate the ability to:
#1. Utilise the
order of operation agreement to simplify expressions containing integers and
exponents.
#2. Add,
subtract, and reduce, if necessary, non-mixed number fractions with different
signs.
#3. Solve an
algebraic equation with one variable that requires two operations to solve.
Attendance Policy
Attendance is not optional. Your timely, consistent
attendance is required for effective learning.
The purpose of the attendance policy is to minimize disruptions in our learning
environment.
Roll call is always taken at class start: Arrive before the end of roll call (and stay),
or you are late.
You
are required to sign the Participation Exceptions
List (located near the classroom door):
- When you arrive late to class. (you will be marked absent for ½ of a class meeting)
- When you have to leave early before
class is dismissed. (you will be marked
absent for ½ class)
Bathroom break: Leave your books and
phone in class - no sign-in or sign-out.
If you leave class for any other reason (café, phone, etc.) take your things
and sign-out.
Instructor
Drop Policy
I
will drop you if you are late or leave early 4 times in the first 3 weeks.
I will drop you if you are absent 3 times in the first 3 weeks. (2 lates = 1
absence)
Drop Dates
for Students
August 30, 2013 - The last day to drop a
full-term course and get a refund.
September 8, 2013 - The last day to drop a
full-term course without a
"W" grade issued.
November 22, 2013 - The last day to drop a
full-term course with a "W" grade issued.
It is YOUR
responsibility to drop this course if you no longer wish to be enrolled. You can
use Eagle Advisor (My MSJC) to drop, or get assistance from the Eagle Access
Center.
After three final grades of D, F or W, a student will NOT be allowed to enroll
in this course again.
(One
additional enrollment may be permitted by petition with documented extenuating
circumstances.)
Accessibility
Mt.
San Jacinto College abides by the Americans with Disabilities Act and Section
504 of the
Rehabilitation Act of 1973 that prohibits federal and state agencies or
programs from discriminating
against qualified individuals with disabilities.If you have a documented disability that
limits major
life activity which may have some impact on your work in this class and for
which you may require
accommodations, please notify the Disabled Students Program and Services. DSPS
is located in
room 1019B.You may call 639-5305 to arrange
for verification of your disability and for
reasonable accommodations.Contact DSPS for scheduling tests in the
DSPS Testing Room.
Classroom
Behavior
Turn off your phone, i-pod or pager before class
begins. Put it away,not on your
desk or lap.
If your phone rings or noticeably vibrates, quickly silence it and see me at
the end of class.
Texting (sending or receiving) is disruptive, and
not allowed.You cannot use your phone
in class,
or leave class to use it, unless you leave for the day. If you are an emergency professional, please
see me to get an exception.
I-Pads, Tablets and Notebook PCs can ONLY be used
for note taking or e-Text access, but sounds
and communications applications must be disabled.NO EMAIL, SURFING or MESSAGING, etc!
Talking
to other students during lecture is rude and disruptive. So is interrupting the
instructor or
other students while they are talking.Please
raise your hand to ask questions or
volunteer answers.
If
your behavior disrupts the class, you will be given only one warning.If you disrupt the class
again, you will be excused from class for the rest of the day, marked absent
for that meeting and
possibly referred to the Dean of Instruction.
Sleepy
or Uncomfortable?Feel free to go to the
back of the classroom to stand or flex silently.
Class Structure
- Roll
call starts promptly at 3:30; arrive (and stay) by end of roll call, or be
marked late.
- Be ready for new material: Before class meets, use the LRC to clarify any
previous topics you still don't understand. If class time remains after the new
material is presented, I will be available for questions.
- My presentations are interactive; you are expected to follow the flow of
discussion; You will be asked many questions. If you say
"I don't know," I may ask you why.
Your Course
Grade
The
scores you earn on twelve (12) homework submissions, five (5) quizzes/projects,
five
(5) tests, any extra credit and the final exam will determine your grade. The points
possible are:
You can access your current scores from a link in this
class syllabus on my instructor website.
Extra credit will be limited to 30 points. It may occur toward the end of
classtime; don't leave early.
Tests,
Quizzes and the Final Exam
There
will be five 60 minute tests and a 110
minute final examination.Use
pencil.
Test questions are similar to exercises assigned as homework.
You must show all your work to a solution to receive full credit for
that exercise.
Partial credit may be given for some questions. The final exam will be
comprehensive. All Test grades count, so make sure that
you take them all. Guessing or using trial and error
receives no points, even for correct answers; you are required to
solve questions using the written notations, techniques and computations taught
in class.
Allowed: One 3"x5" note card per test (two
for the final), as well as a 4"x6" MrV's
Tables card. Not Allowed: Books, detailed notes,
calculators or any other reference materials.
I
will show you complete solutions to test questions in class when graded tests
are returned. It is important to compare your answers and work with those solutions immediately. During the test review, only use a blue/black pen to make
notes/corrections on your returned test.
If you have questions about your grade or the way a particular solution was
graded, you must ask
me before leaving the classroom. Once you have left the classroom, your
test score is permanent.
Each 10 to 15
minute Quiz has four or five exercises
based on the last 2 days of assignments.
You can use your own homework and a
MrV's Tables card for reference, but nothing else.
It's a good habit to always bring your unsubmitted homework with you to class. Quizzes may be given at start of class (be
on time).Quizzes are not announced ahead of time.
If you miss a quiz due to tardiness or absence, your score will be 0.
If you miss more than one quiz, one
Make-up Quiz may be given the last week of class.
Save your tests with corrected solutions
(use blue/black ink) so that you can use them to study for the final.
If you are ABSENT
on a test day …
You have until
the start of the next class to take the test in the LRC (800 Bldg), 8am-8pm M-F Missed a Monday test?Take it anytime between Monday 5:00pm and
Wednesday at 2:30pm. Missed a Wednesday test? Take it anytime
between Weds. 5:00pm and 2:30pm the next Monday.
This is necessary because completed tests are returned promptly and followed by
a class review. You
can use the LRC only once to take a test with no penalty.Otherwise, 10% penalties will apply. If you don't
take a test at all, your score for that test will be 0.Tests cannot be taken early.
If you are ABSENT
for the final examination …
Your
final exam grade is 0 and you won't earn a grade better than "D" for
the course.
If you miss the final examination for unforeseen justifiable reasons, send me
an e-mail immediately.
Requests for Incomplete grades are not always approved. A make-up date is not
usually possible. Work, travel or vacation plans are not
valid excuses for missing the final.
If you are ABSENT for a
Surprise Quiz …
Your
quiz grade is 0; at class end, one make-up quiz may be given if you missed 2 or
more quizzes.
Keep in mind that only the best 4 grades out of 5 quizzes are used.
If you are ABSENT
for any other class day …
Read
the assigned chapter sections you missed, and do the homework before the next class.
Possibly the tutors in the LRC can help you, but review the assigned section before you go there.
Cheating
If
you cheat on a test or the final, you will receive a score of 0 for the whole
test.
Cheating on homework is assumed when you give yourself a score that is 5 or
more above
the real number of correct answers;this
can happen when you: - are very sloppy in counting correct exercises,
or - you don't check your answers with the
book and have incorrect work and answers, or - you have incorrect or missing work
but you claim the book answer without correcting your work.
You will get 0 points for the entire homework if you have serious scoring
errors.
Working with someone else on your homework is not cheating. Do your share of
the thinking.
Copying homework is senseless because you learn so very little to prepare you
for the tests.
Instructor
Website:
To access the latest updated class syllabus,
interactive PowerPoints, your latest grades and
the homework schedule, go to your class web pages within my instructor website: Blackboard is not planned for this
class, but some features may be added during the term.
MSJC Student
e-mail:Check it Daily!
If
I have to unexpectedly cancel a class meeting, I will send a note to your
student e-mail.
Use your student e-mail to contact me for questions, appointment requests or to
let me know when
you are absent for more than 2 class days in a row; put Math51 in the subject
line.
I will usually respond within 2 days. Directions on how to
activate and login to your student e-mail
can be found at or seek help at the Eagle Access Center.
Emergency
Contact Numbers:
MSJC Menifee Campus Police
951- 639-5180, and Instruction Office (951) 639-5400.
Friends and family need to realize that they can leave a message about an
emergency, but these
offices cannot give out any information about any student and cannot promise
how quickly a
student can be tracked down.Use only for serious emergencies.
SI (Supplemental Instruction)
An SI Leader is currently NOT AVAILABLE for this
class.Perhaps next time.
Student participation in SI Sessions would be voluntary.
An SI Leader acts as a model student and hosts out-of-class review sessions that incorporate what to learn (course content) with how to learn it (study
skills).
Math Savings Account:
Do you plan to take Math 90
Introduction to Algebra?Save all
materials from this course
(text, class notes, homework, tests, and test solutions) for review before the
next course.
Homework
You are required to accurately
self-score each Section in each Homework Pack:
- Before scoring, check your answers with the answers in the back of your
textbook.
- Mark any uncorrected exercises. Then count the correct ones and writeScore = #
The
homework assignment list is attached.Two
homework Sections are assigned after most
class meetings, but Packages of 2 to 6 Sections are collected for grading about
once a week.
Each
of the twelve Homework Packages has 2 to 6 section assignments, and is worth 5 grade
points.
Incomplete Packages will receive fewer points.You must show all work steps, complete all
sections, have accurate work and checked answers, use correct format with
scoring for at least 90%
of all exercises to receive full credit.
Late Packages will be
accepted with a 1-point per class day
penalty, but must be turned in
withinthree class days of the original due date. If you are absent on the
day a Package is due,
turn it in at the start of the next class that you attend (no late penalty
unless more than 3 days late).
Retention
of new skills and concepts normally decreases with time … unless it is
reinforced with
homework exercise and study.Suggestion:
break your homework into two parts.Do
the first part
as soon after the class as possible; do the second part a day or two
later.I know it is tempting to do
homework in class during lecture, but your retention will suffer and you may
miss important points. If you just can't work an exercise, go to
the LRC for help.
Tips for Success:
Prepare for
each class meeting: Finish the homework from the last
class; visit the LRC if necessary. Preview the textbook sections to be
covered in this class.
Prepare for
tests/exams: Review your homework for areas that
were difficult. Try the practice tests in the textbook;
visit the LRC if necessary.
During each
class:
Bring your textbook and take notes on the
board examples. Ask questions as soon as you get lost.
Outside of
class: Form a homework/study group with other
students and attend regularly.
Check your student e-mail often; Class
cancellations and schedule changes may be sent to you.
Check my online syllabus for your current grades and assignments, and to run
PowerPoints.
Alternate Textbook
Options:(Search for ISBN-13:
978-0321731548)
Used
copies of this 6th edition are ok,
but be sure the vendor can deliver it before the 3rd class day.
- If you have a PC, Laptop or Tablet, you can rent an E-Text for 180 days for
less than the printed
book price. WiFi access in class in not guaranteed. You can try to use your
Laptopor Tablet..
E-Text Free trial:
How to Format and Score Your
Homework: - Start
each Section on a new page: On the first page, put your name,
section number, assigned exercises in the upper right corner. Within each section you can use both sides of
sheets, but leave a little space between exercises.
Include the Exercise Group Directions at the start of each new group.
- For each exercise: Write down original exercise Show all
work steps Check
each answer in the back of the text.Unchecked work will not get full credit. If your answer is correct, circle it. If your answer is wrong: Either:Correct your work and circle your correct answer. Or:(If the answer or work is left wrong) Mark a
big X over the exercise number.
- After working all exercises in a section, Score it: Only count the exercises that are completely right and checked in the back of the text. To the left of your name, write that number:Score = # If you didn't check all answers in
the textbook, write UncheckedScore=. By marking Unchecked, your work still gets 80% credit, but it's a dangerous
habit. If I find errors that show you didn't mark unchecked work, you will get
no credit)
- For each Homework Package:Staple
all sections together, in order.
- Do not add up your section scores;
I'll do that while grading your package with 0 to 5 points. | 677.169 | 1 |
Support You Need to Succeed…Even on the Go! The Lial Serieshas helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors. With the new editions, the approachable writing and pedagogy, varied exercise sets, and robust ancillary resources have been updated. Teaching and Learning Experience To provide a better teaching and learning experience, for both instructors and students, this program will: Improve Results:MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning. Drive Student Success:The Lial team combines approachable writing with supportive pedagogy, ample exercise sets, and extensive end of chapter material to ensure student success. Support Students and Instructors:Beyond the core support in the text and MyMathLab, the program offers additional supplemental student and instructor support.
Author Biography
Marge Lial became interested in math at an early age—it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology; trips to various digs and ruin sites produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed.
Stan Salzman is a long time resident of Sacramento, California. Stan has taught at American River College for many years, where he was a member of the business department. He is the author of Business Math and Essential Math, published by Pearson Education, Inc., and is coauthor of Basic Math.
Table of Contents
1. Whole Numbers
1.1 Reading and Writing Whole Numbers
1.2 Adding Whole Numbers
1.3 Subtracting Whole Numbers
1.4 Multiplying Whole Numbers
1.5 Dividing Whole Numbers
1.6 Long Division
1.7 Rounding Whole Numbers
1.8 Exponents, Roots, and Order of Operations
1.9 Reading Pictographs, Bar Graphs, and Line Graphs
1.10 Solving Application Problems
2. Multiplying and Dividing Fractions
2.1 Basics of Fractions
2.2 Mixed Numbers
2.3 Factors
2.4 Writing a Fraction in Lowest Terms
2.5 Multiplying Fractions
2.6 Applications of Multiplication
2.7 Dividing Fractions
2.8 Multiplying and Dividing Mixed Numbers
3. Adding and Subtracting Fractions
3.1 Adding and Subtracting Like Fractions
3.2 Least Common Multiples
3.3 Adding and Subtracting Unlike Fractions
3.4 Adding and Subtracting Mixed Numbers
3.5 Order Relations and the Order of Operations
4. Decimals
4.1 Reading and Writing Decimal Numbers
4.2 Rounding Decimal Numbers
4.3 Adding and Subtracting Decimal Numbers
4.4 Multiplying Decimal Numbers
4.5 Dividing Decimal Numbers
4.6 Fractions and Decimals
5. Ratio and Proportion
5.1 Ratios
5.2 Rates
5.3 Proportions
5.4 Solving Proportions
5.5 Solving Application Problems with Proportions
6. Percent
6.1 Basics of Percent
6.2 Percents and Fractions
6.3 Using the Percent Proportion and Identifying the Components in a Percent Problem | 677.169 | 1 |
Textbook Information
What is the difference between "required" and "choose" as listed in the bookstore?
Often times it is cheaper for the bookstore to purchase new versions of text as part of a package. When this happens the bookstore, only buys new books as part of the package and buys back from students used books. Most packages contain online access codes that allow you to utilize textbook specific online supplements.
If the bookstore can obtain used books (in quantity) at a cheaper price then the package AND the teacher doesn't require components in the package, the listing in the bookstore will use the word "choose" to let the student know that they have a choice in purchases.
If the bookstore can not obtain used books (in quantity) at a cheaper price then the package, the listing in the bookstore will use the word "required" despite the fact that all components in the package are not required.
If a teacher requires the components of the package, the package will be listed as "required".
All math classes have material that must be purchased for that class; the exact requirements for each teacher can be found listed by semester under Current Students.
Is a used book really cheaper?
The answer to this depends primarily on whether or not your teacher requires you to purchase an access code in order to complete online homework. Since the cost for a stand alone access code averages $80, it is rarely cheaper to purchase a used book if your teacher requires the access code.
Additionally Math 81, 84 and 31 require the student to complete arranged hours. The material to needed to complete arranged hours is contained in the packages. To purchase these separately can be very expensive (ranging from $27- $101).
I didn't buy the package as required in the bookstore and my teacher requires an Access Code?
If your teacher requires an access code found in the SMC packages and you chose to purchase the text from another vendor, it is your responsibility to purchase the access code that will work with the SMC system as a standalone access code (average cost of standalones about $80).
Is a Custom Book really custom to SMC?
Customized can mean one of two things: the content is identical to national versions but the layout, cover or printing method has been changed to reduce costs OR the book is a merging of multiple texts. Math 28, Math 32 and Math 85 text books are truly different than any national versions and extreme caution should be exercised before purchasing either book from a source other than the SMC bookstore. | 677.169 | 1 |
I'd recommend the book from Pearson its called "Discrete Matematical Structures" and it covers most of the basic stuff. However the algebra in it, is a bit vague, but if you can find a cheap copy of it, do it
Figured this is the best place to post, any tutorials, videos, or just random suggestions would be helpful.
Thanks
I took Discrete last fall term. I would recommend Discrete Mathematics with Applications by Susanna S. Epp to explain the stuff if you want to get a head start. You can buy an older version off Amazon pretty cheap.
Our class required Discrete Mathematics and Its Applications sixth ed by Kenneth H. Rosen. It is a comprehensive text and good for reference or a doorstop but it is horrible to learn from. Plus I had a horrible instructor who decided to give us quizzes and tests on even numbered problems from Rosen which are not explained in the text and no answers in the solutions manual.
If taught correctly, Discrete can be fascinating. If you get a bad instructor it can be like eating stewed poison ivy for lunch.
If you go to Amazon.com you can find used books by both Sue Epps and Ken Rosen for rock bottom prices. It does not matter as to the edition. Because any of those books will serve you well as a reference. | 677.169 | 1 |
South Pasadena CalculusMaham H.
...Finally, I preview limits and derivatives that will form the basis of Calculus. With Trigonometry, it is common that students feel lost, because they haven't understand the basics of trigonometry, that is what the six trigonometric functions Sin, Cos, Tan, Sec, Csc, and Cot mean. Once that is f...
David SIsaac Y.
...Navigate through various word problems that will increase their math literacy. Start looking at the next unit to help them get ahead.
-Students at a medium level of mastery: Pose questions to guide their thinking. Build content mastery through increasing math fluency. | 677.169 | 1 |
When homework is assigned, I will tell you when it is due. Homework
may be turned in early (place it in my mail box, my hand, or gently
slide it under my door). Late homework will be reduced in value
by 50% for each day, or fraction thereof, it is late. Some of the
homework will be easy, some difficult and some may be impossible
to fully complete--but you can show me what effort you made.
Comments:
Number theory is the study of the integers
which includes such things as cryptology, divisibility rules, finding
massive primes, error correcting codes and magic tricks. It is a great course for secondary education
students as well as those looking for undergraduate research projects because of its many elementary and elegant problems that often lead to deep consequences. Yes,
number theory has proofs, though it is nowhere as proof intensive as Abstract Algebra
or Real Analysis.
Honesty & Internet:
Students are encouraged to work together, but you must write up the solutions yourself, independently from others, while you are alone. I urge you to use the internet honestly. You may look up definitions but do not
search for solution to the problems in assignments or ask about them on-line.
The library also has a great deal of useful books, many under the subject heading "elementary number theory." If you use ideas which are not your own, please indicate your source appropriately. If what you find makes the solution trivial, then check with me before submitting to make sure the abbreviated work will get full credit. The point of excises is to develop your understanding, not to borrow from others.
I assume you understand the university policies found in the student handbook.
Departmental
Objectives:
The student will:
Identify and apply various properties of and relating to the
integers including the Well-Ordering Principle, primes, unique
factorization, the division algorithm, and greatest common
divisors.
Identify certain number theoretic functions and their
properties.
Understand the concept of a congruence and use various results
related to congruences including the Chinese Remainder
Theorem. | 677.169 | 1 |
Introduction to Order of Operations Part 1 This video shows the four parts to the order of operations. The first parts is to perform the operations within the parenthesis. Some examples are shown. The second part is to simplify any numbers that have exponents. Examples are once again shown. The third part is perform multiplication and division in order working from left to right. Many examples are shown. The fourth part is perform addition and subtraction in order working from left to right. Examples are shown. Then they show examples us Author(s): No creator set
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Managing the European economy after the introduction of the Euro The Euro was first adopted as a currency in 1999, but what impact has it had on the European economy? This unit looks at the key developments in the economy since that date and examines the challenges of economic policy formation and governance of the EU's expanding economy References and further readingLicensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see - Original copyright The Open University
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5 Next steps The idea of 'family' is very powerful in contemporary UK culture and policy. Family lives have been the subject of many anxieties both at the personal and policy levels. How do public debates relate to people's everyday experiences of families? In this unit, you can explore the many attempts at defining 'family' and why these complex and contradictory meanings are important to us. We begin to unpick questions of power and inequality, to test our everyday assumptions about families, and Author(s): The Open University
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identify and describe what is meant by a formal rule and understand the problems associated with rule making;
explain what is meant by policy and why it is important;
understand how formal rules are constructed;
explain the difference between specific and general rules, and why the difference matters;
explain why the language of formal rules is important;
exSome thoughts on car parking Peter Guest (former president British Parking Association) talks on 'Some thoughts on car parking' as part of the OxTran Seminar Series at the TSU in 2009. Please note: Peter's views do not represent those of the British Parking Association. Author(s): Peter Guest
Predicting the Behaviour of Techno-Social Systems: How Informatics and Computing Help to Fight Off G We live in an increasingly interconnected world of 'techno-social' systems, where infrastructures composed of different technological layers are interoperating within the social component that drives their use and development. The multi-scale nature and complexity of these networks are crucial features in understanding and managing them. In the last decade advances in performance in computer technology, data acquisition and complex networks theory allow the generation of sophisticated simulation Author(s): Alessandro Vespignani
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4.1 Understanding the relationship between data and space3 Maps and the modern worldStudying at the Oxford Internet Institute. Sections: I want to study the Internet - Author(s): William Dutton, Helen Margetts, Ralph Schroeder, L
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2.2 Mental maps How do we use maps? related items provided in this feed
Virtual Maths Data Handling - Light Survey Exercises and resources for conducting a Light Intensity Survey.
"To measure the levels of light in a particular area, we need to use a device called a Light Meter, which measures the intensity of light in the vicinity of the sensor and displays the reading." Author(s): Leeds Metropolitan University
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Active, healthy lifestyles In this unit, aimed at teachers of Physical Education, we begin by looking at some of the common misconceptions relating to fitness and activity levels together with accepted definitions of these concepts. We consider how active young people should actually be, and discuss how PE teachers can ensure they are making an effective contribution to this area of public health. Author(s): The Open University
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Resources on film music can be difficult to come by. There has been a gradual increase in the range and number of books available, and the bibliography you can get by clicking on the link below should help guide you towards useful texts.
There is some confusion over the uses of the terms 'ethical' and 'ethics'. Often people use the adjective 'ethical' to signal things that they would expect virtuous people to do. That is they use the word 'ethical' instead of 'good'. Companies, institutions and even governments might claim to have 'ethical' policies. Probably such a policy declares the ideology. For example, saying that 'sustainability is ethical' may be part of a.2 People knowledge This unit considers two ideas: that health is an ever-present factor in our lives, and that health is something difficult to define. But how can we say that health is everywhere if it is so mysterious? How do we recognise health if it so difficult to define? There are no easy answers to these questions! In this unit we explore this paradox, not just because it is a fascinating dilemma but because understanding health in all its multifaceted complexity is a prerequisite to working for health in i Author(s): The Open University
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Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a | 677.169 | 1 |
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The thinkers of ancient Egypt, Greece and India recognized that numbers governed much of what they saw in their world and hence provided an approach to its divine creator. Robert Lawlor sets out the system that determines the dimension and the form of both…
Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. The new edition of this text includes two additional…
A square is just a square until it becomes a house in this clever book. A circle becomes a spinning ferris wheel, and when you add some string and a tail to a diamond shape, it becomes a kite flying high in the sky! With sprightly rhymes and energetic…
This workbook is designed to supplement optics textbooks and covers all the traditional topics of geometrical optics. Terms, equations, definitions, and concepts are discussed briefly and explained through a series of problems that are worked out in a…
Lucid, well-written introduction to elementary geometry usually included in undergraduate and first-year graduate courses in mathematics. Topics include vector algebra in the plane, circles and coaxial systems, mappings of the Euclidean plane, similitudes,…
Riemannian Geometry includes results discovered during the last few years, which have previously only been available through research papers. It contains an elementary account of twistor spaces, of interest to applied mathematicians and physicists, and the final…
Whenever you are -- inside or outside -- there are shapes to discover. And with Tana Hoban's help you will begin to see them. Look around. How many circles, squares, stars, triangles, hearts, and rectangles can you see? They are everywhere!
King Arthur was a good ruler, but in this math adventure he needs a good ruler. Geometry is explained with humor in SIR CUMFERENCE AND THE FIRST ROUND TABLE, making it fun and accessible for beginners. What would you do if the neighboring kingdom were threatening…
The great work that founded analytical geometry. Included here is the original French text, Descartes' own diagrams, together with the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John…
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence… | 677.169 | 1 |
Summary
Practical Business Math Procedures is a comprehensive introduction to the concepts and applications of mathematics to personal and commercial business problems. The text uses basic arithmetic and problem solving techniques and illustrates their use in retailing, interest and loans, banking, payroll, taxes, investments, insurance, and a variety of other business situations.
The text is well known for the motivating integration of interesting real world examples and photos from the Wall Street Journal, Kiplingerís, and many other business journals. Slater is the most popular and widely used book for this course and is carefully written and developed to support students with little math experience with practice quizzes, thousands of exercises, color coded procedures and diagrams, supporting tutorial videos on DVD, and the highest standards of reliability and cleanliness.
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ThanksJuly 26, 2011
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This is the first time I am taking cl[censored] online and at our bookstore this same book was double the price than on ecampus.com Thanks ecampus you've made studying a lot more relaxing BookSeptember 13, 2010
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This book helped me pass my business math class. My teacher was terrible, so I had to teach myself and this book was great. It was easy to follow and I was able to get a B in the classPractical Business Math Procedures with Business Math Handbook, Student DVD, WSJ Insert: 4.5 out of 5 stars based on 2 user reviews. | 677.169 | 1 |
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NATIONAL BOARD FOR HIGHER MATHEMATICS Research Scholarships Screening Test Saturday, February 2, 2008 Time Allowed: Two
Hours Maximum Marks: 40
Please read, carefully, the instructions on the following page
1
INSTRUCTIONS TO CANDIDATES • Please ensure that this booklet contains 9 numbered (and printed) pages. The back of each printed page is blank and can be used for rough work. • There are five sections, containing ten questions each, entitled Algebra, Analysis, Topology, Applied Mathematics and Miscellaneous. Answer as many questions as possible. The assessment of the paper will be based on the best four sections. Each question carries one point and the maximum possible score is forty. • Answer each question, as directed, in the space provided in the answer booklet, which is being supplied separately. This question paper is meant to be retained by you and so do not answer questions on it. • In certain questions you are required to pick out the qualifying statement(s) from multiple choices. None of the statements, or more than one statement may qualify. Write none if none of the statements qualify, or list the labels of all the qualifying statements (amongst (a), (b), and (c)). • Points will be awarded in the above questions only if all the correct choices are made. There will be no partial credit. • N denotes the set of natural numbers, Z - the integers, Q - the rationals, R - the reals and C - the field of complex numbers. Rn denotes the ndimensional Euclidean space, which is assumed to be endowed with its 'usual' topology. The symbol Zn will denote the ring of integers modulo n. The symbol ]a, b[ will stand for the open interval {x ∈ R | a < x < b} while [a, b] will stand for the corresponding closed interval; [a, b[ and ]a, b] will stand for the corresponding left-closed-right-open and leftopen-right-closed intervals respectively. The symbol I will denote the identity matrix of appropriate order. The space of continuous real valued functions on an interval [a, b] is denoted by C[a, b] and is endowed with its usual 'sup' norm. The space of continuously differentiable real valued functions on [a, b] is denoted by C 1 [a, b] and its usual norm is the maximum of the sup-norms of the function and its derivative.
2
Section 1: Algebra 1.1 Let S7 denote the group of permutations of 7 symbols. Find the order of the permutation: 1 2 3 4 5 6 7 . 6 4 5 7 3 1 2 1.2 Write down the number of mutually nonisomorphic abelian groups of order 195 . 1.3 For two ideals I and J in a commutative ring R, define I : J = {a ∈ R : aJ ⊂ I}. In the ring Z of all integers, if I = 12Z and J = 8Z, find I : J . 1.4 Let P be a prime ideal in a commutative ring R and let S = R\P, i.e. the complement of P in R. Pick out the true statements: (a) S is closed under addition. (b) S is closed under multiplication. (c) S is closed under addition and multiplication. 1.5 Let p be a prime and consider the field Zp . List the primes for which the following system of linear equations DOES NOT have a solution in Zp : 5x + 3y = 4 3x + 6y = 1. 1.6 Let A be a 227 × 227 matrix with entries in Z227 , such that all its eigenvalues are distinct. Write down its trace. 1.7 Let B be a nilpotent n × n matrix with complex entries. Set A = B − I. Write down the determinant of A. 1.8 Let x and y be two non-zero n × 1 vectors. If yT denotes the transpose of y, what are the eigenvalues of the n × n matrix xyT ? 1.9 Let A be a real symmetric n × n matrix whose only eigenvalues are 0 and 1. Let the dimension of the null space of A − I be m. Pick out the true statements: (a) The characteristic polynomial of A is (λ − 1)m λm−n . (b) Ak = Ak+1 for all positive integers k. (c) The rank of A is m. 1.10 What is the dimension of the space of all n×n matrices with real entries which are such that the sum of the entries in the first row and the sum of the diagonal entries are both zero?
Consider its Taylor expansion about a point a ∈ R, an (x − a)n . What is the radius of convergence of this
2.2 Consider the series
∞
(−1)n
n=1
x2 + n . n2
Pick out the true statements: (a) The series converges for all real values of x. (b) The series converges uniformly on R. (c) The series does not converge absolutely for any real value of x.
2.3 Let f : R → R be a continuous function. Which of the following imply that it is uniformly continuous? (a) f is 2π-periodic. (b) f is differentiable and its derivative is bounded on R. (c) f is absolutely continuous.
2.4 Let f : [−1, 1] → R be continuous. Assume that Evaluate:
1 n→∞
1 −1
f (t) dt = 1.
lim
f (t) cos2 nt dt.
−1
2.5 Let f be a continuously differentiable 2π-periodic real valued function on π the real line. Let an = −π f (t) cos nt dt where n is a non-negative integer. Pick out the true statements: (a) The derivative of f is also a 2π-periodic function. 1 (b) |an | ≤ C n for all n, where C > 0 is a constant independent of n. (c) an → 0, as n → ∞.
2.6 Let fn and f be continuous functions on an interval [a, b] and assume that fn → f uniformly on [a, b]. Pick out the true statements: (a) If fn are all Riemann integrable, then f is Riemann integrable. (b) If fn are all continuously differentiable, then f is continuously differentiable. (c) If xn → x in [a, b], then fn (xn ) → f (x).
Pick out the true statements: (a) For any t ∈ R, the set {x ∈ X : f (x) < t} is an open set in X. (b) The function f is continuous. (c) Every sequence {fαn } contained in the above family admits a uniformly convergent subsequence. 3.4 Let D = {x ∈ R2 : |x| ≤ 1} where |x| is the usual euclidean norm of the vector x. Let f : D → X be a continuous function into a topological space X. Pick out the cases below when f will NEVER be onto. (a) X = [−1, 1]. (b) X = [−1, 1]\{0}. (c) X = ]−1, 1[. 3.5 Let Mn (R) denote the set of all n × n matrices with real entries, consid2 ered as the space Rn . Which of the following subsets are compact? (a) The set of all invertible matrices. (b) The set of all orthogonal matrices. (c) The set of all matrices whose trace is zero.
6
3.6 With the notations as in the preceding question, which of the following sets are connected? (a) The set of all invertible matrices. (b) The set of all orthogonal matrices. (c) The set of all matrices whose trace is zero. 3.7 Let f : R → R be a continuous function. Define G = {(x, f (x)) : x ∈ R} ⊂ R2 . Pick out the true statements: (a) G is closed in R2 . (b) G is open in R2 . (c) G is connected in R2 . 3.8 Let X be a topological space and let A ⊂ X. Let ∂A denote the boundary of A, i.e. the set of points in the closure of A which are not in the interior of A. A closed set is nowhere dense if its interior is the empty set. Pick out the true statements: (a) If A is open, then ∂A is nowhere dense. (b) If A is closed, then ∂A is nowhere dense. (c) If A is any subset, then ∂A is always nowhere dense. 3.9 Let V be a complete normed linear space and let B be a basis for V as a vector space. Pick ot the true statements: (a) B can be a finite set. (b) B can be a countably infinite set. (c) If B is infinite, then it must be an uncountable set. 3.10 Let V1 = C[0, 1] with the metric d1 (f, g) = max |f (t) − g(t)|.
t∈[0,1]
Section 4: Applied Mathematics 4.1 Write down the Laplace transform of the function f (x) = cos 2x. 4.2 Let B denote the unit ball in RN , N ≥ 2. Let αN be its (N -dimensional) volume and let βN be its ((N − 1)-dimensional) surface measure. Apply Gauss' divergence theorem to the vector field v(x) = x and derive the relation connecting αN and βN . 4.3 Assume that the rate at which a body cools is proportional to the difference in temperature between the body and its surroundings. A body is heated to 110◦ C and is placed in air at 10◦ C. After one hour, its temperature is 60◦ C. At what time will its temperature reach 30◦ C? 4.4 A body of mass m falls under gravity and is retarded by a force proportional to its velocity. Write down the differential equation satisfied by the velocity v(t) at time t. 4.5 Solve the above equation given that the velocity is zero at time t = 0. 4.6 Write down the critical points of the nonlinear system of differential equations: dx = y(x2 + 1) dt dy = 2xy 2 . dt 4.7 Classify the following differential operator as elliptic, hyperbolic or parabolic: ∂2u ∂2u ∂2u −2 + 2 2. ∂x2 ∂x∂y ∂y 4.8 Let B be the unit ball in the plane and let u be a solution of the boundary value problem: ∆u = C in B ∂u = 1 on ∂B ∂n where ∆ denotes the Laplace operator, ∂B denotes the boundary of B and ∂u denotes the outer normal derivative on the boundary. Evaluate C, given ∂n that it is a constant. L(u) = 2 4.9 Write down the dual of the linear programming problem: Max. : 2x + 3y such that x + 2y = 3 2x + y ≥ 4 x+y ≤ 5 x ≥ 0 , y ≥ 0. 4.10 Write down the Newton-Raphson iteration scheme to find the square root of a > 0, by solving the equation x2 = a. 8
Section 5: Miscellaneous 5.1 Differentiate with respect to t:
a
f (t) =
−t2
e−x dx, (a > 0).
2
5.2 Sum the series: 1+ 5.3 Sum the series: 1 1 1 1 1 1 + + + ··· 3 4 5 42 7 43 5.4 Let A be the point (0, 1) and B the point (2, 2) in the plane. Consider all paths made up of the two line segments AC and CB as the point C varies on the x-axis. Find the coordinates of C for which the corresponding path has the shortest length. 1+ 5.5 Find the area of the pentagon formed in the plane with the fifth roots of unity as its vertices. 5.6 Let A, B, C, D and E be five points marked, in clockwise order, on the unit circle in the plane (with centre at origin). Let α and β be real numbers and set f (P ) = αx + βy where P is a point whose coordinates are (x, y). Assume that f (A) = 10, f (B) = 5, f (C) = 4 and f (D) = 10. Which of the following are impossible? (a) f (E) = 2 (b) f (E) = 4 (c) f (E) = 5 5.7 Let r identical red balls and b identical black balls be arranged in a row. Write down the number of arrangements for which the last ball is black. 5.8 It is known that a family has two children. (a) If it is known that one of the children is a girl, what is the probability that the other child is also a girl? (b) If it is known that the elder child is a girl, what is the probability that the younger child is also a girl? 5.9 A real number is called algebraic if it occurs as the root of a polynomial with integer coefficients. Otherwise it is said to be a transcendental number. Consider the interval [0, 1] considered as a probability space when it is provided with the Lebesgue measure. What is the probability that a number chosen at random in [0, 1] is transcendental? 5.10 List all primes p ≤ 13 such that p divides n13 − n for every integer n. 9 1 + 3 1 + 3 + 32 + + ··· 2! 3! | 677.169 | 1 |
This unit from the Yale-New Haven Teachers Institute is "an attempt to develop a unit in mathematics that will provide topics for students interested in the aviation trades." The unit can be used to cover all areas of...
This lesson from Illuminations asks students to use a geometry applet to analyze the characteristics of a square. Graphs are created to show relationships between characteristics (side length, diagonal length, perimeter...
This document from SpaceTEC National Aerospace Technical Education Center is one of three handbooks for people preparing for mechanic certification with airframe or powerplant ratings, or both. This particular volume...
Based at the University of Plymouth, the Centre for Innovation in Mathematics Teaching has developed many instructional materials designed to help both novice and experienced math teachers. This particular area of the...
This lesson from Illuminations looks at inverse variation. Students are asked to use estimates to measure the height of an object, visualize two-dimensional objects and calculate their area, and sketch graphs to... | 677.169 | 1 |
The 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 10th edition includes new problems, updated figures and examples to help motivate students. The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two or three semester course sequence, or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. | 677.169 | 1 |
ACT Math
Key Problems and Concepts CoveredLearn
Master
About This Course
Course Description
If you are looking to get into a great college or University you will need an excellent ACT score and this course will help you get that higher ACT math score that you need and want.
You can complete this course all in one sitting or break it up into parts whichever works better for you.
In this course we will be covering 21 key concept areas that are covered on the math portion of the ACT exam to assist you in boosting your Math ACT score.
There will be a teaching segment for each area where we will discuss important formulas and background information that you need to know.
You will have opportunities to pause the video and work on solving examples independently. We will then go over these examples together and I will show you how to solve them effectively and efficiently.
Each lesson you will be provided with a worksheet with problems for additional practice and an answer key to check your answers to further reinforce what you have learned.
As a private professional math tutor, I have worked individually with hundreds of students helping them prepare for the Math portion of the ACT. I know the stumbling blocks that students have with the test and common mistakes that are made. By being able to recognize what is being asked for in a given problem you will be able to take the correct approach and use the correct formula(s) to solve the problem. I will give you the tips and insights that you need to be more confident, faster, and most importantly accurate, thus boosting your score and helping you get into your desired College or University. Join the course now and let's get started learning.
What are the requirements?
There are no prerequisites for this course, however you may want to take a practice ACT test prior to taking this course then another practice test after taking this course to see your improvement.
What am I going to get from this course?
Increase your Math ACT score.
Increase you speed, confidence and accuracy on the test.
Position yourself with a better ACT score to help with your college admissions.
What is the target audience?
Students that are struggling with the math section of the ACT will benefit from this course.
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Instructor Biography
My name is Mario DiBartolomeo and I am a graduate from the University of Michigan's college of Education. I have made a career out of privately tutoring middle school, high school and college students. I have worked INDIVIDUALLY with HUNDREDS of students in my local area in Southeast Michigan and now am offering training to new and part-time tutors to teach them how to turn tutoring into a career. I specialize in tutoring mathematics including Algebra, Geometry, Trigonometry, Algebra 2, PreCalculus, Calculus as well as helping students prepare for the math portion of the ACT exam.
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Please confirm that you want to add Start a Successful Tutoring Business as a High Paid Tutor to your Wishlist. | 677.169 | 1 |
2007-03-15T00:16:46ZFluxBB from England, so yes. ]]> "advanced" texts I notice that "log" is used instead of "ln". I'm not sure why they don't save themselves a letter and stick with "tradition", but I can see how they justify replacing the base 10 log notation with base e: base 10 logarithms just aren't that commonly used farther down the road. I think that ln is the clearest notation though. Is ln used in England?]]> wrote:
mathsyperson wrote:
I usually use log = log(10) and ln = log(e).
Is that because you were mostly taught that?
Pretty much. That's what I was taught when I was first introduced to logs, and I've just stuck to it. I don't know which is used most throughout the world though. Don't worry too much, anyone who knows enough about logs to understand that section will be able to figure out what base you're using pretty quickly.
]]> in my math books "ln" was always used for base e, and "log" was assumed to be base 10 when no base was given. However, in programming "log" itself tends to go by base e. So I guess it depends on what you're familiar with. At any rate, I think people from both fields will recognize "ln" so maybe you should use that. Or at least display what base you are using.]]> wrote:
I usually use log = log(10) and ln = log(e).
Is that because you were mostly taught that? Do you think I will also confuse most people?
especially if you consider a system of equations such as xy = 2 and y = 2x + 3, substituting you get y = 4/y + 3 which becomes y^2 - 3y - 4 = 0 which is obviously a 2nd degree equation.
]]> xy would be order 2 then? That makes sense.
I think the loggy limits addition looks good. I was a bit worried that it would be too advanced, but it's explained very well so people could probably follow along anyway. I was confused by your example for a bit before I realised that you were using logs with base e, but that's probably just me. I usually use log = log(10) and ln = log(e).
]]> just thought I might mention. I recall reading that in multivariable equations, the degree of each term is the sum of the exponants of the variables in the term, and the degree of the expression or equation is equal to the degree of its highest degree term.
At least thats what I recall. I might have forgotten the precise definiton.
]]> agree with Toast. You've pretty much said everything you can say about degree, and explained it very well.
I'm not sure whether you should include the bit about loggy limits, because it's on a substantially higher level than the rest of the page.
]]> job on that page, I never knew about the fractions thing. Well... there isn't really much to talk about regarding degree apart from what you've already said... and perhaps that limit thing... so yeah ]]> fine and i tottaly agree (top one)]]> am thinking of adding that you can also work out the Degree by taking the limit of log(f(x))/log(x) as x goes to infinity.]]> am still working on creating some pages on Limits, and along the way I made this page: | 677.169 | 1 |
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About the Book
About the Contents:
Pretest
Helps you pinpoint where you need the most help and directs you to the corresponding sections of the book
Topic Area Reviews
Math Basics
Numbers (Signed Numbers and Fractions)
Linear Equations and Algebraic Fractions
Polynomials and Factoring
Inequalities, Absolute Value Inequalities, and Radicals
Introducing Quadratic Equations--Testing Solutions
Graphing and Systems of Equations
Functions
Story Problems
Customized Full-Length Exam
Covers all subject areas
Pretest that pinpoints what you need to study most
Clear, concise reviews of every topic
Targeted example problems in every chapter with solutions and explanations | 677.169 | 1 |
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The Sixth Edition uses all strands of the Rule of Four - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. | 677.169 | 1 |
Details about Mathematica Navigator:
Mathematica Navigator contains a great deal of material not easily found elsewhere in a well-organized form, with sufficient detail and illustrative examples. This book will serve excellently as a Mathematica handbook; it starts with the basics, goes carefully through the main material of Mathematica, and covers some advanced topics. Mathematica packages are integrated into the text, so that the reader gets a comprehensive overview of the features of Mathematica. This book allows a new user to begin working with Mathematica and proceed to quite a high level. Old users will find much new material, allowing them to raise their knowledge and skill to an even higher level. In addition, registered readers can send questions to the author concerning the use of Mathematica in areas treated in the book. * Gives a careful, overall introduction to Mathematica * Explores graphics in detail,both for functions and data * Covers procedural, functional, and rule-based programming * Presents useful standard Mathematica packages throughout the text * Emphasizes methods of applied mathematics and numerical analysis * CD-ROM contains the entire book, including all animations, and data sets presented in the book
Back to top
Rent Mathematica Navigator 1st edition today, or search our site for other textbooks by Heikki Ruskeepaa. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Elsevier Science & Technology Books.
Need help ASAP? We have you covered with 24/7 instant online tutoring. Connect with one of our tutors now. | 677.169 | 1 |
Course
3 Unit 7 - Discrete Models of Change 1st Edition
Discrete Models
of Change is the final unit from the discrete mathematics strand in
Courses 1-3 of the Contemporary Mathematics in Context program.
(See the descriptions of Course 3 Units.)
Unit Overview
Discrete Models
of Change extends student ability to represent, analyze, and solve
problems in situations involving sequential and recursive change. It summarizes
and formalizes much of the work with recursion across Courses 1-3, while
at the same time reviewing linear, exponential, and power functions.
Unit Objectives
To use iteration and recursion as tools to represent, analyze,
and solve problems involving sequential change
To formalize and consolidate previous study of NOW-NEXT
equations, particularly through the use of subscript notation
and the introduction of recursive formulas
To understand and apply recursive formulas, particularly combined
recursive formulas of the form An = rAn -
1 + b
To review linear, exponential, and polynomial models from
a recursive perspective
Sample Overview
The sample material
from Discrete Models of Change is the second lesson of the unit.
In the first lesson, recursive formulas were used to model situations,
and the effect of parameter changes on long-term behavior in these situations
was examined. Lesson 2, "A Discrete View of Function Models," develops
student understanding of arithmetic and geometric sequences and their
connections to linear and exponential functions. Finite differences tables
are used to find power function formulas for selected recursive formulas.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a common pattern as elaborated under Instructional
Design. | 677.169 | 1 |
Description
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Review quote
R. Hartshorne Algebraic Geometry "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions."-MATHEMATICAL REVIEWS
Review Text
R. Hartshorne
Algebraic Geometry
"Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions."- MATHEMATICAL REVIEWS | 677.169 | 1 |
4th edition of Collins GCSE Maths has been fully revised and updated for the new GCSE specifications and endorsed by Edexcel. The new edition of this well-established text has a new focus on mathematical reasoning and problem solving. The course coverage ensures that you will have the confidence to tackle the new curriculum and succeed.
•Bring awe and wonder with a chapter opener that puts the maths in context •Provide rigourous maths practice with hundreds of high quality questions •Focus on literacy skills with key words per topic •Reason, interpret and communicate mathematically with flagged mathematical reasoning questions (labelled MR and CM) •Solve problems within mathematics and in other contexts with flagged problem-solving questions (labelled PS and EV) •Show step by step working through worked examples (numbered sequentially throughout the chapter) •Differentiate at the top end with more challenging questions •Access answers online, in the Teacher's Pack and in the Collins Connect edition • Endorsed by Edexcel | 677.169 | 1 |
Foundations of GeometryFoundations of Geometry, Second Editionimplements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers ;and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Editionstreamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. | 677.169 | 1 |
Discovering Calculus with Maple
Author:Kent Harris - Robert J. Lopez
ISBN 13:9780471009733
ISBN 10:471009733
Edition:2
Publisher:Wiley
Publication Date:1995-01-03
Format:Paperback
Pages:352
List Price:N/A
 
 
This substantially illustrated manual describes how to use Maple as an investigative tool to explore calculus concepts numerically, graphically, symbolically and verbally. Every chapter begins with Maple commands employed in the chapter, an introduction to the mathematical concepts being covered, worked examples in Maple worksheet format, followed by thought-provoking exercises and extensive discovery projects to encourage readers to investigate ideas on their own. | 677.169 | 1 |
Basic Math and Pre-Algebra For Dummies, 2nd Edition
Book Description
Tips for simplifying tricky basic math and pre-algebra operations
Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. | 677.169 | 1 |
These popular and proven workbooks help students build confidence before attempting end-of-chapter problems. They provide short exercises that focus on developing a particular skill, mostly requiring students to draw or interpret sketches and graphs. New to the Third Edition are exercises that provide guided practice for the textbookâ s Problem-Solving Strategies, focusing in particular on working symbolically. Author : Randall D. Knight (Professor Emeritus) ISBN : 0321753097 Language : English No of Pages : 384 Edition : 3 Publication Date : 1/15/2012 Format/Binding : Paperback Book dimensions : 10.8x8.5x0.8 Book weight : 0.02 | 677.169 | 1 |
Ch 15 Review Sheet Algebra II Honors Mr. Petach Please write your answers on a separate sheet! 1. Find the cross product a b for each of the following vectors. Use the determinant method and the distributive property method for each set of vectors. (a) a
Ch 13 Review Sheet Algebra II Honors Mr. Petach Please write your answers on a separate sheet! The Apollo 13 astronauts need to get back to Earth. To the astronauts, the Earth appears to be moving relative to the moon (due to the Earths orbit around the s
01/14/2011 PIB Algebra II Mr. Petach Evaluation The most important part of mathematics is the ability to solve problems. Tests, quizzes, take-home projects, and graded projects show how well you solve math problems. However, daily practice and an engaged
Name:
KEY Chapter 5 Exam 04/14/2011 Algebra II Honors Mr. Petach
Please circle your answers and show your work for credit. Calculators may be used on this exam. 1. Simplify the following expressions. Use only positive fractional exponents in your answer. | 677.169 | 1 |
This document promotes computer symbolic mathematics and computer algebra as ideal instructional materials for mathematics, science, and engineering students. Further, computer algebra is viewed as appropriate for all students throughout the mathematics curriculum, by serving a vast area of mutual reinforcement and cross-motivation between mathematics and computer science. Some of the problems with most popular programing languages in mathematics instruction are listed, along with many of the obstacles that must be met if a computer algebra language is to be developed and assigned widespread use. Several steps to possible remedies are proposed, and a summary of an educational computer symbolic mathematics system as implemented on the Intel 8080 is included in an appendix. (MP) | 677.169 | 1 |
Mathematics for Informatics and Computer ways do exist to mix different ingredients, how many chances to win a gambling game, how many possible paths going from one place to another in a network ? To this kind of questions Mathematics applied to computer gives a stimulating and exhaustive answer. This text, presented in three parts (Combinatorics, Probability, Graphs) addresses all those who wish to acquire basic or advanced knowledge in combinatorial theories. It is actually also used as a textbook. Basic and advanced theoretical elements are presented through simple applications like the Sudoku game, search engine algorithm and other easy to grasp applications. Through the progression from simple to complex, the teacher acquires knowledge of the state of the art of combinatorial theory. The non conventional simultaneous presentation of algorithms, programs and theory permits a powerful mixture of theory and practice.
All in all, the originality of this approach gives a refreshing view on combinatorial theory. | 677.169 | 1 |
Gauss elimination is a method of solving a system of linear equations. This site contains an interactive tool that performs...
see more
Gauss elimination is a method of solving a system of linear equations. This site contains an interactive tool that performs Gauss elimination procedure one step at a time. The result is displayed after each step. A user can also use this tool to invert a matrix Gaussian Elimination to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Gaussian Elimination
Select this link to open drop down to add material Gaussian Elimination to your Bookmark Collection or Course ePortfolio
Growing out of classes in computer music at Dartmouth College this is web version of a book that is intended as a...
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Growing out of classes in computer music at Dartmouth College this is web version of a book that is intended as a "user-friendly" introduction to music and computers. AN excellent introduction to what is sound and Computers to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Music and Computers
Select this link to open drop down to add material Music and ComputersThis site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations,...
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This site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations, determinants, eigenvectors and eigenvalues. S.O.S. Mathematics--Matrix Algebra is a part of an independent, commercial site that offers straightforward technical assistance primarily to high school and college.O.S. Mathematics--Matrix Algebra to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material S.O.S. Mathematics--Matrix Algebra
Select this link to open drop down to add material S.O.S. Mathematics--Matrix Math--Secondary Interactives to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Seeing Math--Secondary Interactives
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This site is designed to answer many important questions regarding carrers and professional placement of math majors. It...
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This site is designed to answer many important questions regarding carrers and professional placement of math majors. It contains very useful statistical data on the subject as well as information on different connections between mathematics and real life. The site can be very useful for all kinds of professional orientation sessions for math majors When will I use math? to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material When will I use math?
Select this link to open drop down to add material When will I use math? to your Bookmark Collection or Course ePortfolio
LiveGraphics3D is a non-commercial Java 1.1 applet that enables users to put almost any three-dimensional graphics computed...
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LiveGraphics3D is a non-commercial Java 1.1 applet that enables users to put almost any three-dimensional graphics computed by Mathematica directly onto an HTML page. It can then be viewed and interactively rotated without any additional software. LiveGraphics3D also shows animations and supports parametrized graphicsGraphics3D to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material LiveGraphics3D
Select this link to open drop down to add material LiveGraphics3D to your Bookmark Collection or Course ePortfolio
An interactive scatterplot applet that allows users to put in their own data that is part of a large collection of platform...
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An interactive scatterplot Scatterplot to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material National Library of Virtual Manipulatives: Scatterplot
Select this link to open drop down to add material National Library of Virtual Manipulatives: Scatterplot to your Bookmark Collection or Course ePortfolio
This applet is a web based lab that explores the properties of linear functions. It is one in a series of other precalculus...
see more
This applet is a web based lab that explores the properties of linear to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Linear Functions
Select this link to open drop down to add material Linear Functions to your Bookmark Collection or Course ePortfolio | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This is a serious - but not solemn - textbook that attempts to make a clear, conceptual understanding of calculus accessible to all liberal arts students. It presents mathematics as growing out of the classical liberal arts to form a natural bridge between the humanities and the sciences, integrating the history and pedagogy of mathematics in a way that may be of interest to prospective teachers as well. Instead of a pre-calculus review, this book offers an historical development of much of the geometry and algebra needed, emphasizing the fundamental need for students to develop a clear style of writing. Calculus is here largely restricted to the study of algebraic functions, but all the usual aspects of the interplay between functions and derivatives are covered: optimization, instantaneous rates, Newton's method, freely falling bodies, antiderivatives, integrals, areas, volumes, etc. The fundamental theorem is prominently featured and carefully treated. A brief final chapter about the intellectual climate surrounding the development of calculus offers students further insight into the place of mathematics as an element in the history of thought.
Synopsis
reason for delaying its study has to do with the question of mathematical maturity. * No use is made here of trigonometric, logarithmic, or expo nential functions except in occasional optional material indicating how such functions can be handled. A perceptive remark made by George P6lya suggests how we can simultaneously learn mathematics and learn "about" mathematics-i.e., about the nature of mathematics and how it is developed: If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference. The reader will find plenty of opportunity here for guessing. The early chapters go at a gentle pace and invite the reader to enter into the spirit of the investigation. Exercises asking the reader to "make a guess" should be taken in this spirit-as simply an invitation to speculate about what is the likely truth in a given situation without feeling any pressure to guess "correctly." Readers will soon realize that a matter about which they are asked to guess will likely be a topic of serious discussion later on."
Synopsis
Presenting mathematics as forming a natural bridge between the humanities and the sciences, this book makes calculus accessible to those in the liberal arts. Much of the necessary geometry and algebra are exposed through historical development, and a section on the development of calculus offers insights into the place of mathematics in the history of thought.
Table of Contents
1: Tokens from the Gods. 2: Rational Thoughts. 3: To Measure is to Know. 4: Sherlock Holmes Meets Pierre de Fermat. 5: Optimistic Steps. 6: Chains and Change. 7: The Integrity of Ancient and Modern Mathematics. 8: Romance in Reason. | 677.169 | 1 |
How To Learn Calculus Of One Variable
4.11 - 1251 ratings - Source
How To Learn Calculus Of One Variable A Central Part In Many Branches Of Physics And Engineering. The Present Book Tries To Bring Out Some Of The Most Important Concepts Associates With The Theoretical Aspects Which Is Quite Exhaustively. The Entire Book In A Manner Can Help The Student To Learn The Methods Of Calculus And Theoretical Aspects.These Techniques Are Presented In This Book In A Lucid Manner With A Large Number Of Example, Students Will Easily Understand The Principles Of Calculus. It Helps To Solve Most Examples And Reasonings.This Book Mainly Caters To The Need Of Intermediate And Competitive Students, Who Will Find It A Pleasure In This Book. It Can Also Be Useful For All Users Of Mathematics And For All Mathematical Modelers.6. y = i. y = Ve -*)(*- 2) 1 V^ Answers: I. (-2. +Al) : -f| 3. (-oo, l)u (2, +co) 1 2a#39; , 2a#39;2, 5. (-
1, 3) 6. (1, 2) 7. (-00, 6). jTv/?ta#39; 6: W/7e/7 the given function is put in the form: y =
Exercise 1.10 Find the domain of each of the following functions: i. y = 2. y = 3.
Title
:
How To Learn Calculus Of One Variable
Author
:
J. D. Ghosh
Publisher
:
New Age International - 2004-01-01
ISBN-13
:
Continue
You Must CONTINUE and create a free account to access unlimited downloads & streaming | 677.169 | 1 |
Math Bridge
Three items are added to Geometry section.
Length (Pythagorean theorem)
Area (Triangle, rectangle and circle)
Geometry with Algebra (Triangle figured by three linear functions)
Description
In this Math App, there are no words to explain except at index. So let me introduce the concept of Math Bridge in English. You can try free sample version on web.
This App is not Math itself, but Math-related supplemental program. Math can only exist when you are doing it as if your thinking exists when you think.
1. Calculation
In this App, there are three levels and one challenge mode in following calculations.
i) Addition:
ii) Subtraction:
iii) Multiplication:
iv) Division:
After every five questions, quick review is set to check right and wrong. All four challenge modes for calculations have a five seconds timer to answer the question. They are difficult but concentration can enable us to get right answers.
5 Differentiation
In calculus, a branch of mathematics, the derivatives is a measure to know how a function changes as its input changes. (from wikipedia)
In this App, you can find points of extreme by a quadratic derivative in trinomials.
6 Integration
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. (from wikipedia)
In this App, you can learn the calculation of an area between quadratic function and linear function. At first, the cross-points of two functions are calculated by factoring and calculate the area by integration. Please touch screen to take steps.
An Orbit of thrown object as quadratic curve can be a bridge connected between the real world and math. Math is a tool as well as a world. The difference of the real world and a world is ambiguous, because we can't see the real world without a world, which is our own world. Math has a history over 3000 years as well as language, both of which are very powerful to explore the real world. Life may be a problem much more complex than math, but logic is useful for both of them. To handle logic or theory requires much energy in brain so that doing math is a good training for thinking about the world and life with your own logic. These can be reasons why we learn math. How about you?
Have fun!
ver 1.1
"Quadratic formula" and "Trinomial" are added in Equation.
In Quadratic formula, you can see the course from a general quadratic equation to the quadratic formula by 7 steps. The logic of four arithmetic operations and notion of equal is the basic skill.
In trinomial, you can solve cubic equations by factoring. Please note that plus and minus notations are needed to be cared for as well as calculating fraction. When f(a) = 0 in f(x)=0, it means that the "a" can be factoredTonline
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Symmetry*
Symmetry* is simple yet sophisticated brain challenging puzzle game.
Each stage, only 1/4 of the symmetry pattern is revealed and it is your job to finish up the rest!
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Tlaloc's Temple
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Thank you everybody who tried it and shared this adventure with me ! I stay on touch for your feedback to tell me what to change and improve !
Trapped in the temple of the Aztec's god of water, sadistics and cunning traps awaits you in the…
Rebuild 2
Reclaim a city from the zombie hordes while managing supplies, housing and morale. Featuring new buildings, plotlines, characters, customizable survivors with skills and equipment, new & improved art and all new hidden endings to discover.
***WAIT 15 MINUTES FOR THE GAME UP LOAD***
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Publisher's Summary
Have you ever wanted to be able to make complex math calculus in your mind, without a calculator? You've come to the right place!Here's a gist of what you'll learn:
Addition and subtraction
Multiplication
Division
The famous walk on the number line
Find the sum of one to 100
Multiplying two-digit numbers with 11
Simultaneously doubling and halving terms in a problem, incorporating even terms | 677.169 | 1 |
Popular in Mathematics (M)
Reviews for LINEAR OPTIM 407 7 Linear Optimization 1 Introduction 11 What is optimization A mathematical optimization problem is one in which some function is either maximized or minimized relative to a given set of alternatives The function to be minimized or maximized is called the objective function and the set of alternatives is called the feasible region or constraint region In this course the feasible region is always taken to be a subset of R real n dimensional space and the objective function is a function from R to R We further restrict the class of optimization problems that we consider to linear program ming problems or LPs An LP is an optimization problem over R wherein the objective function is a linear function that is the objective has the form 01 C z Cnxn for some 0 E R i 1 n and the feasible region is the set of solutions to a nite number of linear inequality and equality constraints of the form ai1iai2239amn bi 1778 and anxiai2x2amxnbi is1m Linear programming is an extremely powerful tool for addressing a wide range of applied optimization problems A short list of application areas is resource allocation produc tion scheduling warehousing layout transportation scheduling facility location ight crew scheduling portfolio optimization parameter estimation 12 An Example To illustrate some of the basic features of LP we begin with a simple two dimensional example In modeling this example we will review the four basic steps in the development of an LP model H Identify and label the decision variables 3 Determine the objective and use the decision variables to write an expression for the objective function 00 Determine the eaplicit constraints and write a functional expression for each of them 4 Determine the implicit constraints PLASTIC CUP FACTORY A local family owned plastic cup manufacturer wants to optimize their production mix in order to maximize their pro t They produce personalized beer mugs and champaign glasses The pro t on a case of beer mugs is 25 while the pro t on a case of champaign glasses is 20 The cups are manufactured with a machine called a plastic extruder which feeds on plastic resins Each case of beer mugs requires 20 lbs of plastic resins to produce while champaign glasses require 12 lbs per case The daily supply of plastic resins is limited to at most 1800 pounds About 15 cases of either product can be produced per hour At the moment the family wants to limit their work day to 8 hours We will model the problem of maximizing the pro t for this company as an LP The rst step in our modeling process is to identify and label the decision variables These are the variables that represent the quanti able decisions that must be made in order to determine the daily production schedule That is we need to specify those quantities whose values completely determine a production schedule and its associated pro t In order to determine these quantities one can ask the question If I were the plant manager for this factory what must I know in order to implement a production schedule77 The best way to identify the decision variables is to put oneself in the shoes of the decision maker and then ask the question What do I need to know in order to make this thing work7 In the case of the plastic cup factory everything is determined once it is known how many cases of beer mugs and champaign glasses are to be produced each day Decision Variables B of cases of beer mugs to be produced daily 0 of cases of champaign glasses to be produced daily You will soon discover that the most dif cult part of any modeling problem is identifying the decision variables Once these variables are correctly identi es then the remainder of the modeling process usually goes smoothly After identifying and labeling the decision variables one can now specify the problem objective That is one can write an expression for the objective function Objective Function Maximize pro t where pro t 25B 200 The next step in the modeling process is to express the feasible region as the solution set of a nite collection of linear inequality and equality constraints We separate this process into two steps 1 determine the explicit constraints and 2 determine the implicit constraints The explicit constraints are those that are explicitly given in the problem statement In the problem under consideration there are explicit constraints on the amount of resin and the number of work hours that are available on a daily basis Emplicit Constraints resin constraint 20B 120 S 1800 work hours constraint B 0 3 8 This problem also has other constraints called implicit constraints These are constraints that are not explicitly given in the problem statement but are present nonetheless Typically these constraints are associated with natural77 or common sense77 restrictions on the deci sion variable In the cup factory problem it is clear that one cannot have negative cases of beer mugs and champaign glasses That is both E and 0 must be non negative quantities Implicit Constraints 0 S B 0 S O The entire model for the cup factory problem can now be succinctly stated as 73 max 25B 200 subject to 20B 120 3 1800 3 T150 8 0 S B O l Since it is an introductory example the Plastic Cup Factory problem is particularly easy to model As the course progresses you will be asked to model problems of increasing dif culty and complexity In this regard let me emphasize again that the rst step in the modeling process identi cation of the decision variables is always the most dif cult In addition the 4 step modeling process outlined above is not intended a process that one steps through in a linear fashion As the model unfolds it is often necessary to revisit earlier steps for example by adding in more decision variables a very common requirement Cycling through these steps several times is often required before the model is complete In this process the greatest stumbling block experienced by students is the overwhelming desire to try to solve the problem as it is being modeled lndeed every student who has taken this course over the last 20 years has made this error and on occasion I continue to make this error myself Perhaps the most common error in this regard is to try to reduce the total number of decision variables required This often complicates the modeling process blocks the ability to fully characterize all of the variability present makes it dif cult to interpret the solution and understand its robustness and makes it dif cult to modify the model as it evolves Never be afraid to add more decision variables either to clarify the model or to improve its exibility Modern LP software easily solves problems with tens of thousands of variables and in some cases tens of millions of variables It is more important to get a correct easily interpretable and exible model then to provide a compact minimalist model 3 We now turn to solving the Plastic Cup Factory problem Since this problem is two dimensional it is possible to provide a graphical representation and solution The rst step is to graph the feasible region To do this7 rst graph 15 20B 120 1800 W 12 7 objective normal 71 solution 45 optimal value 2625 feasible region 1 1 7 2 W MEBE078 1 lllllllll l lllllB 12 3 4 5 6 7 89101 12131415 the line associated with each of the linear inequality constraints Then determine on which side of each of these lines the feasible region must lie dont forget the implicit constraintsl To determine the correct side7 locate a point not on the line that determines the constraint for exarnple7 the origin is often not on the line7 and it is particularly easy to use Plug this point in and see if it satis es the constraint If it does7 then it is on the correct side of the line If it does not7 then the other side of the line is correct Once the correct side is determined put little arrows on the line to remind yourself of the correct side Then shade in the resulting feasible region which is the set of points feasible for all of the linear inequalities The next step is to draw in the vector representing the gradient of the objective function This vector may be placed anywhere on your graph7 but it is often convenient to draw it emanating from the origin Since the objective function has the form f9617 962 01961 02962 the gradient of f is the same at every point in R2 mexz Cl 02 4 Recall from calculus that the gradient always points in the direction of increasing function values Moreover since the gradient is constant on the whole space the level sets of f associated with different function values are given by the lines perpendicular to the gradient Consequently to obtain the location of the point at which the objective is maximized we simply set a ruler perpendicular to the gradient and then move the ruler in the direction of the gradient until we reach the last point or points at which the line determined by the ruler intersects the feasible region In the case of the cup factory problem this gives the solution to the LP as g 71 We now recap the steps followed in the solution procedure given above Step 1 Graph each of the linear constraints indicating on which side of the constraint the feasible region must lie with an arrow Don7t forget the implicit constraints Step 2 Shade in the feasible region Step 3 Draw the gradient vector of the objective function Step 4 Place a straight edge perpendicular to the gradient vector and move the straight edge either in the direction of the gradient vector for maximization or in the oppo site direction of the gradient vector for minimization to the last point for which the straight edge intersects the feasible region The set of points of intersection between the straight edge and the feasible region is the set of solutions to the LP The solution procedure described above for two dimensional problems reveals a great deal about the geometric structure of LPs that remains true in 71 dimensions We will explore this geometric structure more fully as the course evolves For the moment note that the solution to the Plastic Cup Factory problem lies at a corner point of the feasible region Indeed it is easy to convince oneself that every 2 dimensional LP has an optimal solution that is such a corner point The notion of a corner point can be generalized to n dimensional space where it is refered to as a vertex These vertices play a big role in understanding the geometry of linear programming Before leaving this section we make a nal comment on the modeling process described above We emphasize that there is not one and only one way to model the Cup Factory problem or any problem for that matter In particular there are many ways to choose the decision variables for this problem Clearly it is suf cient for the shop manager to know how many hours each day should be devoted to the manufacture of beer mugs and how many hours to champaign glasses From this information everything else can be determined For example the number of cases of beer mugs that get produced is 15 times the number of hours devoted to the production of beer mugs However in the end they should all point to the same optimal process 13 Sensitivity Analysis One of the most important things to keep in mind about real world77 LPs is that the input data associated with the problem speci cation can change over time is subject to mea surernent error and is often the product of educated guesses another name for fudging For example in the case of the cup factory the pro t levels for both beer mugs and charn paign glasses are subject to seasonal variations Prior to the New Year the higher demand for charnpaign glasses forces up the sale price and consequently their pro tability As St Patricks Day approaches the demand for charnpaign glasses drops but the demand for beer rnugs soars In June demand for charnpaign glasses again rises due to the increase in rnar riage celebrations Then just before the Fourth of July the demand for beer rnugs returns These seasonal uctuations may effect the optimal solution and the optimal value A natural question to ask in this regard is What is the smallest pro t level required for charnpaign glasses remain in the optimal production rniX7 or equivalently What is the smallest pro t level at which rnanufacturing charnpaign glasses rernains e cient The lowest level of pro tability for charnpaign glasses to remain in the optimal production mix is called the break even pro t77 for charnpaign glasses Correspondingly the lowest sale price for charnpaign glasses to remain in the optimal production mix is called the break even sale price77 for charnpaign glasses 131 Breakeven Prices The break even price for charnpaign glasses is easily computed Recall that the optimal solu tion is obtained by holding a ruler perpendicular to the objective gradient and then moving the ruler in the direction of the objective gradient to the furthest point at which the line determined by the ruler and the feasible region intersect Thus to determine the break even price for charnpaign glasses we need to determine the smallest tilt of the objective gradi ent for which the optimal solution changes from producing both beer mugs and charnpaign glasses to producing just beer rnugs This occurs when the objective gradient is parallel to any normal to the constraint line associated with the resin bound That is if the objective is fBO a3 60 then we want 04 7 20 B T E where the numbers 20 and 12 are coef cients in the resin constraint Holding 04 xed at 25 we get 12 7 25 15 B 20 That is the break even price for charnpaign glasses is 15 a case Similarly one computes the break even price for beer rnugs by considering the labor hours constraint and arrives at 20 per case of beer rnugs Observe that if we set the per case pro tability of champaign glasses to 15 while keeping the pro tability of beer mugs xed we nd that every point on the line segment connecting the two points and 30 is optimal for the new LP Thus the set of optimal solutions to an LP can be in nite 132 Marginal Values Next we consider the effect of uctuations in the availability of resources on both the optimal solution and the optimal value In the case of the cup factory there are two basic resources consumed by the production process plastic resin and labor hours In order to analyze the behavior of the problem as the value of these resources is perturbed we rst observe a geometric property of the optimal solution namely that the optimal solution lies at a corner point77 or vertex of the feasible region More will be made of the notion of a vertex later but for the moment suf ce it to say that if an optimal solution to an LP exists then there is at least one optimal solution that is a vertex of the feasible region Next note that as the availability of a resource is changed the constraint line associated with that resource moves in a parallel fashion along a line normal to the constraint Thus at least for a small range of perturbations to the resources the vertex associated with the current optimal solution moves but remains optimal We caution that this is only a generic property of an optimal vertex and there are examples for which it fails For example the feasible region can be made empty under arbitrarily small perturbations of the resources These observations lead us to conjecture that the solution to the LPs l6162 max 25B 200 subject to 20B 120 3 1800 61 1 1 EB 0 E 9 62 0 g B 0 lies at the intersection of the two lines 20B 120 1800 61 and 1175B 0 8 62 for small values of 61 and 62 namely B 4576261 C 75 77562 7 el and 06162 2625 62 261 It can be veri ed by direct computation that this indeed yields the optimal solution for small values of 61 and 62 Next observe that the value 161 62 can now be viewed as a function of 61 and 62 and that this function is differentiable at g with WWW 3392 l 39 7 The number 2 is called the marginal value of the resin resource at the optimal solution 2 71 and the number L5 is called the marginal value of the labor time resource at the optimal solution We have the following interpretation for these marginal values each additional pound of resin beyond the base amount of 1800 lbs contributes 2 to the pro t and each additional hour of labor beyond the base amount of 8 hours contributes to the pro t Using this information one can answer certain questions concerning how one might change current operating limitations For example7 if we can buy additional resin from another supplier7 how much more per pound are we willing to pay than we are currently paying Answer 2 per pound is the most we are willing to pay beyond what we now pay7 why Or7 if we are willing to add overtime hours7 what is the greatest overtime salary we are willing to pay Of course7 the marginal values are only good for a certain range of uctuation in the resources7 but within that range they provide valuable information 14 Duality Theory We now brie y discuss the economic theory behind the marginal values and how the hidden hand of the market place77 gives rise to them This leads in a natural way to a mathematical theory of duality for linear programming Think of the cup factory production process as a black box through which the resources ow Raw resources go in one end and exit the other When they come out the resources have a different form7 but whatever comes out is still comprised of the entering resources However7 something has happened to the value of the resources by passing through the black box The resources have been purchased for one price as they enter the box and are sold in their new form as they leave The difference between the entering and exiting prices is called the pro t Assuming that there is a positive pro t the resources have increased in value as they pass through the production process The marginal value of a resource is precisely the increase in the per unit value of the resource due to the production process Let us now consider how the market introduces pressures on the pro tability and the value of the resources available to the market place We take the perspective of the cup factory vs the market place The market place does not want the cup factory to go out of business On the other hand7 it does not want the cup factory to see a pro t It wants to keep all the pro t for itself and only let the cup factory just break even It does this by setting the price of the resources available in the market place That is7 the market sets the price for plastic resin and labor and it tries to do so in such a way that the cup factory sees no pro t and just breaks even Since the cup factory is now seeing a pro t7 the market must gure out by how much the sale price of resin and labor must be raised to reduce this pro t to zero This is done by minimizing the value of the available resources over all price increments that guarantee that the cup factory either loses money or sees no pro t from both of its products If we denote the per unit price increment for resin by R and that for labor by L7 then the pro t for beer mugs is eliminated as long as 1 20B 7L gt 25 15 7 since the left hand side represents the increased value of the resources consumed in the production of one case of beer mugs and the right hand side is the current pro t on a case of beer mugs Similarly7 for champaign glasses7 the market wants to choose R and L so that 1 12B 7L gt 20 15 7 Now in order to maintain equilibrium in the market place7 that is7 not drive the cup factory out of business since then the market realizes no pro t at all7 the market chooses R and L so as to minimize the increased value of the available resources That is7 the market chooses R and L to solve the problem D minimize 1800B 8L subject to 20R L 25 12B L 2 20 0 3 R7 L l V This is just another LP It is called the dual77 to the LP 73 in which the cup factory tries to maximize pro t Observe that if is feasible for 73 and is feasible for D7 then 25B 200 3 20B LlB 12R Ljo R2OB 120 L B 0 1800B 8L Thus7 the value of the objective in 73 at a feasible point in 73 is bounded above by the objective in D at any feasible point for D In particular7 the optimal value in 73 is bounded above by the optimal value in D The strong duality theorem77 states that if either of these problems has a nite optimal value7 then so does the other and these values coincide ln addition7 we claim that the solution to D is given by the marginal values for 73 That is7 1 32 is the optimal solution for D In order to show this we need only show that R7 58ii R7 58 L i 3752 is feasible for D and that the value ofthe objective in D at L i 3752 coincides with the value of the objective in 73 at First we check feasibility K o 8 7 2 20 7LEgt25 8 15 2 5 1 375 12777220 8 15 2 Next we check optimality 5 375 254520752625 1800 87 This is a most remarkable relationship We have shown that the marginal values have three distinct and seemingly disparate interpretations H The marginal values are the partial derivatives of the value function for the LP with respect to resource availability7 D The marginal values give the per unit increase in value of each of the resources that occurs as a result of the production process7 and C40 The marginal values are the solutions to a dual LP7 D 15 LPS in Standard Form and Their Duals Recall that a linear program is a problem of maximization or minimization of a linear func tion subject to a nite number of linear inequality and equality constraints This general de nition leads to an enormous variety of possible formulations In this section we propose one xed formulation for the purposes of developing an algorithmic solution procedure and developing the theory of linear programming We will show that every LP can be recast in this one xed form We say that an LP is in standard form if it has the form 73 maximize mm ngg cnzn subject to ailzl aigzg amzn lt bl forz3917277m 0 zj forj17277n Using matrix notation7 we can rewrite this LP as 73 maximize cTz subject to Az S b 0 S x 7 where c 6 R72 b 6 RT A E Rm and the inequalities Az S b and 0 S x are to be interpreted componentwise Following the results of the previous section on LP duality7 we claim that the dual LP to 73 is the LP D minimize blyl bzyz bnym subjectto a1jy1azjy2amjym Z ijOFj17277n 0 yiforz3917277m7 10 or equivalently using matrix notation we have D minimize bTy subject to ATy 2 c 0 S y Just as for the cup factory problem the LPs 73 and D are related via the Weak Duality Theorem for linear programming THEOREM WEAK DUALITY Ifz E R is feasible for andy E R is feasible for D then ch S yTA S bTy Thus if is unbounded then D is necessarily infeasible and ifD is unbounded then 73 is necessarily infeasible Moreover if cTi bTy with i feasible for 73 and y feasible for D then i must solve 73 and y must solve D PROOF Let x E R be feasible for 73 and y E R be feasible for D Then CT 1 Ci 1 x H m m since 0 3 7 and 07 3 Z aijyi so cjxj S aijyi jl i1 i1 l 1M 4M3 s s S F yTAz m 1 XXX ai alyz i1 11 m 1 7L 2 biyl lSinCe 0 S in and bi E Z ai j SO biyi S ai j il i1 11 11 bTy To see that cTi bTy plus 737D feasibility implies optimality simply observe that for every other 737D feasible pair Ly we have ch S bTy cTi S bTy I We caution that the infeasibility of either 73 or D does not imply the unboundedness of the other Indeed it is possible for both 73 and D to be infeasible as is illustrated by the following example EXAMPLE maximize 2x1 7 2 1 7 2 S 1 1 2 S 2 0 S 1 2 151 Transformation to Standard Form Every LP can be transformed to an LP in standard form This process usually requires a transformation of variables and occasionally the addition of new variables In this section we provide a step by step procedure for transforming any LP to one in standard form minimization a maximization To transform a minimization problem to a maximization problem just multiply the objective function by 71 linear inequalities If an LP has an equality constraint of the form a 1 al z cumin 2 bi This inequality can be transformed to one in standard form by multiplying the inequal ity through by 71 to get aiih ai z 39 39 39 am n S ibi linear equation The linear equation 011 1min bi can be written as two linear inequalities duh quot39 1min lt bi and ai i am n Z bi The second of these inequalities can be transformed to standard form by multiplying through by 71 variables with lower bounds If a variable al has lower bound ll which is not zero li 3 07 one obtains a non negative variable wl with the substitution In this case7 the bound li 3 x1 is equivalent to the bound 0 S w variables with upper bounds If a variable x has an upper bound ul S one obtains a non negative variable iv with the substitution i u 7 wi In this case the bound z lt u is equivalent to the bound 0 S w variables with iriterval bounds An interval bound of the form Z 3 z lt U can be transformed into one non negativity constraint and one linear inequality constraint in standard form by making the substi tution In this case the bounds l g z lt u are equivalent to the constraints 0 3 iv and w 3 iii 7 li free variables Sometimes a variable is given without any bounds Such variables are called free vari ables To obtain standard form every free variable must be replaced by the difference of two non negative variables That is if z is free then we get M u 7 Ni with 0 3 iii and 0 3 vi To illustrate the ideas given above we put the following LP into standard form minimize 3x1 7 2 subject to 7z1 6x2 7 3 4 2 73 72 4 5 3 4 S 2 71 23 572 4 2 The hardest part ofthe translation to standard form or at least the part most susceptible to error is the replacement of existing variables with non negative variables For this reason I usually make the translation in two steps In the rst step I make all of the changes that do not involve variable substitution and then in the second step I start again and do all of the variable substitutions Following this procedure let us start with all of the transformations that do not require variable substitution First turn the minimization problem into a maximization problem by rewriting the objective as maximize 7 3x1 m Next we replace the rst inequality constraint by the constraint 1762374 The equality constraint is replaced by the two inequality constraints 7 4 S 5 772 7 4 S Finally7 the double bound 72 3 x4 3 2 indicates that we should group the upper bound with the linear inequalities All of these changes give the LP maximize 73m 2 subject to 1 7 6x2 3 7 x4 3 3 7M 4 S 5 7 72 7 4 S 75 3 4 S 2 4 S 2 71 S 273 S 5772 S 4 We now move on to variable replacement Observe that the variable 1 is free7 so we replace it by zlzf7zf with0 2170 zf The variable 2 has a non zero lower bound so we replace it by 22z21 or 22271 with 0 22 The variable 3 is bounded above7 so we replace it by 2357z3 or 35723 with 0 23 The variable 5 is bounded below7 so we replace it by 24z42 or 4z472 with 0 z4 After making these substitutions7 we get the following LP in standard form maximize 732r 32 22 subjectto 2f 7 2f 7 622 7 23 7 24 S 710 722 24 S 14 7 722 7 24 S 714 7 23 24 S 71 24 S 4 0 3 21721722723724 | 677.169 | 1 |
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Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of a researcher. It would not be an exaggeration to say that the ability to do mathematical research lies essentially asking "well-posed" questions. The approach taken by the authors in Problems in Algebraic Number Theory is based on the principle that questions focus and orient the mind. The book is a collection of about 500 problems in algebraic number theory, systematically arranged to reveal ideas and concepts in the evolution of the subject. While some problems are easy and straightforward, others are more difficult. For this new edition the authors added a chapter and revised several sections. The text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition facilitates independent study, and students having taken a basic course in calculus, linear algebra, and abstract algebra will find these problems interesting and challenging. For the same reasons, it is ideal for non-specialists in acquiring a quick introduction to the subject. less
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From the reviews of the second edition:
"Problems in Algebraic Number Theory is intended to be used by the students for independent study of the subject. It provides the reader with a large collection of problems (about 500) … . The reviewer thinks that the authors have done a fantastic job choosing the problems, which are perfectly arranged so the students can progressively move from topic to topic … . the book is an excellent resource for the instructor and the student as a companion to any algebraic number theory course." (Álvaro Lozano-Robledo, MathDL, May, 2005)
"This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and L-Functions highlighting some of the analytic aspects of algebraic number theory. … the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory." (Zentralblatt für Didaktik der Mathematik, August, 2005)
"This is the second edition of Problems in algebraic number theory. ... errors have been corrected … . The decision to expand the book by including a chapter on density theorems is most welcome." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1055)
"This is the second edition of an unusual introduction to algebraic number theory. … each chapter is written in straightforward textbook style. All chapters contain a very large number of problems. … it presents a good way of acquiring a working knowledge of basic algebraic number theory by using it for independent study or as supplementary reading." (Ch. Baxa, Monatshefte für Mathematik, Vol. 149 (4), 2006) | 677.169 | 1 |
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Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving wer...
This paper investigates the reasoning of first year non-mathematics students in non-routine calculus tasks. The students in this study were accustomed to imitative reasoning from their primary and secondary education. In order to move from imitative reasoning toward more creative reasoning, non-routine tasks were implemented as an explicit part of the students' calculus course. We examined the reasoning of six students in the middle of the calculus course and at the end of the course. The ana...
This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…
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Full Text Available Thisals of mathematics had been duly informed by letter of the new discovery of the concordance of prime numbers spirals with regular number spirals, but for the sake of fidelity. Mathematics is not complexity, but simplicity, the configuration of 1 is spiral .The relationship between pure mathematical numbers and empty space is a primordial relationship, and well defined by gaps, plus it has been validated by the author by the Publishing of the pure continuous Den-Otter Prime number sieve at 1/6 and 5/6 ( and 1/3 and 2/3,and these prime sieves are reversible .Thus the relationship of the configuration of 1 is in two planes that expand in the frame of (5/6 and 1/6 and (1/3 and 2/3are represented by spiral configuration , expressed by these numbers, as in :All prime numbers spirals are assigned infinitely by the simple -1 offset of the two spiral numbers cords 1/3+2/3=1 5/6+1/6=1 1/3-1/6=1/6 5/6-2/3=1/6 1/3+1/6=0.5 5/6+2/3=1.5 1.5/0.5=3 Note: the above is also confirmed by Arabian numerical shown below. Primordial mathematics as created by the creator is absolute and precise whilst the mathematics invented by man is approximate .Current Mathematics of a thousand years has accomplished much by approximate theory, and it is very possible to land a man on the moon by approximate mathematics, but to precisely understand mass and energy, the nucleus of mass and the vastness of space, one must understand the precise nature and curvature of space
Full Text Available This paper presents the results of a documentary investigation with the intention of substantiate how and why, and the level and depth of the topics used by the teacher in the classroom for the development of the mathematical knowledge on the part of higher level engineering students. The analysis of the mathematical object was made through the construction of conceptual cartography, being the core of the derivative concept. To construct the axes, the socio-formative theory of Sergio Tobón was used, together with the semiotic representation register of Raychmond Duval and Tall's mathematical advanced thought in the engineering context. The topic is a part of the Unit of learning: Differential and Integral Calculus. This corresponds to the first semester. The course lasts for a semester and is intended for students aged between 18 and 20 years. The research shows that by constructing a conceptual cartography involving at least 8 axes of analysis that the socio-formation orientates, and taking mathematics in the context of careers offered by the educational institution, the teacher is allowed to place the thematic content in the appropriate level and depth, guiding in a possible treatment of knowledge to be brought into the classroom.
Calculus, Second Edition discusses the techniques and theorems of calculus calculus…
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MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…
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One goal of our Discovering the Art of Mathematics project is to empower students in the liberal arts to become confident creators of art and imaginative creators of mathematics. In this paper, we describe our experience with using string art to guide liberal arts students in exploring ideas of calculus. We provide excerpts from our inquiry-based…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math easy by teaching "calculus without limits" using the new realistic philosophy of zeroism, different from Platonic idealism or formalist metaphysics. Despite its demonstrated advantages, it is being resisted because of the existing colonial hangover.
Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK) CalStudents often use imitative reasoning, i.e. copy algorithms or recall facts, when solving mathematical tasks. Research show that this type of imitative reasoning might weaken the students' understanding of the underlying mathematical concepts. In a previous study, the author classified tasks from 16 final exams from introductory calculus courses at Swedish universities. The results showed that it was possible to pass 15 of the exams, and solve most of the tasks, using imitative reasoning. Th... attitudes toward mathematics during a 'mainstream' calculus course while controlling for student backgrounds. The attitude measure combines students' self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted 'good teaching' practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational 'technology' (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students' attitudes towards mathematics. (3) 'Ambitious teaching' (e.g. group work, word problems, 'flipped' reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional 'good teaching' practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do
Many people suffer from an inferiority complex where mathematics is concerned, regarding figures and equations with a fear based on bewilderment and inexperience. This book dispels some of the subject's alarming aspects, starting at the very beginning and assuming no mathematical education.Written in a witty and engaging style, the text contains an illustrative example for every point, as well as absorbing glimpses into mathematical history and philosophy. Topics include the system of tens and other number systems; symbols and commands; first steps in algebra and algebraic notation; common fr
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed ...Data spanning fifteen semesters and including more than 1200 students showed far less than the anticipated difference in performance between students with quite diverse levels of physics preparation. Students ranged from those with no prior physics course work to those with two or more years of HS physics and prior courses in college physics. Less prior physics training frequently coincided with better performance in the first calculus-based course. Preparation in mathematics, on the other hand, appeared critically important; students at the extremes of the math preparation spectrum were concentrated at the corresponding extremes of the physics grade distribution.
A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.
This essay investigates the rhetoric surrounding the appearance of the concept of the infinitesimal in the seventeenth-century Calculus of Sir Isaac Newton and Gottfried Wilhelm Leibniz. Although historians often have positioned rhetoric as a supplemental discipline, this essay shows that rhetoric is the "material" out of which a new and powerful…
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions. The basic rules of multivector differentiation are derived explicitly, as well as a variety of basic m...
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- * Student Solutions Manual- To come * Instructor
Full Text Available This study from the Norwegian University of Science and Technology (NTNU examines students' learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ is advanced from current literature with two additions: (1 a course specific context using introductory college calculus students, and (2 participation of Norwegian students.Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors' aspirations. A significant increase in "Mastery Avoidance" and "Work Avoidance" was accompanied with a drop in "Mastery Approach" and "Performance Approach". Variables such as value, motivation and enjoyment decreased along with a significant drop in self-confidenceThe aim of this paper is to provide a cross-national comparative analysis of the introduction of calculus in Spanish and French military educational institutions through the works of Pedro Padilla y Arcos (1724-1807?) and Étienne Bézout (1730-1783), respectively. Both authors developed their educational work in the context of military schools and academies. Padilla's Curso Militar de Mathematicas (1753-1756) was the first work published in Spain which introduced the teaching of calculus in formal education. Bézout's Cours de Mathématiques (1764-1769) was the first work on calculus explicitly addressed to French military students and can be considered a representative of the canonical knowledge on eighteenth-century mathematics, both in France and abroad. Eighteenth-century Spain has traditionally been regarded as a country in the periphery whose scientific culture and education were pervaded by French science and education. This centre-periphery framework is often represented by a static model of one-way transmission from the centre to the periphery. A crossnational comparative analysis can help revisit this monolithic centre-periphery framework. A recent historiographical stream places the emphasis on appropriation, hence moving away from the idea of passive reception. In my paper I focus on the reading and writing of educational books, as practices which contribute actively to the development and circulation of knowledge. To assist the analysis, I explore the differences in communication practices in each case, in contents and approaches, and in particular, I give special attention to their inspiration in mathematical streams other than the French standpoint.
This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…
A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplicatio...This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculusComprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Mathematics' skills and knowledge lay the basis for engineering studies. However, the resources targeted to mathematics' teaching are in many cases very limited. During the past years in our university the reduction of mathematics' contact hours has been significant while at the same time the study groups have grown. However, the mathematical…
It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…
When first published posthumously in 1963, this book presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a
Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples o...
Quaternion derivatives in the mathematical literature are typically defined only for analytic (regular) functions. However, in engineering problems, functions of interest are often real-valued and thus not analytic, such as the standard cost function. The HR calculus is a convenient way to calculate formal derivatives of both analytic and non-analytic functions of quaternion variables, however, both the HR and other functional calculus in quaternion analysis have encountered an essential tech...Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix's large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix's account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix's large Traité... was a...In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra. Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis. Following an introdu
This unit considers the application of calculus in determining price discrimination and consumer surplus in a competitive market. Producer surplus and two-tier price discrimination are also developed in problems. It is noted that calculus cannot usually provide numerical answers for practical economic problems. The importance of calculus…
In this paper we discuss flipping pedagogy and how it can transform the teaching and learning of calculus by applying pedagogical practices that are steeped in our understanding of how students learn most effectively. In particular, we describe the results of an exploratory study we conducted to examine the benefits and challenges of flipping a…
The dynamism of the natural world means that it is constantly changing, sometimes rapidly, sometimes gradually. By mathematically interpreting the continuous change that characterizes so many natural processes, analysis and calculus have become indispensable to bridging the divide between mathematics and the sciences. This comprehensive volume examines the key concepts of calculus, providing students with a robust understanding of integration and differentiation. Biographies of important figures will leave readers with an increased appreciation for the sometimes competing theories that informe
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the prior fear of mathematics. The students today cant live without using computer technology. The uses of computer for teaching and learning can transform the boring traditional methodology of teach to more active and attractive method. In this paper, we will sh...Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Visualization is key in helping a student understand the fundamentals of Calculus. The new generation of computer literate students, raised in a video-based environment, will expect more than the traditional chalkboard methods in assisting them in this visualization. By integrating computers into the classroom and developing software to assist in mathematics instruction, we can enhance student comprehension of, and ability to apply, mathematics in solving real world problems of interest to th...
This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation p
The Rho-calculus is a new calculus that integrates in a uniform and simple setting first-order rewriting, lambda-calculus and non-deterministic computations. This paper describes the calculus from its syntax to its basic properties in the untyped case. We show how it embeds first-order conditional rewriting and lambda-calculus. Finally we use the Rho-calculus to give an operational semantics to the rewrite based language Elan administering the CCR as a readiness examination in calculus are provided along with data to guide others in using the CCR as a readiness examination for beginning calculus.
Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…
Jennifer Ouellette never took maths in the sixth form, mostly because she – like most of us – assumed she wouldn't need it much in real life. But then the English graduate, now an award-winning science-writer, had a change of heart and decided to revisit the equations and formulas that had haunted her youth. The Calculus Diaries is the fun and fascinating account of a year spent confronting her numbers-phobia head on. With wit and verve, Ouellette explains how she discovered that maths could apply to everything from petrol mileages to dieting, rollercoaster rides to winning in Las VegasCompletely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...
How THIS BOOK DIFFERS ThisStone in the urinary tract has fascinated the medical profession from the earliest times and has played an important part in the development of surgery. The earliest major planned operations were for the removal of vesical calculus; renal and ureteric calculi provided the first stimulus for the radiological investigation of the viscera, and the biochemical investigation of the causes of calculus formation has been the training ground for surgeons interested in metabolic disorders. It is therefore no surprise that stone has been the subject of a number of monographs by eminent urologists, but the rapid development of knowledge has made it possible for each one of these authors to produce something new. There is still a technical challenge to the surgeon in the removal of renal calculi, and on this topic we are always glad to have the advice of a master craftsman; but inevitably much of the interest centres on the elucidation of the causes of stone formation and its prevention. Professor Pyrah has had a long anIn the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to model its behavior with the symbolic language of mathematics. In this essay, I examine an ambitious 16th and 17th-century intellectual agenda from the perspective of Wigner's question, namely, what historian Paolo Rossi calls "the quest to create a universal language." While many elite thinkers pursued related ideas, the most inspiring and forceful was Gottfried Leibniz's effort to create a "universal calculus," a pictorial language which would transparently represent the entirety of human knowledge, as well as an associated symbolic calculus with which to model the behavior of physical systems and derive new truths. I suggest that a deeper understanding of why the efforts of Leibniz and others failed could shed light on Wigner's original question. I argue that the notion o...Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.
We investigate Calculus teaching at university mathematics departments and in particular research math-ematicians' teaching practice in the context of lectures. We are interested in how lecturers draw mathematics students into mathematical culture. In this paper, we focus on the teaching of a lecturer of a large cohort of students that we analyse using grounded techniques and the Teaching Triad construct (Jaworski, 1994). In spite of the lecture format, the analysis suggests that this lecture...Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…
The limit concept is a fundamental mathematical notion both for its practical applications and its importance as a prerequisite for later calculus topics. Past research suggests that limit conceptualizations promoted in introductory calculus are far removed from the formal epsilon-delta definition of limit. In this article, I provide an overview…Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus
Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus administe...
Fundamentals of CalFull Text Available The purpose of this study was to investigate the effects of using writing activities on students' understanding and achievement in Calculus. The design of this study was quasi-experimental. The subjects of this study consisted of two secondary schools in one of the states in Malaysia. Each school was assigned one intact class of Form Four to be the experimental group and another one intact class as the control. The experimental group learned mathematics by using the writing activities for five weeks, while the control group learned mathematics by using traditional whole-class instruction. A 20-item Calculus Achievement test was designed with reliability .87. The findings showed that the experimental group exhibited significantly greater improvement on calculus achievement. The students showed positive reaction towards the use of writing. Findings of this study provide information to schools to take advantage of writing activities to promote understanding.
Only a subset of adults acquires specific advanced mathematical skills, such as integral calculus. The representation of more sophisticated mathematical concepts probably evolved from basic number systems; however its neuroanatomical basis is still unknown. Using fMRI, we investigated the neural basis of integral calculus while healthy subjects were engaged in an integration verification task. Solving integrals activated a left-lateralized cortical network including the horizontal intrapariet...
Homeschooling in the United States has grown considerably over the past several decades. This article presents findings from the Factors Influencing College Success in Mathematics (FICSMath) survey, a national study of 10,492 students enrolled in tertiary calculus, including 190 students who reported homeschooling for a majority of their high…
The benefits of high-level mathematics packages such as Matlab include both a computer algebra system and the ability to provide students with concrete visual examples. This paper discusses how both capabilities of Matlab were used in a multivariate calculus class. Graphical user interfaces which display three-dimensional surfaces, contour plots,…Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces, it has to be redesigned when applied to other generalized cohomology theories such as the equivariant, the quantum cohomology, K-theory, and cobordism. All this cohomology theories are different deformations of the ordinary cohomology. In this note, we show that there is, in some sense, the universal deformation of Schubert calculus which produces the above mentioned by specialization of the appropriate parameters. We build on the work of Lerche Vafa and Warner. The main conjecture these authors made was that the classical cohomology of a Hermitian symmetric homogeneous manifold is a Jacobi ring of an appropriate potential. We extend this conjecture and provide a simple proof. Namely, we show that the cohomology of the Hermitian symmetric space is a Jacobi ring of a certain potential and the equivariant and the quantum cohomology and the K-theory is a Jacobi ring of a particular deformation of this potential. This suggests to study the most general deformations of the Frobenius algebra of cohomology of these manifolds by considering the versal deformation of the appropriate potential. The structure of the Jacobi ring of such potential is a subject of well developed singularity theory. This gives a potentially new way to look at the classical, the equivariant, the quantum and other flavors of Schubert calculus.
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as lim
One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool.The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a ""mini-calculus"" which brings out t
Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…
Full Text Available Modern undergraduates join science and engineering courses with poorer mathematical background than most contemporaries of the current faculty had when they were freshers. The problem is very acute in the United Kingdom but more and more countries adopt less resource intensive models of teaching and the problem spreads. University tutors and lecturers spend more and more time covering the basics. However, most of them still rely on traditional methods of delivery which presuppose that learners have a good memory and considerable time to practice, so that they can memorize disjointed facts and discover for themselves various connections between the underlying concepts. These suppositions are particularly unrealistic when dealing with a large number of undergraduates who are ordinary learners with limited mathematics background. The first author has developed a teaching system that allows such adult learners achieve relatively deep learning of mathematics – and remarkably quickly – through a teacher-guided (often called Socratic dialog, which aims at the frequent reinforcement of basic mathematical abstractions through Eulerian sequencing. These ideas have been applied to create a prototype of a Cognitive Mathematics Tutoring System aimed at teaching basic mathematics to University freshers., an electronic Personal Algebra and Calculus Tutor (e- PACT.Cal) is one of learning model based IT which can be used in Calculus I learning. This learning model have aim to enhance conc...
Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem...
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where integrals are of convolution form with weakly singular kernels of power law type. In recent decades fractional calculus has won more and more interest in applications in several fields of applied sciences. In this lecture we devote our attention to wave propagation problems in linear viscoelastic media. Our purpose is to outline the role of fractional calculus in providing simplest evolution processes which are intermediate between diffusion and wave propagation. The present treatment mainly reflects the research activity and style of the author in the related scientific areas during the last decades.
This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated with...
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...
Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition. PMID:24082453
A main challenge of programming component-based software is to ensure that the components continue to behave in a reasonable manner even when communication becomes unreliable. We propose a process calculus, the Quality Calculus, for programming software components where it becomes natural to plan...
This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...In education theory, Bloom's taxonomy is a well-known paradigm to describe domains of learning and levels of competency. In this article I propose a calculus capstone project that is meant to utilize the sixth and arguably the highest level in the cognitive domain, according to Bloom et al.: evaluation. Although one may assume that mathematics is…
This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and…
The calculus of variationsThis textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory
The $\\rho$-calculus is a new calculus that integrates in a uniform and simple setting first-order rewriting, $\\lambda$-calculus and non-deterministic computations. This paper describes the calculus from its syntax to its basic properties in the untyped case. We show how it embeds first-order conditional rewriting and $\\lambda$-calculus. Finally we use the $\\rho$-calcul- us to give an operational semantics to the rewrite based language ELAN.
Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency
Differential Calculus is a staple of the college mathematics major's diet. Eventually one becomes tired of the same routine, and wishes for a more diverse meal. The college math major may seek to generalize applications of the derivative that involve functions of more than one variable, and thus enjoy a course on Multivariate Calculus. We serve this article as a culinary guide to differentiating and integrating functions of more than one variable -- using differential forms which are the basis for de Rham Cohomology.
This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculusThis study is part f a larger one whose general objective is to investigate and to develop a new strategy for teaching Differential and Integral Calculus I, specifically for physics majors, through a possible integration with the teaching of General and Experimental Physics I. With the specific objective of identifying physics problem-situations that may help in making sense of the mathematical concepts used in Calculus I, and languages and notations that might be used in the teaching of Calc...
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems.This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other toWe present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (such as Lie derivatives) which are important in applications. Previous attempts at discrete exterior ca...
Excellent text provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations ca...
The properties of the Bigeometric or proportional derivative are presented and discussed explicitly. Based on this derivative, the Bigeometric Taylor theorem is worked out. As an application of this calculus, the Bigeometric Runge-Kutta method is derived and is applied to academic examples, with known closed form solutions, and a sample problem from mathematical modelling in biology. The comparison of the results of the Bigeometric Runge-Kutta method with the ordinary Runge-Kutta method shows...
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topiFractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Additional topics include black holes, gravitational waves, and a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume's appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. calculus argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.
This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…
The Dual Calculus, proposed recently by Wadler, is the outcome of two distinct lines of research in theoretical computer science: (A) Efforts to extend the Curry–Howard isomorphism, established between the simply-typed lambda calculus and intuitionistic logic, to classical logic. (B) Efforts to establish the tacit conjecture that call-by-value (CBV) reduction in lambda calculus is dual to call-by-name (CBN) reduction. This paper initially investigates relations of the Dual Calculus t...
A first order inference system, named R-calculus, is defined to develop the specifications.This system intends to eliminate the laws which are not consistent with users' requirements. TheR-calculus consists of the structural rules, an axiom, a cut rule, and the rules for logical connectives.Some examples are given to demonstrate the usage of the R-calculus. Furthermore, the propertiesregarding reachability and completeness of the R-calculus are formally defined and proved.
Cirquent calculus is a new proof-theoretic framework, originally motivited by the needs of computability logic (see ). Its main distinguishing feature is sharing: unlike the more traditional frameworks that manipulate tree- or forest-like objects such as formulas, sequents or hypersequents, cirquent calculus deals with circuit-style structures called cirquents. The present article elaborates a deep-inference cirquent calculus system CL8 for classical propositional logic and the corresponding fragment of the resource-conscious computability logic. It also shows the existence of polynomial-size analytic CL8-proofs of the pigeonhole principle -- the family of tautologies known to have no such proofs in traditional systems. Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need onThis textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers. In addition to the standard results of advanced calculus, the book contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each sectionThe basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research. PMID:20615808This applications-related introductory treatment explores facets of modern symbolic logic useful in the exposition of elementary mathematics. The authors convey the material in a manner accessible to those trained in standard elementary mathematics but lacking any formal background in logic. Topics include the statement calculus, proof and demonstration, abstract mathematical systems, and the restricted predicate calculus. The final chapter draws upon the methods of logical reasoning covered in previous chapters to develop solutions of linear and quadratic equations, definitions of order andUnderstanding Maxwell's equations in differential form is a prerequisite to study the electrodynamic phenomena that areThe rewriting calculus is a rule construction and application framework. As such it embeds in a uniform way term rewriting and lambda-calculus. Since rule application is an explicit object of the calculus, it allows us also to handle the set of results explicitly. We present a simply typed version of the rewriting calculus. With a good choice of the type system, we show that the calculus is type preserving and terminating, i.e. verifies the subject reduction and strong normalization properties....
, statically typed model for virtual classes has been a long-standing open question. This paper presents a virtual class calculus, vc, that captures the essence of virtual classes in these full-fledged programming languages. The key contributions of the paper are a formalization of the dynamic and static...
Network calculus, a theory dealing with queuing systems found in computer networks, focuses on performance guarantees. This title presents a comprehensive treatment for the stochastic service-guarantee analysis research and provides basic introductory material on the subject, as well as discusses the various researches in the area problems and exercises accompany each chapter.This paper outlines a technique for teaching a rigorous course in calculus and differential equations which stresses applicability of the mathematics to problems in civil engineering. The method involves integration of subject matter and team teaching. (SD)
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit… "flipping" (or inverting) their classrooms. By flipping, we of set operation, introducing the notation for 'intersection,' 'union,' and 'element of,' many years before it was accepted. Despite its uniqueness, Calcolo Geometrico has been strangely neglected by histor III includes vector analysis, real valued functions, partial differentiation, multiple integrations, vector fields, and infinite series I covers functions, limits, basic derivatives, and integrals...... case studies and it has been extended in several directions. The aim of this paper is to provide a thorough presentation of the logic....
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, incl...
The paper significantly extends and generalizes our previous paper. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of (p+1)x(p+1) complex matrices. For many variables we give a general construction of the differentiation algebras. Some particular examples are related to the multiparametric quantum deformations of the harmonic oscillators. 18 refs Pre-Calculus reviews sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents
This introduction to Malliavin's stochastic calculus of variationsIntroduction to the Operational Calculus is a translation of ""Einfuhrung in die Operatorenrechnung, Second Edition."" This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work ""Operational Calculus."" Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)
This monograph explores the early development of the calculus of variations of variationsThe aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined
A simple partial version of the Fundamental Theorem of CalThis article presents an example of how middle school teachers can lay a foundation for calculus. Although many middle school activities connect directly to calculus concepts, the authors have decided to look in depth at only one: the concept of change. They will show how teachers can lead their students to see and appreciate the calculus…
This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...
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 Calculus I Super Review includes a review of functions, limits, basic derivatives, the definite integral, combinations, and permutations. 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
Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. More than 1,200 problems appear in the text, with concise explanations of the basic notions and theorems to be used in their solution. Many are followed by complete answers; solutions for the others appear at the end of the book. Topics include sequences, functions of a single variable, limit of a function, differential calculus for functions of a single variable, fundamental theorems and applications of dif
We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the rational homology type of the input functor, whose layers are given by rational spectra with an action of $O(n)$. By work of Greenlees and Shipley, we see that these layers are classified by torsion $H^*(B SO(n))[O(n)/SO(n)]$-modules.
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av
This thesis presents a type system, Provability Calculus of 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.
Dartmouth College mathematicians have developed a free online calculus course called "Open Calculus." Open Calculus is an exportable distance-learning/self-study environment for learning calculus including written text, nearly 4000 online homework problems and instructional videos. The paper recounts the evaluation of course elements since 2000 in…This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in ap...Discusses the progress and challenges of a new reformed calculus sequence for science, engineering, and mathematics students developed by the Institute of Technology Centre for Educational Programs and School of Mathematics at the University of Minnesota. Compares achievement and retention of Initiative students with a control group from a…
Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts - not just the number crunching - and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for
The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus ofWritten by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.
This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.
Full Text Available Cal is one of learning model based IT which can be used in Calculus I learning. This learning model have aim to enhance concept mastery and to improve the learning attitude of students a multimedia interactive based tutorial model of Calculus I is applied. This research is quasi experimental with subject on SBI class from the faculty of teacher training and education Sebelas Maret University with mathematical education as a experiment class and physic education as a control class. Research data were collected by using a concept mastery pretest, posttest and a questionnaire. Data analysis was conducted by using t –test. The result of this research show that the MMI learning have significance on improve Calculus learning quality and also improve the learning attitude of students. Keywords: Calculus; Interactive multimedia; learning attitude
This report presents a new distributed process calculus, called the -calculus. Key insights for the calculus are similar to those laid out by L. Cardelli for its calculus of ambients. Mobile Ambients and other recent distributed process calculi such as the Join calculus or the D-calculus introduce notions of distributed locations or localities, corresponding to a spatial partitioning of computations and embodying different features of distributed computations (e.g. failures, access control, p...
Mathematical Statistics with Applications provides a calculus-based theoretical introduction to mathematical statistics while emphasizing interdisciplinary applications as well as exposure to modern statistical computational and simulation concepts that are not covered in other textbooks. Includes the Jackknife, Bootstrap methods, the EM algorithms and Markov chain Monte Carlo methods. Prior probability or statistics knowledge is not required.* Step-by-step procedure to solve real problems, making the topic more accessible* Exercises blend theory and modern applications*This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp
Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for tIn this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary This paper presents a brief overview of the life story and professional career of Prof. R. Gorenflo - a well-known mathematician, an expert in the field of Differential and Integral Equations, Numerical Mathematics, Fractional Calculus and Applied Analysis, an interesting conversational partner, an experienced colleague, and a real friend. Especially his role in the modern Fraction... ofAbout the Book: This book Engineering Mathematics-II is designed as a self-contained, comprehensive classroom text for the second semester B.E. Classes of Visveswaraiah Technological University as per the Revised new Syllabus. The topics included are Differential Calculus, Integral Calculus and Vector Integration, Differential Equations and Laplace Transforms. The book is written in a simple way and is accompanied with explanatory figures. All this make the students enjoy the subject while they learn. Inclusion of selected exercises and problems make the book educational in nature. It shou
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo... | 677.169 | 1 |
Integration By Parts
Students investigate integration and its use in the study of Calculus. They use the two methods of substitution and integration by parts as application to mathematical problems of integration. The lesson includes examples for the teacher to use | 677.169 | 1 |
Scientific Computing (Coursera)
Investigate the flexibility and power of project-oriented computational analysis, and enhance communication of information by creating visual representations of scientific data.
Practice using this technique to resolve complicated problems in a range of fields including the physical and engineering sciences, finance and economics, medical, social and biological sciences. Enhance communication of information by creating visual representations of scientific data.
This course is a survey of numerical solution techniques for ordinary and partial differential equations. Emphasis will be on the application of numerical schemes to practical problems in the engineering and physical sciences. Apply advanced MATLAB routines and toolboxes to solve problems. Review and practice graphical techniques for information presentation and learn to create visual illustrations of scientific results.
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Based on Next Generation Science Standards, this course provides an introduction to the role of science in society, feedback and regulation mechanisms, and using a systems approach to solve scientific problems. Participants will explore the nature of scientific inquiry and learn how to analyze scientific data. | 677.169 | 1 |
Concepts in Competitive Mathematics
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This short reference book contains fundamental concepts crucial to solving math competition problems such as those found on the Mathematical Association of America's AMC 10, AMC 12, and AIME, as well as those found in local or regional competitions. Full of formulas as well as examples and solutions, this book shows how specific problems can be best solved in order to succeed in math competitions. Content is organized by mathematical topic and has been selected for its diversity. Topics include Number Theory, Combinatorics, Probability, Statistics, Sequences and Series, Algebra, Geometry, Trigonometry, and Coordinate Mathematics. The book even contains a section containing the author's own tips from past experience in math competitions. All in all, this is a must buy for math competition participants and teachers alike. Contains: Nine Chapters, Table of Contents, Index.The book even contains a section containing the authora#39;s own tips from past experience in math competitions. All in all, this is a must buy for math competition participants and teachers alike.
Title
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Concepts in Competitive Mathematics
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:
Zachary M. Boazman, Richard Newcomb
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:
Zachary Boazman - 2010-05-27
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Practice makes perfect! Get perfect with a thousand and one practice problems! 1,001 Geometry Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems that deal with core geometry topics, such as points, lines, ...
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Leo Corry tells the story behind the idea of number, from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the ...
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The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of ...
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Mathematics is a human endeavour of long standing and is deeply ingrained in Western philosophy and thinking. This illustrated book presents the science of mathematics in an innovative and engaging way. Its aim is to make maths more accessible ...
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A funny and enlightening romp through the world of numbers with one of Australias best-loved broadcasters.By popular demand, Australias funniest and most famous mathematician is back with a brilliant new book. Adam Spencers World of Numbers ...
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Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of
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Algebra I For Dummies, 2nd Edition (9781119293576) was previously published as Algebra I For Dummies, 2nd Edition (9780470559642). While this version features a new Dummies cover and design, the content is the same as the prior release and ...
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Algebra I Workbook For Dummies, 2nd Edition, tracks to a typical high school Algebra class with hundreds of practice problems to guarantee understanding and retention?now with 25 percent new and revised content to ensure it meets the needs of ...
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Your complete guide to acing Algebra II Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have ...
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Overview—from algebra review to study tips—Additional Product Information
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Revised! Section-ending Business Capsules and accompanying exercises address business situations related to the mathematical concepts covered in the chapter.
Revised! At the beginning of each exercise set, Skills Review exercises help students practice those skills covered in previous sections; answers are provided at the back of the text to reinforce understanding.
Updated! Exercise Sets offer opportunities for practice and review. Approximately 6,000 exercises progress from skill-development problems to more challenging, real-world applications—all of which can be customized to the difficulty level of the instructor's choiceTable of Contents
Note: Chapters 1-7 include a Mid-Chapter Review and conclude with an Algebra Review, Chapter Summary and Study Strategies, Review Exercises, and a Chapter Test.
0. A PRECALCULUS REVIEW. The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization. 1 The General Power Rule and Substitution Partial Fractions and Logistic Growth Appendix A. Alternate Introduction to the Fundamental Theorem of Calculus. Appendix B. Formulas. Differentiation and Integration Formulas. Formulas from Business and Finance. Appendix C. Differential Equations. Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations. Appendix D. Properties and Measurement (web only). Review of Algebra, Geometry, and Trigonometry. Units of Measurements. Appendix E. Graphing Utility Programs (web only). Graphing Utility Programs.
What's New
ThisNew! Make a Decision multi-step exercises reinforce students' problem-solving skills by taking real-life applications further, testing what students know about a given problem and prompting them to make decisions within the context of that problem.
New! Non-computational Concept Check questions appear at the end of each section, allowing students to pause and check their understanding of the concepts covered in that section.
New! App Your passkey is needed in order to access an Eduspace Plus course. Individual passkeys must be purchased for each course enrollment. Eduspace is Houghton Mifflin's online learning tool. It may be required by your instructor to complete online homework and assignments. Eduspace also offers powerful tools and text-specific content that will help you get a better grade. Eduspace Plus courses contain:Your passkey is needed in order to access an Eduspace Plus course. Individual passkeys must be purchased for each course enrollment.Eduspace is Houghton Mifflin's online learning tool. It may be required by your instructor to complete online homework and assignments. Eduspace also offers powerful tools and text-specific content that will help you get a better grade.Eduspace Plus courses contain: | 677.169 | 1 |
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The New TEKS A.b.3 Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions.
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The New TEKS A.b.3 Students will use technology to collect and explore data and analyze statistical relationships.
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The New TEKS A.b.3 Students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents. Students will generate and solve linear systems with two equations and two variables and will create new functions through transformations.
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The New TEKS A.c.3 Linear Functions, Equations, Inequalities The student will determine
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Motion Sensor TI CBR2
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What Other Scenarios?
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How Can I Walk? a line that goes up? a line that is steep? a curve that opens up? a curve that opens down? a graph that starts at 6? a horizontal line?
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Math is Figure-out- able Give kids a chance to build intuition Its about relationships: - Between what you know and the new, build to the new - Between teachers and students to build young mathematicians | 677.169 | 1 |
9780821835Isaac Newton encrypted his discoveries in analysis in the form of an anagram that deciphers to the sentence, 'It is worthwhile to solve differential equations'. Accordingly, one can express the main idea behind the orbit method by saying 'It is worthwhile to study coadjoint orbits'. The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient 'User's Guide' and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists | 677.169 | 1 |
1 Math 71 Outline Lecture Notes (Prepared by Stefan Waner)
1. The Cartesian Plane and Distance The coordinate plane is the infinite plane with two perpendicular axes-the x-axis and the y-axis. The axes divide the plane into four quadrants-shown in c
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This course focused on the beginning of various calculus theorems and their applications. The professor provides multiple examples during class, as well as excellent and easy to follow notes. In addition, the office hours established by the professor are consistent and she is always willing to take the time to thoroughly run through problems from class, extra examples, and any other questions that will help the students fully understand what is being taught in class. At the same time, she also answers questions about the homework and class over email. The syllabus provided at the beginning of the semester provides a clear idea about what to expect throughout the course, including grading, attendance, and contact information. Homework is assigned online and is very helpful for studying and improving the students understanding of the material.
Course highlights:
Throughout this course, I have learned how to properly take the derivative of different functions. In addition, I learned how to take integrals by also finding the antiderivative of different functions among other materials. As well as improved some older skills like factoring among other skills.
Hours per week:
3-5 hours
Advice for students:
The grade you get in the class is up to you. The professor provides students with all necessary materials for passing the class; however, the student must take the time to complete the homework and seek out help if it is needed. In addition, it never hurts to take more than one night to study and to ask questions as soon as you don't understand something. | 677.169 | 1 |
Analyze this:
Our Intro to Psych Course is only $329.
*Based on an average of 32 semester credits per year per student. Source
Tutorial
From the YouTube website:
Published on Oct 28, 2013
Shop.TutorMeMath.net
This video by Fort Bend Tutoring shows the process of solving quadratic inequalities using a sign chart. This math concept is used in algebra, precalculus, trigonometry and calculus courses. Six (6) examples are shown in detail. Intro/Outro done by Chuck Knipp's Shirley Q. Liquor. Instruction by Larry "Mr. Whitt" Whittington.
Factoring Quadratic Trinomials: Part 1
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This Donation button is secured using PayPal. | 677.169 | 1 |
Explore More Items Similar to Mathematics - Class XII
Overview: Mathematics - Class XII
About the Book: Mathematics Class XII: Volume - 1 and 2: 11th Edition + This text book is based on the latest syllabus prescribed by the CBSE. The whole syllabus has been divided into two volumes. Volume - I consists of Chapter 1 - 19 and Volume - II consists of Chapter 20 - 33. In this revised edition new chapters on Relations, Functions, Binary Operations and Inverse Trigonometric Functions have been included. All other chapters have been thoroughly revised and up-dated. In each chapter all concepts and definitions have been discussed in detail with suitable illustrative examples. At the end of each chapter an exercise consisting of multiple choice questions (MCQs), summary for quick revision of concepts and formula have been given. NCERT text book problems in the Exercises have been solved in the section Hints to NCERT and Selected Problems. Some new and unique features of this book :- Detailed theory with illustrations Algorithmic approach Large number of graded solved examples Large number of unsolved exercises. Contents: Volume - I Relations Functions Binary Operations Inverse Trigonometric Functions Algebra of Matrices Determinants Adjoint and Inverse of a Matrix Solution of Simultaneous Linear Equations Continuity Differentiability Differentiation Higher Order Derivatives Derivative as a Rate Measure Differentials, Errors and Approximations Mean Value Theorems Tangents and Normals Increasing and Decreasing Functions Maxima and Minima Indefinite Integrals Volume - II Definite Integrals Areas of Bounded Regions Differential Equations Algebra of Vectors Scalar or Dot Product Scalar Triple Product Direction Cosines and Direction Ratios Straight Line in Space The Plane Linear Programming Probability Mean and Variance of a Random Variable Binomial Distribution Appendix
Product Details
Language
English
Publication Date
January 1, 2014
Publisher
Dhanpat Rai Publications
Contributor(s)
R.D. Sharma
Binding
Paperback
Edition
REVISED EDITION 2011
Page Count
186
ISBN 10
9383182369
ISBN 13
9789383182367
Dimensions and Weight
Product Weight
3 kg
Product Dimensions
28 cm x 23 cm x 14 cm
Customer Reviews on Mathematics - Class XII
Rd Sharma is one of the best authoR in the subject of maths .he had written so many books based on their experience on maths like in algebra,trigonometry ,coordinate geometry.this book is one of them.i had buyed this book when I was in class 12 for the practice of board level.after solving from this book ,I observed that I was gaining confidence in maths .the question given in this book is quite nice .this book also consists of ncert text solutions.additional questions for practice but note that it is not good for JEE mains and advance..... | 677.169 | 1 |
Laxmi Calculus I (Math 264)
Product Code : 9789351380177
Quick Overview
The book 'Golden Co-ordinate Geometry' has been designed to meet the requirements of students of Degree and Honours classes of various Universities. It will also be found useful by the students preparing for various competitive examinations. The author has more than four decades of experience of teaching mathematics to graduate classes and has first hand experience of problems and difficulties faced by students. The book has been written with the conviction that a good book needs minimum guidance from the teacher and is self-sufficient for clarity of basic concepts. The author has endeavoured to present the fundamental concepts in a comprehensive and lucid mannerContents:
1. The Point 2. The Straight Line 3. Two or More Straight Lines 4. Change of Axes 5. The Circle 6. Two or More Circles 7. The Parabola 8. The Ellipse 9. Hyperbola 10. The General Equation of the Second Degree and Tracing of Conics | 677.169 | 1 |
Mathematical Problem Solving and New Information Technologies
4.11 - 1251 ratings - Source
A strong and fluent competency in mathematics is a necessary condition for scientific, technological and economic progress. However, it is widely recognized that problem solving, reasoning, and thinking processes are critical areas in which students' performance lags far behind what should be expected and desired. Mathematics is indeed an important subject, but is also important to be able to use it in extra-mathematical contexts. Thinking strictly in terms of mathematics or thinking in terms of its relations with the real world involve quite different processes and issues. This book includes the revised papers presented at the NATO ARW qInformation Technology and Mathematical Problem Solving Researchq, held in April 1991, in Viana do Castelo, Portugal, which focused on the implications of computerized learning environments and cognitive psychology research for these mathematical activities. In recent years, several committees, professional associations, and distinguished individuals throughout the world have put forward proposals to renew mathematics curricula, all emphasizing the importance of problem solving. In order to be successful, these reforming intentions require a theory-driven research base. But mathematics problem solving may be considered a qchaotic fieldq in which progress has been quite slow.In: The teaching and assessing of mathematical problem solving (R. Charles aamp; E.
Silver, eds.), pp. ... T., Hiebert, J., aamp; Moser, J.: Problem structure and first grade
childrena#39;s initial solution processes for simple addition and subtraction problems.
Title
:
Mathematical Problem Solving and New Information Technologies
Author
:
Joao P. Ponte, Joao F. Matos, Jose M. Matos, Domingos Fernandes
Publisher
:
Springer Science & Business Media - 2013-06-29
ISBN-13
:
Continue
You Must CONTINUE and create a free account to access unlimited downloads & streaming | 677.169 | 1 |
This text provides a comprehensive introduction to the mathematical theory of probability, its application to the modeling of random phenomena encountered in electrical and computer engineering, and its uses in making optimal decisions and inferences. Fine meets the needs of engineering students by addressing both highly conceptual mathematical methods and their real-world applications. He offers a sound introduction to the many elements of applied probability - the presentation is thorough, yet does not require a more advanced mathematical background beyond basic integral calculus. | 677.169 | 1 |
This college-prep physics course is designed for the student who has completed algebra and has had an introduction to the definitions of sine, cosine, and tangent. It provides a detailed introduction to the methods and concepts of general physics.
Heavily emphasizing vector analysis, this text is ideal preparation for a university-level physics course. It provides the student with a strong background in one-dimensional and two-dimensional motion, Newton's laws and their application, gravity, work and energy, momentum, periodic motion, waves, optics, electrostatics, electrodynamics, electrical circuits, and magnet | 677.169 | 1 |
A survey of basic mathematics
4.11 - 1251 ratings - Source
1.12 SCIENTIFIC NOTATION AND APPROXIMATIONS Since most
measurements and many other numbers are only ... and the resulting number is
multiplied by the integral power of 10 that is required to make a number of the
proper size.
Title
:
A survey of basic mathematics
Author
:
Fred Winchell Sparks, Charles Sparks Rees
Publisher
:
McGraw-Hill Science, Engineering & Mathematics - 1979-06
ISBN-13
:
Continue
You Must CONTINUE and create a free account to access unlimited downloads & streaming | 677.169 | 1 |
Year 13 students study:
Further Maths students study the further Pure Module FP2, and 3 applications modules (S2, S3 and M2).
From September 2013 all modules will be examined in June.
Students wishing to complete only the AS Further Mathematics would drop Further Mathematics and continue with A Level Maths.
There is no course work. Each module is examined by a 1 hour and a half exam, and the scores combined equally to give the final grade.
AS/A Level Mathematics (Statistics, Decisions and Mechanics)
Specification Edexcel
Why study Mathematics?
Mathematics is a popular subject choice because of its importance to a wide range of careers, and to the high value employers place on potential employees having studied mathematics beyond GCSE. Potential scientists, engineers, accountants and computer specialists should take mathematics, but it can just as successfully be chosen to complement a variety of arts and humanities subjects.
What will I study?
All students study the core pure mathematics topics along with a choice of mechanics, statistics or decision mathematics for their applied modules.
Mechanics provides grounding for courses and careers in Physics, Sports Studies and Engineering. Statistics is useful for Biology, Business, Geography and Psychology. Decision mathematics is applicable to Business and for careers in logistics.
How will I be assessed?
There is no coursework in mathematics. Assessment is by 90 minute examinations.
From September 2013 all modules will be examined in June.
Entry requirements
Grade A or better in Maths GCSE.
Course expenses
£10 deposit, which is returnable when you finish the course, for three books. | 677.169 | 1 |
ISBN 9788126521821
ISBN-10
8126521821
Binding
Paperback
Number of Pages
500 Pages
Language
(English)
Subject
Engineering Entrance
The Book Has A Two-Fold Advantage: (A) Conceptual Strength Provided By Accurate, Precise But Sufficient Coverage Of Topics; (B) Solved And Unsolved Problems As Per Jee (Main & Advanced) Pattern For Strengthening Concepts. The Main Idea Is To Make Students Understand The Theory Behind To Enable Them To Strategize A Given Problem And Tactically Solve It. The Topics Covered In This Volume Are: Sets, Relations And Functions; Exponentials And Logarithms; Complex Numbers; Quadratic Numbers; Progressions, Sequences And Series; Permutations And Combinations; Binomial Theorem; Matrices, Determinants And System Of Equations; Partial Fractions. | 677.169 | 1 |
The National Extension College has a great deal of experience of producing materials which are flexible enough to be used in many different ways and these two packages have been carefully tailored to meet the needs of specific groups of students.
The Resource Bank is designed for use at key stage 4, with students who are aiming for the top grade at intermediate level GCSE, or a good grade at Higher level. It could also be used by students who are making the transition from GCSE to A-level. The whole pack is photocopiable, and comprises eight sets of activities along with a comprehensive tutor's guide. The activities are not designed to teach the mathematics involved, but to give further practice and consolidate skills.
The activities in each section are largely independent of each other, and as well as practice sheets, there are investigations and explorations. The topics covered include number, vectors, trigonometry and handling data. It is a pity that the worksheets are fairly dull to look at; although students at this level are usually well-motivated, I feel they will not be immediately stimulated by the presentation of the tasks.
There is a useful section of hints, and the tutor's guide gives a thorough classification of the tasks with details of equipment needed and the intended target levels. It is claimed that the package would be suitable for independent study but I cannot envisage students being able to use the materials unaided. There are some good materials here, let down by unimaginative presentation.
The A-level materials are designed to cover the modular courses such as the AEB, and currently consist of a binder and two books covering the pure mathematics core. The materials covering mechanics, further pure mathematics and statistics will shortly be published, so that teachers will be able to purchase simply the mix of options they require. A course guide in the binder explains the different courses and gives tips on how to study the material and prepare for the final examination. The books are written in a very pleasant and discursive style, with many explanations; it is easy to imagine the author talking directly to you.
The working out of examples is very clear, with the sort of "signs" or footnotes that a good teacher would use when explaining the work on the board. The section on sequences and series is particularly good in this respect. I was slightly worried though by the definition of an asymptote as a dotted line on a graph, and by the speed with which differentiation was covered.
There are lots of exercises with worked answers, and these are supplemented by further skills sections in the binder. There is also a booklet of assignments covering the core, based on past A-level questions.
The books and other material are well suited to individual study but could also be profitably used by teachers with classes of A-level students. If the forthcoming materials are up to the standard of those published already, the NEC will have a winner on its hands. | 677.169 | 1 |
Fun Self-Discovery Tools
Factoring by Grouping
Rating:
Description:
This video, by Fort Bend Tutoring on YouTube, discusses how to factor a polynomial by grouping.
Published on Feb 20, 2013
This video by Fort Bend Tutoring shows the process of factoring by grouping. This math concept is used in algebra, precalculus, trigonometry and calculus classes. Intro/Outro by Shirley Q. Liquor. Instruction by Larry "Mr. Whitt" Whittington.
Please donate to assist us in bringing the world more free videos through our YouTube Channel using the link:
This Donation button is secured using PayPal. | 677.169 | 1 |
This introduction to the basic mathematical theory of the finite element method is geared toward readers with limited mathematical backgrounds. Its coherent demonstrations explain the use of these techniques in developing the theory of finite elements, with detailed proofs of the major theorems and numerous examples. 1976 edition.
Descrizione libro Dover Publications Inc., ThisThis | 677.169 | 1 |
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Learn Multimedia Algebra in Win95
08/01/96
Algebra in Simplest Terms is a 24-lesson CD-ROM series that reviews fundamental and teaches advanced algebra concepts, using an electronic textbook format. Based on the successful PBS College Algebra series produced by COMAP's Sol Garfunkel, Ph.D., the course combines professionally produced video and text narration with an online dictionary and graphing calculator, management system, placement tests and more. More than 2,000 instructional screens as well as 2,200 tests and exercise questions are integrated. The program starts with a lesson on the Language of Algebra and concludes with a Probabilities lesson. It also provides feedback for questions and exercises, reinforcing key concepts. Liafail, Inc., Minneapolis, MN, (612) 925-3727.W
This article originally appeared in the 08 | 677.169 | 1 |
Laboratories in Mathematical Experimentation
4.11 - 1251 ratings - Source
This text is composed of a set of 16 laboratory investigations which allow the students to explore diverse ideas and concepts in mathematics. The approach is hands-on and experimental. The course provides the necessary transition to the study of higher, abstract mathematics.This text is composed of a set of 16 laboratory investigations which allow the students to explore diverse ideas and concepts in mathematics.
Title
:
Laboratories in Mathematical Experimentation
Author
:
Mount Holyoke College
Publisher
:
Springer Science & Business Media - 1997-03-01
ISBN-13
:
Continue
You Must CONTINUE and create a free account to access unlimited downloads & streaming | 677.169 | 1 |
Enrollment Info
Florida Algebra I
Prerequisites:Introductory or Pre-Algebra Length:Two Semesters
Florida Algebra I focuses on the understanding of key algebraic topics and the mastery of critical reasoning skills. It is aligned with Florida's Next Generation Sunshine State Standards and prepares students for Florida's end-of-course assessment for Algebra I. Through a "Discovery-Confirmation-Practice"-based exploration of algebraic concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to extend their knowledge in a variety of problem-solving applications. Course topics include algebraic expressions and equations; problem solving with functions; graphing; linear equations and inequalities; polynomials; radical expressions and equations; rational expressions and functions; and matrices.
Florida Algebra I features ample opportunity for students to hone their computational skills by working through practice problem sets before moving on to formal assessment. Throughout the course, diagnostic assessments help students to quickly identify areas of weakness and improve performance while summative assessments chart progress and skill development.
The content is specifically aligned with Florida's Next Generation Sunshine State Standards and Benchmarks | 677.169 | 1 |
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