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Featuring exercises that can be played in practice and in actual performances, Drum Solos & Fill-ins for the Progressive Drummer contains 4-, 8-, and 16-bar sol—Buddy Rich. Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra. All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding ... STUDENT TESTED AND APPROVED!. If you suffer from math anxiety, then sign up for private tutoring with Bob Miller!. Do mathematics and algebraic formulas leave your head spinning?. If so, you are like ... An examination of several approaches for establishing visions, strategic plans and implementation plans for the Chancellor's office to develop a strategic and performance planning process. The report ... Reflecting the success of the first workshop of the Cyprus Institute entitled Climate Change and Energy Pathways for the Mediterranean held in Cyprus in 2005, these proceedings present an overview of ... This much-needed resource helps trainers cut through the jungles of their own generational learning habits and clear a path to the emerging generations of learners. How to Design and Deliver Training ...
Pre-Algebra 9780078651083 ISBN: 0078651085 Pub Date: 2005 Publisher: Glencoe/McGraw-Hill School Pub Co Summary: "Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.78651085 Student Edition. Missing up to 3 pages. Heavy wrinkling from liquid damage. Does not affect the text. Light wear, fading or curling of cover or spine. May have use [more] 0078651085
Microsoft Mathematics 4.0.1108.0: Free Download Microsoft Math software was designed to help student to learn to solve equations step-by-step, while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry and calculus. From basic math to precalculus, Microsoft Mathematics includes tools and features to help you achieve a better understanding of fundamental concepts and... [read more >>] NOTE: If you have problems downloading Microsoft Mathematics
March 2013 A lot of new material this month. Firstly, a very nice set of six lessons on Angles and Polygons. Secondly, some Non-Calculator work on Percentages. Thirdly, a comprehensive treatment of Inequalities for GCSE. Answers to all exercises are included.
This classThis noteSimilar is the case with other topics coming next year like 3-Dimensional Geometry, Probability , Inverse trigonometric functions, vectors , Linear Programming and so on. Before these topics are introduced at Plus 2 level, you are supposed to have the basics in Coordinate (2-dimensional) Geometry, Elementary Probability, Elementary vectors, graph drawing , Permutations and combinations , logarithms, and so on. So I have decided to introduce a crash course for you in revising these elementary areas during these holidays, i.e. before you enter plus two. Being well-experienced, I know the relevant areas which you should have mastered before you enter Plus 2 . This will enable you to get better grades in your final examination and also to perform very well in the subsequent Engineering Entrance Examinations. This course will prolong 10 weeks during these holidays beginning from Monday, 5th April, 2010. You will be taught 2 hours a week and each hour will cost Rs 50 /- or 2 US dollars Altogether the fees for this course will be Rs 1000/- which you can also pay on a monthly basis at the rate of Rs 500- a month. This amount should reach my bank account in advance . My Bank particulars are given below : Account Name : IGNATIUS GEORGE Bank name : ICICI, Bank Branch : KOTTAYAM ACCOUNT NUMBER : 626701520746 If you are interested in this course, first you register for my first class I have scheduled on 5th April. After registering , you may have to pay Rs. 500 as the course fee for the first month. Once the money has reached my account , I will communicate the same to WiZiQ . Once you are paid , you are through and you can walk in to my class straight away. For further clarifications please contact me at e-mail: gntsgeorge@yahoo.co.in Skype ID : georgeignatius9 About IGNATIUS GEORGE (Teacher) I am an Indian by nationality and a mathematics teacher by profession. I was employed in Africa as a school teacher (mathematics) for many years .(Sierra Leone , Nigeria and Botswana). Currently ,I am attached to a CBSE High School in India as part-time maths teacher for Std 11 and 12 I am also engaged now giving online tuition (private) to students all over the world; USA , UK , Canada , Australia, Singapore , Saudi Arabia , Qatar ans so on
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics. This lesson teaches students how to add and subtract expressions that contain radicals. Students are taught to simplify each radical expression individually and add the simplified forms according to the rules of algebra. Grades 8-12. 28 minutes on DVD.
Abstract A common approach used for introducing algebra to young adolescents is an exploration of visual growth patterns and expressing these patterns as functions and algebraic expressions. Past research has indicated that many adolescents experience difficulties with this approach. This paper explores teaching actions and thinking that begins to bridge many of these difficulties at an early age. A teaching experiment was conducted with two classes of students with an average age of eight years and six months. From the results it appears that young students are capable not only of thinking about the relationship between two data sets, but also of expressing this relationship in a very abstract
Visit this daily schedule regularly to find the latest updates of suggested problems and other useful course information. You are responsible for any material covered in class, in our textbook, or in WEBWORK. Your main course activities will consist of working out homework problems on WEBWORK and preparing for quizzes and exams. As preparation for the quizzes and exams and also to improve your learning during class lectures, you should do the suggested problems below (third column of the following table). If at all possible, try to read the material for each day and attempt some of the problems BEFORE coming to class. Even if you don't get it all, the reading will probably make the lectures more valuable. You may find a graphing calculator helpful in checking your work, but there aren't any problems assigned that require anything more than a simple scientific calculor (at most). If you find that you need a graphing calculator for a problem, then you may be too "calculator dependent."
Introduction to $-adic Analytic Number Theory This book is an elementary introduction to $-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $-adic $-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $-adic analog of the Riemann zeta function and $-adic analogs of Dirichlet's $-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory. The book treats the subject informally, making the text accessible to non-experts. It would make a nice independent text for a course geared toward advanced undergraduates through beginning graduate students. This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In ... This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. The capstone of the book is a brief presentation of the ...
Developmental Math What is the Problem? More than 60 percent of all students entering higher education in the United States are required to complete remedial/developmental courses as a first step towards earning associate's or bachelor's degrees. A staggering 70 percent of these students never complete the required mathematics courses, blocking their entry to higher education and a wide array of careers. Improving Developmental Math in Community Colleges Recognizing the grave consequences for both individual opportunity and the nation's social and economic well being, Carnegie has engaged networks of faculty members, researchers, designers, students, and content experts in the creation of two new pathways, one in statistics and the other in quantitative reasoning. Our goal is to dramatically increase—from 5 to 50 percent—the proportion of students who earn college math credit within a year of continuous enrollment. We aim to put college students on a pathway of success, not just in college, but in their lives and careers as well. The Pathways Statway™ is a one-year pathway focused on statistics, data analysis, and causal reasoning that culminates in college-level statistics. Learn more about theCarnegie Statway NIC » Quantway™is a pathway focused on quantitative reasoning with the aim of promoting success in college mathematics. Learn more about theCarnegie Quantway NIC » The Instructional System Version 1.0 of the Statway™ and Quantway™ lessons were created by The Charles A. Dana Center at The University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching, and are copyrighted by both organizations. Participants in both Carnegie's Statway™ and Quantway™ Networked Improvement Communities are not using Version 1.0, but instead are using Version 1.5 of the lessons, which have been co-developed and improved by the Network. These materials are part of an Instructional System that includes: Ambitious learning goals leading to deep and long lasting understanding; Lessons and out-of-class materials to advance these goals; Formative and summative assessments, including end of module and end of course assessments; Productive Persistence — an evidence-based package of practical student activities and faculty actions integrated throughout the instructional system to increase student motivation, tenacity and skills for success; Language and literacy — a component that interweaves necessary supports in instructional materials and classroom activities so that learning is accessible to all; Dynamic online environment for network engagement and collaboration; Advancing Quality Teaching — a component to provide instructors with the knowledge, skills, and habits necessary to experience efficacy in initial use of the Pathways and develop increasing expertise over time; Rapid Analytics to support the continuous improvement of teaching and of the materials. Improving Continuously To promote consistently high performance as the project scales and to ensure effective implementation at scale across contexts, Carnegie has organized its collaborators and cooperative members into Carnegie Networked Improvement Communities (NICs) to strengthen mathematics teaching and learning at the college level. It is the Foundation's intent that over time the NICs will promote continuous improvement strategies throughout their member institutions. What Makes Carnegie's Work Different? We steward Networked Improvement Communities focused on the lack of student success in developmental mathematics. We join the worlds of research and practice, making faculty co-developers and research partners. We focus on continuous evidence-based improvement. We learn from practice to improve continuously. We believe that much more can be accomplished together than even the best of us can accomplish alone. Use of Materials Statway™ and Quantway™ are trademarks of the Carnegie Foundation for the Advancement of Teaching that Carnegie secured as the steward of the Networked Improvement Communities to provide quality assurance to its members. To maintain the NIC's quality standards, however, it is essential that the NIC control the use of these brand names. Thus, the Statway™ or Quantway™ name would not apply to any third party derivatives of this work. Survey software for Carnegie's work with the Networked Improvement Communities is powered by Qualtrics
Costs T.B.A.AP Calculus AB is a college-level course covering such concepts as derivatives, integrals, limits, approximation, applications, and modeling. In the second semester students�continue by reviewing function notation, then exploring absolute value, piecewise, exponential, logarithmic, trigonometric, polynomial, and rational functions. After studying limits and continuity, students move on to concepts of derivatives, including the chain rule, differentiation, implicit differentiation, and logarithmic differentiation. Toward the end of the course, students will apply what they have learned to solve integration problems. A TI-83+ or TI-84+ graphing calculator is required.
IBDŽ Home Study: Level 1 - Beginning Strategies for Successful Investing With the current volatility of the market, it's never been more important to use a time-tested, successful strategy for investing.The IBDŽ Home Study Program makes it easier than ever to learn our proven method for selecting stocks that have the traits of a big winner! The Home Study Program is an interactive kit that provides investing education to fit your schedule!"The Twisted World of Trigonometry. The DVD Super Pack contains Modules 1 through 6. Programs Included in this Series: Module 1: The Basics The Standard Deviants serve-up all sorts of useful trig vocabulary. Get your fill of degree, radian measurements and a sampler platter of right triangle trigonometry. Module 2: Trigonometry Functions The Standard Deviants take you to the junction of all functions. Together, we'll learn about six trigonometry functions. Module 3: Triangles It's time to clean out your brain to make room for triangles! The Standard Deviants cover lots of material including: right triangles, oblique triangles, the law of sines and the law of cosines. Module 4: Graphing Functions The Standard Deviants get graphic. It's off to the world of x and y axes, origins and amplitude. Learn some helpful rules to make your trig gig much easier. The Standard Deviants even hook you up with some key trig formulas. Module 5: Identities Discover the amazing secrets behind identities! The Standard Deviants start with a quick look at some common trig graphs which can be lines, curves or even parts of a circle. Then they plow headfirst into identities and the formulas that you'll need to make them happen. Module 6: Angle Formulas It's time to angle yourself for some trig learning because the Standard Deviants are here to discuss angle formulas, identities and proofs. And no trig experience would be complete without examples, lots and lots of examples to help solidify your trig knowledge." "Whether you need help with high school chemistry, need to review for a college chemistry class, or you're studying for the AP Chemistry Exam, the Standard Deviants can help! The Standard Deviants will help you "bond" with the material as this chemistry tutorial demonstrates the states and properties of matter, atomic and molecular weight, thermochemistry, Lewis structures, VSPER Theory, molarity and molality, and much more." Investigate the many ways to convert and transform color images into beautiful black and white images. Join artist, author, and educator Katrin Eismann as she guides you through this step-by-step tutorial-based class that demonstrates the many options for transforming your images from color to black and white. You'll learn how to work with Adobe Camera Raw and adjustment layers to interpret and add subtle toning and tinting effects, along with many other spectacular techniques. Katrin will also give you an overview of the Advanced Black and White print option for Epson inkjet printers to ensure your finished images are as beautiful in print as they appear on your computer screen. "The Standard Deviants are more fun than a textbook and cheaper than hiring a calculus tutor! Beginning with a review of functions and graphing, these DVDs cover limits, vertical and horizontal asymptote, slopes and derivatives, antiderivatives, the definite integral, and more." The video series follows one of the industry's best photographers as he explains some of his techniques for creating spectacular lighting EddieTwo internationally renowned cinematographers light the same shots from the same dramatic script in this back-to-back workshop. Don McAlpine ( Patriot Games, Breaker Morant and My ********* Career ) and Denis Lenoir ( Monsieur Hire, Clear and Present Danger and Mrs. Doubtfire ) vividly demonstrate how differences in creative style and approach affect the impact and tone of the scene. This program is packed with technical information, demonstrations & insights into the role of the cinematographer. This is a Whole set of 58 videos Showing How to hack! Thanks to the makers for Their effort.You time and all are awesome. Please use this videos Only for Study Purposes and research. Anyone do not harm
Enhance your GCSE Statistics lessons with exciting digital resources that will put statistics into a real-life context for students. * Enhance your lessons with 120 digital resources, matched to the Collins GCSE Statistics student books. * Allow students to access the GCSE Statistics student books at home, with SCORM compliant pages for your VLE. * Boost student confidence with video worked exam questions. * Introduce new topics to the class with ease, with 36 differentiated Powerpoint starters. * Practice key skills with multiple choice and matching pair questions. * Show students how statistics are used in real life, with news clips and career videos. * Find Foundation and Higher content all in one place. * Suitable for both AQA and Edexcel exam boards. * Resources produced by an expert team of authors. You can earn a 5% commission by selling GCSE Statistics Resource Pack and VLE - AQA and Edexcel (Collins GCSE Statistics
Geometric Sequences We already know that an arithmetic sequence is one where the difference between successive terms is constant. The distance each term is the same. A geometric sequence is a lot like an arithmetic sequence, but it is completely different at the... Please purchase the full module to see the rest of this course Purchase the Sequences Pass and get full access to this Calculus chapter. No limits found here.
Leaving Certificate Mathematics usually is a requirement for a great many areas of employment and courses. In terms of the word of work, employers look for numeracy skills in all areas including apprenticeships, nursing and the Gardai. All Institutes of Technology insist on at least Ordinary Level Maths as a basic entry requirement. There are some exceptions, for example, Art Degrees/Courses. A Grade C or higher in Ordinary Level Maths is required for many Science or Commerce courses – this reflects the amount of Maths and Statistics involved in studying Science, Commerce or Psychology. Knowledge of the Junior Certificate Higher Course will be assumed. The syllabus is presented in the form of a core and a list of options. Students study the whole of the core and one option: CORE: ALGEBRA Algebraic operations on polynomials and rational functions, unique solutions of simultaneous linear equations with two or three unknowns, inequalities, complex numbers, proof by induction of simple identities and matrices.
EL1150Introductory Matlab Course1.5 credits Introduktionskurs till Matlab Course Syllabus In this course you will learn how to use Matlab as an effective tool in science and engineering. From the course content: The possibilities and limitations in Matlab, syntax and interactive computations, programming in Matlab, visualisation, optimizing code for fast computations. Learning outcomes The course will give the fundamental knowledge and practical abilities in MATLAB required to effectively utilize this tool in technical numerical computations and visualisation in other courses. After the course you will be Able to use Matlab for interactive computations. Familiar with memory and file management in Matlab. Able to generate plots and export this for use in reports and presentations. Able to program scripts and functions using the Matlab development environment.
Re: if using Mathematica to solve an algebraic problem is like copying To: mathgroup at smc.vnet.net Subject: [mg108887] Re: if using Mathematica to solve an algebraic problem is like copying From: "David Park" <djmpark at comcast.net> Date: Tue, 6 Apr 2010 07:23:27 -0400 (EDT) Why is using Mathematica similar to copying someone else's homework? Putting the question of the motivation and economics of student cheating aside, the question is: how can Mathematica be used to promote learning by students actually interested in learning? How about the following as one possible method? Use an Axiom Set - Problems approach. Give the students the axioms or rules of his subject (with descriptive names) in an active form and then have them solve problems by choosing and applying the axioms step by step. If they could do that, would it satisfy you, even though the computer was doing the dog work? Would you object if the students didn't actually memorize the axioms but worked from a table or palette? Would they sort of memorize them just by repeated use? Or is it your position that students have only learned what they can recall from memory and apply using pencil and paper? More generally, is it your position that Mathematica can't ever be helpful in learning, or that it hasn't been shown to be useful, or that we just haven't learned ourselves how to make it useful. David Park djmpark at comcast.net From: Richard Fateman [mailto:fateman at cs.berkeley.edu] from someone else, then consider this article, which suggests that students (at MIT, at least) learn significantly less, in some sense by copying their homework. Of course this would be similarly true for other computer systems. While the details of the experimental setup may not match, the results are startling.
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The goals we have set for this project are broad and far reaching. Here are our priorities: 1. Make mathematics welcome and even indispensable across the entire curriculum In the same way that all students should be able to write an essay in any subject they have studied, all students should be able to look at a problem or situation or experiment and ask suitable mathematical questions. They should then have some idea of how to seek the answers to their questions. This is inevitably tied to the reduction of a lot of anxiety about the use of mathematics among the students and, we cautiously point out, the faculty. 2. Motivate students to take mathematics seriously We believe we need to change the way mathematics seems to put off budding scientists and social scientists so that they attempt to minimize their use of it throughout their undergraduate career and (one suspects) later in life. An interdisciplinary approach to mathematics, allowing students to focus on their discipline, should prove a motivator to do otherwise. 3. Broaden the diversity of those undergraduates enrolling in math or science courses In addition to ethnic diversity this project is designed to reach out to students in the humanities and fine arts with courses and materials highlighting the mathematics that intersects their current interests. The presence of these people in mathematics courses will make those courses richer for those inclined more toward the mathematics and science and will make the mathematics important and beautiful to those not initially drawn to it. 4. Increase the ability of students to approach data in a mathematical manner This applies primarily to students in the natural sciences, social sciences and psychology. Faculty in these fields find that students have a weak grasp of what it means to fit a curve to data, how to measure variances, how to interpret the results of various statistical tests, how to interpret a graph, etc. 5. Increase the ability and willingness of students to use mathematics they already know to facilitate their understanding of other subjects and to draw upon other subjects to improve their mathematics We have in mind here the issue of modelling real world phenomena using calculus, differential equations, linear algebra, discrete mathematics, Fourier series, probability, dynamical systems and other topics normally addressed through the mathematics curriculum. 6. Stem the flow away from science and math of students with talent and ability 7. Make the methods and materials designed to further these goals available, accessible and outright friendly to the broad national audience of faculty in undergraduate institutions Impact Information In its first four years the Dartmouth Mathematics Across the Curriculum project created sixteen new courses: a six-course mathematics and physical sciences sequence (IMPS), two intermediate mathematics applications for science courses, and eight courses linking mathematics with a humanistic discipline. Additionally, it has influenced another thirteen, supporting the creation of new mathematics modules, case studies, or other interventions that add a mathematical lens. The evaluation team was charged with evaluating the effects of these courses on student learning, faculty development and institutional culture. Apportioning our resources for maximum impact, we focused on four categories of courses where the MATC influence was greatest: the IMPS sequence, the Introduction to Calculus featuring real-life applications, intermediate math applications for science, and the math and humanities courses. The evaluation results are based on extensive assessmentusing attitude and achievement surveys, content tests, and in-depth interviews with students and facultyof nineteen courses (a total of 36 course iterations) taught by 27 different faculty (a total of 44 "faculty-courses") and involving over 1800 "student-courses." Looking at a broad range of courses over time allowed us to identify patterns in student learning and faculty experience that transcend a single course or discipline as well as to assess the effectiveness of MATC courses.
Hello Students and Parents, This will be an exciting year for my 8th grade advanced, gifted, and regular pre-Algebra classes. This course is filled with knowledge to help hone skills that will be applicable to all forms of mathematics in the future. For those of you who strive for excellence and enjoy working hard, this class will be particularly easy for you. I have high expectations for my students and hopefully they have high expectations for themselves as well. All the class rules, supplies, and contact information are on the syllabus. I am always checking my email so if you have a question or would like to discuss something about the class I will be available at marlonjr@dadeschools.net. Thank you and I hope we all have a wonderful and productive school year! ***ALL MR. CARTER'S CLASSES** updated August 29, 2011 LOOK UNDER THE 8TH GRADE PRE- ALGEBRA TAB TO ACCESS EXTRA CREDIT HW PAGES. OTHER THAN THAT YOUR SUPPLIES WILL BE DUE TUE/WED DEPENDING ON YOUR PERIOD. IF YOU WANT THE EXTRA CREDIT THIS IS ALSO DUE... This course reinforces mathematical skills taught in the sixth and seventh grade classes with additional advanced computation including an emphasis on Algebraic concepts. Students will study fractions, decimals,percents, positive and negative integers and rational numbers. They will become more proficient in using ratios, proportions and solving algebraic equations. Students will develop and expand problem solving skills (creatively and analytically) in order to solve word problems. A strong emphasis will be placed on understanding mathematical principles required for success in this course and as a foundation for future mathematics courses.
Nine PlanetsA Multimedia Tour of the Solar System: one star, eight planets, and more Search for San MarinoIt goes into the use and calculation of sequences and series, the binomial theorem (expanding a binomial expression that is to an exponent greater than 3), the necessity of vectors, parametric equations (such as x = t, y = f(t)), matrices and determinants. Lastly, Pre-Calculus starts students on... ...I have a unique range of skills from analog to digital methods, and I get excited about learning new things and sharing the knowledge.Digital Photography - Developing the Digital (Adobe Lightroom Basics) You've been using a DSLR and capturing loads of images, now what? Making great pictures star
Welcome to my home page. Algebra I is one of my favorite courses to teach because I get to work with students new to high school math. I hope throughout the year your student develop to learn the importance of math and maybe even enjoy it too. If you ever need to contact me please email me at givensa@rcschools.net Attachedis a copy of the syllabus and supply list for Algebra 1. Algebra I Algebra I is a Tennessee state tested course focusing on standards and grade-level expectations ranging from graphing one and two-step equations to graphing and solving quadratic formulas. The website to access your textbook is my.hrw.com Your student has a unique username and password I have given to them.
Description Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on why future teachers are learning the content as well as when and how they will use it in the classroom. The Sixth Edition has been streamlined throughout to make it easier to focus on the important concepts. The authors continue to make the course relevant for future teachers by adding new features such as questions connected to School Book Pages; enhancing hallmark features such as Responding to Students exercises; and making the text a better study tool through the redesigned Chapter Summaries. To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit Table of Contents 1. Thinking Critically 1.1 An Introduction to Problem Solving 1.2 Pólya's Problem-Solving Principles 1.3 More Problem-Solving Strategies 1.4 Algebra as a Problem-Solving Strategy 1.5 Additional Problem-Solving Strategies 1.6 Reasoning Mathematically 2. Sets and Whole Numbers 2.1 Sets and Operations on Sets 2.2 Sets, Counting, and the Whole Numbers 2.3 Addition and Subtraction of Whole Numbers 2.4 Multiplication and Division of Whole Numbers 3. Numeration and Computation 3.1 Numeration Systems Past and Present 3.2 Nondecimal Positional Systems 3.3 Algorithms for Adding and Subtracting Whole Numbers 3.4 Algorithms for Multiplication and Division of Whole Numbers 3.5 Mental Arithmetic and Estimation 4. Number Theory 4.1 Divisibility of Natural Numbers 4.2 Tests for Divisibility 4.3 Greatest Common Divisors and Least Common Multiples 5. Integers 5.1 Representations of Integers 5.2 Addition and Subtraction of Integers 5.3 Multiplication and Division of Integers 6. Fractions and Rational Numbers 6.1 The Basic Concepts of Fractions and Rational Numbers 6.2 Addition and Subtraction of Fractions 6.3 Multiplication and Division of Fractions 6.4 The Rational Number System 7. Decimals, Real Numbers, and Proportional Reasoning 7.1 Decimals and Real Numbers 7.2 Computations with Decimals 7.3 Proportional Reasoning 7.4 Percent 8. Algebraic Reasoning and Connections with Geometry 8.1 Algebraic Expressions, Functions, and Equations 8.2 Graphing Points, Lines, and Elementary Functions 8.3 Connections Between Algebra and Geometry 9. Geometric Figures 9.1 Figures in the Plane 9.2 Curves and Polygons in the Plane 9.3 Figures in Space 9.4 Networks 10. Measurement: Length, Area, and Volume 10.1 The Measurement Process 10.2 Area and Perimeter 10.3 The Pythagorean Theorem 10.4 Surface Area and Volume 11. Transformations, Symmetries, and Tilings 11.1 Rigid Motions and Similarity Transformations 11.2 Patterns and Symmetries 11.3 Tilings and Escher-like Designs 12. Congruence, Constructions, and Similarity 12.1 Congruent Triangles 12.2 Constructing Geometric Figures 12.3 Similar Triangles 13. Statistics: The Interpretation of Data 13.1 Organizing and Representing Data 13.2 Measuring the Center and Variation of Data 13.3 Statistical Inference 14. Probability 14.1 Experimental Probability 14.2 Principles of Counting 14.3 Permutations and Combinations 14.4 Theoretical Probability Appendices A. Manipulatives in the Mathematics Classroom B. Getting the Most out of Your Calculator C. A Brief Guide to the Geometer's Sketchpad D.
The Cartoon Guide to Calculus "In Gonick's work, clever design and illustration make complicated ideas or insights strikingly clear." —New York Times Book Review Larry Gonick, master cartoonist, former Harvard instructor, and creator of the New York Times bestselling, Harvey Award-winning Cartoon Guide series now does for calculus what he previously did for science and history: making a complex subject comprehensible, fascinating, and fun through witty text and light-hearted graphics. Gonick's The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere. Book Description A complete—and completely enjoyable—new illustrated guide to calculus Master cartoonist Larry Gonick has already given readers the history of the world in cartoon form. Now, Gonick, a Harvard-trained mathematician, offers a comprehensive and up-to-date illustrated course in first-year calculus that demystifies the world of functions, limits, derivatives, and integrals. Using clear and helpful graphics—and delightful humor to lighten what is frequently a tough subject—he teaches all of the essentials, with numerous examples and problem sets. For the curious and confused alike, The Cartoon Guide to Calculus is the perfect combination of entertainment and education—a valuable supplement for any student, teacher, parent, or professional. "How do you humanize calculus and bring its equations and concepts to life? Larry Gonick's clever and delightful answer is to have characters talking, commenting, and joking-all while rigorously teaching equations and concepts and indicating calculus's utility. It's a remarkable accomplishment-and a lot of fun." Larry Gonick's sparkling and inventive drawings make a vivid picture out of every one of the hundreds of formulas that underlie Calculus. Even the jokers in the back row will ace the course with this book. — David Mumford, Professor emeritus of Applied Mathematics at Brown University and recipient of the National Medal of Science I always thought that there are no magic tricks that use calculus. Larry Gonick proves me wrong. His book is correct, clear and interesting. It is filled with magical insights into this most beautiful subject. — Persi Diaconis, Professor of Mathematics, Stanford It has no mean derivative results about the only derivatives that matter…. A spunky tool-toting heroine called Delta Wye seems the perfect role model for our next generation. — Susan Holmes, Professor of Statistics, Stanford A creative take on an old, and for many, tough subject…Gonick's cartoons and intelligent humor make it a fun read. — Amy Langville, Recipient of the Distinguished Researcher Award at College of Charleston and South Carolina Faculty of the YearThe Cartoon History of the Modern World Part 1,...
fun and easy way® to understand the basic concepts and problems of pre-algebra Whether you're a student preparing to take algebra or a parent who needs a handy reference to help kids study, this easy-to-understand guide has the tools you need to get in gear. From exponents, square roots, and absolute value to fractions, decimals, and percents, you'll build the skills needed to tackle more advanced topics, such as order of operations, variables, and algebraic equations.
Algebra for the IPad Generation Feb 24, 2012 For many students, algebra inspires apprehension and dread. Today, students are increasingly dependent on tools, such as iPads and even their phones, that can do the work of algebra for them. This makes the job of a teacher trying to convey algebra's importance difficult. Yet there are still ways to make algebra relevant, interesting and fun. The Problem with Algebra Algebra has its fair share of young critics. When students first encounter algebra, with its x's and y's, they may find it incomprehensible and foreign. Many students argue that the word problems with which they are presented are unnecessarily obtuse. For example, a student may be asked to determine how many boys and girls there in a class of 25 students, given that there are five more girls than boys. Of course, in order to formulate this problem, the person asking the question must already know the answer. A reluctant algebra student might protest that the question is merely an excessively elaborate way of arriving at information that's already known. Algebra as a Puzzle One key to making algebra compelling is to present it as a puzzle to be solved. Algebra is less about mathematics and more about logic. Treating the above problem, and others like it, like puzzles can helpt a student overcome the psychological barrier that often arises with a challenging math problem. It's important that students who struggle with algebra avoid getting bogged down with focusing on finding the answer. It's true that many algebra textbooks are full of seemingly arbitrary questions with little relevance. Yet this isn't much different than trivia games, jigsaw puzzles or video games. While there's a thrill in completing a jigsaw puzzle, most of the joy in the activity is the process of figuring it out. Algebra is no different. Algebra's Origins Another method for helping students connect with algebra is to explore its origins. Students with an interest in history and culture may appreciate the story of how algebra came to exist. Algebra's earliest origins date back to the ancient Egyptians, who solved algebraic problems almost entirely with words. The Babylonians subsequently developed a more sophisticated approach, though it was still hindered by a lack of symbols. It was the Arabs in the 9th century, who then controlled significant portions of modern day Asia, Africa and Europe, who are largely considered to be the first masters of algebra. They combined the rhetorical algebra of the Egyptians, Babylonians and Greeks with the Hindus' number system. They gave algebra its name, though the innovations would continue for hundreds more years. Algebra for Cash There will be students who are uninterested in algebra as a puzzle or algebra's fascinating history. These students might be more concerned with how algebra can help them. For these practical students, algebra should be acknowledged as a gatekeeper subject, as it's often called. These students may be more receptive to learning algebra when they understand that without algebra, countless desirable and lucrative jobs are off the table. This includes jobs in fields such as architecture, chemistry, biology, business and, notably, computer engineering, a field with both a high need and one of the highest average starting pays among major professions
One of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, convincing answer; others hem and haw and stare at the floor. The real response to the question should be, "Yes, you will, because algebra gives you power" the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on. Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, Algebra I For Dummies can provide the help you need. This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works. In Algebra I For Dummies, you'll discover the following topics and more: All about numbers rational and irrational, variables, and positive and negative Figuring out fractions and decimals Explaining exponents and radicals Solving linear and quadratic equations Understanding formulas and solving story problems Having fun with graphs Top Ten lists on common algebraic errors, factoring tips, and divisibility rules. No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, Algebra I For Dummies can give you the tools you need to succeed. Few beginning graduate students in mathematics and other quantitative subjects possess the daunting breadth of mathematical knowledge expected of them when they begin their studies. This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations. [via] More editions of All the Mathematics You Missed: But Need to Know for Graduate School: A fully annotated and illustrated version of both ALICE IN WONDERLAND and THROUGH THE LOOKING GLASS that contains all of the original John Tenniel illustrations. From "down the rabbit hole" to the Jabberwocky, from the Looking-Glass House to the Lion and the Unicorn, discover the secret meanings hidden in Lewis Carroll's classics. [via] More editions of Annotated Alice : Alice's Adventures in Wonderland and Through the Looking Glass: Designed for students who are not from a mathematical background, this introductory statistical text emphasizes ideas over computation. It highlights the relevance of statistical concepts and their applications. Examples are based on real data drawn from a variety of disciplines. An early emphasis on distribution makes difficult topics such as sampling distributions, confidence intervals and significance tests less confusing. Exercises, bullet lists and highlighted boxes are used to reinforce information. [ comeExcellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some knowledge of differential equations and multivariate calculus required. Many problems and exercises (some solutions) integrated into the text. 1979 edition. Bibliography. This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in the widest sense, with an interest in physics and mathematics, will gain from its study. [via] This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters identify important themes and establish the notation used throughout the book, and subsequent chapters explore the normal and arithmetical structures of groups as well as applications. Includes 679 exercises. 1978 edition. René Descartes (15961650) is one of the towering and central figures in Western philosophy and mathematics. His apothegm Cogito, ergo sum marked the birth of the mind-body problem, while his creation of so-called Cartesian coordinates have made our physical and intellectual conquest of physical space possible. But Descartes had a mysterious and mystical side, as well. Almost certainly a member of the occult brotherhood of the Rosicrucians, he kept a secret notebook, now lost, most of which was written in code. After Descartess death, Gottfried Leibniz, inventor of calculus and one of the greatest mathematicians in history, moved to Paris in search of this notebookand eventually found it in the possession of Claude Clerselier, a friend of Descartes. Leibniz called on Clerselier and was allowed to copy only a couple of pageswhich, though written in code, he amazingly deciphered there on the spot. Leibnizs hastily scribbled notes are all we have today of Descartess notebook, which has disappeared. Why did Descartes keep a secret notebook, and what were its contents? The answers to these questions lead Amir Aczel and the reader on an exciting, swashbuckling journey, and offer a fascinating look at one of the great figures of Western culture. [via] More editions of Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe: An[via] More editions of Fooled By Randomness: The Hidden Role Of Chance In Life And In The Markets: Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale. A coastline, for instance, is a fractal, with each bay or headland having its own smaller bays and headlands--as is a tree with a trunk that separates into two smaller side branches, which in their turn separate into side branches that are smaller still. No longer mathematical curiosities, fractals are now a vital subject of mathematical study, practical application, and popular interest. For readers interested in graphic design, computers, and science and mathematics in general, Hans Lauwerier provides an accessible introduction to fractals that makes only modest use of mathematical techniques. Lauwerier calls this volume a "book to work with." Readers with access to microcomputers can design new figures, as well as re-create famous examples. They can start with the final chapter, try out one of the programs described there (preferably in a compiled version such as TURBO BASIC), and consult the earlier chapters for whatever is needed to understand the fractals produced in this way. The first chapter, which builds on the relationship of binary number systems to the "tree fractal" described above, is the best place to start if one has no computer. There will be much to enjoy on the way, including the beautiful color illustrations. [via] Classic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics include Lebesque and Stieltjes integrals, Hilbert and Banach spaces, self-adjunct transformations, spectral theories for linear transformations of general type, more. Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, and methodological principles of noncooperative and cooperative game theory. Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information. Game Theory will be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential [via] Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.A clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. It then considers the application of symbolic logic to the clarification and axiomatization of theories in mathematics, physics, and biology. Hundreds of problems, examples, and exercises. 1958 edition. Ivars Peterson has come up with another itinerary of Mathland - where the habitat is mysterious and the inhabitants fascinating. He explores uncharted islands, introducing strange vibrations in the shadows of chaos, new twists in knot physics, and the straight side of circles. The tour is enjoyable to experienced travellers and first-time tourists alike. Peterson, a journalist with Science News, makes the arcane intelligible by interpreting mathematics into engaging prose. [via] Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953. [via] This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large Numbers and Three-Series Theorem are proved by martingale techniques. A proof of the Central Limit Theorem is also given. The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints. [via] Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems interesting to beginning and advanced readers. Divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, many other aspects produce ingenious puzzles. Solutions to all problems. This book provides a modern introduction to the representation theory of finite groups. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Amongst those applications covered are Burnside's paqb theorem, the use of character theory in studying subgroup structure, and a description of how to use representation theory to investigate molecular vibration. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book. This will be suitable as a text for those teaching a course in representation theory, and in view of the applications of the subject, will be of interest to chemists and physicists as well as mathematicians. [via] Striking just the right balance between formal and abstract approaches, this text proceeds from generalities to specifics. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics. "First-rate. . . deserves to be widely read." American Mathematical Monthly. 1980 edition. This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come. Although we seldom think of it, our lives are played out in a world of numbers. Such common activities as throwing baseballs, skipping rope, growing flowers, playing football, measuring savings accounts, and many others are inherently mathematical. So are more speculative problems that are simply fun to ponder in themselves--such as the best way to score Olympic events. Here Robert The This book, which requires of its readers only a basic understanding of high school or college math, is for anyone fascinated by the workings of mathematics in our everyday lives, as well as its applications to what may be imagined. All will be rewarded with a myriad of interesting problems and the know-how to solve them.
0618783768 9780618783762 1111809321 9781111809324 Elementary Linear Algebra: The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding technology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice. «Show less Elementary Linear Algebra: The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications,... Show more» Rent Elementary Linear Algebra 6th Edition today, or search our site for other Falvo
Ok you people out there that want the easy way out in your geometry, algabra, and pre-calc class i got a math program for you that does most of what you need for these classes. ne thing from: Area, surface area, volume, cramers rule, Conics, distance formula, end behavior, midpoint, pascals triangle, quadratic formula, reducing radicals, and slope. It runs right out of the program menu, or if you really want to be secretive, it works under mirage (which can hide it from teachers) I was hoping to sell it for like 2 bucks....but don't know if it will work that way... but if you want it..email me and i'll give it to you for free Because I like to help people learn programming and stuff, I have setup a few yahoo groups where people can learn from me/eachother, share files/programs, post messages, etc. - Trust me, I am among the best, so I think it would be very beneficial. I am very willing to teach people everything I know whenever I have free time (I like to work on a one-to-one basis). Check out my groups if you are at all interested or curious. Below are the web addresses for my groups (CAREFUL, I had to put a space after each slash, so if you copy and paste, delete the spaces): You could try searching for one first. For example, you could probably find one or more in 83plus/basic/math (such as baseic.zip or bases.zip) or in 83/basic/math. I don't want to sound rude or condescending, but you really should look first for what you want before you ask someone to do something for you. This site especially has most math programs a beginner like you or I would need. Once you've learned enough and need a program that doesn't exist (at least on ticalc), one should hope that you would have the ability and knowledge to write what you need by yourself or at least to search the many resources available to you on the Internet and other places. This goes for most every beginner, not just you. I'm not trying to be high and mighty by calling you and others a beginner; I still consider myself to be a beginner in many ways. hi i am taking AP Calculus. please, i am begging you. someone has to create a super program for this class. it isn't a hard class, but it takes time to solve some stuff. also, a calculus program would save me time in contests. well see you and thanks A lot of programs calculate everything for you in the background, giving you a final answer. What about a program that gives you the formula? I can't remember formula, and I don't trust values of programs, I'd prefer to just see the formula. Option 1: If it is Mirage compatible (add a ":" to the beginning of the first line), you simply highlight it in Mirage and press "tan(". To the right, the properties should read either "LOCKED:Y" or "L:Y". Option 2: Send it to your computer (PC or Mac) and open it with 83+ Graph Link. There should be a box next to "Protected". Check the box. If you don't have either of those two programs, e-mail me at SSpyro64@AOL.com Ok, this is kind of similar. I'm the only person at my school who knows any bit how to program calculators, so, like anyone would do, I sell them. However, lately, people have been giving each other the programs instead of buying them from me. Is there a way to stop people from being able to send programs???? thats pretty underhanded ... but, back to the point if you aren't sending then mirage its easy to send them a shell that can detect hidden progrsms and run them but not unhide them. You can send them the program from mirage so you dont have to unhide it. they will be able to run the program from the shell but if you dont give anyone mirage then they cant send them.
. 60+ examplesMath software for students studying precalculus. Can be interesting for teachers teaching precalculus. Math Center Level 1 consists of Graphing calculator 2D, Advanced Calculator, and Simple Calculator called from the Control Panel. Simple calculator is a general purpose calculator.Advanced Calculator is a step farther in complexity comparing to the Simple Calculator.Graphing Calculator 2D has two panels
The content. Analysis is about the concepts of function, derivative, and integral (quoted from the preface for the Shilov's book). As a starting point in this study we will look into the structure of real line and explore some of the axioms of the real number system. The primary focus in the initial part of the course will be on the Completeness Axiom and various equivalent forms of it. We will study in detail the concepts of limit, derivative, integral , and the series. Although you have already study all those concepts in your Calculus courses, I am sure that you will realize that there is a lot of room to improve our basic understanding of those concepts. Real Analysis is one of the key courses in the foundations of mathematics, and most of the time in this course will be spent into looking back into the foundations of Calculus. However, we would also like to use our improved understanding of Calculus to move toward the greater level of abstractions, and to learn something about some of the more "modern" developments of Analysis. In particular, we will study the concept of Metric Spaces a little bit. 1. Program Assessment - Course Objectives Here is a concise list of course goals following the format of Math Department Assessment Plan. In Section 1 2 MATH 420 - REAL ANALYSIS SPRING 2005 Course-level Outcomes. Students shall study foundations of the real number system, limits, continuity, derivative and integral. Mathematical Reasoning: Students will try to achieve an in-depth understanding of the ideas presented. This includes making sure statements and claims made are checked for accuracy, and an appropriate justification is given. Problem Solving: A number of calculus problems will be revisited, and many new solved. This course will challenge and develop students' problems solving skills to the limit. Communication: The main mode of communication in this course will be written (homework, exams). However, in-class participation (oral communication) is essential, as well. Technology: Use of a Computer Algebra System (Derive, Maxima) and LATEX. 2. Course Philosophy and Procedure In order to succeed in this course, you should really immerse yourself totally in doing mathematics. The key strategy in solving problems is "not to give up". This course is truly a problem solving course. Most of the course time will be spent on limits, derivatives, integrals, ... . You will see again some of the stuff that you are familiar with, but sooner or later you will stumble over some basic stuff that you actually do not know very well. You should certainly build up on your strengths (the stuff you more or less know), but make sure that you do not neglect working on the weaknesses, as well. Use homework and exams as directions, but you should really guide yourself in the work of filling in the gaps in your knowledge in order to be able to meet the goals set up by the homework and exam problems. Mathematics is not a spectator sport. It is learned by doing. Viterbo University is striving to be a Learner-centered institution. That entails an expectation of maturity and taking responsibility for their learning on the part of students. I see my job as one helping you succeed in this learning process. In spite of my best efforts, I may not always manage to say things the way which best leads to your full comprehension. You can also help me by providing as much of a feedback as you can. I will try to do a formal evaluation survey around the middle of the semester. Other than that, I find the questions in class, and especially when someone comes to my office for assistance, very helpful. As a further assistance to you: • About a week prior to any exam, you will receive a practice exam which will be, in terms of format and type of problems, very much like the actual exam. • I am asking you to keep a The Learner's Journal. This is to be a separate notebook that should contain a record of your study/practice on daily basis. I would also like you to keep a time log - date, hour from-to - for each study session. I would prefer that you use a pen for writing in that journal. If you are going to use pencil, then please do not use erasers, and in any case, do not tear pages out. For a learning to take place, you have to try to do MATH 420 - REAL ANALYSIS SPRING 2005 3 something. In trying, you are likely to make mistakes. The real learning will start taking place once you start understanding and correcting your mistakes. You turn that journal in together with your exam, and then you will be graded for the portion of that journal that covers the period preceding that current exam. Up to 30% of the exam score is possible to earn this way. The elements that will play the key role in grading the journal are – Organization - readability: In order to evaluate, I have to able to read it first. I should not have a difficult time navigating through those notes. – Mathematical correctness. – The quality of the work and the amount of time spent on studying. • Take-home problems: These assignments should test/help a better integration of material. Some will include more difficult problems. One of those assignments will be a group HW. In general, I encourage you to find some time to study together, but unless stated otherwise, the HW is to be written up on your own. I will try to space those assignments so that you could have some time to catch up. This should leave significant room for exploring the book on your own, and I encourage you to find your own balance between solving some problems in full, and just sketching solutions to some. You should try to read, meaning to the point where you really understand the question, most of the book problems. The work in class, your book, HW, and practice exams should give you a pretty clear idea what is that you are expected to learn. It is your job to, perhaps through trial and error, find learning strategies that work best for you. Remember, learning is something you do, rather than something I do to you. Help. I am used to you asking questions in class, coming to my office, working in groups, asking questions by e-mail. Hope all of that will continue. There is a growing mount of Internet resources, too. Just go to Yahoo, or Google and search for "real analysis". In particular, you may want to look at Some of the HW will involve some use of technology (CAS and LATEX). The details will be given later. One of the writing assignments will be graded in two parts - the second part will require you to come to my office and explain your reasoning, answer some questions. In all your work, written and oral, it is essential to provide explanations, justify your reasoning. My grading scale is A=80%, B=60% , C=40%, D > 30% . The following exceptions to that scale are possible: • An A on the final exam (more than 180/200 points) will mean an A for the final grade as well. 4 MATH 420 - REAL ANALYSIS SPRING 2005 • If one is passing the course by the time of the final exam, but earns less than 30% points (a score less than 60/200), that will result in an F for the final grade. 3. Some details and examples Specific Course Goals. To study rigorous foundations of calculus; extend basic knowledge of functions, limits, derivatives and integrals. Students are expected to learn to state definitions and theorems precisely, and be able to prove theorems stated. In particular, the proofs involving the concept of limit are going to be of central importance. The process of working toward those goals will involve looking back into everything you have learned in mathematics so far, and to subject those concepts to the following key questions: • What do I really know about ...? • What does ...mean? • Is what I just said about ...true? • How do I know if (why) it is true? Let me try to clarify this a little bit by looking into an example. Example: For some Math 155 students, conquering a problem such as p8 + p32 − p18 = 3p2 represents a major undertaking; something they consider worth of including into their portfolio for the semester. Now, when you look at what is involved into justifying the above result, a number of problems present themselves. For example, we have to use the rule pAB = pApB , A,B 0. Can you prove that rule? Another key rule here is AC + BC = (A + B)C . How about proving this one It is much more difficult question than one before. In fact, it is so basic that there is nothing more basic to use as a help in proving it. So, we have to accept that rule as an axiom. Note: I would like to encourage you to read [4, Chapter 4] here! Moreover, the rules are used by applying them to "existing" mathematical objects (in this case, real numbers). But, what do we mean by p2. Can you prove that such a number exists? What do we even mean by asking a question like that? The goal of this course is not only to learn how to answer the questions as those (that is how to do certain rigorous proofs), but we would also like to develop the corresponding mathematical awareness, so that we do not overlook those "simple" questions when solving problems. Ultimately, this kind of training leads to deepening our understanding of what mathematics is about. We would like to use that improved understanding to bring about other two basic goals of this course, which are: • Move beyond the concepts we are familiar with. We will study the concept of metric spaces. Fall 1999 - Final. To illustrate the goal of "improving Calculus skills", let's consider the final exam I gave to the Real Analysis class in Fall 1999. Problem 1. • State the definitions of a lower/upper bound of a set of real numbers. • State the definition of infimum. • State the theorem about existence of an infimum of a set bounded below. • Extra credit: Should I say "the infimum"? • Prove that the set S = 3, 5 2, 7 3, 9 4, . . . has an infimum, and find that infimum. • State the Completeness Axiom. • Prove that the Completeness Axiom is equivalent to the Infimum Theorem above. Problem 2. Define f(x) = 1Xn=1 n2 + 1 n! xn . (a) Use the ratio test to show that f is defined for all real x. (b) Prove that f is continuous at x = 0. Problem 3. State the definition of the derivative f0(a) of a function f at the point a of its domain. Use that definition to find the derivative of f(x) = 3x at an arbitrary point of Df . Problem 4. Find, lim x!0 sin (ln (1 + x)) ln (1 + sin (x)) . State and prove all the rules used in the process. In the case of L'Hospital's rule, just state it. The proof would be an extra credit. Problem 5. Probably most of the functions we have encountered so far would be continuously differentiable. That is, if f is differentiable at x = a, then f0 is a continuous function at x = a. Is this statement a theorem? Hint: Show that the function f(x) = (x2 sin 􀀀1 x , if x 6= 0 0, if x = 0 is a counterexample. 6 MATH 420 - REAL ANALYSIS SPRING 2005 A student that has passed a Calculus sequence should have no difficulty in understanding almost all of the questions on that final. Being able to answer them completely is a different matter. Americans with Disability Act. If
Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers some of the best researchers and educators in a particular field to present diverse sets of lectures. This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry, three very active research areas in mathematics and theoretical physics. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics. Two major themes at this institute were supersymmetry and algebraic geometry, particularly enumerative geometry. The volume contains two lecture series on methods of enumerative geometry that have their roots in QFT. The first series covers the Schubert calculus and quantum cohomology. The second discusses methods from algebraic geometry for computing Gromov-Witten invariants. There are also three sets of lectures of a more introductory nature: an overview of classical field theory and supersymmetry, an introduction to supermanifolds, and an introduction to general relativity. This volume is recommended for independent study and is suitable for graduate students and researchers interested in geometry and physics. This comprehensive and progressive new text presents a variety of topics that are only briefly touched on in other books; this text provides a thorough introduction to the techniques of quantum field ... This text explains the features of quantum and statistical field systems that result from their field-theoretic nature and are common to different physical contexts. It supplies the practical tools ... Quantum field theory has undergone extraordinary developments in the last few decades and permeates many branches of modern research such as particle physics, cosmology, condensed matter, statistical ... This book is a modern introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, ...
Young scholars explore the Fundamental Theorem of Calculus. In the Calculus lesson, students investigate indefinite and definite integrals and the relationship between the two, which leads to the discovery of the Fundamental Theorem of Calculus. Students explore the concept of differential calculus. In this differential calculus lesson, students use the derivative definition as h approaches zero to find the derivative of quadratic and 4th degree functions. Students use their Ti-89 to find the gradient of the secant and tangent. Twelfth graders investigate the limitations of the Fundamental Theorem of Calculus. In this calculus instructional activity, 12th graders explore when one can and cannot use the Fundamental Theorem of Calculus and explore the definition of an improper integral. Students explore the concept of area under a curve. In this area under a curve instructional activity, students find integrals of various functions. Students use their Ti-Nspire to graph functions and find the area under the curve using the fundamental theorem of calculus.
students acquire conceptual understanding of key geometric topics, work toward computational fluency, and expand their problem-solving skills. Course topics include reasoning, proof, and the creation of sound mathematical argumentsExtensive scaffolding aids below-proficient readers in understanding academic math content and in making the leap to higher-order thinking. Mathematical vocabulary is supported with rollover definitions and usage examples that feature audio and graphical representations of terms. Situational interest that promotes a relevant, real-world application of math skills serves to engage and motivate students. The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards (available on request).
High School Workshops (1997 – present) These day-long workshops, held on the University of Arizona campus, are designed for high school classes. (We also occasionally hold workshops designed for middle school classes, as well as workshops geared specifically towards school teachers.) The workshops cover topics that are not commonly taught in school math classes. Through an intuitive approach to each subject, students are exposed to both interesting and active areas of contemporary mathematics research. A secondary purpose of the high school workshops is to expose high school students to what an undergraduate education in mathematics includes, and to encourage them to add math classes to their schedule when they enter college. If you are a teacher interested in bringing your class to a workshop, please contact the current program coordinator (see below). Workshop topics Listed here are past workshop topics. We are always open to ideas for new topics. Introduction to Fourier Series and Harmonic Analysis Advanced topics in Fourier Series and Harmonic Analysis Introduction to Cryptology Public Key Cryptography and Digital Signature Verification Factoring and Primality Testing Introduction to Quantum Mechanics Einstein's Way Cool Notion of Motion Elasticity and Bridge Design Rate of Change and Functions Probability and Game Theory The symmetric road to the Rubik's Cube Knot Theory Graph Theory Biomathematics Additional information on particular workshops (topic descriptions, dates, and participants) is available at various workshop-related websites: Current program coordinator History and Participants Workshops in this outreach program are organized and run entirely by graduate students (with faculty encouragement and departmental administrative support). The program came into existence in Spring 1997 as one aspect of the SWRIMS project, when SWRIMS director Dr. William Vélez suggested this outreach program—and allocated SWRIMS funding—to graduate students Jennifer Christian-Smith, Aaron Ekstrom, and Alexander Perlis. (SWRIMS had already been involved in high school workshops on Population Biology and Honey Bees, which were organized by Dr. Joseph Watkins.) Initially, graduate student program coordinators and workshop organizers were funded by SWRIMS. Since around 2000, the primary incentive for graduate student participation has been the vertical integration requirement for graduate students funded by the department's VIGRE Grant. Reports Talks about (aspects of) this outreach program Katrina Piatek-Jimenez and Jennifer Christian-Smith. Graduate Students in the High School Classroom: Enriching the School Mathematics Curriculum and Students' Perceptions of Mathematics. Radio show interview by Dr. Patricia Kenschaft, host of radio show Math Medley, February 16, 2002. Jennifer Christian-Smith. The Saturday Mathematics Workshop Series at the University of Arizona: An Outreach Project Connecting Undergraduate and Graduate Students to High School Students. AMS/MAA Joint Meetings, New Orleans, Louisiana, January 2001. Aaron Ekstrom and Alexander Perlis. Fourier Series for high school students. AMS/MAA Joint Meetings, San Antonio, Texas, January 1999.
Question 565853 <font face="Times New Roman" size="+2"> You are kidding, right? Which one of several hundred math books in use today, each of which costing in excess of $75, shall I pull off of my shelf of all possible math books so that I can see the diagram? This is Algebra.com. It is NOT the Psychic Hot Line
News Archive MATLAB® Becomes the Tool of Choice Across Universities A standard instructional tool for mathematics, engineering and science courses in universities, MATLAB® has rapidly become the tool of choice for high productivity research, development and analysis in industry. MATLAB® is a high-performance language for technical computing that integrates computation, visualization and programming in an easy-to-use environment. It is a standard instructional tool for mathematics, engineering and science courses in universities and has rapidly become the tool of choice for high productivity research, development and analysis in industry. This two-day hands-on workshop is designed for beginning and intermediate MATLAB users. No prior knowledge of MATLAB is required. Taught in WPI's Computing and Communications Center by Dr. Adriana Hera, the workshop includes topics such as working with matrices; plotting and visualization; scripts and user defined functions; basic statistics and data analysis, nonlinear fitting; and, solving differential equations. In addition, the course includes a variety of engineering and scientific problems solved using MATLAB.
Introductory and Intermediate Algebra through Applications 9780321535788 ISBN: 0321535782 Edition: 2 Publisher: Addison Wesley Summary: This text aims to teach by example, while expanding understanding with exercise sets and applications. The design offers a side-by-side format that pairs each example and its solution with a corresponding practise exercise. Real-world applications show how integral mathematical understanding is to a variety of situationsPresented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are fully integrated throughout the text [more] Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are fully integrated throughout the text and exercise sets. Akst/Bragg's user-friendly design offers a
Improve your Study skills is a free ebook for College and High School students to develop and improve your study skills. Tired of endless studying? 200 pages of everything you need to spend less time studying, get better grades, pass your exams. A word-processor-like editor specifically designed for use in high school and college-level algebra-based physics courses. Equator helps high school and college physics students to easily navigate the algebra. Attendance Robot is a Microsoft Excel Add-In that turns your attendance sheet into self-service attendance machine. Save time. - No more need to have someone manually take attendance. No more need to manually calculate total attendees, dues, etc. Time and Attendance Plus is an affordable software solution that allows you to record and track the attendance of employees. It will then output simple easy to read reports that can be passed onto your payroll department. Improve grades and test scores Multimedia learning system makes even the toughest physics concepts come alive Great for new learners or students studying for college entrance exams,build science skills fast! Deductions is educational software designed to help students learn proofs in formal logic. It is intended to be used by instructors and students of college-level logic courses in philosophy, mathematics and computer science.
Advanced Instructional Schools (AIS) Objectives of AIS After students gain basic knowledge in algebra, analysis and topology in the annual foundation schools, they are ready for studying several subjects in mathematics at research level. In any AIS, lectures are delivered by experts in two closely related areas. The emphasis in these schools will be, in addition to imparting basic knowledge, in understanding connections between various areas of mathematics and problem solving. Towards the end of these schools special expository lectures will be arranged which introduce the audience to major open problems. Subject areas of advanced instructional schools Keeping in mind the expertise available in the country, the following subjects have been chosen for these schools at present: Commutative algebra and algebraic geometry Algebraic and differential topology Functional and harmonic analysis Differential Geometry and Lie groups Representation theory and its applications Algebraic and analytic number theory Partial Differential equations and their applications Combinatorics and graph theory Eligibility Students who perform well in the Annual Foundation Schools will have the option of further training in Advanced Instructional Schools. In addition, Ph. D. students having fellowship, post doctoral fellows and a few university faculty members will be selected for these based on recommendation letters and performance in M. Sc. and/or Ph. D. courses. Format of Advanced Instructional Schools 09.00-10.30 10.30-11.00 11.00-12.30 12.30-2.00 2.00-4.00 4.00-4.15 4.15-5.15 5.15-5.45 Lecture Tea Lecture Lunch Tutorial Tea Special Lecture Refreshments Resource Persons and lecture notes The lectures will be delivered by course instructors and the tutorials will be conducted by course assistants. The suggested load is a minimum of 8 lectures for each speaker. A typical school will require a total of 6 instructors and 3 course assistants. A few Special expository lectures highlighting current developments andopen problems will be arranged. The instructors will prepare notes of their lectures and send them to the conveners before the programme starts so that copies can be distributed to the students. The notes of lectures will contain all the problems sets to be discussed in the tutorials. The notes will be more comprehensive than the lectures as the students will use them later for self-study. The guest speakers for special lectures will prepare lecture notes outlining recent developments or work done on an important open problem. Effort will be made to provide comprehensive literature survey so that participants may use the notes for self-study. After the school is over, the speakers will be encouraged to revise their notes and send them to the secretary of ATM Schools for posting on the web-pages of the schools.
Peer Review Ratings Overall Rating: This site provides written explanations (in .pdf format) as well as flash videos demonstrating many uses of the TI-83 or TI-83+ graphing calculator. The keystrokes given in the written explanations and almost all of the keystrokes given in the videos can also be used for the TI-83+ Silver Edition, TI-84+, and TI-84+ Silver Edition. The following calculator topics are addressed: order of operations, graphing, setting the viewing window, solving linear equations, solving linear inequalities, solving three-part inequalities, finding x and y intercepts, creating tables, finding the line of best fit, solving systems of equations using matrices, finding the local maxima and minima, using the numeric solver, evaluating functions, graphing piecewise-defined functions, creating a scatter diagram, and statistical calculations. Learning Goals: This site provides written and video explanations of many uses of the TI-83 or TI-83+ graphing calculators. The topics covered range from algebra to basic statistical concepts. The written content is presented in .pdf format for easy printing and the videos are delivered through Flash videos. Recommended Uses: This site can be used as a resource for students to learn or refresh their understanding of how to use the TI-83 or TI-83 Plus graphing calculator for algebraic and statistical concepts. Technical Requirements: Adobe Acrobat Reader is needed to view .pdf files. A Flash plug-in is needed if the latest version of Internet Explorer is not being used. Evaluation and Observation Content Quality Rating: Strengths: This site provides both written and video explanations of content that appeal to all learning styles. In the videos and written instructions, algebraic explanations are given, when applicable, alongside the instructions for the utilization of the graphing calculator. In the video instruction, an actual image of the TI-83 is shown. There is a cursor that points to buttons that are pressed and comments that are presented in the left margin. The author's commentaries are synchronized with the moving cursor. The text instructions are well formatted and include color coding that makes it easier to follow. Concerns: Often there is only one example presented for a topic. Potential Effectiveness as a Teaching Tool Rating: Strengths: Because of the clarity of explanation and the incorporation of video explanations, a student with no experience can learn to use the TI-83 or TI-83 Plus graphing calculator. The selected examples are well selected in that they show the student how to accomplish the less intuitive operations of the TI 83 calculator such as graphing piecewise-defined functions. In the text portion, the author points out common mistakes such as using the minus sign when the negative sign should be used. Concerns: The written instructions (.pdf files) cover the keystrokes for the TI-83+ calculator; however, the videos demonstrate a TI-83 calculator. Though almost all keystrokes will be the same for both models, this is not always the case (for example, accessing the matrix menu). Ease of Use for Both Students and Faculty Rating: Strengths: The site has a very simplistic format. Written explanations can be printed for use while the videos are playing. The pace of the video is slow enough for a student to follow and take notes if desired. Concerns: No explanation of how to use the site is given. If the user has a pop-up blocker, then it must be turned off in order to use this site. The calculator is too large for some small computer screens. A note that dial-up users may have to allow the "choppy" play of the video to run first and then select rewind to see the video smoothly would be helpful.
Basic math Basic Mathematics (Vakcode) Course ID SOW-DGCN12 (Studiepunten) Credits 3 (Periode) Scheduled 1st semester, 1 st period Objectives(Doelstelling) The data considered in cognitive neuroscience studies are typically of a considerable complexity: multiple time-series of haemodynamic responses recorded in numerous voxels (fMRI, PET) or electrophysiological activity recorded through many electrode channels (EEG) or sensors (MEG). Both the acquisition and analysis of such data rely on sometimes pretty sophisticated quantitative techniques. Also, increasingly, models for the neurocognitive processes underlying these data are specified at a quantitative level. Consequently, for a basic understanding of data acquisition, analysis and modelling, some minimum amount of mathematical 'literacy' is required. The aim of this course is to provide (or refresh) such a minimal background. Both technical detail and mathematical rigor will be bypassed; instead, focus is on familiarizing the student with the basic mathematical concepts and tools to be encountered in the other courses of the master's programme and possibly to be applied in the second-year research training.
Differentiation Differentiation is the chief chapter in Differential Calculus. It is these concepts which form the basis of entire Calculus. This further helps in the subsequent chapter of Tangents and Normal and Maxima Minima. Normally a dependent variable is expressed in terms of independent variables by means of an equation. Now when we find the differential coefficient of the dependent variable with respect to the independent variable, what we are doing is to try to find out another equation by which the change in the dependent variable (for any infinitesimal change in independent variable) is relatable to the independent variable, whatever be the value of the independent variable. "Differentiation" is one of the easiest and important chapters of Calculus in the Mathematics syllabus of IIT JEE, AIEEE and other engineering examinations. In this section we'll discuss in detail the geometrical significance of differential co-efficient and various ways to carry out the differentiation of different functions. These laws are not only important from the point of view of Mathematics but they are also very useful to a large extent in Physics and Physical Chemistry. The examples based on this are very easy and can be helpful in mastering the topic. The chapter is important not only because it fetches 3-4 questions in most of the engineering examination but also because it is prerequisite to the subsequent chapters of Differential Calculus. Differentiation is important from the perspective of scoring high in IIT JEE as there are few fixed pattern on which a number Multiple Choice Questions are framed on this topic. You are expected to do all the questions based on this to remain competitive in IIT JEE examination. It is very important to master these concepts at early stage as this forms the basis of your preparation for IIT JEE, AIEEE, DCE,EAMCET and other engineering entrance examinations.
For various parts of quant you can read specific books, e.g., books on combinatorics, probability, geometry etc. You don't have to read them all. Only the ones where you feel that you lack understanding of concepts.
Algebra: A Combined Approach, CourseSmart eTextbook, 4th Edition Description Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Algebra: A Combined Approach, Fourth Edition was written to provide students with a solid foundation in algebra and help them effectively transition to their next mathematics course. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success. Table of Contents Chapter R: Prealgebra Review R.1 Factors and the Least Common Multiple R.2 Fractions R.3 Decimals and Percents Chapter 1: Real Numbers and Introduction to Algebra 1.1 Tips for Success in Mathematics 1.2 Symbols and Sets of Numbers 1.3 Exponents, Order of Operations, and Variable Expressions 1.4 Adding Real Number 1.5 Subtracting Real Numbers Integrated Review 1.6 Multiplying and Dividing Real Numbers 1.7 Properties of Real Numbers 1.8 Simplifying Expressions Chapter 2: Equations, Inequalities, and Problem Solving 2.1 The Addition Property of Equality 2.2 The Multiplication Property of Equality 2.3 Further Solving Linear Equations Integrated Review 2.4 An Introduction to Problem Solving 2.5 Formulas and Problem Solving 2.6 Percent and Mixture Problem Solving 2.7 Linear Inequalities and Problem Solving Chapter 3: Graphing Equations and Inequalities 3.1 Reading Graphs and The Rectangular Coordinate System 3.2 Graphing Linear Equations 3.3 Intercepts 3.4 Slope and Rate of Change Integrated Review 3.5 Equations of Lines 3.6 Graphing Linear Inequalities in Two Variables Chapter 4: Systems of Equations 4.1 Solving Systems of Linear Equations by Graphing 4.2 Solving Systems of Linear Equations by Substitution 4.3 Solving Systems of Linear Equations by Addition Integrated Review 4.4 Systems of Linear Equations and Problem Solving Chapter 5: Exponents and Polynomials 5.1 Exponents 5.2 Negative Exponents and Scientific Notation 5.3 Introduction to Polynomials 5.4 Adding and Subtracting Polynomials 5.5 Multiplying Polynomials 5.6 Special Products Integrated Review 5.7 Dividing Polynomials Chapter 6: Factoring Polynomials 6.1 The Greatest Common Factor 6.2 Factoring Trinomials of the Form x2 + bx + c 6.3 Factoring Trinomials of the Form ax2 + bx + c 6.4 Factoring Trinomials of the Form ax2 + bx + c by coupling 6.5 Factoring by Special Products Integrated Review 6.6 Solving Quadratic Equations by Factoring 6.7 Quadratic Equations and Problem Solving Chapter 7: Rational Expressions 7.1 Simplifying Rational Expressions 7.2 Multiplying and Dividing Rational Expressions 7.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator 7.4 Adding and Subtracting Rational Expressions with Different Denominators 7.5 Solving Equations Containing Rational Expressions Integrated Review 7.6 Proportions and Problem Solving with Rational Equations 7.7 Simplifying Complex Fractions Chapter 8: Graphs and Functions 8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines 8.2 Introduction to Functions 8.3 Polynomial and Rational Functions Integrated Review 8.4 Interval Notation, Finding Domains and Ranges from Graphs and Graphing Piecewise-Defined Functions 8.5 Shifting and Reflecting Graphs of Functions Chapter 9: Systems of Equations and Inequalities and Variation 9.1 Solving Systems of Linear Equations in Three Variables and Problem Solving 9.2 Solving Systems of Equations Using Matrices Integrated Review 9.3 Systems of Linear Inequalities Variation and Problem Solving Chapter 10: Rational Exponents, Radicals, and Complex Numbers 10.1 Radical Expressions and Radical Functions 10.2 Rational Exponents 10.3 Simplifying Radical Expressions 10.4 Adding, Subtracting, and Multiplying Radical Expressions 10.5 Rationalizing Numerators and Denominators of Radical Expressions Integrated Review 10.6 Radical Equations and Problem Solving 10.7 Complex Numbers Chapter 11: Quadratic Equations and Functions 11.1 Solving Quadratic Equations by Completing the Square 11.2 Solving Quadratic Equations by Using the Quadratic Formula 11.3 Solving Equations by Using Quadratic Methods Integrated Review 11.4 Nonlinear Inequalities in One Variable 11.5 Quadratic Functions and Their Graphs 11.6 Further Graphing of Quadratic Functions Chapter 12: Exponential and Logarithmic Functions 12.1 The Algebra of Functions 12.2 Inverse Functions 12.3 Exponential Functions 12.4 Exponential Growth and Decay Functions 12.5 Logarithmic Functions Integrated Review 12.6 Properties of Logarithms 12.7 Common Logarithms, Natural Logarithms, and Change of Base 12.8 Exponential and Logarithmic Equations and Problem Solving Chapter 13: Conic Sections 13.1 The Parabola and the Circle 13.2 The Ellipse and the Hyperbola Integrated Review 13.3 Solving Nonlinear Systems of Equations 13.4 Nonlinear Inequalities and Systems of Inequalities Appendices A Transition Review: Exponents, Polynomials, and Factoring Strategies B. Transition Review: Solving Linear and Quadratic Equations C. Sets and Compound Inequalities D. Absolute Value Equations and Inequalities E. Determinants and Cramer's Rule F. Review of Angles, Lines, and Special Triangles G. Stretching and Compressing Graphs of Absolute Value Functions H. An Introduction to Using a Graphing Utility Student Resources Study Skills Builders Bigger Picture Study Guide Outline Practice Final Exam Answers to Selected Ex
Category Archives: TI-84 Lessons The table feature allows you to quickly scroll the an x vs. y chart on your TI-84. This lesson demonstrates how the table can be used from beginning algebra graphs to finding a limit in calculus
focus in ALGEBRA: INTRODUCTORY & INTERMEDIATE is on you, the student. You are encouraged to be active participants both in the classroom and in your own studies as you work through the How To examples and the paired Examples and You Try It problems. The role of "active participant" is crucial to your success. ALGEBRA: INTRODUCTORY & INTERMEDIATE presents worked examples, and then provides you with the opportunity to immediately work similar problems, helping to build your confidence and eventually master the concepts. This simple framework, known as the Aufmann Interactive Method (AIM) is the foundation for your success. All lessons, exercise sets, tests, and supplements are organized around a carefully-constructed hierarchy of objectives. This "objective-based" approach helps you clearly organize your thoughts around the content making the pages easier for you to follow
iv. Differentiation from first Principles for x squared, integral of x and cosine x v. Implicit differentiation Brendan GuildeaVideo eLesson(31min)Exam Questions & Answers(19min)(3897 views)Calculus - Differentiation II View Topic »This RevisionPack guides you through worked solutions to example questions that include: - Standard derivatives (including exp and ln) - Using product and quotient rules with the chain rule - Working with the root of natural logarithms (e) - Second derivatives - Parametric equations of a curve This RevisionPack guides you through worked solutions to example questions that include: - Standard derivatives (including exp and ln) - Using product and quotient rules with the chain rule - Working with the root of natural logarithms (e) - Second derivatives - Parametric equations of a curve Brendan GuildeaVideo eLesson(29min)Exam Questions & Answers(27min)(3378 views)Calculus - Differentiation III View Topic »Topics dealt with in this pack include: 1. using the Newton-Raphson formula to find approximate roots 2. The addition rule from first principles 3. Finding maximum, minimum and inflection points, plus their applications 4. How to graph a curve with no turning points and find its asympotes The pack includes solutions to some of the most challenging questions on Math Paper I higherTopics dealt with in this pack include:
Buy PDF List price: $49.95 Our price: $45.99 You save: $3.96 (8%) The essential guide to MATLAB as a problem solving tool This text presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. Stressing the importance of a structured
0764113607 9780764113604. Readers follow along and learn to solve many different problems that can be reduced to triangular diagrams. They learn the laws of sine and cosine, trigonometric functions and inverse functions, waves, conic sections, polynomial approximation, and much more. The book is filled with instructive exercises and their solutions, plus illustrative drawings, graphs, and diagrams. This new edition contains updated coverage on using graphing calculators and computer spreadsheets for solving trigonometric problems. «Show less.... Show more» Rent Trigonometry 3rd Edition today, or search our site for other Downing Trigonometry
For courses in data mining. Thorough in its coverage from basic to advanced topics, this text presents the algorithms and techniques used in data mining. It introduces readers to various data mining concepts and algorithms. Introduction to Data Mining presents fundamental concepts and algorithms for those learning data mining for the first time. Each concept is explored thoroughly and supported with numerous examples. The text requires only a modest background in mathematics. Each major topic is organized ...
By testing expert Mike Bryon, How to Pass Advanced Numeracy Tests provides a wealth of practice questions and detailed explanations to boost your ability in a range of numeracy assessment tests. With over 500 practice questions and four realistic tests, it is ideal for graduate and management level candidates who want to revise the basics and progress... more... in which to tackle both simple and complex conceptsThe Clemsons' clear and readable book takes the reader from debates about how children learn and what children know and can do when they start school; through to a discussion of how mathematics can be managed, assessed and evaluated in the school and classroom. Linking these two parts of the book is a section on the subject of mathematics itself, from... more... Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and,... more...
Fall Start Math Skills Self-Assessment (UPDATED AS OF AUGUST 8th, 2011: Summer Start students should view the information at the bottom of the page) UPDATED AS OF JULY 28th, 2011 Your core course faculty requires that you be proficient in certain math skills before you begin the program. The Math Self-Assessment will help you to assess your skills in this area. The Math Workshop is designed for you to learn or refresh your skills in order to help you be as prepared as possible for your first year's core courses. Math Skills Requirement For the economics, statistics, and finance core courses, you will need to be proficient in: We strongly advise you to study and/or review these self-study materials before you start your core classes at Stern as your professors will assume that you have this knowledge, and many of the concepts that you will be learning will rely on these skills. Your Core Course Faculty has created a 20 question Math Skills Self-Assessment to help you assess your skills in this area. It should take you between 20-45 minutes to complete. We ask that you take the self-assessment before arriving at Stern. Use the Answer Key to score your exam to learn your results. Your results will be a good indicator as to whether you need to take the Math Workshop. Note: the in-class Math Assessment that was originally scheduled for August 25th has been canceled, and this Self-Assessment has replaced the in-class exam. This workshop is designed to help you refresh or learn the required Math Skills so that you are best prepared for your first year core classes. Professor Avi Giloni will conduct an 8 hour Math Workshop during Launch 2011 (formerly Pre-Term) on these skills. The cost of the workshop is $350. Once you register, your Bursar account will be charged. The deadline to register is Wednesday, August 17, 2011.
Starting from governing differential equations, a unique and consistently weighted residual approach is used to present advanced topics in finite element analysis of structures, such as mixed and hybrid formulations, material and geometric nonlinearities, and contact problems. This book features a hands-on approach to understanding advanced concepts of the finite element method (FEM) through integrated Mathematica and MATLAB® exercises. Designing structures using composite materials poses unique challenges due especially to the need for concurrent design of both material and structure. Students are faced with two options: textbooks ...
...I look forward to hearing from you.In Algebra 1 students will learn how to identify and do the operations on real numbers. Also, they will learn to know how to solve and graph the linear equations, inequalities and system of two equations and inequalities. In Algebra 2 students will learn how to identify the mathematical concepts such as real and complex numbers as well as absolute value.
This student-friendly textbook for the Statistics 1 Module of A-Level Maths comprehensively covers the Edexcel exam specification. It contains straightforward, accessible notes explaining all the theory, backed up with useful step-by-step examples. There are practice questions throughout the book to test understanding, with recap and exam-style questions at the end of each section (detailed answers to all the questions are included at the back). Finally, there's a CD-ROM containing two complete Statistics 1 practice exam papers - ideal to print out for realistic practice before the final tests
Provides clear, well organized presentation of calculus with applications to engineering and the sciences. Emphasizes the methods and applications of the calculus with some coverage of relevant theory, including functions, limits, continuity, differentiation, integrations in higher dimensions, and line and surface integrals. Pays particular attention to those aspects of calculus that are important in developing effective problem solving methods--often involving estimating errors or constructing numerical approximations. Supplies more thorough treatment of some major topics than most books, such as: comparison tests for improper integrals; use of power series representations for functions; and the relation between linear approximations and differentiation. Also covers elementary transcendental functions, infinite series, Taylor's approximation, polar coordinates, and vectors and three dimensional geometry. [via]
Overview Working through the practice problems in this book and then consulting the detailed solutions will help you understand not only what the correct answer is, but why it is correct and the most efficient way to arrive at the answer. More About This Book Overview Working through the practice problems in this book and then consulting the detailed solutions will help you understand not only what the correct answer is, but why it is correct and the most efficient way to arrive at the
The theory of group representations is a fundamental subject at the intersection of algebra, geometry and analysis, with innumerable applications in other domains of pure mathematics and in the physical sciences: chemistry, molecular biology and physics, in particular crystallography, classical and quantum mechanics and quantum field theory. Topics include: - brisk review of the basic definitions and fundamental results of group theory, illustrated with examples; - detailed study of the group of rotations, the special unitary group in dimension 2 and their representations; - spherical harmonics; - representations of the special unitary group in dimension 3 (roots and weights) with quark theory as a consequence of the mathematical properties of the symmetry group. This book is an introduction to both the theory of group representations and its applications in quantum mechanics. Unlike many other texts, it deals with finite groups, compact groups, linear Lie groups and their Lie algebras, concisely presented in one volume. With only linear algebra and calculus as prerequisites, it is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom or for independent study
Mathematics with Business Applications Chapter 18: Business Math in Action A Virtually Perfect Fit Fashion designers are in a race against time. Seasons change quickly and so do styles, which means designers must constantly come up with fresh ideas that can be worn each season. If a new trend suddenly explodes, designers have to scramble to keep up. They must design new clothes and get them manufactured-fast. Sometimes as little as two or three weeks' lag time in processing customers' orders can mean the difference between making and losing money. The most time-consuming part of the clothing industry is manufacturing the garments. It takes about 27 weeks to have garments made in the Far East, and six weeks in the U.S. The finished garments are shipped to distribution centers, and from there they are trucked to retail stores across the nation. When the clothing finally lands at your local store, it must be unpacked, priced, security tagged, and finally folded or placed on hangers. One way to shortcut the process is to deliver garments directly to consumers, bypassing the store altogether. In the past, companies did this through mail-order catalogues. When the Internet became popular in the 1990s, stores could advertise their clothing online as well as in catalogues. Ideally, shopping for clothes online would be more dynamic and interactive than looking at catalogues. Above all, clothing sites might be able to overcome the biggest problem with mail-order clothes: getting the size right without being able to try on the garment. Enter the virtual dressing room. Virtual dressing technology allows you to create a virtual self by entering your weight, height, and other dimensions. A model based on these dimensions will then show you how a piece of clothing will look on your body type. You can view how long a jacket might hang or how the neckline of a sweater might look on your body as opposed to that of the skinny catalogue model. On some sites, your virtual model will rotate so you can view the item from the side and back as well as the front. It's a big improvement over traditional sizing charts. Still, the virtual dressing room has not solved all the problems of online shopping. About a third of all clothing bought online is returned, usually because the buyer didn't like the way it fit. Consumers also dislike the hassle of having to ship items back to the retailer, and they're frustrated with not being able to judge the quality of the fabric, how it feels, or what its true color is. When a customer returns an item, the retailer must spend more money to have it packaged again for resale. The worst part for retailers is that more than half of all customers who return a garment will never shop at that site again, according to a study by iMarketing News. Lands' End is among the most successful of the online clothing retailers. Its virtual dressing technology has improved the company's online sales, and shoppers who use the program tend to make larger purchases than those who don't. Customized garments, such as monogrammed jackets, account for 40 percent of LandsEnd.com's business. Because bricks-and-mortar retailers (that is, stores you can walk into) don't want to bother with customizing garments, LandsEnd.com was able to fill a consumer need. If other retailers can discover similar niches, they too might find that online sales are worth the risks.
Exploring Algebra VHS Introduce middle school students to more advanced properties of functions and algebra. 3 - 5 VHS $39.95 Equations, Roots & Exponents Mastery DVD A 12-lesson pre-algebra program that teaches selected critical concepts, skills, and problem-solving strategies needed to recognize and work with different types of equations problems. 5 - 8 DVD $39.95 Statistics and Data Analysis in Sports VHS Using only a calculator, a stat book, and some custom equations, a new generation of baseball statisticians believes it's possible to accurately predict a player's true value to his team.
Numerical Mathematics and ComputingAuthors Cheney and Kincaid show students of science and engineering the modern computer's potential for solving numerical problems and gives them ample opportunity to hone their skills in programming and problem solving. The text helps students learn about errors that inevitably accompany scientific computing and arms them with methods for detecting, predicting, and controlling these errors. In this edition a discussion of how to locate codes for numerical algorithms on the World Wide Web has been added. A new section on iterative methods for solving large systems of linear equations has also been added.A less scholarly approach and a different menu of topics sets this book apart from the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, SECOND EDITION.
Representation of real numbers on a line. Complex numbers – basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications. 2.Matrices and Determinants: Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications – Solution of a system of linear equations in two or three unknowns by Cramer's rule and by Matrix Method. Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.
Additional Resources In this workshop you will see how the visual and kinesthetic approach of Hands-On Equations demystifies the learning of algrbra, thereby providing students with a foundation for algebraic thinking and for a traditional Algebra 1 course. Since algebra is the language of mathematics, success with algebra is essential to the further study of mathematics and science.
Main menu Post navigation Calculator Now every gadget – phone, tablet, and even game consoles have a calculator. But what is interesting, in my case, I did when they were not used . In other matters this refers not only to electronic calculators but their notebooks I do not use it, preferring an ordinary paper notebook. Calculators are very different from each other: there are simple functions of calculators, which only multiplication, division, subtraction and addition. There are more "wired" calculators, which can among other things, to build a power, etc. There are also online calculators. Online calculator can save you a lot of time to solve various mathematical problems. In computing any non-trivial engineering problems have a good calculator (even online fit calculator) is necessary. Calculator – a tool for automatic computation. If not at hand or simply engineering mathematics (arithmetic) calculator, you can always use a simple and convenient online calculator. So you can easily calculate the sine (sin), cosine (cos), tangent (tan), the logarithm (log), to build number to a power – all this and more in the online calculator. We know that mathematics (algebra and geometry) as well as other items can not be represented without calculations.
Mathcentre provide this refresher resource for basic differentiation, which has been designed to enable students to prepare for their university mathematics programme. There is a comprehensive review including differentiation of a general power multiplied by a constant, simple fractions and general brackets. Although it has been… Mathcentre provide this numeracy refresher resource, which was developed and trialled by staff of the University of Birmingham Careers Centre and subsequently used widely throughout the HE Sector. There are sections which review decimals, fractions, averages, percentages and ratios, making it a useful resource for Key Stage Three… Mathcentre provide this algebra refresher resource which has been designed to enable students to prepare for their university mathematics programme. There is a comprehensive review of algebraic manipulation including, removing brackets, surds, solving linear equations, transposition of formulae, quadratic equations and completing…
AS/A2 Further Mathematics (level 3) Develop understanding of mathematics and its processes in a way that promotes confidence and fosters enjoyment Develop skills in logical reasoning and recognise incorrect reasoning Develop an understanding of coherence and progression in mathematics and extend your range of skills and techniques Represent real world problems in a mathematical model Is it for me? The course is taken alongside AS/A2 Maths and suits those who have enjoyed and excelled at GCSE Mathematics. Students aiming to pursue Higher Education courses in Mathematics, Physics, Engineering or other courses with a high level of mathematical content should seriously consider this course. Assessment is exam based. What's involved? AS Mechanics 1 This unit uses mathematics to model real world situations. You will study displacement, velocity and acceleration, including motion under gravity in one and two dimensions. Vectors are used to model forces and Newton's Laws of Motion are studied and allow us to model some interesting static and dynamic problems in mechanics. The concept of momentum is introduced to model such things as snooker balls colliding. Further Pure Mathematics 1 This unit extends our understanding of number and it introduces complex numbers. Inequalities involving algebraic fractions are studied. Matrices are introduced and their use in describing and manipulating plane transformations of points and figures is explored. The solutions of trigonometrical equations are extended to general solutions and logarithms are used to reduce relations to a linear form. Decision Mathematics 2 Decision Mathematics is an area that provides practical techniques for solving real-world problems. Critical path analysis involves the representation of compound projects by activity networks and the sequencing of activities to complete projects in the shortest time and use the resources efficiently. Dynamic programming is introduced to find shortest and longest paths through a network and algorithms are also developed to find the maximum flow through a network. Ideas in linear programming are extended to the use of the Simplex method and the Simplex tableau. A2 Further Pure Mathematics 4 All students complete this unit. You will look at geometry in 3 dimensions primarily by studying algebraic structures called vectors and matrices. You will see that these operate in non-intuitive ways and do not behave like normal numbers. The other two units will be selected from the following four units, (with all members of the groups doing the same units), dependent on the interests of the students in the group: Mechanics 2, Statistics 2, Mechanics 3, Further Pure Mathematics 3. Entry Requirements: A minimum of 5 GCSEs at grades A* to C, with: grade A* or A in Maths grade C or above preferred in English Language. Which courses go well with this? This course is only taken with AS Maths. It combines well with all science subjects but especially Physics. Progression: A2 Further Mathematics provides a firm foundation for the more academic mathematical courses offered by most universities.
Subject Guide: Mathematics & Computer Science Welcome! This subject guide is the result of an ongoing collaborative effort between the library and the Mathematics & Computer Science Department to support undergraduate and faculty research needs. Please let us know if there are any significant omissions in the site, and we will do our best to remedy the situation as soon as possible! The Mathematics Department has a reference librarian that specifically focuses on helping the members of the department and the student math majors with any library needs. If you have any questions regarding math resources, ordering math books, math journals available at SU, or need help going about your research, please contact her immediately - she is there to help you! Websites Biographies of Mathematicians Hall of Great Mathematicians: a work in progress. Includes a list of biographies that have been requested but not yet added to the collection. Women in Mathematics: The Women in Math Project of the Department of Mathematics at the University of Oregon in Eugene. Includes biographies of women in mathematics, jobs, grants, scholarship opportunities for women in mathematics, and much more. Calculators and Converters The Calculators-On-Line Center: Links to thousands of on-line calcuators in every area of human endeavor, including beekeeping, fire engine design, and cosmetics. Simon Fraser University: The mandate of the Centre for Experimental and Constructive Mathematics (CECM), a research center within the department of mathematics is "to explore and promote the interplay of conventional mathematics with modern computation and communication in the mathematical sciences." Also at Simon Fraser University: the pi pages, including the history of the computatio of pi, current records of computation, the literature of pi, pi news, pi aesthetics, and pi on the net. Swarthmore College: Numerous pages on various topics in mathematics and in mathematics education at all levels from elementary to college. University of Saint Andrews: "The MacTutor History of Mathematics Archive" has ain index to biographies of mathematicians, an index to "famous curves", index to topics in the history of mathematics, and even a "Mathematicians of the Day" feature that will tell you which famous mathematicians died or were born on the day in question. This is truly a wonderful site for the curious mathematician. University of Tennessee at Knoxville: This site has something for almost everyone: mathematics education at all levels, plus the usual suspects (calculus, algebra, geometry, etc.), plus some outliers (fluid dynamics, art and music). University of Texas at El Paso: This seems to be a commercial site hosted by UTEP. It claims to be "your free resource for math review material from Algebra to Differential Equations". Get help with your homework, referesh your memory, prepare for a test..." Also has a collection of important stuff, such as tables of logarithms, algebraic identities, binomial coefficients, and so on. Perhaps an excellent page for students. Vanderbilt University: The title of this page is "Most common errors in undergraduate mathematics". This page is maintained by a professor at Vanderbilt. In every class he shows his students his collection of common undergraduate mistakes and he tells them how much they will regret it if they commit one or more of these mistakes. Miscellaneous Math Topics: Dozens of links to mathematical sites, including pi, history, measurement, careers, and so on. Maintained by the Eisenhower Ntional Clearinghouse.
Precalculus Functions and Graphs: A Graphing Approach 5e 9780618851508 061885150X Summary: Part of the market-leading "Graphing Approach Series" by Larson, Hostetler, and Edwards, "Precalculus Functions and Graphs: A Graphing Approach," 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.Continuing ...the series' emphasis on student support, the Fifth Edition introduces "Prerequisite Skills Review." For selected examples throughout the text, the "Prerequisite Skills Review" directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.The."New!" The "Nutshell Appendix" reviews the essentials of each function, discussed in the "Library of Functions" feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students."New!" "Progressive Summaries" outline newly introduced topics every three chapters and contextualize them within the framework of the course."New!" "Make a Decision" exercises--extended modeling applications presented at the endof selected exercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data."Updated!" The Library of Functions, threaded throughout the text, defines each elementary function and its characteristics at first point of use. The Fifth Edition incorporates new exercises that tests students' understanding of these functions. All elementary functions are also presented in a summary on the front endpapers of the text for convenient reference."Updated!" The "Chapter Summaries" have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review."Updated!" The "Proofs of Selected Theorems" are now presented at the end of each chapter for easy reference.The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. "Technology Tips" point out the pros and cons of technology use in certain mathematical situations. They also provide alternative methods of solving or checking a problem using a graphing calculator. Students may sometimes be misled by the visuals generated by graphing calculators, so the authors use color to enhance the graphing calculator displays in the textbook, where appropriate. This enables students to visualize concepts accurately and efficiently. "Technology Support" notes appear throughout the text and refer students to the "Technology Support Appendix," where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The "TechnologySupport" notes also direct students to the "Graphing Technology Guide," on the textbook's website, for keystroke support for numerous calculator models.Carefully positioned throughout the text, "Explorations" engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts."What You Should Learn" and "Why You Should Learn It" appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additi
Core Maths for the Biosciences The ideal text for any bioscience student wanting a guide to mathematics for the duration of their degree course. Starting with the essentials, the book covers a wide range of mathematical concepts to which a student might be exposed during the course of a bioscience degree, in a self-contained and consistent presentation. Emphasises the power of computation in solving mathematical problems, reflecting how mathematical tools are applied in biology today. Extensive free online support, including a suite of interactive Excel (R) spreadsheets, encourages hands-on learning, helping students to master even the most challenging concepts. Biological systems are often best explored and explained using the power of maths - from the rate at which enzymes catalyse essential life processes, to the way populations ebb and flow as predators and prey interact. Mathematical tools lie at the heart of understanding biological systems - and mathematical skills are essential for success as a bioscientist. Core Maths for the Biosciences introduces the range of mathematical concepts that bioscience students may encounter - and need to master - during the course of their studies. Starting from fundamental concepts of arithmetic and algebra, the book blends clear explanations and biological examples throughout as it takes the reader towards some of the most sophisticated yet elegant mathematical tools in use by biologists today: differential equations, dynamical systems and chaos theory. Three case studies appear in instalments throughout the text, illustrating the theory: Models of Population Growth, Models of Cancer, and Predator-Prey Relationships. Reflecting the use of maths in modern biology, the book shows how computational approaches are applied to probe biological questions, and makes extensive use of computer support to help readers develop intuitive mathematical skills - both through graph-plotting software, and interactive Excel® workbooks for each chapter. Core Maths for the Biosciences is the ideal course companion as you master the mathematical skills you need to complete your undergraduate studies and will remain a valuable resource at professional and research level. Online Resource Centre The Online Resource Centre to accompany Core Maths for the Biosciences features For registered adopters of the book: Figures from the book in electronic format Solutions to all end of chapter exercises For students: Solutions to half of the end of chapter exercises For PC users, access to FNGraph, the graph-plotting software featured in the book, and associated graph files An extensive range of interactive Excel workbooks, to help you master the concepts presented in the book through hands-on learning - Links to useful learning resources on other web sites Readership: Undergraduates studying biosciences and bioscience-related subjects at degree and foundation level. Postgraduates will also find useful numerical techniques in the Extension sections at the end of most chapters. Martin B. Reed, Department of Mathematical Sciences, University of Bath Dr Martin Reed is a lecturer in the Department of Mathematical Sciences at the University of Bath, and was for the last five years its Director of Teaching. He has taught maths in universities since 1973, both in the UK and overseas (Swaziland, Papua New Guinea, Tanzania); the latter experience has developed his ability to explain subtle concepts in simple, clear language. Prior to his position at Bath, Martin was a member of the Biosciences Department at Brunel University, where he taught core skills to all first year students. Martin's research interests are in numerical methods and optimization. He has lately worked in the field of evolutionary computation, where biological principles such as natural selection and swarm intelligence are used as inspiration for computer algorithms which can solve challenging practical problems. "Exactly the sort of thing that will be helpful in showing those with biological problems how mathematics can be very useful - and that what is really important is maintaining an intuitive understanding between the mathematics - which is essentially no more, but no less, than a way of thinking very precisely - and the actual phenomena they are dealing with...Very fine indeed." - Professor Lord May of Oxford, Department of Zoology, University of Oxford "Fantastic. Easy to understand, interactive, biologically relevant and dictated in a way that seemed as though you are almost having a conversation with the author." - James Sleigh, Student, University of Oxford "Coherent and clear. The best I have seen this kind of material treated." - Stephen Hubbard, University of Dundee "This book is by far the best of its kind, a spectacular diamond in the rough." - Helen Smith, student, University of Salford "The interactive spreadsheets are a work of genius." - Stuart Fisk, student, University of Essex
Extra Examples shows you additional worked-out examples that mimic the ones in your book. These requirements include the benchmarks from the Sunshine State Standards that are most relevant to this course. The benchmarks printed in regular type are required for this course. The portions printed in italic type are not required for this course. Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.
In this section Lifeskills Mathematics New National Qualifications Lifeskills Mathematics sits within the Mathematics curriculum area. Finalised Course and Unit documents are now available for all the new qualifications, from National 2 to Advanced Higher. These documents contain both mandatory information (in the Specifications) and advice and guidance (in the Support Notes). You can download all of these documents for this subject from our download page, using the button below, or use our check-box facility to download a selection of documents. Assessment support materials are also now available for all the new National 2, National 3, National 4 and National 5 qualifications. Information on Course assessment support material (such as Specimen Question Papers and coursework information) is available on the National 5 subject page and, for all National 2 to National 5 qualifications, information on how to access Unit assessment support materials can be found on each subject page. Following the development of these support materials, some documents with mandatory information (Course Assessment Specifications, in particular) have been updated with further information and clarifications. In line with our standard practice, these documents contain version information and, if necessary, a note of changes. This ensures you can recognise the most up-to-date documents. Development process The final documents have been published following a lengthy engagement process. Find out how we got here. Considerable work has been carried out by the Curriculum Area Review Groups (CARGs), the Qualifications Design Teams (QDTs) and Subject Working Groups (SWGs) to develop the final documents. At each stage of the qualification development process, we publish draft documents outlining our proposals and plans. Visit our timeline to find out when the next documents for each qualification will be published. Key points National 3 to National 5 develops confidence and independence in being able to handle information and mathematical tasks in both personal life and in the workplace motivates and challenges learners by enabling them to think through real-life situations involving mathematics has mathematical skills underpinned by numeracy and is designed to develop learners' mathematical reasoning skills relevant to learning, life and work provides opportunities in Units for combined assessment has a hierarchical Unit structure that provides progression from National 2 to National 5 has a test as the added value assessment at National 4, and question papers at National 5 National 2 Lifeskills Mathematics offers opportunities for flexible delivery through the use of Units which can be delivered sequentially, in parallel or in a combined way offers increased opportunities for personalisation, choice and flexibility in Unit assessment, with opportunities for integrated assessment provides increased opportunities for interdisciplinary and cross-curriculum working includes both mathematical operational and reasoning skills in the Units provides an opportunity to use mathematical skills in real-life contexts The Unit titles have been changed to better reflect the Unit content, which has been reorganised. Units, including the National 4 Added Value Unit Outcomes, Assessment Standards and Evidence Requirement statements, have all been revised to increase flexibility. Additional information is provided in the Evidence Requirements for all Units. At National 2, there has been a change of Unit title from Personal Mathematics to Shape, Space and Data to better reflect content. There is now a range of small optional Units, which aims to improve accessibility for learners at this level.
Welcome to Math 126. This is the third quarter of an introductory course in calculus. What makes this course interesting? The use of calculus and its consequences cuts across many disciplines, ranging from biology to business to engineering to the social sciences. At the risk of oversimplifying, calculus provides powerful tools to study "the rate of change." For example, we might want to study how fast a disease is spreading through a population, by studying the "number of diagnosed cases per day". We hope that seeing how calculus can be used to solve real world problems will be interesting. This course first expands upon the idea of linear approximations learned in math 124. You will learn how to make better approximations and to estimate how good these approximations are. Many practical applications of calculus involve functions that depend on more than one variable. You will learn about the geometry of curves and surfaces and get an introduction to differentiation and integration of functions two variables. What makes this course difficult? The hardest thing about calculus is precalculus. The hardest thing about precalculus is algebra. You all know from previous math classes how one course will build upon the next, and calculus is no exception. Math 126 will not only use material from precalculus and algebra, but it will use material you learned in Math 124 and Math 125. Very few of you will go on to major in mathematics or computer science, but most of you will eventually see how calculus is applied in your chosen field of study. For this reason, we aim for ability to solve application problems using calculus. Some of the homework problems are quite lengthy and building up your "mathematical problem solving stamina" is just one of the aims of this course. If you have taken the Math 120 at UW, you know what this all means. If you have not, it means that a large number of "word problems" ("story problems") or "multi-step problems" are encountered in the course. This is one key place Math 126 will differ from a typical high school course. In addition, it is important to note that the ability to apply calculus requires more than computational skill; it requires conceptual understanding. As you work through the homework, you will find two general types of problems: calculation/skill problems and multi-step/word problems. A good rule of thumb is to work enough of the skill problems to become proficient, then spend the bulk of your time working on the longer multi-step problems. Five common misconceptions Misconception #1: Theory is irrelevant and the lectures should be aimed just at showing you how to do the problems. The issue here is that we want you to be able to do ALL problems – not just particular kinds of problems – to which the methods of the course apply. For that level of command, the student must attain some conceptual understanding and develop judgment. Thus, a certain amount of theory is very relevant, indeed essential. A student who has been trained only to do certain kinds of problems has acquired very limited expertise. Misconception #2: The purpose of the classes and assignments is to prepare the student for the exams. The real purpose of the classes and homework is to guide you in achieving the aspiration of the course: command of the material. If you have command of the material, you should do well on the exams. Misconception #3: It is the teacher's job to cover the material. As covering the material is the role of the textbook, and the textbook is to be read by the student, the instructor should be doing something else, something that helps the student grasp the material. The instructor's role is to guide the students in their learning: to reinforce the essential conceptual points of the subject, and to show their relation to the solving of problems. Misconception #4: Since you are supposed to be learning from the book, there's no need to go to the lectures. The lectures, the reading, and the homework should combine to produce true comprehension of the material. For most students, reading a math text won't be easy. The lectures should serve to orient the student in learning the material. Misconception #5: Since I did well in math, even calculus, in a good high school, I'll have no trouble with math at UW. There is a different standard at the college level. Students will have to put in more effort in order to get a good grade than in high school (or equivalently, to learn the material sufficiently well by college standards). How do I succeed? Most people learn mathematics by doing mathematics. That is, you learn it by active participation; it is very unusual for someone to learn calculus by simply watching the instructor and TA perform. For this reason, the homework is THE heart of the course and more than anything else, study time is the key to success in Math 126. We advise an average of 15 hours of study per week, OUTSIDE class. Also, during the first week, the number of study hours will probably be even higher as you adjust to the viewpoint of the course and brush up on precalculus/algebra skills. In effect, this means that Math 126 will be roughly a 20 hour per week effort; the equivalent of a half-time job! This time commitment is in line with the University Handbook guidelines. In addition, it is much better to spread your studying evenly as possible across the week; cramming 15 hours of homework into the day before an assignment is due does not work. Pacing yourself, using a time schedule throughout the week, is a good way to insure success; this applies to any course at the UW, not just math. What is the course format? On Monday, Wednesday and Friday, you will meet with the Instructor for the course in a class of size approximately 160; these classes are each 50 minutes long. On Tuesday and Thursday you will have a 50 minute section of about 40 students run by a TA. During these sections, you will take quizzes and exams, work in small groups on worksheets, and participate in question and answer sessions. The worksheets are designed to lead you through particular ideas related to this course. The TA for the course will circulate around the individual groups to insure everyone is progressing. What resources are available to help me succeed? Calculus is a challenging course and the math department would like to see every one of you pass through with a positive experience. To help, a number of resources are available. Your instructor and TA will be accessible to help you during office hours, which will be announced early the first week of the term. If you are new to the university, you might have the false impression that professors are aloof and hard to approach. Our faculty and TA's make themselves very accessible to help their students and you should not be afraid to ask for advice or help. The math department operates a Math Study Center (MSC), located in B-14 of Communications. This facility is devoted to help students in our freshman math courses only. The center has extensive hours of operation that will be announced the first week of class. The MSC is staffed by advanced undergraduate and graduate students who can help you with difficulties as you work through the course. In addition, many faculty hold office hours there as well. One useful piece of advice: The MSC is often overcrowded the day before homework is due; this is another good reason to spread your study time out over the week. Some students use the MSC as a place to meet a small group of fellow students in the course and work through problems together. Explaining solutions to one another is often the best way to learn. A large amount of material is available on line (including old quizzes, midterms, finals and worksheets) at
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Math Algebra 1 Algebra is the branch of mathematics concerned with representing numbers and ideas with symbols. Students have been using symbols for many years, but this is the first course that is entirely about algebra. All year, students will create and solve equations using many methods: trial-and-error, algebraic manipulation, tables, graphs and technology (computers and calculators). Students learn many new concepts but will focus on linear equations, quadratic equations, polynomials, systems of linear equations, exponential equations, and probability distributions. Many "real-world" examples are used, so that students can see how the math applies to jobs, science, and other academic subjects; this course starts to prepare students for these areas of study. Graphing calculators will be used in the classroom, but students are not expected to purchase one. Algebra 2 In Advanced Algebra, students become better at understanding the concepts of algebra. Mostly, students study functions: Linear equations in one variable; Systems of linear equations in several variables; Matrices; Quadratic functions; Power functions; Root functions; Exponential functions; Logarithms and logarithmic functions; Trigonometric functions; And polynomials. Conic sections (circles, ellipses, hyperbolas…) are also studied. Arithmetic and geometric series are introduced in this course, and statistics are studied in more detail than before. Technology is integrated throughout the curriculum. Graphing calculators are used extensively as visualization tools, and as symbolic manipulators to expedite algebraic computations, or to check answers arrived at by paper-and-pencil means. There will be many problems that students cannot solve without graphing calculators (like problems involving matrices). Students are required to own a graphing calculator because they are used so much. Applied Mathematics Applied Mathematics helps students to develop mathematically by engaging them in hands-on, open-ended, context-rich explorations that incorporate authentic data and the use of real-worlds tools, particularly the tools of technology. Through study mathematics from an applied perspective, students learn to see mathematics as a powerful set of processes, models and skills that can be used to solve non-routine problems, both in and out of the classroom. Students are asked to take the initiative and are given the latitude to explore. Geometry Graphing Calculators: Helpful, but not required in this course. (TI-84 plus Silver Edition is recommended.) In this course, we will use traditional methods and interactive, electronic resources like Geogebra to learn about the geometry of plane figures. Initial topics that will be covered will include parallel and perpendicular lines, triangles (congruent and otherwise), and other types of polygons. Students will be introduced to inductive reasoning using Geogebra, then they will learn to formalize their findings using deductive logic and formal proof. Geogebra will continue to be an especially powerful tool to help us examine the geometries of similarity and transformations – reflections, rotations, translations, dilations, and compositions. Lastly, we will learn about the geometry of 3-Dimensional figures (Surface Area and Volume), as well as the geometry of lines and angles in circles. Pre-Calculus Graphing Calculator: A graphing calculator is required for this course. (TI-84 plus Silver Edition is recommended.) Precalculus is a course designed to prepare students for the further study of calculus in general, and specifically for AP Calculus AB. About half of the course consists of a further study of functions, including polynomial, rational, power, and exponential functions, as well as their inverses, including logarithmic functions. The other half of the course will consist of a further study of trigonometry, including trigonometric identities, relationships, and graphs of the six trigonometric functions and their inverses. Graphing calculators, interactive Geogebra drawings, and other electronic resources will be used in most class sessions to deepen students' understandings of these topics, including function transformations, domain and range, end-behavior, asymptotic behavior, increasing and decreasing intervals, maxima and minima, and real-world problems applying these ideas. Other topics to be addressed are the Binomial Theorem, Synthetic Division & the Rational Root Theorem, elementary matrix and vector operations, parametric equations, and polar coordinates. Some calculus topics will be introduced throughout the year (but not mastered), including limits, continuity, and the average change function. AP Calculus Graphing Calculators: A graphing calculator is required for this course. (TI-84 plus Silver Edition is recommended.) AP Calculus is a course designed to introduce students to differential and integral calculus, and to prepare students for the culminating AP Calculus Exam given the following month of May. The course can be broken into three sections: Limits, Differential Calculus, and Integral Calculus. To begin, students will formally learn about limits, and limiting situations. This will culminate in several forms of the limit-definition of the derivative. In the Differential Calculus section of the course, students will learn about a multitude of differentiating techniques (including the product rule, quotient rule, chain rule, and implicit derivatives) for a multitude of familiar and unfamiliar functions (including polynomial, rational, power, trigonometric, exponential, and combination functions). Calculus techniques will be used to work on real-world applications, including kinematic problems (position, velocity, and acceleration), problems involving related rates, problems involving maxima and minima, and other applications. In the Integral Calculus section of the course, we will learn about a multitude of anti-differentiation techniques with, again, numerous familiar and unfamiliar functions. Applications of the integral will be introduced as well. Ideally, we will finish the AP Calculus AB syllabus near the end of March, so that we have 4-6 weeks to review topics before the AP Calculus Exam in early in the month of May. After the AP Calculus Exam, we will examine a few other topics and applications of calculus.
The course was designed with the goal that a student completing the course will have a thorough knowledge of the most basic and essential math skills as well as develop skills for critical thinking and problem solving. Throughout this course you will be manipulating numbers in a way that will help you understand how to use them on paper as well as everyday life. The course is designed to help you realize the importance of mathematics. It is my hope that you will take the skills that you learn and begin to utilize them in your daily life.
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News Further Mathematics Why choose Further Mathematics A/AS Level? 'The highest form of pure thought is in mathematics.' (Plato) Further mathematics will extend your mathematical knowledge and understanding. It is an enjoyable and rewarding subject and explores new concepts and ideas to a high level. It provides an additional challenge for any students who enjoy maths and are confident in their ability in the subject. It develops students' understanding of mathematical processes and enables them to model real life problems. Your modules The course develops skills in four areas of mathematics; pure maths, statistics, mechanics and decision mathematics. Pure maths extends the core maths covered at A level, whilst introducing new topics such as complex numbers. Statistics and mechanics also extends the concepts covered at A level, while decision maths studies algorithms and networks. On your marks... Year 12 Raw Score Max Mark UMS Examination Decision 1 75 100 1.5hr Calc Decision 2 75 100 1.5hr Calc Further Pure 1 75 100 1.5hr Calc Year 13 Mechanics 2 75 100 1.5hr Calc Statistics 2 75 100 1.5hr Calc Further Pure 2 75 100 1.5hr Calc Edexcel ( scheme of learning. Click on the following link to access more information on the scheme of learning, formula booklet and support materials: Who takes this course? We advise that anyone who achieves a grade A or above in their GCSE. You must also study Maths A Level as well. What skills will I learn? All sorts of skills, relevant to your life and the other subjects that you study: Logical reasoning You will be able to tackle problems mathematically and analyse and refine models that you produce Communication skills, both through written and oral explanations IT skills will improve as you use computer software and graphical calculators Increased responsibility for your own learning and gain a deeper understanding of mathematical problems. What could this lead to in the future/How will this fit into my life? Mathematics and Further Mathematics is one of those subjects that can fit in with many things you may want to do in the future. It is especially vital if you want to study a Mathematics, Physics or Chemistry based course at Higher Education. Further Mathematics is a requirement for most Mathematics degrees. Further Mathematics AS Level is becoming more common as a requirement of Physics, Chemistry or Engineering degrees as well. It is extremely useful for students wishing to pursue a career in engineering or in computer science. What do I do now? Talk to your Mathematics teacher and get some advice as to whether the course could be right for you. Making an appointment to see your school careers advisor is also a good idea.
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MATH 155: Mathematics, A Way of Thinking Course Description:An investigation of topics including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for General Education. Text: Mathematics, One of the Liberal Arts. Miles, Thomas & Nance, Douglas. Brooks/Cole Publishing, 1997. Core Skill Objectives: THINKING SKILLS: The students will ... (a) ... use reasoned standards in solving problems and presenting arguments. COMMUNICATION SKILLS: The students will ... (a) ... read with comprehension and the ability to analyze and evaluate. (b) ... listen with an open mind and respond with respect. LIFE VALUE SKILLS: The students will ... (a) ... analyze, evaluate and respond to ethical issues from an informed personal value system. CULTURAL SKILLS: The students will ... (a) ... understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior. (b) ... demonstrate knowledge of the signs and symbols of another culture. (c) ... participate in activity that broadens their customary way of thinking. AESTHETIC SKILLS: The students will ... (a) ... develop an aesthetic sensitivityCourse Objectives: THINKING SKILLS: The students will ... (a) ... explore writing numbers and performing calculations in various numeration systems. (b) ... solve simple linear algebraic equations. (c) ... explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models. (d) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system. (e) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms. (f) ... explore the basics of probability. (g) ... learn descriptive statistics, including making the connection between probability and the normal distribution table. (h) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations. (i) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course. COMMUNICATION SKILLS: The students will ... (a) ... write a mathematical autobiography. (b) ... collect a portfolio of their work during the course and write a reflection paper. (c) ... do group work (labs and practice exams), involving both written and oral communication. (d) ... turn in written solutions to occasional problems. LIFE VALUE SKILLS: The students will ... (a) ... develop an appreciation for the intellectual honesty of deductive reasoning. (b) ... understand the need to do one's own work, to honestly challenge oneself to master the material. CULTURAL SKILLS: The students will ... (a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples. (b) ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages". (c) ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry. AESTHETIC SKILLS: The students will ... (a) ... develop an appreciation for the austere intellectual beauty of deductive reasoning. (b) ... develop an appreciation for mathematical elegance. This course is aimed at the needs of elementary education majors and as such is the first part of a three-course, 12-credit sequence (MATH 155-255-355). This is a "content" course rather than a "methods" course (teaching methods are addressed in the latter two courses in the above sequence). It is what people generally call a "Liberal Arts Mathematics Course", meaning that it covers a wide variety of topics, has an emphasis on problem solving, and uses a historical and humanistic approach. Consequently, the course is considered appropriate for the general education requirements and is open to all students. There will be a few assignments not generally included in a mathematics course, but which will, I hope, make your experience in this class more well-rounded than in a typical algebra course. These include the following: Mathematical Autobiography: Due: Monday, September 13. Point value: 25. This will be a 3-5 page paper in which you explore your life as a math student. I think it is especially appropriate for education majors to reflect on your past mathematical life, and to consider what methods and styles worked for you in the classrooms throughout your K-12 career. Try to be specific and try not to make this a "blame the teacher" paper. Portfolio: Due: Friday, December 10. Point value: 40. It is important to an artist or a photographer to assemble a "portfolio", a collection of their work which is representative of their skills and interests. The same is true for a student of mathematics. During this course you will be working many problems, some of which will be "breakthrough" efforts, when you finally understood how to do something or which you are proud of because your write-up was so well done. You will choose FIVE problems along the way which you want to include in your portfolio; for each of these problems you will include a nicely organized re-write of the problem along with a brief reflection paper on why you chose that particular problem and on what you learned from the problem. Each of the five problems (the write-up and the reflection paper combined) will be worth 8 points. I expect at least one page for each problem. Group Labs: At a number of points during the course you will be working on a "lab" in small groups. I believe that students learn in a variety of ways, and that while studying alone can be valuable, for many working on problems in small groups can enhance student learning significantly. Even though you will be working in a group of three or four people, each person should turn in a paper; I want to see each person's expression of the solutions to the problems - and if you each get a graded paper back it will give you something to study from. It is important that each person contributes their input into these labs. I will randomly assign groups, although I am willing to consider rearranging them as time passes, when, for example, a student drops the course. It happens. The grading procedure is quite straight-forward. "A" = 90% or more of total possible points, "AB" = 87% or more, "B" = 80% or more, "BC" = 77% or more, "C" = 70% or more, "CD" = 67% or more, and "D" = 60% or more. We will probably end up with about 800 possible points. My advice is simple: if you wish to earn a decent grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. I find that the surest way to receive less than a "C" is to make sure you miss some classes and fail to turn in all your work! Attendance is important in this class. There is really never a "good day" to miss because we will either be covering new material or working in groups on some problems. I will not formally reduce your grade for poor attendance, but I will take attendance throughout the course so that I can apply the 2-day rule when we take those practice exams (see above). I can also tell you that poor attendance is one of the best ways to hurt you overall chances of success. Late assignments is also something you should avoid. For one thing, if I am going to be able to get your work graded in a timely fashion so that it will do you some good for study purposes, you need to get it turned in on time. Another reason is that since we will be moving from one topic to the next, it is important that you are not spending your time doing work you should have done a week or two earlier instead of focusing on what we are doing at the moment. Therefore, I have a rule on late assignments: 10% of the total point value of a given assignment will be subtracted from your score for each of the first 3 days past the due date. Beyond 3 class periods, I will no longer accept late work. In general it is better to turn in work even if it is not entirely finished than to hold on to it. Final Comments: I believe firmly that you as the student are the learner, and that
Motivating readers by making maths easier to learn, this work includes complete past exam papers and student-friendly worked solutions which build up to practice questions, for all round exam preparation. It also includes a Live Text CDROM which features fully worked solutions examined step-by-step, and animations for key learning points. Engineering A Level covers each of the compulsory AS and A2 units from Edexcel in a dedicated chapter. Full coverage is given to the three units required at AS Level, and the 3 additional A2 units required for completion of the A Level award. Students following the GCE courses will find this book essential reading, as it covers all the material they will be following through the duration of their study. Knowledge-check questions and activities are included throughout, along with learning summaries, innovative 'Another View' features, and applied maths integrated alongside the appropriate areas of engineering study. All examples relate directly (and exclusively) to engineering practice, to emphasise application of theory in real-world engineering contexts. for students of a wide range of abilities, especially for those who find the theoretical side of mathematics difficult. This course aims to provide a basis for Maths for the Artist that says If Id known Maths would have been central to effects and animation I would have paid attention in school! so you can understand the principles and approaches we use maths for everyday in production and post. This short course hopes to give you all the maths you need for day-to-day life. After completing the course, you should never again have to say either to yourself or to someone else, "I wish I could do that, but I'm no good at figures." The Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. ... For some people, the opportunities to use maths in everyday situations are opportunities that are best avoided. This text is aimed at teaching you all the maths you need to know for everyday living including: how to work with numbers; how to change between different types of measurements; understanding fractions, decimals and percentages; how to make sense of simple graphs and tables; and using maths at work, shopping and around the home. Whilst suitable for complete beginners, this book progresses steadily to a more complex level and is also designed to enable parents to help their children with maths problems. Some games and puzzles are included throughout the text. This course aims to provide a basis for Maths for the Artist that says "If I'd known Maths would have been central to effects and animation I would have paid attention in school!" - so you can understand the principles and approaches we use maths for everyday in production and post.
The best selling 'Algorithmics' presents the most important, concepts, methods and results that are fundamental to the science of computing. It starts by introducing the basic ideas of algorithms, including their structures and methods of data manipulation. It then goes on to demonstrateThis book is a concise introduction to the key mathematical ideas that underpin computer science, continually stressing the application of discrete mathematics to computing. It is suitable for students with little or no knowledge of mathematics, and covers the key concepts in a simple and stra...
30 Common Street, Watertown MA 02472 Math Department -- Grades 6-12 The Watertown Public Schools Math Department strives to bring every student to their mathematical potential by providing a rigorous and comprehensive curriculum complemented by teacher support and technology. Students are offered multiple paths for four years of mathematics, all designed for mathematical success in post-high school programs. Support is available in many forms, including a Math Lab open all periods, as well as access to teachers both before and after school. Students will be expected to bring their own calculator to every math class. For classes up to Pre-Calculus, a scientific calculator will suffice. We are supporting the TI-30XS MultiView (TM). Pre-calculus students may use a scientific calculator or graphing calculator. Calculus and Statistics students at all levels must bring a graphing calculator with them daily. We are using TI-83+ and TI-84 series (regular, Plus and Silver Edition) graphing calculators. Text Book Companion Sites Some of our text books at the high school have web sites created by the publishers to help you with your school work. Click on the link below to see if your book is one of them. Want to be student of the month? Work hard, and your picture could grace the WPS Math Department Page. Not everyone can be chosen, but keep on doing your best and maybe, just maybe, you'll make the list.
famous stage actress was once asked if she had ever suffered from stage-fright, and if so how she had gotten over it. She laughed at the interviewer's naive assumption that, since she was an accomplished actress now, she must not feel that kind of anxiety. She assured him that she had always had stage fright, and that she had never gotten over it. Instead, she had learned to walk on stage and perform – in spite of it. Like stage fright, math anxiety can be a disabling condition, causing humiliation, resentment, and even panic. Consider these testimonials from a questionnaire we have given to students in the past several years: When I look at a math problem, my mind goes completely blank. I feel stupid, and I can't remember how to do even the simplest things. I've hated math ever since I was nine years old, when my father grounded me for a week because I couldn't learn my multiplication tables. In math there's always one right answer, and if you can't find it you've failed. That makes me crazy. Math exams terrify me. My palms get sweaty, I breathe too fast, and often I can't even make my eyes focus on the paper. It's worse if I look around, because I'd see everybody else working, and know that I'm the only one who can't do it. I've never been successful in any math class I've ever taken. I never understand what the teacher is saying, so my mind just wanders. Some people can do math – not me! What all of these students are expressing is math anxiety, a feeling of intense frustration or helplessness about one's ability to do math. What they did not realize is that their feelings about math are common to all of us to some degree. Even the best mathematicians, like the actress mentioned above, are prone to anxiety – even about the very thing they do best and love most. In this essay we will take a constructive look at math anxiety, its causes, its effects, and at how you as a student can learn to manage this anxiety so that it no longer hinders your study of mathematics. Lastly, we will examine special strategies for studying mathematics, doing homework, and taking exams. Let us begin by examining some social attitudes towards mathematics that are especially relevent. magine that you are at a dinner party, seated with many people at a large table. In the course of conversation the person sitting across from you laughingly remarks, "of course, I'm illiterate . . . !" What would you say? Would you laugh along with him or her and confess that you never really learned to read either? Would you expect other people at the table to do so? Now imagine the same scene, only this time the guest across from you says, "of course, I've never been any good at math . . . !" What happens this time? Naturally, you can expect other people at the table to chime in cheerfully with their own claims to having "never been good at math" – the implicit message being that no ordinary person ever is. The fact is that mathematics has a tarnished reputation in our society. It is commonly Poor teaching leads to the inevitable idea that the subject (mathematics) is only adapted to peculiar minds, when it is the one universal science, and the one whose ground rules are taught us almost in infancy and reappear in the motions of the universe. – H.J.S. Smith accepted that math is difficult, obscure, and of interest only to "certain people," i.e., nerds and geeks – not a flattering characterization. The consequence in many English-speaking countries, and especially in the United States, is that the study of math carries with it a stigma, and people who are talented at math or profess enjoyment of it are often treated as though they are not quite normal. Alarmingly, many school teachers – even those whose job it is to teach mathematics – communicate this attitude to their students directly or indirectly, so that young people are invariably exposed to an anti-math bias at an impressionable age. It comes as a surprise to many people to learn that this attitude is not shared by other societies. In Russian or German culture, for example, mathematics is viewed as an essential part of literacy, and an educated person would be chagrined to confess ignorance of basic mathematics. (It is no accident that both of these countries enjoy a centuries-long tradition of leadership in mathematics.) Students must learn that mathematics is the most human of endeavors. Flesh and blood representatives of their own species engaged in a centuries long creative struggle to uncover and to erect this magnificent edifice. And the struggle goes on today. On the very campuses where mathematics is presented and received as an inhuman discipline, cold and dead, new mathematics is created. As sure as the tides. – J.D. Phillips Our jaundiced attitude towards mathematics has been greatly exacerbated by the way in which it has been taught since early in this century. For nearly seventy years, teaching methods have relied on a behaviorist model of learning, a paradigm which emphasizes learning-by-rote; that is, memorization and repetition. In mathematics, this meant that a particular type of problem was presented, together with a technique of solution, and these were practiced until sufficiently mastered. The student was then hustled along to the next type of problem, with its technique of solution, and so on. The ideas and concepts which lay behind these techniques were treated as a sideshow, or most often omitted altogether. Someone once described this method of teaching mathematics as inviting students to the most wonderful restaurant in the world – and then forcing them to eat the menu! Little wonder that the learning of mathematics seems to most people a dull and unrewarding enterprise, when the very meat of the subject is boiled down to the gristle before it is served. This horror story of mathematics education may yet have a happy ending. Reform efforts in the teaching of mathematics have been under way for several years, The mind is not a vessel to be filled. It is a fire to be kindled. – Plutarch and many – if not all – teachers of mathematics have conscientiously set about replacing the behaviorist paradigm with methods based on constructivist or other progressive models of learning. As yet, however, there remains no widely accepted teaching methodology for implementing these reform efforts, and it may well be that another generation will pass before all students in the primary and secondary grades are empowered to discover the range and beauty of mathematical ideas, free of the stigmas engendered by social and educational bias. Finally, young women continue to face an additional barrier to success in mathematics. Remarkably, even at the start of the 21st century, school-age girls are still discouraged by parents, peers, and teachers with the admonition that mathematics "just isn't something girls do." Before we became teachers, we would have assumed that such attitudes died out a generation ago, but now we know better. Countless of our female students have told how friends, family members, and even their junior and senior high school instructors impressed upon them the undesirability of pursuing the study of mathematics. My own wife (a mathematician) recalls approaching her junior high school geometry teacher after class with a question about what the class was studying. He actually patted her on the head, and explained that she "didn't need to know about that stuff." (And, needless to say, he didn't answer her question.) Rank sexism such as this is only part of the problem. For all adolescents, but especially for girls, there is concern about how one is viewed by members of the opposite sex – and being a "geek" is not seen as the best strategy. Peer pressure is the mortar in that wall. And parents, often even without knowing it, can facilitate this anxiety and help to discourage their daughters from maintaining an open mind and a natural curiosity towards the study of science and math. Together these social and educational factors lay the groundwork for many widely believed myths and misconceptions about the study of mathematics. To an examination of these we now turn. host of common but erroneous ideas about mathematics are available to the student who suffers math anxiety. These have the effect of justifying or rationalizing the fear and frustration he or she feels, and when these myths are challenged a student may feel defensive. This is quite natural. However, it must be recognized that loathing of mathematics is an emotional response, and the first step in overcoming it is to appraise one's opinions about math in a spirit of detachment. Consider the five most prevalent math myths, and see what you make of them: MYTH #1: APTITUDE FOR MATH IS INBORN. This belief is the most natural in the world. After all, some people just are more talented at some things (music and athletics come to mind) and to some degree it seems that these talents must be inborn. Indeed, as in any other field of human endeavor, mathematics has had its share of prodigies. Karl Gauss helped his father with bookkeeping as a small child, and the Indian mathematician Ramanujan discovered deep results in mathematics with little formal training. It is easy for students to believe that doing math requires a math brain, one in particular which they have not got. MATH BRAIN But consider: to generalize from "three spoons, three rocks, three flowers" – to the number "three" – is an extraordinary feat of abstraction, yet every one of us accomplished this when we were mere toddlers! Mathematics is indeed inborn, but it is inborn in all of us. It is a human trait, shared by the entire race. Reasoning with abstract ideas is the province of every child, every woman, every man. Having a special genetic make-up is no more MATH GENES necessary for success in this activity than being Mozart is necessary to humming a tune. Ask your math teacher or professor if he or she became a mathematician in consequence of having a special brain. (Be sure to keep a straight face when you do this.) Almost certainly, after the laughter has subsided, it will turn out that a parent or teacher was responsible for helping your instructor discover the beauty in mathematics, and the rewards it holds for the student – and decidedly not a special brain. (If you ask my wife, on the other hand, she will tell you it was orneriness; she got sick of being told she couldn't do it.) MYTH #2: TO BE GOOD AT MATH YOU HAVE TO BE GOOD AT CALCULATING. Some people count on their fingers. Invariably, they feel somewhat ashamed about it, and try to do it furtively. But this is ridiculous. Why shouldn't you count on your fingers? What else is a Chinese abacus, but a sophisticated version of counting on your fingers? Yet people accomplished at using the abacus can out-perform anyone who calculates figures mentally. Modern mathematics is a science of ideas, not an exercise in calculation. It is a standing joke that mathematicians can't do arithmetic reliably, and I often admonish my students to check my calculations on the chalkboard because I'm sure to get them wrong if they don't. There is a serious message in this: being a wiz at figures is not the mark of success in mathematics. This bears emphasis: a pocket calculator has no knowledge, no insight, no understanding – yet it is better at addition and subtraction than any human will ever be. And who would prefer being a pocket calculator to being human? This myth is largely due to the methods of teaching discussed above, which emphasize finding solutions by rote. Indeed, many people suppose that a professional mathematician's research involves something like doing long division to more and more decimal places, an image that makes mathematicians smile sadly. New mathematical ideas – the object of research – are precisely that. Ideas. And ideas are something we can all relate to. That's what makes us people to begin with. MYTH #3: MATH REQUIRES LOGIC, NOT CREATIVITY. The grain of truth in this myth is that, of course, math does require logic. But what does this mean? It means that we want things to make sense. We don't want our equations to assert that 1 is equal to 2. Logic is the anatomy of thought. – John Locke This is no different from any other field of human endeavor, in which we want our results and propositions to be meaningful – and they can't be meaningful if they do not jive with the principles of logic that are common to all mankind. Mathematics is somewhat unique in that it has elevated ordinary logic almost to the level of an artform, but this is because logic itself is a kind of structure – an idea – and mathematics is concerned with precisely that sort of thing. But it is simply a mistake to suppose that logic is what mathematics is about, or that being a mathematician means being uncreative or unintuitive, for exactly the opposite is the case. The great mathematicians, indeed, are poets in their soul. How can we best illustrate this? Consider the ancient Greeks, such as Pythagoras, who first brought mathematics to the level of an abstract study of ideas. The moving power of mathematics is not reasoning but imagination. – Augustus De Morgan They noticed something truly astounding: that the musical tones most pleasing to the ear are those achieved by dividing a plucked string into ratios of integers. For instance, the musical interval of a "fifth" is achieved by plucking a taut string whilst pressing the finger against it at a distance exactly four-fifths along its total length. From such insights, the Pythagoreans developed an elaborate and beautiful theory of the nature of physical reality, one based on number. And to them we owe an immense debt, for to whom does not music bring joy? Yet no one could argue that music is a cold, unfeeling enterprise of mere logic and calculation. If you remain unconvinced, take a stroll through the Mathematical Art of M.C. Escher. Here is the creative legacy of an artist with no advanced training in math, but whose works consciously celebrate mathematical ideas, in a way that slips them across the transom of our self-conscious anxiety, presenting them afresh to our wondering eyes. MYTH #4: IN MATH, WHAT'S IMPORTANT IS GETTING THE RIGHT ANSWER. If you are building a bridge, getting the right answer counts for a lot, no doubt. Nobody wants a bridge that tumbles down during rush hour because someone forgot to carry the 2 in the 10's place! But are you building bridges, or studying mathematics? Even if you are studying math so that you can build bridges, what matters right now is understanding the concepts that allow bridges to hang magically in the air – not whether you always remember to carry the 2. That you be methodical and complete in your work is important to your math instructor, and it should be important to you as well. This is just a matter of doing what you are doing as well as you can do it – good mental and moral hygiene for any activity. But if any instructor has given you the notion that "the right answer" is what counts most, put it out of your head at once. Nobody overly fussy about how his or her bootlace is tied will ever stroll at ease through Platonic Realms. MYTH #5: MEN ARE NATURALLY BETTER THAN WOMEN AT MATHEMATICAL THINKING. If there is even a ghost of a remnant of a suspicion in your mind about gender making a whit's difference in students' mathematics aptitude, slay the beast at once. Special vigilance is required when it comes to this myth, because it can find insidious ways to affect one's attitude without ever drawing attention to itself. For instance, I've had female students confide to me that – although of course they do not believe in a gender gap when it comes to ability – still it seems to them a little unfeminine to be good at math. There is no basis for such a belief, and in fact a sociological study several years ago found that female mathematicians are, on average, slightly more feminine than their non-mathematician counterparts. Sadly, the legacy of generations of gender bias, like our legacy of racial bias, continues to shade many people's outlooks, often without their even being aware of it. It is every student's, parent's, and educator's duty to be on the lookout for this error of thought, and to combat it with reason and understanding wherever and however it may surface. Across the centuries, from Hypatia to Amalie Nöther to thousands of contemporary women in school and university math departments around the globe, female mathematicians have been and remain full partners in creating the rich tapestry of mathematics. For outstanding web sites with information about historical and contemporary women in mathematics, check the subject index in the "biography" section of the Math Links Library. ven though all of us suffer from math anxiety to some degree – just as anyone feels at least a little nervous when speaking to an audience – for some of us it is a serious problem, a burden that interferes with our lives, preventing us from achieving our goals. The first step, and the one without which no further progress is possible, is to recognize that math anxiety is an emotional response. (In fact, severe math anxiety is a learned emotional response.) As with any strong emotional reaction, there are constructive and unconstructive ways to manage math anxiety. Unconstructive (and even damaging) ways include rationalization, suppression, and denial. By "rationalization," we mean finding reasons why it is okay and perhaps even inevitable – and therefore justified – for you to have this reaction. The myths discussed above are examples of rationalizations, and while they may make you feel better (or at least less bad) about having math anxiety, they will do nothing to lessen it or to help you get it under control. Therefore, rationalization is unconstructive. By "suppression" is meant having awareness of the anxiety – but trying very, very hard not to feel it. I have found that this is very commonly attempted by students, and it is usually accompanied by some pretty severe self-criticism. Students feel that they shouldn't feel this anxiety, that it's a weakness which they should overcome, by brute force if necessary. When this effort doesn't succeed (as invariably it doesn't) the self-criticism becomes ever harsher, leading to a deep sense of frustration and often a severe loss of self-esteem – particularly if the stakes for a student are high, as when his or her career or personal goals are riding on a successful outcome in a math class, or when parental disapproval is a factor. Consequently, suppression of math anxiety is not only unconstructive, but can actually be damaging. Finally, there is denial. People using this approach probably aren't likely to see this essay, much less read it, for they carefully construct their lives so as to avoid all mathematics as much as possible. They choose college majors, and later careers, that don't require any math, and let the bank or their spouse balance the checkbook. This approach has the advantage that feelings of frustration and anxiety about math are mostly avoided. However, their lives are drastically constrained, for in our society fewer than 25% of all careers are, so-to-speak, "math-free," and thus their choices of personal and professional goals are severely limited. (Most of these math-free jobs, incidentally, are low-status and low-pay.) People in denial about mathematics miss out on something else too, for the student of mathematics learns to see aspects The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. It is written in the language of mathematics. – Galileo of the structure and beauty of our world that can be seen in no other way, and to which the "innumerate" necessarily remain forever blind. It would be a lot like never hearing music, or never seeing colors. (I understand that some people have these disabilities – but they didn't choose to have them.) Okay, so what is the constructive way to manage math anxiety? I call it "taking possession." It involves making as conscious as possible the sources of math anxiety in one' own life, accepting those feelings without self-criticism, and then learning strategies for disarming math anxiety's influence on one's future study of mathematics. (These strategies are explored in depth in the next section.) Begin by understanding that your feelings of math anxiety are not uncommon, and that they definitely do not indicate that there is anything wrong with you or inferior about your ability to learn math. For some this can be hard to accept, but it is worth trying to accept – since after all it happens to be true. This can be made easier by exploring your own "math-history." Think back across your career as a math student, and identify those experiences which have contributed most to your feelings of frustration about math. For some this will be a memory of a humiliating experience in school, such as being made to stand at the blackboard and embarrassed in front of one's peers. For others it may involve interaction with a parent. Whatever the principle episodes are, recall them as vividly as you are able to. Then, write them down. This is important. After you have written the episode on a sheet(s) of paper, write down your reaction to the episode, both at the time and how it makes you feel to recall it now. (Do this for each episode if there is more than one.) After you have completed this exercise, take a fresh sheet of paper and try to sum up in a few words what your feelings about math are at this point in your life, together with the reason or reasons you wish to succeed at math. This too is important. Not until after we lay out for ourselves in a conscious and deliberate way what our feelings and desires are towards mathematics, will it become possible to take possession of our feelings of math anxiety and become free to implement strategies for coping with those feelings. At this point it can be enormously helpful to share your memories, feelings, and goals with others. In a math class I teach for arts majors, I hand out a questionnaire early in the semester asking students to do exactly what is described above. After they have spent about twenty minutes writing down their recollections and goals, I lead them in a classroom discussion on math anxiety. This process of dialogue and sharing – though it may seem just a bit on the goopy side – invariably brings out of each student his or her own barriers to math, often helping these students become completely conscious of these barriers for the first time. Just as important, it helps all my students understand that the negative experiences they have had, and their reactions to them, are shared one way or another by almost everyone else in the room. If you do not have the opportunity to engage in a group discussion in a classroom setting, find friends or relatives whom you trust to respect your feelings, and induce them to talk about their own experiences of math anxiety and to listen to yours. Once you have taken possession of your math anxiety in this way, you will be ready to implement the strategies outlined below. athematics, as a field of study, has features that set it apart from almost any other scholastic discipline. On the one hand, correctly manipulating the notation to calculate solutions is a skill, and as with any skill mastery is achieved through practice. On the other hand, such skills are really only the surface of mathematics, for they are only marginally useful without an understanding of the concepts which underlie them. The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver. – I.N. Herstein Consequently, the contemplation and comprehension of mathematical ideas must be our ultimate goal. Ideally, these two aspects of studying mathematics should be woven together at every point, complementing and enhancing one another, and in this respect studying mathematics is much more like studying, say, music or painting than it is like studying history or biology. In view of mathematics' unique character, the successful student must devise a special set of strategies for accomplishing his or her goals, including strategies for lecture taking, homework, and exams. We will examine each of these in turn. Keep in mind that these strategies are suggestions, not laws handed down from the mountain. Each student must find for him or herself the best way to implement these ideas, fitting them to his or her own unique learning styles. As the Greek said, know thyself! TAKING LECTURES. Math teachers are a mixed bag, no question, and it's easy to criticize, especially when the criticism is justified. If your own math teacher really connects with you, really helps you understand, terrific – and be sure to let him or her know. But if not, there are a couple of things you will want to keep in mind. To begin with, think what the teacher's job entails. First, a textbook must be chosen, a syllabus prepared, and the material being taught (which your teacher may or may not have worked with in some time) completely mastered. This is before you ever step into class on that first day. Second, for every lecture the teacher gives, there is at least an hour's preparation, writing down lecture notes, thinking about how best to present the material, and so on. This is on top of the time spent grading student work – which itself can be done only after the instructor works the exercises for him or herself. Finally, think about the anxiety you feel about speaking to an audience, and about your own math anxiety, and then imagine what a math teacher must do: manage both kinds of anxiety simultaneously. It would be wonderful if every instructor were a brilliant lecturer. But even the least brilliant deserves consideration for the difficulty of the job. The second thing to keep in mind is that getting the most out of a lecture is your job. Many students suppose that writing furiously to get down everything the instructor puts on the board is the best they can do. Unfortunately, you cannot both write the details and focus on the ideas at the same time. Consequently, you will have to find a balance. Particularly if the instructor is lecturing from a set text, it may be that almost everything he or she puts on the board is in the text, so in effect it's written down for you already. In this case, make some note of the instructor's ideas and commentary and methods, but make understanding the lecture your primary focus. One of the best things you can do to enhance the value of a lecture is to review the relevent parts of the textbook before the lecture. Then your notes, instead of becoming yet another copy of information you paid for when you bought the book, can be an adjunct set of insights and commentary that will help you when it comes time to study on your own. Finally, remember that your success is your instructor's success too. He or she wants you to achieve your goals. So develop a rapport with the instructor, letting him or her know when you are feeling lost and requesting help. Don't wait until after the lecture – raise your hand or your voice the minute the instructor begins to discuss an idea or procedure that you are unable to follow. Use any help labs or office hours that are available. If you are determined to succeed and your instructor knows it, then he or she will be just as determined to help you. SELF STUDY AND HOMEWORK There you are, just you and the textbook and maybe some lecture notes, alone in the glare of your desk lamp. It's a tense moment. Like most students, you turn to the exercises and see what happens. Pretty soon you are slogging away, turning frequently to the solutions in the back of the book to check whether you have a clue. If you're lucky, it goes mostly smoothly, and you mark the problems that won't come right so that you can ask about them in class. If you're not so lucky, you get bogged down, stuck on this problem or that, while the hours slide by like agonized glaciers, and you miss your favorite TV show, and you think of all the homework for your other classes that you haven't got to yet, and you begin to visualize burning your textbook . . . except that the stupid thing cost you 80 bucks . . . Let's start over. There you are, just you and the textbook and maybe some lecture notes, alone in the glare of your desk lamp. Relax. What are you here for? For whom are you doing this homework? Your teacher? Your parents? No, homework is for you, and you alone. It is your opportunity to learn, and to begin to gain mastery – and that is what you are here for. Not a grade – knowledge. Presumably, your instructor has just lectured the material, but have you read the material in the textbook yourself yet? You haven't? Then do so. Reading the textbook is something practically no student does, yet it can make a world of difference in how difficult the material seems to you. When reading a textbook, remember that it is not a novel, nor indeed like any other kind of book. Written math is dense. Each paragraph – sometimes even each line – contains deep ideas, which may require a novel way of thinking to understand. It may take you 20 minutes or longer just to absorb and understand a single page. That is normal. Read it with blank paper available and a pencil in your hand. Work through the examples yourself, until you thoroughly understand each step. Writing things down is far more effective than high-lighting or underlining. Read the footnotes. After you have done these things, then you are ready to look at the exercises. (NB: If you are reading a college-level text, it may be helpful to familiarize yourself with the Latin terms and Greek letters commonly used in mathematics.) Many instructors (but not all) encourage their students to work together on homework problems. Modern learning theories emphasize the value of doing this, and I find that students who collaborate can develop a synergy among themselves which supports their learning, helping them to learn more, more quickly, and more lastingly. Find out how your instructor feels about this, and if it is permitted find others in class who are interested in studying together. You will still want to put in plenty of time for self-study, but a couple of hours a week spent studying with others may be very valuable to you. WORKING PROBLEMS. Most problem sets are designed so that the first few problems are rote, and look just like the examples in the book. Gradually, they begin to stretch you a bit, testing your comprehension and your ability to synthesize ideas. Take them one at a time. If you get completely stuck on one, skip it for now. But come back to it. Give yourself time, for your subconscious mind will gradually formulate ideas about how to work the exercise, and it will present these notions to your conscious mind when it is ready. As an experienced math instructor, it is my sad duty to report that about a third of the students in any given class, on any given assignment, will look the exercises over, and conclude that they don't know how to do it. They then tell themselves, "I can't do something I don't understand," and close the book. Consequence: no homework gets done. About another third will look the exercises over, decide that they pretty much get it, and tell themselves, "I don't need to do the homework, because I already understand it," and close the book. Consequence: no homework gets done. I keep the subject constantly before me and wait till the first dawnings open little by little into the full light. – Sir Isaac Newton Don't let this be you. If you've pretty much already got it, great. Now turn to the hard exercises (whether they were assigned or not), and test how thorough your understanding really is. If you are unable to do them with ease, then you need to go back to the more routine exercises and work on your skills. On the other hand, if you feel you cannot do the homework because you don't understand it, then go back in the textbook to where you do understand, and work forward from there. Pick the easiest exercises, and work at them. Compare them to the examples. Work through the examples. Try doing the exercises the same way the examples were done. In short, work at it. You will learn mathematics this way – and in no other way. STORY PROBLEMS. Everybody complains about story problems, sometimes even the instructor. One is tempted to feel that math is hard enough without some sadist turning it into wordy, dense, hard-to-understand story problems. But again, ask yourself: "Why am I studying math? Is it so that I'll always know how to factor a quadratic equation?" Hardly. The study of math is meant to give you power over the real world. And the real world doesn't present you with textbook equations, it presents you with story problems. Your boss doesn't tell you to solve for x, he tells you, "We need a new supplier for flapdoodles. Bob's Flapdoodle Emporium wholesales them at $129 per gross, but charges $1.25 per ton per mile for shipping. Sally's Flapdoodle Express wholesales them at $143 per gross, but ships at a flat rate of $85 per ton. Figure out how each of these will impact our marginal cost, and report to me this afternoon." The real world. Personally, I love story problems – because if you can work a story problem, you know you really understand the math. It helps to have a strategy, so you might want to check out the Solving Story Problems article in the PRIME sometime soon. TAKING EXAMS. For many students, this is the very crucible of math anxiety. Math exams represent a do-or-die challenge that can inflame all one's doubts and frustrations. It is frankly not possible to eliminate all the anxiety you may feel about exams, but here are some techniques and strategies that will dramatically improve your test-taking experience. Don't cram. The brain is in many ways just like a muscle. It must be exercised regularly to be strong, and if you place too much stress on it then it won't function at its peak until it has had time to rest and recover. You wouldn't prepare for a big race by staying up and running all night. Instead, you would probably do a light work-out, permit yourself some recreation such as seeing a movie or reading a book, and turn-in early. The same principle applies here. If you have been studying regularly, you already know what you need to know, and if you have put off studying until now it is too late to do much about it. There is nothing you will gain in the few hours before the exam, desperately trying to absorb the material, that will make up for not being fresh and alert at exam time. On exam day, have breakfast. The brain consumes a surprisingly large number of calories, and if you haven't made available the nutrients it needs it will not work at full capacity. Get up early enough so that you can eat a proper meal (but not a huge one) at least two hours before the exam. This will ensure that your stomach has finished with the meal before your brain makes a demand on the blood supply. When you get the exam, look it over thoroughly. Read each question, noting whether it has several parts and its overall weight in the exam. Begin working only after you have read every question. This way you will always have a sense of the exam as a whole. (Remember to look on the backs of pages.) If there are some questions that you feel you know immediately how to do, then do these first. (Some students have told me they save the easiest ones for last because they are sure they can do them. This is a mistake. Save the hardest ones for last.) It is extremely common to get the exam, look at the questions, and feel that you can't work a single problem. Panic sets in. You see everyone else working, and become certain you are doomed. Some students will sit for an hour in this condition, ashamed to turn in a blank exam and leave early, but unable to calm down and begin thinking about the questions. This initial panic is so common (believe it or not, most of the other students taking the exam are having the same experience), that it's just as well to assume ahead of time that this is what is going to happen. This gives you the same advantage as when the dentist alerts you that "this may hurt a little." Since you've been warned, there's far less tendency to have an uncontrollable panic reaction when it happens. So say to yourself, "Well, I may as well relax because I expected this." Take a deep breath, let it out slowly. Do this a couple of times. Look for the question on the exam that most resembles what you know how to do, and begin poking it and prodding it and thinking about it to see what it is made of. Don't bother about the other students in the room – they've got their own problems. Before long your brain (remember, it's a muscle) will begin to unclench a bit, and some things will occur to you. You're on your way. Math exams are usually timed – but remember, it's not a race! You don't want to dally, but don't rush yourself either. Work efficiently, being methodical and complete in your solutions. Box, circle, or underline your answers where appropriate. If you don't take time to make your work neat and ordered, then not only will the grader have trouble understanding what you've done, but you can actually confuse yourself – with disastrous results. If you get stuck on a problem, don't entangle yourself with it to the detriment of your overall score. After a few minutes, move on to the rest of the exam and come back to this one if you have time. And regardless of whether you have answered every question, give yourself at least two or three minutes at the end of the exam period to review your answers. The "oops" mistakes you find this way will surprise you, and fixing them is worth more to your score than trying to bang out something for that last, troublesome question. In math, having the right answer is nice – but it doesn't pay the bills. SHOW YOUR WORK. Finally, place things in perspective. Fear of the exam will make it seem like a much bigger deal than it really is, so remind yourself what it does not represent. It is not a test of your overall intelligence, of your worth as a person, or of your prospects for success in life. Your future happiness will not be determined by it. It is only a math test – it tests nothing about you except whether you understand certain concepts and possess the skills to implement them. You can't demonstrate your understanding and skills to their best advantage if you panic through making more of it than it is. When you get the exam back, don't bury it or burn it or treat it like it doesn't exist – use it. Discover your mistakes and understand them thoroughly. After all, if you don't learn from your mistakes, you are likely to make them again. AFTERWORD ath anxiety affects all of us at one time or another, but for all of us it is a barrier we can overcome. In this article we have examined the social and educational roots of math anxiety, some common math myths associated with it, and several techniques and strategies for managing it. Other things could be said, and other strategies are available which may help you with your own struggle with math. Talk to your instructor and to other students. With determination and a positive outlook – and a little help – you will accomplish things you once thought impossible. The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty. Building on the Platonic Realms' "Coping With Math Anxiety" article, which has won international recognition since being posted in 1997, the authors' new book includes a reedited and expanded version of the original article together with a new introduction, interactive exercises and student activities, and a full chapter devoted to understanding the specific courses and programs of study offered by college math departments. An invaluable resource for every high school and college student, and an important teaching tool for all math instructors. An instructor's guide is freely available on request.
At the conclusion of their studies, Mathematics majors will demonstrate the following learning outcomes: 1. Develop mathematical thinking and communication skills: progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction and formal proof; gain experience in careful analysis of data; become skilled at conveying their mathematical knowledge in a variety of settings, both orally and in writing. Particularly, students will be exposed to a number of contrasting but complementary points of view: continuous and discrete, algebraic and geometric, deterministic and stochastic, theoretical and applied. These will be assessed by means of a comprehensive examination in Senior Year.
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Mathematics and Statistics What is Maths A level about? Mathematics and Statistics is comprised of two main areas: Pure Mathematics and Statistics. Pure Mathematics is the study of the basic principles of Mathematics that underpin many real life processes. During this part of the course you will extend your knowledge of such topics as algebra, trigonometry and sequences. You will also learn new concepts such as calculus. Statistics is the study of data. This part of the course will teach you how to critically analyse data and how probability theory can be used to model real life situations. Is this course for me? All students wishing to undertake an A level in Mathematics are required to achieve a grade B at GCSE with a minimum of 300 UMS marks. In addition to this, students will be required to pass the entry level algebra competency test What else do I need to know? There is the opportunity for Year 12 students to undertake community service. The Mathematics department also offer a weekly clinic on a Thursday. This is to support students with their studies. All pupils are welcome to come along and receive help from a variety of teachers. What do other students say? "You have not lived till you have done Maths at Charters!" "Always brings a new challenge". Where could it lead? Mathematics is a highly employable A level to have. Most students who study Mathematics go on to careers in Engineering, Computer Science and Finance. How is this course structured? All units are equal weighting. Unit Content Unit Assessment AS Unit 1: Core Maths 1 This extends your GCSE knowledge of Algebra, Indices and Co-ordinate systems. It also teaches you how to express your Mathematics correctly. Module examination in January of Year 12. AS Unit 2: Core Maths 2 This builds upon the work you did in Core 1. In this module you begin to look at such topics as Calculus and Trigonometry. Module examination in June of Year 12. AS Unit 3: Statistics 1 This module covers how to analyse data, the binomial distribution, probability theory and how to test whether a particular result is significant Module examination in June of Year 12. A2 Unit 4: Core Maths 3 This module extends the calculus techniques that you learnt in Core 2. It also looks at functions and natural logarithms. You will be required to produce a piece of coursework. 20% coursework. 80% examination in January of Year 13. A2 Unit 5: Core Maths 4 This module is called Applications of Advanced Mathematics. The module extends all the topics you have learnt thus far and asks you to apply them in more complex situations. Module examination in June of Year 13. A2 Unit 6: Statistics 2 This module introduces you to two more distributions. It also extends your knowledge of hypothesis testing and teaches you new techniques for testing the validity of results.
MathScopeis a support unit for those of you who may experience difficulties with mathematics in whatever subject you are studying. MathScope is staffed and resourced throughout the year and offers a comprehensive service for students who are having difficulty coping with the mathematical demands of their course at whatever level. There is much evidence to show that, if steps are taken early enough, the initial reluctance of students to get involved with maths in their subject can be avoided. MathScope has sympathetic, experienced tutors who don't want students to be afraid of mathematics. MathScope is a place for you to go if you start to feel anxious about not being able to cope with mathematics. MathScope is a place where you will find solutions to your mathematics problems - whatever level. MathScope is open 5 days a week. You can phone us with your problems: 0161 295 4787
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General resources Aligned lesson plans Systems of equations can be used to solve many different kinds of problems. One application is in making solutions such as is done in chemistry. In this lesson, students will set up a system of equations to determine the volume of a solution. In this lesson, student use a system of equations to determine the number of each type of "atom" in a closed container. Format: lesson plan (grade 9–12 Mathematics and Science) By Jennifer Elmo
for students intending to earn an Associate of Science degree and then transfer to a mathematics, engineering program, or other calculus-based major at a four-year institution. Students will gain a basic understanding of calculus, the mathematics of motion and change. Topics include limits and continuity, differentiation, applications of differentiation, integration, applications of integration, derivatives of exponential functions, logarithmic functions, inverse trigonometric functions, hyperbolic functions and related integrals. Students must have a working knowledge of college algebra and trigonometry. In this course, we will study the foundations of calculus, the study of functions and their rates of change. We want you to learn how to model situations in order to solve problems. If you have already taken calculus before, we want you to gain an even deeper understanding of this fascinating subject. The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two ideas form the basis for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. This examples, and figures. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The videos were created by renowned mathematics professor Gilbert Strang who has taught at MIT since 1962. The video series reviews the key topics and ideas of calculus with applications to real-life situations and problems and then fully covers the concept of Derivatives. This is a two-semester course in n-dimensional calculus with a review of the necessary linear algebra. It covers the derivative, the integral, and a variety of applications. An emphasis is made on the coordinate free, vector analysis. This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals. C work. This will be true no matter where you are or what computer you use, as long as it is connected to the internet and has a web browser. The student component of COW (called the Manager) generates calculus examples and exercises in "modules" for studying, tutoring and practice. A number of the modules allow you to experiment by letting you change values or parameters in a function or graph and then see the effect. These modules are called "hands on" modules, and are marked with an asterisk. The component of the COW accessible by instructors (called the Reporter) handles assignment and automatic grading of homework, reporting on student work and class management. This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and L'hopital's Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using Newton's Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005) This elementary transcendental functions. The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going right at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.
Algebra And Trigonometry - 01 edition ISBN13:978-0534434120 ISBN10: 0534434126 This edition has also been released as: ISBN13: 978-0534380298 ISBN10: 0534380298 Summary: James Stewart, the author of the worldwide best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. Algebra and Trigonometry was designed specifically to help readers learn to think mathematically an...show mored to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, College Algebra, Third Edition, and Precalculus, Third EditionGoodwill Savannah Savannah, GA No comments from the seller $2.95 +$3.99 s/h Good Savannah Goodwill Savannah, GA Good
Calculus Calculus is a branch of mathematics that expands upon the principles used in algebra and geometry to include the idea of limits. There are two main sub-categories of calculus—differential calculus and integral calculus. Each has a different focus. Integral calculus deals with the idea of accumulation, while differential calculus examines the rate of change. Common calculus terminology includes words such as integrals, functions and derivatives. The following academic lectures are designed to give you insight into this branch of mathematics and help you understand the concepts involved in calculus.
A: Students taking general education or introductory collegiate courses in the mathematical sciences General education and introductory courses enroll almost twice as many students as all other mathematics courses combined [1]. They are especially challenging to teach because they serve students with varying preparation and abilities, many of whom have had negative experiences with mathematics. Perhaps most critical is the fact that these courses affect life-long perceptions of and attitudes toward mathematics for many students—and hence many future workers and citizens. For all these reasons these courses should be viewed as an important part of the instructional program in the mathematical sciences. This section concerns the student audience for these entry-level courses that carry college credit. An important resource for discussions about these courses is Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, published by the American Mathematical Association of Two-Year Colleges and available in its entirety on the Internet. A.1: Offer suitable courses Mathematical sciences departments should ensure that all students meeting general education or introductory requirements in the mathematical sciences are enrolled in courses designed to Engage students in a meaningful and positive intellectual experience; Increase quantitative and logical reasoning abilities needed for informed citizenship and in the workplace; Strengthen quantitative and mathematical abilities that will be useful to students in other disciplines; Improve every student's ability to communicate quantitative ideas orally and in writing; Encourage students to take at least one additional course in the mathematical sciences. General Introductory Courses At Princeton University, the Math Alive course is designed for those who haven't had college mathematics but would like to understand some of the mathematical concepts behind important modern applications. It consists of largely independent 2-week units in cryptography, error correction and compression; probability and statistics; birth, growth, death and chaos; geometry and motion control; and voting and social choice. Each unit is divided into two parts. For each part students can download lecture notes in pdf or ps format. Each part has a problem set and a corresponding online lab. Links for the lecture notes, online labs, and problem sets through corresponding links are on the course website. Each problem set is posted on the web one week before it is due. Solutions to the problem are available on the web after the submission deadline. The syllabus describes class topics, lists due dates and posts problem sets and labs. A widely-used text for a similar but somewhat less mathematically demanding course is For All Practical Purposes by COMAP. The companion website contains extensive resources for students and teachers. At The University of Texas at Austin, the mathematics course developed for the liberal arts honors program is designed to present "culturally significant and beautiful concepts with concomitant emphasis on potent strategies of discovery and exploration." The course presents infinity, the fourth dimension, geometric gems, topology, coincidence, chaos, fractals, and other topics. Each topic is intended to illustrate the process of starting with a simple observation and applying techniques of effective thinking that lead to the creation of new ideas, such as making errors and learning from them, breaking complicated questions into simple components, understanding simple things deeply, and finding the essence of an issue. One project directs students to take a non-mathematical issue they care about and apply the methods of analysis, not the mathematics itself, to analyze the issue or produce a creative work about it. The text used is The Heart of Mathematics: An invitation to effective thinking, by E. Burger, and M. Starbird. The introductory course in Contemporary Mathematics at Virginia Commonwealth University is taken by more than 2000 students each year. It uses the text Excursions in Modern Mathematics Peter Tannenbaum and Robert Arnold and includes topics such as voting and fair division, applications of graph theory/networks, population growth, symmetry, and fractal geometry. In the context of these applications of mathematics, students strengthen their algebraic and graphing skills. The course serves as a prerequisite for the statistics course that is required in most humanities and social science degree programs. Students take three exams and four quizzes; write two papers; participate in making a group presentation; make a poster session presentation; turn in a dozen in-class/homework worksheets; and respond to weekly prompts in a Learning Log. Grades are based on tests (30%), quizzes (20%), presentations (20%), papers (20%), worksheets etc. (20%). Students who complete a learning log may drop the lowest 10% of the grades for their assignments. A detailed instructor's guide, discusses the use of writing-to-learn, group projects, independent study projects, poster sessions and other approaches that expect active student engagement. Mount Holyoke College offers a variety of courses to incoming students not enrolling in a calculus sequence. The introductory "explorations" in algebra, number theory, geometry, and fractals and chaos offer a way for students to begin their study of mathematics. These courses emphasize mathematics as an art and as a way of seeing and understanding. The explorations presuppose neither special talent for nor prior strong interest in mathematics. They intend to awaken interest by demonstrating either the pervasiveness of mathematics in nature and its power as a tool that transcends disciplines or its qualities as an art that brings aesthetic pleasure to the participant. Another alternative for students is an interdisciplinary case-study course in quantitative reasoning. Resources that can be used to introduce students to contemporary topics in general education courses include the AMS website What's New in Mathematics and PLUS magazine, an Internet magazine from the United Kingdom, which aims to introduce readers to the beauty and the practical applications of mathematics. A number of articles in the MAA journal Math Horizons are also appropriate for a general undergraduate student audience. Precalculus – New Approaches Based on her workshop program in calculus, Nancy Baxter-Hastings has developed a workshop program in precalculus, designed to eliminate the distinction between classroom and laboratory work. Her text is Workshop Precalculus: Discovery With Graphing Calculators. The method alternates between three primary components: summary discussions, introductory remarks, and collaborative activities. Students are expected to learn by working in groups, discussing problems as a class, and writing individual reports. The book encourages students to do initial computations and symbolic manipulations by hand in order to understand how results are produced, turning to calculators once they understand a concept. The book offers the following suggestions for workshop instructors: take control of the course, keep the class roughly together, allow students to discover, promote collaborative learning among students, encourage students' guessing and development of intuition, lecture when appropriate, have students do some work by hand, use technology as a tool, be proactive in approaching students and give them access to "right" answers, provide plenty of feedback, stress good writing, implore students to read well, and have fun! Precalculus with Applications, based on Functioning in the Real World: A PreCalculus Experience by Sheldon Gordon et al., is taught at Farmingdale State University of New York. It is designed to prepare students for calculus as well as for quantitative courses in the natural and social sciences. The course introduces students to the fundamental families of functions using contextual, tabular, graphical, and algebraic representations. A common theme is the notion of fitting functions to real-world data. Each family of functions is introduced in context and the emphasis throughout is on realistic applications. Matrices and their use in solving systems of linear equations are also introduced, as are the notion of recursion and applications via models involving difference equations. The course requires three class tests, a series of three individual investigatory projects (which count as equivalent to two class tests), and a cumulative final exam. The Precalculus Weblet consists of an online textbook, syllabi, homework, and exams developed by the members of The Washington State Board for Community College Education. It contains links for exploring precalculus concepts using current information on the Internet. All the material on the website is freely available for personal use. The article "Who Are the Students who take Precalculus" by Mercedes McGowen, William Rainey Harper College, examines the numbers of students in precalculus courses, their backgrounds and motivations for taking the courses, and the subsequent mathematics courses in which they enroll. Integrating Precalculus and Calculus In 1988 Moravian College replaced the traditional 2-term Precalculus-Calculus I sequence with a one-year course, Calculus I with Review. The course addressed the problem of making calculus accessible to students with weak algebra and problem-solving skills. The idea was that by providing conceptual background and discussing specific algebra techniques just prior to introducing a calculus topic, the students are motivated to understand the usefulness of the techniques and immediately apply them to calculus problems. The developers of the course believed that it is important to have good supplemental material, and to this end they prepared a text, A Companion to Calculus, which can be used with scheduled or informal tutoring sessions or as a supplement for individual study. Chapters are keyed to primary topics in any first calculus course, and the text approaches all concepts in four ways: descriptive (verbal and written), symbolic, numeric, and graphic. With assistance from the Fund for the Improvement of Post-Secondary Education (FIPSE), the Moravian project team mentored a number of other institutions in creating similar courses. In fact the idea of integrating precalculus material into calculus course became so successful that textbooks have been written specifically for such a course. Two of these are Calculus 1 With Precalculus: A One Year CoursebyRon Larson, et al., and Integrated Calculus: Calculus with Precalculus and Algebra by Laura Taalman. An example of a calculus course that integrates calculus and precalculus and places special emphasis on active learning is the Workshop Calculus Program. The textbooks Workshop Calculus: Guided Explorations with Review, vol. 1 and vol. 2, and Workshop Calculus with Graphing Calculators Guided Exploration with Review, vol. 1 and vol. 2, developed by Nancy Baxter-Hastings, Dickinson College, seeks to help students develop the confidence, understanding, and skills necessary for using calculus in the natural and social sciences and for continuing their study of mathematics. Lectures are replaced by an interactive teaching format that does not distinguish between classroom and laboratory work. Students are expected to learn by doing and by reflecting on what they have done, and the instructor is expected to respond to students as they learn. ARTIST stands for Assessment Resource Tools for Improving Statistical Thinking. "This website, with support from the National Science Foundation, provides a variety of assessment resources for teaching first courses in Statistics: 1. Assessment Builder: a collection of about 1100 items, in a variety of item formats, according to statistical topic and type of learning outcome assessed. This database can be used to generate files to be edited and manipulated by statistics instructors. 2. Resources: * Information guidelines, and examples of alternative assessments (such as projects, article critiques, and writing assignments) * Copies of articles or direct links to articles on assessment in statistics. References and links for other related assessment resources. 3. Research Instruments: instruments that may be useful for research and evaluation projects that involve assessments of outcomes related to teaching and learning statistics. 4. Implementation issues: questions and answers on practical issues related to designing, administering, and evaluating assessments. 5. Presentations: copies of conference papers and presentations on the ARTIST project, and handouts from ARTIST workshops. 6. Events: information on past and upcoming ARTIST events. 7. Participation: ways to participate as a class tester for ARTIST materials." The article "An Activity-Based Statistics Course" by M. Gnanadesikan et al. from the Journal of Statistics Education includes examples of types of activities that work well in various classroom settings along with comments from colleagues and students on their effectiveness. Another source for the activity-based approach is Teaching Statistics: A Bag of Tricks, by A. Gelman and D. Nolan. The software Fathom, developed with support from the National Science Foundation, allows users to type in their own data, to use the over 300 data files that come with Fathom, or to import data from text files or directly from the Internet. Laurie J. Burton, Western Oregon University, reported about a technique used in a general education mathematics survey course aimed at engaging students and improving their communication skills. She incorporated weekly projects by dividing the class into groups of four and requiring the groups to write summaries of their projects On a rotating basis, one student was responsible for the written submission, while the others served as editors. Over the semester each student was responsible for two weekly, typed "write ups," each worth 12.5% of the course grade. In the written submissions the students were required to include an introduction, a statement of assumptions, a rewriting of each problem, a display of all steps the mathematics, and a clear sentence reporting he answer. Burton reported that "The class started off slowly to say the least! I wrote an extensive set of directions for them, but clearly many of them didn't bother to read their packet! The first three weeks of projects were dismal. Eventually they all sort of clued in and by the end of the term students were turning in really nice projects. Clearly they had learned something. I was really impressed and happy as a teacher that the students were making such clear progress." Information about the nature and use of current projects for the course, Introduction to Contemporary Math, is available through a link on her website. The University of South Carolina Spartanburg (USCS) developed Project-Based Instruction in Mathematics for the Liberal Arts. The website provides projects and resources for instructors and students who wish to teach and learn college mathematics or post-algebra high school mathematics via project-based instruction. In 1994 a group of faculty members at USCS began to develop and test an innovative pedagogy integrating technology and activity- or project-based instruction in mathematics for liberal arts majors. The group collected, modified, and wrote items for a packet of activities designed to form the core of material that would be used to supplement and eventually replace the textbook in the "College Mathematics" course. Subsequently, M.B. Ulmer wrote a booklet to lend structure to the use of the activities, which supplanted used of a regular textbook in many sections. Ulmer reports that success rates have risen dramatically for students who have gone through the program and that their subsequent performance in required statistics courses has also shown improvement. Quantitative Literacy Using the recent anthrax crisis as an example, NSF Director Rita Colwell observed,"When we have little direct control over our fate, a firm understanding of probability can alleviate some of the stress." Colwell's remarks were made at a 2001 forum on quantitative literacy held at the National Research Council and jointly sponsored by the National Council on Education and the Disciplines, the Mathematical Sciences Education Board, and the Mathematical Association of America. The forum's white paper defined quantitative literacy (also called "numeracy") as the "quantitative reasoning capabilities required of citizens in today's information age." Relevant documents include Mathematics and Democracy: The Case for Quantitative Literacy (Steen, 2001) and Quantitative Literacy: Why Numeracy Matters for Schools and Colleges. The Mathematical Association of America recently established a Special Interest Group on Quantitative Literacy (SIGMAA QL). Information about previous work of the CUPM subcommittee on Quantitative Literacy Requirements is maintained by Rick Gillman, Valparaiso University. The Quantitative Literacy webpage of MAA Online contains links for information a reports concerning quantitative literacy that were formerly located on the website of the National Council on Education and the Disciplines at the Woodrow Wilson National Fellowship Foundation. In "General Education Mathematics: New Approaches for a New Millennium," Jeffrey O. Bennett, University of Colorado at Boulder, and William L. Briggs, University of Colorado at Denver present some observations regarding the problems of developing appropriate mathematics curricula for non-science, engineering, mathematics (SEM) students, along with recommendations for their solution The authors state that the ways students need mathematics are for college, for career, and for life. When a committee at the University of Colorado examined what mathematics would be appropriate to meet these needs, four content areas emerged: logic, critical thinking, and problem solving; number sense and estimation; statistical interpretation and basic probability; and interpretation of graphs and models. Bennett and Briggs advocate a context-driven approach for instruction in these areas. Developing Mathematical and Quantitative Literacy across the Curriculum The University of Nevada, Reno, established a Mathematics Center with a focus on integrating mathematics across the curriculum. The main goal of the Center is to improve the quantitative and mathematical skills of all students, and to help them better appreciate the importance and utility of mathematics. The Center does this primarily by working with faculty in various disciplines to assist them in enhancing the quantitative and mathematical content of their courses, and then providing them and their students with the necessary support. The plan calls for influencing courses ranging from the natural and social sciences to English and the fine arts. It also calls for bringing applications from other disciplines into the elementary mathematics classes. The Core Curriculum is a high priority for the project. Macalester College has established an interdisciplinary program, Quantitative Methods for Public Policy, that involves many different departments in teaching quantitative literacy in the context of public policy analysis. This work is supported by a grant from the Department of Education's Fund for the Improvement of Post-Secondary Education. Offering Choices to Satisfy a General Mathematics Requirement Stetson University offers students a wide variety of mathematics courses to complete the mathematics requirement. Courses meeting the general mathematics requirement include Finite Mathematics, Mathematical Game Theory, Chaos and Fractals, In Search of Infinity, Great Ideas in Mathematics, Mathematics and Multiculturalism, Geometry, Introduction to Mathematical Modeling, and Cryptology, as well as the calculus courses. Goucher College also offers a variety of courses to students completing their general mathematics requirement. Available courses include Topics in Contemporary Mathematics, Introduction to Statistics, Problem Solving and Mathematics-Algebra, Problem Solving and Mathematics-Geometry, Functions and Graphs, Discrete Mathematics, various levels of calculus courses and Linear Algebra. The Math Lab Program at Francis Marion University is designed to give students access to mathematics across a wide range of entry-level courses and to make it possible for students to work at their own pace. The Math Lab features an individualized format that makes it possible for a student to complete the course in more or less time than the regular semester. However, to succeed in the Math Lab program students must have motivation and self-discipline. Francis Marion strongly recommends that students use the available resources including extra help sessions, extensive mini-lab hours, computer tutorials, videotapes, and instructor office hours. The Math Lab Program offers the introductory courses of College Algebra with Analytic Geometry I, College Algebra with Analytic Geometry II, College Trigonometry with Analytic Geometry II, and Calculus I. All but the first course satisfy the General Education Requirement. The first course does, however, earn credit toward graduation. Syllabi for all courses are located at the site indicated above. Faculty teaching developmental mathematics courses at various institutions can often feel isolated and may have little information on what is new in the field. A committee of the MAA has started a web page, a mailing list and other activities to support these instructors. Support is also available from AMATYC, which focuses considerable attention on developmental mathematics. See the section on developmental mathematics on their Electronic Proceedings pages. Mathematical sciences departments at institutions with a college algebra requirement should Clarify the rationale for the requirement and consult with colleagues in disciplines requiring college algebra to determine whether this course—as currently taught— meets the needs of their students; Determine the aspirations and subsequent course registration patterns of students who take college algebra; Ensure that the course the department offers to satisfy this requirement is aligned with these findings and meets the criteria described inA.1. Refocusing College Algebra Founded in 1996, the Historically Black College and University (HBCU) Consortium for College Algebra Reform developed the Contemporary College Algebra program. Its purpose is to refocus college algebra to address the quantitative proficiencies that students need for mathematics and other disciplines, society, and the workplace. Thus emphasis is placed on trying to empower students as problem solvers in the modeling sense rather than making them try to master lists of algebraic rules. To support the purpose, the course emphasizes developing communication skills, engaging students in small group activities/projects, using technology for doing mathematics, and trying to build student confidence. Discussions with faculty in different disciplines and with people in the workplace influenced the development of the program. In particular, the heavy emphasis placed on data as well as on graphical and numerical analysis reflects these discussions. Data analysis is used to generate the need for functions, which in turn leads to modeling situations in various disciplines using recursive sequences. Creators of the program believe that the ability to understand elementary data analysis, to extract functional relationships from data, and to model real-life situations mathematically is fundamental to the education of every student. The pedagogical environment is focused on student learning, which includes a strong emphasis on small-group in-class activities and out-of-class projects. Technology is used extensively as part of discovery activities. The program has expanded beyond the HBCU Consortium to include majority schools and tribal colleges. A conference on College Algebra was sponsored by the HBCU College Algebra Reform Consortium in December 2002. Two articles that resulted from a workshop sponsored by the Consortium are "College Algebra" by Arnold Packer, Johns Hopkins University, "An Urgent Call to Improve Traditional College Algebra Programs" by Don Small, U.S. Military Academy, and "Who Are the Students Who Take Precalculus?" by Mercedes A. McGowen, William Rainey Harper College. Conference participants recommended the following as major characteristics of a college algebra program: * Real-world problem based: a topic is introduced through a real-world problem and then the mathematics necessary to solve the problem is developed. Example problem: Schedule a multi-faceted process. * Modeling (transforming a real-world problem into mathematics): - using power and exponential functions, systems of equations, graphing, and difference equations – primary emphasis is placed on creation of a model and interpretation of the results. Example: Model the stopping time versus speed data presented in a driver's manual by plotting the data and fitting a curve to the plot. Interpret how well the resulting stopping time function models reality at small speeds. Revise the model, if necessary, to account for zero stopping time at zero speed. Use the (revised) function to predict stopping times for speeds not given by the data. Revise the model to account for different road surfaces. * Emphasize communication skills: as needed in society as well as in academia – reading, writing, presenting, and listening. Example: Students learn how to read, understand, and critique news articles that include quantitative information and to make informed decisions based on the articles. * Small group projects: involving inquiry and inference. Example: Analyze the soda preference of students by conducting a survey and comparing the results with data from the school's dining hall or a local fast food restaurant. * Appropriate use of technology to enhance conceptual understanding, visualization, and inquiry, as well as for computation. Example: "What-if" a model for paying off a credit card debt by changing the monthly payment, interest rate, size of debt, etc. Plot the results to visually compare the different scenarios. * Use of hands-on activities rather than all-lecture format. The Texas Southern Consortium for College Algebra Reform, part of Project Intermath, has two goals: (1) to develop a contemporary college algebra course that educates students for the future rather than training them for the past; and (2) to change the culture surrounding the college algebra program. The primary goal of its contemporary college algebra course is to empower students to become exploratory learners. Most of the topics in the course begin with the analysis of data. The course involves the use of small-group projects developed by interdisciplinary faculty teams, incorporates a strong technology component, emphasizes the development of students' communication skills, and attempts to improve students' mathematical self-esteem and confidence in their problem-solving skills. The specific objectives of the goal of changing the college algebra culture are to energize faculty to develop modes of instruction that actively engage students in their learning, instill in faculty a sense of ownership and pride about teaching college algebra, encourage faculty in disciplines that require college algebra to develop a sense of involvement and responsibility for the college algebra program, and obtain administrative support for a reformed college algebra program. Three faculty members at the University of Houston Downtown, William Waller, Linda Becerra, and Ongard Sirisaengtaksin, wrote a case study about the process of initiating change in their college algebra course. They write that the challenges they believed needed addressing in their previous course were student performance and student preparation, and that traditional methods were not effective in meeting these challenges. Their aims were to provide students with numerous opportunities to learn, lead students to learn fundamental concepts and skills through solving real-world problems, stimulate student interest and increase motivation (thereby improving retention), increase mathematical literacy, use diverse teaching strategies, and offer a technology-dependent curriculum. "A Research Evaluation of a Reform College Algebra Course" by Joan Cohen Jones, Eastern Michigan University and Andrew Balas, University of Wisconsin Eau Claire, describes how the authors, a mathematics educator and a mathematician, structured a college algebra course with the aim of empowering students by having them construct their own understanding through discussing concepts in small cooperative groups. In the course, students had to apply traditional algebra skills to problems in real-life situations. Research conducted by the authors indicated that the students improved in their attitudes toward mathematics and their confidence in their ability to solve problems, that students attributed their success less to the instructors and more to themselves and their peers, that successful groups bonded well, and that the groups served as a forum to explore and test ideas. The College Algebra Reform Papers website at the State University of New York – Oswego contains articles by William Fox, Francis Marion University, Scott Herriott, Maharishi University of Management, and Laurie Hopkins, Columbia College, discussing the appropriateness of college algebra practices and offering suggestions for improvement. William Fox addresses the issue of integrating modeling and problem solving in developing new courses to replace the traditional college algebra course. Scott Herriott compares the traditional college algebra curriculum with more recent reform approaches and also discusses related issues of national and local educational policy. Laurie Hopkins focuses on the role of technology, and specifically the use of handheld computer algebra systems in the college algebra classroom. The website also includes two "provacateur" responses to the articles. Hamid Behmard's college algebra course at Chemeketa Community College uses College Algebra and Trigonometry with Modeling and Visualization by Gary Rockswold. It covers polynomial, rational, exponential, logarithmic, and related piece-wise defined functions. The algebra of functions, complex numbers, sequential functions, and linear systems are also included. The course incorporates group activities and writing and the syllabus states: "Upon successful completion of this course, students shall be able to: 1. Create mathematical models of abstract and real world situations using linear, quadratic, polynomial, rational, exponential, and logarithmic expressions. 2. Use inductive reasoning to develop mathematical conjectures involving these function models. 3. Use deductive reasoning to verify and apply mathematical arguments involving these models. (Distinguish between the uses of inductive and deductive reasoning.) 4. Represent these functions in graphical, tabular, symbolic and narrative form, and then use mathematical problem solving techniques to solve problems involving these functions. 5. Make mathematical connections to, and solve problems from other disciplines involving these functions. 6. Use oral and written skills to individually and collaboratively communicate about these function models. 7. Apply appropriate technology to enhance mathematical thinking and understanding, solve mathematical problems, and judge the reasonableness of their results. After examining the student population in the college algebra course and consulting with departments that required that course, the Hiram College Department of Mathematics eliminated the course and replaced it with Mathematical Modeling in the Liberal Arts. In this course, students use data together with linear, quadratic, polynomial, exponential, and logarithmic functions to model naturally occurring phenomena in medicine, economics, business, ecology, and other disciplines. The course uses numerical, graphical, verbal, and symbolic modeling methods. Bonnie Gold's article "Alternatives to the One-Size-Fits-All Precalculus/College Algebra Course" describes Monmouth University's mathematics department's experience replacing a single college algebra course taken by almost all students by four courses designed for particular student populations: elementary education majors, biology majors, social science majors, and students who eventually go on to a standard calculus course. The three new courses were designed in consultation with faculty from the relevant departments. In addition, the course that prepares students for calculus no longer satisfies the general education mathematics requirement, whereas the other three courses – as well as a pre-existing quantitative reasoning and problem solving course – do satisfy the requirement. For an electronic copy of the article, contact Bonnie Gold. At American University, Elementary Mathematical Models is a course at the level of college algebra or precalculus that uses simple discrete growth models to provide a context for the study of elementary real functions. The mathematical content has a large degree of overlap with traditional college algebra or precalculus courses and includes properties and applications of linear, polynomial, rational, exponential, and logarithmic functions. The course goals emphasize looking realistically at the methodology of applying mathematics through models, with consistent use of numerical, graphical, and symbolic methods over the entire course. The use of simple difference equation models throughout is intended to provide a unifying theme. The course begins with arithmetic growth and linear functions, and concludes with logistic growth models. A qualitative discussion of how chaos can arise in discrete logistic models is the climax of the course. At Georgia College and State University a new college algebra course focuses on integrating technology in the form of graphing calculators and providing learning support: strategies for test taking, dealing with math anxieties, mastering mathematical concepts, and developing graphing calculator skills. The article College Algebra, Learning Support, and Technology: What is the Connection? by Margo Alexander briefly describes a study done to compare college algebra students who concurrently took a learning support course against those who did not have additional support. Paul Dirks, Miami-Dade Community College, developed a course entitled Contemporary College Algebra that incorporated group activities, a heavy use of technology, and outside-of-class group projects. He reported that he was guided by the description below (from a 2002 AMS-MAA-MER session on education reform): Contemporary College Algebra, a data-driven modeling course, is an example of a reformed college algebra course that serves as a base course for a quantitative literacy program. The course focuses on problem solving in the modeling sense rather than the exercise sense. Communications (reading, writing, presenting), use of technology, small group interdisciplinary projects, analysis of real data sets, graphical analysis, and recursive sequence models are all strongly emphasized. The course is designed to prepare students to be mathematically literate in today's information society. The focus is on preparing students for the future rather than training them for the past. Dirks stated that he was at first unsure about whether his students had the mathematical and communication skills required to succeed in this course, but after three semesters of teaching it, he reported that they have exceeded his expectations. He said that he has observed improved student engagement in critical thinking (outlining issues clearly, posing non-trivial questions, organizing their discoveries, and presenting results in a variety of forms), increased exercise of creativity and autodidactic activity (learning new mathematics and adapting old, learning and using new technologies, creatively presenting results); and a phenomenon best expressed by the statement, "The whole is more than the sum of its parts" (group work pushing toward a better solution). Dirks stated that he has forever changed the way he teaches as a result of this experience, that even if this is not the "final answer," he feels his teaching is moving in the right direction. All of the content of Suzanne Dorée's Applied Algebra course at Augsburg College is presented in applied contexts: the examples, exercises, and the text narrative itself, and the topics were chosen in consultation with client disciplines. They are organized into three groups: linear models, exponential models, and polynomial models. The course is equivalent to intermediate algebra but does not presume that students have mastered introductory material. Concepts and skills are included only if needed in subsequent study or for everyday life. The applications are intended to be relevant and meaningful for both traditionally aged and adult learners and for students from a diversity of cultures, life experiences, and areas of interest. The locally produced text materials, sections of which are available on Dorée's website, have been used since 1997 by instructors who have employed a variety of pedagogical approaches. Slides from a talk about the course are also on her website. At the University of Arkansas students can enroll in a special section of College Algebra taught in conjunction with the Mathematics Resource and Tutoring Center (MRTC). The course consists of in-class and MRTC activities plus computer work. The computer work consists of eight interactive modules where the student must demonstrate understanding of the concepts and techniques from the text by scoring 90% or above in order to move to the practice problems for the module. Once students complete all module practice problems correctly, they may take the associated test. This purpose of the course is to prepare students for higher-level mathematics courses. As a consequence, the course offers every student as many different opportunities to learn or re-learn fundamental algebraic material as possible. In designing general education and introductory courses, mathematical sciences departments should ensure that students taking subsequent courses, such as calculus, statistics, discrete mathematics, or mathematics for elementary school teachers, are appropriately prepared. In particular, departments should Determine whether students that enroll in subsequent mathematics courses succeed in those courses and, if success rates are low, revise introductory courses to articulate more effectively with subsequent courses; Use advising, placement tests, or changes in general education requirements to encourage students to choose a course appropriate to their academic and career goals. College Algebra – New Approaches Tim Warkentin and Mark Whisler, Cloud County Community College, wrote "Questions about College Algebra" to describe their experience assessing alternative formats for their college algebra course. They conclude that "The change with the greatest impact is likely to be the change in format that we instituted in the fall of 2002 in College Algebra. We are offering all of our daytime sections of College Algebra as classes that, along with its companion class, College Algebra Explorations, meet every day." "A Research Evaluation of a Reform College Algebra Course" was conducted by Joan Cohen Jones, Eastern Michigan University, and Andrew Balas, University of Wisconsin Eau Claire. The research indicated that "that the students improved in their attitudes toward mathematics and their confidence in their ability to solve problems. They attributed their success less to the instructors and more to themselves and their peers. Successful groups bonded well, and the group served as a forum to explore and test ideas." In "Analysis of Effectiveness of Supplemental Instruction (SI) Sessions for College Algebra, Calculus, and Statistics," Sandra Burmeister, Patricia Ann Kenney, and Doris L. Nice explore data from 177 courses in mathematics for which SI support was given (1996). The SI sessions are based on theoretical notions of "metacognition" and aim to help students develop a cognitive monitoring system and make effective use of learning strategies. The data indicate that SI sessions promote student success. There were positive differences in grades for students who participated in SI sessions in college algebra, calculus, and statistics when compared with students who did not participate. Additionally, in 1994 Kenney and James Kallison reported on research studies on the effectiveness of SI in mathematics classes. In "Precalculus in Transition: A Preliminary Report" by Trisha Bergthold and Ho Kuen Ng, San Jose State University, the authors discuss their initial investigation of low student achievement in our five-unit precalculus course. We investigated issues related to course content, student placement, and student success. As a result, we have streamlined the course content, we are planning to implement a required placement test, and we are planning a 1–2 week preparatory workshop for students whose knowledge and skills appear to be weak. Further study is ongoing. Integrating Precalculus and Calculus An evaluation of the Moravian College integrated calculus and precalculus course by the Fund for the Improvement of Post-Secondary Education examined student persistence rates, the performance of integrated-course students compared to students in the traditional sequence on a set of problems included in the final examinations of both courses, instructor attitudes, and student attitudes. It concluded: "Uniformly, student persistence through the sequence was higher for the integrated course than for calculus preceded by precalculus. Integrated-sequence students performed at least as well on a set of common problems as the traditional-course students, and sometimes better. In general, both faculty and students liked the integrated sequence better." [1] According to the CBMS study in the Fall of 2000, a total of 1,979,000 students were enrolled in courses it classified as "remedial" or "introductory" with course titles such as elementary algebra, college algebra, Pre-calculus, algebra and trigonometry, finite mathematics, contemporary mathematics, quantitative reasoning. The number of students enrolled in these courses is much greater than the 676,000 enrolled in calculus I, II or III, the 264,000 enrolled in elementary statistics, or the 287,000 enrolled in all other undergraduate courses in mathematics or statistics. At some institutions, calculus courses satisfy general education requirements. Although calculus courses can and should meet the goals of Recommendation A.1, such courses are not the focus of this section.
Promethean Flipchart Libraries Sign up for a Webinar to get an Overview of Media4Math+! Do you use Promethean Whiteboards in your classroom? Are you looking for Active Isnpire resources for Algebra, Geometry, and Graphing Calculators? Media4Math has three extensive flipchart libraries in these areas that will bring your Promethean-based lessons to life. Each of our Promethean Flipcharts includes the following features: Video Hands-on activities using technology (the TI-Nspire or Geogebra) Teaching notes Applications of key concepts from Algebra and Geometry Download free samples from our Promethean Flipchart Libraries for Algebra, Geometry, or the TI-Nspire CX. Click on one of the links below to download your sample Flipchart. If you have installed the Active Inspire software, then you can display Promethean Flipcharts running on your computer that is connected to the overhead device. What kind of computer do I need to play the Promethean Flipcharts? Our Promethean Flipcharts will run on either a Mac or a PC. How do I get your Promethean Flipcharts? You can purchase the Algebra, Geometry, and TI-Nspire CX Flipcharts as individual downloads, which you can download directly to your computer. You can also purchase the entire Flipchart library on DVDR. This collection of 23 Flipcharts includes all key topics from a full-year Geometry course. Nearly 20 minutes of video per Flipchart Geogebra (Geometry software) activities Below you will find a summary of each of the 23 Flipcharts in the Geometry Library. Promethean Flipcharts for Geometry: Points Lean about the geometry of points in the context of physics. What is the relationship between subatomic particles and geometric points? How can geometry help us understand subatomic physics? Geometry concepts: points, collinear points Promethean Flipchart for Geometry: Points Promethean Flipcharts for Geometry: Lines Visit Houston, Texas, and learn why city grids are laid in a rectangular pattern. Why do such grids rely on parallel and perpendicular lines? Why is this the most efficient way of organizing a city? Why is it the most fuel efficient? How can the geometry of lines help with city planning? Geometry concepts: lines, parallel lines, perpendicular lines Promethean Flipchart for Geometry: Lines Promethean Flipcharts for Geometry: Angles Visit Himeji Castle in Japan and learn why castles and other fortifications are built the way they are and how they take advantage of the properties of angles. When constructing a building for defensive purposes, knowing the properties of angles is important. Investigate fossils and the geology of sedimentary rocks. In the process you will learn a great deal about parallel and intersecting planes. The Burgess Shale fossils in Canada provide a real-world application. Geometry concepts: Planes, parallel planes, perpendicular planes Promethean Flipchart for Geometry: Planes Promethean Flipcharts for Geometry: Triangles Why does the Eiffel Tower have so many triangular shapes? In this Flipchart, use the properties of triangles to better understand the architecture of one of the world's most famous landmarks. Geometry concepts: triangles, properties of triangles Promethean Flipchart for Geometry: Triangles Promethean Flipcharts for Geometry: Right Triangles Learn about sailing at the same time that you apply your knowledge of right triangles. In this Flipchart students will also learn about the area of a triangle and right triangle trig ratios. Geometry concepts: right triangles, properties of right triangles Promethean Flipchart for Geometry: Right Triangles Promethean Flipcharts for Geometry: Squares and Rectangles Learn about Frank Lloyd Wright's architecture and apply the concepts of squares and rectangles. Geometry concepts: properties of quadrilaterals, squares, rectangles Promethean Flipchart for Geometry: Squares and Rectangles Promethean Flipcharts for Geometry: Parallelograms and Trapezoids Visit Madrid, Spain, and explore the Puerta de Europa Towers, two slanted, paralleogram-shaped towers. Learn how center of gravity and its relationship to its parallelogram design play a role in the architecture of this building. Visit the ancient city of Marrakesh and learn how Islamic artesans created elaborate tile patterns using the properties of polygons. Geometry concepts: polygons, regular hexagons Promethean Flipchart for Geometry: Regular Polygons Promethean Flipcharts for Geometry: Composite Figures The Petronas Towers in Kuala Lumpur provide an ideal application of composite figures. Students analyze the composite shapes in the building's design. Geometry concepts: properties of composite figures Promethean Flipchart for Geometry: Composite Figures Promethean Flipcharts for Geometry: Circles 1 Visit the Roman Coliseum to see circles at work. Even though the Coliseum itself is in the shape of an oval, the properties of circles are crucial to understanding how it was built. Geometry concepts: circles, arcs Promethean Flipchart for Geometry: Circles 1 Promethean Flipcharts for Geometry: Circles 2 Domed buildings have often been a way to study the stars. The Roman Pantheon was built to align with the sun in such a way that on key times of the year, a stunning solar display within the Pantheon could be seen. The properties of inscribed angles and intercepted arcs are key to understanding how the Pantheon was built. Geometry concepts: arc lengths, inscribed angles Promethean Flipchart for Geometry: Circles 2 Promethean Flipcharts for Geometry: Rectangular Prisms Mayan pyramids can be studied as stacks of rectangular prisms. In fact, the change in volume from the first tier to the last can be summarized with a geometric sequence. Students analyze this sequence and calculate the series. Geometry concepts: three-dimensional figures, rectangular prisms Promethean Flipchart for Geometry: Rectangular Prisms Promethean Flipcharts for Geometry: Cylinders The Shanghai Tower in China provides an opportunity to study cylinders in depth. Not only is the interior of the tower a stack of cylinders, the change in surface area from the first tier to the last can be generated by a geometric sequence. Students analyze the sequence and calculate the series. Geometry concepts: properties of three-dimensional figures, cylinders Promethean Flipchart for Geometry: Cylinders Promethean Flipcharts for Geometry: Volume and Density Why did the Titanic sink? How does this relate to volume and density? In this video-based Flipchart, students construct a mathematical model for the Titanic's ability to stay afloat. Through their analysis students see why the Titanic sank and how close it came to surviving the disaster. Geometry concepts: volume, density Promethean Flipchart for Geometry: Volume and Density Promethean Flipcharts for Geometry: Surface Area The glass pyramid at the Louvre Museum provides an opportunity to explore surface area, similar figures, tessellations, rhombuses, and triangles. Students calculate the number of quadrilateral-shaped glass panels to cover the pyramid shape. Geometry concepts: surface area, pyramids Promethean Flipchart for Geometry: Surface Area Promethean Flipcharts for Geometry: Surface Area and Volume The Citibank Tower in New York City has to content with heat loss, due to its large surface area. However, by analyzing the ratio of its surface area to volume, it is possible to come up with an energy-efficient building. Geometry concepts: the ratio of surface area to volume Promethean Flipchart for Geometry: Surface Area and Volume Promethean Flipcharts for Geometry: Longitude and Latitude Learn the history of the development of the longitude and lattitude scale and how this coordinate system still is an important system. Geometry concepts: Longitude, latitude, coordinate systems Promethean Flipchart for Geometry: Latitude Promethean Flipcharts for Geometry: Rectangular Coordinates Among treasure hunters off the coast of Florida, the quest for the gold from the Atocha remained long elusive. Learn how rectangular coordinates were a key part of isolating and locating the treasure. Geometry concepts: Coordinate systems, rectangular coordinate system Promethean Flipchart for Geometry: Rectangular Coordinates Promethean Flipcharts for Geometry: Polar Coordinates The Guggenheim Museum in New York City is itself an artistic treasure. Its innovative design is best understood as an application of polar coordinates. Geometry concepts: Coordinate systems, polar coordinates Promethean Flipchart for Geometry: Polar Coordinates Promethean Flipcharts for Geometry: Transformations Roller coasters are ideal examples of geometric translations and rotations. See how a roller coaster ride can be a great application of geometry! Geometry concepts: transformations, translations, rotations Promethean Flipchart for Geometry: Transformations Promethean Flipcharts for Geometry: 3D Translations The use of logistics in the field of shipping involves managing a great deal of data. This is also an application of translations in three dimensions. This collection of 27 Flipcharts includes all key topics from a full-year Algebra course. Nearly 10 minutes of video adapted from our Applications video series Geogebra activities. Below you will find a summary of each of the 27 Flipcharts in the Algebra Library. Promethean Flipchart Library for Algebra: Cycling The relationship between slope and grade in cycling is explored. Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope. Algebra concepts: slope, slope formula, slope-intercept form Promethean Flipchart for Algebra: Cycling Promethean Flipchart Library for Algebra: Drilling for Oil The potential for oil exploration in the controversial Alaska National Wildlife Refuge (ANWR) sets the scene for this problem. A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. How could new oil fields like ANWR help in breaking our dependence on foreign oil? Algebra concepts: linear functions, linear regression Promethean Flipchart for Algebra: Drilling for Oil Promethean Flipchart Library for Algebra: Health and Fitness Exercise needs to become a consistent part of everyone's lifestyle. In particular, aerobic exercises, which vigorously exerts the heart, is an important form of exercise. The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function. Algebra concepts: linear functions Promethean Flipchart for Algebra: Health and Fitness Promethean Flipchart Library for Algebra: Fireworks Displays Fireworks displays are elegant examples of quadratic function. In this segment the basics of quadratic functions in standard form are developed visually and students are guided through the planning of a fireworks display. Algebra concepts: quadratic functions Promethean Flipchart for Algebra: Fireworks Displays Promethean Flipchart Library for Algebra: Accident Investigation The distance a car travels even after the brakes are applied can be described through a quadratic function. But there is also the reaction time, the split second before the brakes are applied. The total distance is known as the stopping distance and this segment analyzes the quadratic equation that can be used by accident investigators. Algebra concepts: quadratic equations Promethean Flipchart for Algebra: Accident Investigation Promethean Flipchart Library for Algebra: Childhood Growth and Development From the time a baby is born to the time it reaches 36 months of age, there is dramatic growth in height and weight. An analysis of CDC data reveals a number of quadratic models that doctors can use to monitor and growth and development of children. Algebra concepts: Quadratic regression Promethean Flipchart for Algebra: Childhood Growth and Development Promethean Flipchart Library for Algebra: Honey Production Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Algebra concepts: Variables, data analysis Promethean Flipchart for Algebra: Honey Production Promethean Flipchart Library for Algebra: River Ratios Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river's length to its straight-line distance tell us? In this segment the geological forces that account for a river's motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to π. Algebra concepts: Ratios and proportions Promethean Flipchart for Algebra: River Ratios Promethean Flipchart Library for Algebra: Hybrid Cars With the increasing demand worldwide for cars, the cost of gasoline continues to rise. The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. The city of Venice is slowly sinking into the Adriatic Sea. So what does a city whose streets are full of water do about flooding? Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding, rising sea levels, and sinking have on this grand, ancient city. Students use the Lists and Spreadsheets and the Program Editor features of the TI-Nspire. Algebra concepts: inequalities in one variable Promethean Flipchart for Algebra: Floods in Venice Promethean Flipchart Library for Algebra: What Is a Mortgage? Students explore the dramatic events of 2008 related to the mortgage crisis. Brought about principally through mortgage defaults, the effect on the overall economy was severe. Yet, this situation offers an ideal case study for the exploration of Algebra concepts in data analysis and probability. By exploring these questions students get a front row seat to the historical events of the world's largest economy. The time value of money is at the basis of all loans. Students learn about the key factors that determine monthly mortgage payments and use the TI-Nspire to create an amortization table. This table is used throughout the rest of the program to explore different scenarios. Algebra concepts: business math Promethean Flipchart for Algebra: What Is a Mortgage? Promethean Flipchart Library for Algebra: What Is a Subprime Mortgage? Having learned the general features of a mortgage, students learn the specifics of a subprime mortgage. With this comes the notion of a credit score, and with credit scores come the probabilities for a loan default. Students use the amortization table to run probability simulations to determine possible loan defaults on subprime mortgages. Algebra concepts: business math Promethean Flipchart for Algebra: What Is a Subprime Mortgage? Promethean Flipchart Library for Algebra: What Is an Adjustable Mortgage? Another factor in the mortgage crisis was the use of adjustable rate mortgages Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis. Algebra concepts: business math Promethean Flipchart for Algebra: What is an Adjustable Rate Mortgage? The path of a rocket lifting offcan be modeled with the equation of a parabola. Students explore the quadratic function and the parametric equations that can be used to model the path of a spacecraft lifting off. Algebra concepts: conic sections, parabolas Promethean Flipchart for Algebra: Space Travel—Parabolic Paths Promethean Flipchart Library for Algebra: Space Travel—Circular Paths The path of a rocket orbiting the Earth can be modeled with the equation of a circle. Students explore the quadratic relation and the parametric equations that can be used to model the path of a spacecraft orbiting Earth. The planets orbiting the sun follow elliptical paths. In fact, the trajectory of a spacecraft traveling to Mars would also be elliptical. Students explore these various ellipses. Algebra concepts: conic sections, ellipses Promethean Flipchart for Algebra: Space Travel—Elliptical Paths Promethean Flipchart Library for Algebra: What Is an Earthquake? This Flipchart focuses on the Sichuan earthquake in China in 2008. The basic definition of an exponential function is shown in the intensity function for an earthquake. Students analyze data and perform an exponential regression based on data from the Sichuan earthquake. Algebra concepts: exponential functions Promethean Flipchart for Algebra: What Is an Earthquake? Promethean Flipchart Library for Algebra: What Is Earthquake Intensity? An exponential model describes the intensity of an earthquake, while a logarithmic model describes the magnitude of an earthquake. In the process students learn about the inverse of an exponential function. Algebra concepts: exponential functions Promethean Flipchart for Algebra: What Is Earthquake Intensity? Promethean Flipchart Library for Algebra: How Is Earthquake Magnitude Measured? An earthquake is an example of a seismic wave. A wave can be modeled with a trigonometric function. Using the TI-Nspire, students link the amplitude to an exponential function to analyze the dramatic increase in intensity resulting from minor changes to magnitude. Algebra concepts: exponential functions, trigonometric functions Promethean Flipchart for Algebra: How Is Earthquake Intensity Measured? Promethean Flipchart Library for Algebra: Hearing Loss We live in a noisy world. In fact, prolonged exposure to noise can cause hearing loss. Students analyze the noise level at a rock concert and determine the ideal distance where the noise level is out of the harmful range. Using the TI-Nspire's Geometry tools, student create a mathematical simulation of the decibel level as a function of distance. Algebra concepts: logarithmic functions, decibel scale Promethean Flipchart for Algebra: Hearing Loss Promethean Flipchart Library for Algebra: Tsunamis In 1998 a devastating tsunami was triggered by a 7.0 magnitude earthquake off the coast of New Guinea. The amount of energy from this earthquake was equivalent to a thermonuclear explosion. Students analyze the energy outputs for different magnitude earthquakes. Using the Graphing tools, students explore the use of a logarithmic scale to better analyze exponential data. Algebra concepts: logarithmic functions Promethean Flipchart for Algebra: Tsunamis Promethean Flipchart Library for Algebra: Submarines In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine. Algebra concepts: rational functions Promethean Flipchart for Algebra: Submarines Promethean Flipchart Library for Algebra: Submarines All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms. Algebra concepts: rational functions, ratio of surface area to volume Promethean Flipchart for Algebra: Animal Evolution Promethean Flipchart Library for Algebra: The Hubble Space Telescope The Hubble Telescope, like all telescopes, relies on the lens formula to focus an image. The lens formula results in a rational equation that can be solved for determining the settings on the lens. Algebra concepts: rational functions, the lens formula Promethean Flipchart for Algebra: The Hubble Space Telescope Promethean Flipchart Library for Algebra: Profit and Loss Profit and loss are the key measures in a business. A system of equations that includes an equation for income and one for expenses can be used to determine profit and loss. Students solve a system graphically. Algebra concepts: linear systems Promethean Flipchart for Algebra: Profit and Loss Promethean Flipchart Library for Algebra: Encryption Secret codes and encryption are ideal examples of a system of equations. In this activity, students encrypt and decrypt a message. Algebra concepts: linear systems, matrices Promethean Flipchart for Algebra: Encryption Promethean Flipchart Library for Algebra: Ballistic Missiles A ballistic missile shield allows you to shoot incoming missiles out of the sky. Mathematically, this is an example of a quadratic system. Students graph such a system and find the points of intersection between two parabolas. Over 20 minutes of video Hosted by internationally recognized educator Monica Neagoy. Below you will find a summary of each of the 10 Flipcharts in the TI-Nspire CXLibrary. Promethean Flipchart Library for the TI-Nspire CX: Linear Functions In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use of the TI-Nspire CX. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. In this program, the TI-Nspire is used to explore the nature of quadratic functions. Examples ranging from space travel and projectile motion provide real-world examples for discovering algebraic concepts. All examples are solved graphically. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Ever since the mathematics of the Babylonians, equations have played a central role in the development of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video traces the history and evolution of equations. It explores the two principal equations encountered in an introductory algebra course – linear and quadratic – in an engaging way. The foundations of algebra are explored and fundamental questions about the nature of algebra are answered. In addition, problems involving linear and quadratic equations are solved using the TI-Nspire graphing calculator. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Used in just about any industry, inequalities, like equations, are fundamental building blocks of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video explores inequalities—concepts, properties, solutions, and notations— connects them to real-world contexts, and uses the TI-Nspire to make the algebra meaningful. The focus of this program is on linear inequalities in one and two variables. Algebra concepts: Equations, inequalities Promethean Flipchart Library for the TI-Nspire CX: Relations and Functions Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Almost everyone has an intuitive understanding that exponential growth means rapid growth. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video builds on students' intuitive notions, explores exponential notation, and analyzes properties of exponential function graphs, with the help of TI-Nspire features such as sliders and graph transformations. Using exponential functions to model finance applications and a Newton's law of cooling problem further help students build a solid foundation for these fundamental algebraic concepts. What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video introduces students to systems of linear equations in two or three unknowns. To solve these systems, the host illustrates a variety of methods: four involve the TI-Nspire (spreadsheet, graphs and geometry, matrices and nSolve) and two are the classic algebraic methods known as substitution and elimination, also called the linear combinations method. The video ends with a summary of the three possible types of solutions. Algebra concepts: equations, linear equations, linear systems Promethean Flipchart Library for the TI-Nspire CX: Rational Functions After briefly reviewing the concept of inverse variation, this video explores Boyle's law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. This video begins with the historical invention of logarithms that forever changed the world of computation—until the advent of calculators more than 300 years later. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it proceeds to derive the properties of logs, examine logarithmic functions and graphs, and finally explore the well-known Richter logarithmic scale. Algebra Jeopardy: Our most popular Flipchart. This Jeopardy-style Algebra game provides enough questions for a review of key concepts from linear and quadratic functions. FREE Square Numbers: This video-based Algebra and Geometry Flipchart provides a compelling introduction to square numbers. Included are two hands-on activities, one that can be done on an interactive whiteboard by the students, and one using the TI-Nspire CAS graphing calculator. FREE Functions, Relations, and...Star Trek: This video-based Algebra Flipchart uses the idea of the transporter in Star Trek as a way to explore the concepts of functions and relations. Using the idea of a transport as a mapping, we look at a "functional" transport and a "relational" transport. FREE. TI-Nspire Mini-Tutorial: Exploring Slope-Intercept Form: In this video-based Algebra tutorial, students are shown how to use the TI-Nspire graphing calculator to explore the slope-intercept form of a linear function. The use of sliders is explored so that values of m and b can be modified easily. FREE TI-Nspire Mini-Tutorial: Exploring Quadratics: In this video-based Algebra tutorial, students explore the standard form of a quadratic function using sliders. FREE Solving Equations in One Variable: This Algebra Flipchart goes through a comprehensive review of solving equations in one variable, as well as multiple examples. FREE
This is the most important section of the website. The aim of it is to get you understanding and enjoying your maths a bit more. Here you will find links to notes and examples, ways to check your work, video solutions, tutorials, revision websites, exam advice, podcasts, everything you could possibly need to help you get as good as possible at your maths Big News: You can now download the full set of GCSE notes to print out or view on your phone/tablet by clicking here.
High School Math High school math is the mid level of the math curriculum. Students prepare themselves for colleges at high school. This the time which asks parents and educator to be very careful about the teenager students. The main topics in the high school math include Mastering the order of operations involving fractions, exposnets and paranthesis. Kids should be able to do operation with fractions such as how to multiply fractions. Understaing and apply the basic algebraic concepts such as algebraic expressions, polynomials, equations such as linear equations and quadratic equations. Introduction to tringonomentry and application of tringonometric ratios in othe areas of math. Coordinate geometry including lines, circels and conics. Application of lines such as slopes in daily life situations or in physics. Finding area of a circle from its radius or finding area and volume of solids. Mensuration such as finding the surface area and volume of simple three dimensional shapes and composite figures.
Algebra - 9. Inequalities.Powerpoint lesson. KS4 A few years ago I wrote a set of notes for pupils and put them on my website. The notes were supposed to be written in a "pupil-friendly" way, and different to notes students might find in textbooks or elsewhere on the internet. I have converted the notes to PowerPoint slides so you can download the More…m, adapt them if needed, use them in revision lessons or perhaps give your students a set to take home with them to help them prepare for exams. The chances are there will be a few mistakes here and there, so if you spot any please email me & I will correct them. Hope they are of use! Reviews (1) Very accessible and comprehensive notes on inequalities. Covers basics through to solving inequalities graphically - including quadratic inequalties. Simple explanations and clearly commented examples throughout makes them ideal for students to use during independent study.
Numerical Mathematics And Computing - 6th edition Summary: Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' high...show morely regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION

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