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Intermediate Math Journal
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687 KB|6 pages
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Product Description
This is a booklet for students to communicate their mathematical thinking. It is focused on the use of math journals and problem solving techniques for students to use.
The booklet includes steps for students, a description of the journal process, tips on problem solving, a blank template, and a math journal rubric. | 677.169 | 1 |
1. For Students – Home
In the following module, you will learn the mathematics behind differential equations—specifically those describing exponential and logistic growth. You will also study a system of differential equations describing an infectious disease.
The module is divided into three sections: Exponential Growth, Logistic Growth and Infectious Disease. Each section contains a few pages. Please read and complete the activities on each page before moving on to the next.
You can use the menu bar above to return to this page, open the simulator, or open the simulator help page.
You can navigate through this site by using the arrows at the bottom of each page, or by using the sidebar on the left.
You will need Adobe Flash Player 10 to use many of the components found in the module. If you do not have the latest version of Flash Player, you can download it for free here.
Many interactive questions will appear throughout the text. These questions appear in boxes. Try to answer the question on your own, only revealing the answer after you have attempted an answer yourself. | 677.169 | 1 |
Circuit Training - Limits (calculus)
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216 KB|2 pages
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Your students will work every single one of these 24 limits problems because of the circuit format. To advance in the circuit, students must find their answers -- this element of self-check is essential! My students don't get up when the bell rings and they are working on a circuit! The problems are progressive in nature and contain a little bit of everything, including trig and transcendentals.
No answer key is included as the answers are part of the circuit. This can be used as guided notes, independent practice, cooperative work, or even a test! | 677.169 | 1 |
"Anytime you can use real life examples in teaching is a positive experience for the students. Studying the cars on the track and translating the data from runs will help the students learn how calculus has many uses." | 677.169 | 1 |
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PowerPoint Slideshow about ' Welcome Back ' goal of this course is to provide students with a thorough and extensive study of linear and quadratic functions and graphing on the xy-coordinate system. By the end of this course, students will have all the knowledge necessary to solve and graph equations and inequalities. They will also be able to apply this knowledge to other areas of math, such as word problems, ratios and proportions. | 677.169 | 1 |
Designed for a one or two-semester Applied Calculus course, this innovative text features a graphing calculator approach, incorporating real-life applications and such technology as graphing utilities and Excel® spreadsheets to help students learn mathematical skills that they will use in their lives and careers. The texts overall goal is to improve learning of basic calculus concepts by involving students with new material in a way that is different from traditional practice. The development of conceptual understanding coupled with a commitment to make calculus meaningful to the student are guiding forces. The material involves many applications of real situations through its data-driven, technology-based modeling approach. The ability to correctly interpret the mathematics of real-life situations is considered of equal importance to the understanding of the concepts of calculus.
CALCULUS CONCEPTS, Fifth Edition, presents concepts in a variety of forms, including algebraic, graphical, numeric, and verbal. Targeted toward students majoring in liberal arts, economics, business, management, and the life and social sciences, the text's focus on technology along with its use of real data and situations make it a sound choice to help students develop an intuitive, practical understanding of concepts.
Iris B. Reed,
Clemson University
Laurel R. Carpenter,
Cynthia R. Harris,
University of Nevada
Sherry Biggers,
Clemson University
What's New
Many of the book's examples and activities are new. In addition, many data sets have been revised to incorporate more recent data.
All solutions have been reworked and answers have been rewritten to be concise. Activities requiring essay-style answers are clearly marked.
The concept of limits is introduced early in Chapter 1 and used throughout the discussion of models in the remainder of that chapter. The concept is also used to help students understand differentiation and integration.
Formerly presented in a self-contained chapter, coverage of sine models has been incorporated throughout the text in optional sections and activities.
Differential equations and slope fields are introduced in a pair of optional sections located at the end of the integration chapters.
The text has been carefully rewritten so that narrative sections are as clear and concise as possible.
While a real-world context is still used as the platform for most of the discussion, some of the less critical details of these contextual descriptions are now presented to the side of the primary narrative in Notes, allowing students to focus on key ideas without potentially getting distracted.
Definitions and other important mathematical elements are highlighted in boxes for easy reference, and selected mathematical and interpretation skills are illustrated in Quick Examples.
Each section's activity set has been reworked to incorporate an orderly development of the skills and concepts presented in that section.
Many activities have been rewritten to be more student-friendly, and others have been replaced with up-to-date applications. Even-numbered activities are similar to, but not necessarily identical to, odd-numbered activities.
Features
Each chapter opens with a real-life situation and several questions about the situation that can be answered using the concepts and skills to be covered.
Each section incorporates a brief concept development narrative, interspersed with Quick Examples that highlight specific skills as well as formal examples that illustrate the application of the skills and concepts in a real-world setting.
A NAVG (numeric, algebraic, verbal, and graphical) compass icon indicates places in the text where a concept is demonstrated through multiple representations. This feature helps students recognize connections between different representations, and is particularly helpful for students who use alternative learning styles.
A Concept Inventory listed at the end of each section gives students a brief summary of the major ideas developed in the section.
A Concept Review activity section at the end of each chapter provides practice with techniques and concepts. Complete answers to the Concept Review activities are included in the answer key located at the back of the text.
Concept Check is an end-of-chapter checklist that describes the main concepts and skills taught in the chapter and identifies sample odd-numbered activities corresponding to each item. Students can complete these representative activities to help them assess their understanding of the chapter content and identify the areas on which they need to focus their study.
A Chapter Summary reviews and connects major chapter topics and concepts, and further emphasizes their practical importance.
Activities, such as online Projects and Writing Across the Curriculum, reinforce the authors' innovative approach. Spreadsheet and Graphing Calculator Activities give students the opportunity to use technology as they learn difficult calculus concepts.
Section Activities at the end of each section reinforce concepts and allow students to explore topics using, for the most part, actual data in a variety of real-world settings. These activities, designed to encourage students to communicate in written form, include questions and interpretations pertinent to the data. The activities do not mimic the examples in the chapter discussion, requiring students to think more independently. Possible answers to odd-numbered activities are given at the end of the book.
End-of-chapter Projects are optional group assignments that allow students to practice composing reports and giving oral presentations.
Supplements
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
FOR INSTRUCTORS
PowerLecture DVD
ISBN: 9780538735407
This DVD provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing, featuring algorithmic equations. There's also a link to the Solution Builder online solutions manual, making it easy to build solution sets for homework or exams.
Student Solutions Manual
ISBN: 9780538735414
This manual contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. | 677.169 | 1 |
Synopses & Reviews
Publisher CommentsNew Side-by-side Example Solutions for select examples include multiple problem solving approaches—such as algebraic, graphical, and numerical—to appeal to a variety of teaching and learning styles.
New Checkpoints after each Example/Solution refer students to similar drills in the Section Exercises, allowing students to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book.
New Vocabulary Checks open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts.
Exercise Sets have been carefully analyzed and revised to improve the categorization of problems from basic skill-building to challenging; improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications.
New Make a Decision applications—presented throughout the text at the end of selected exercise sets—are based on large sets of real data. These extended modeling applications give students the opportunity to use all the mathematical concepts and techniques they've learned and apply them to large sets of real date—analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format.Eduspace, powered by Blackboard, Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the College Algebra text. This content is paired with the recognized course management tools of Blackboard.
For copyright 2007, two titles have been added to the Precalculus Series: Precalculus with Limits and Precalculus: A Concise Course. These titles enhance the scope of the series, making it even more flexible and adaptable to a variety of learning and teaching styles.
Synopsis The | 677.169 | 1 |
Geometric Tools for Computer Graphics (Hardback)$22.65
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Condition
VERY GOOD: The book's pages and spine are in excellent condition; however, there is what appears to be a manufacturing defect at the bottom of the inside front cover where the cover material falls short of the glued-in endpaper. This book is printed on acid-free paper.
Description
From the back cover: "Do you spend too much time creating the building blocks of your graphics applications or finding and correcting errors? Geometric Tools for Computer Graphics is an extensive, conveniently organized collection of proven solutions to fundamental problems that you'd rather not solve over and over again, including building primitives, distance calculation, approximation, containment, decomposition, intersection determination, separation, and more.
"If you have a mathematics degree, this book will save you time and trouble. If you don't, it will help you achieve things you may feel are out of your reach. Inside, each problem is clearly stated and diagrammed, and the fully detailed solutions are presented in easy-to-understand pseudo-code. You also get the mathematics and geometry background needed to make optimal use of the solutions, as well as an abundance of reference material contained in a series of appendices.
"FEATURES
Filled with robust, thoroughly tested solutions that will save you time and help you avoid costly errors.
Covers problems relevant for both 2D and 3D graphics programming.
Presents each problem and solution in stand-alone form allowing you the option of reading only those entries that matter to you.
Provides the math and geometry background you need to understand the solutions and put them to work.
Clearly diagrams each problem and presents solutions in easy-to-understand pseudocode.
Resources associated with the book are available at the companion Web site Catalan numbers crop up in chess boards, computer programs, and even train tracks. This comprehensive text presents a clear introduction to one of the truly fascinating topics in mathematicsThe origins of computational group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics." — From the back coverThis self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative | 677.169 | 1 |
3. Differentiation 3.1 Tangents and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Related Rates 3.9 Linearization and Differentials
5. Integration 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Substitution and Area Between Curves
10. Infinite Sequences and Series 10.1 Sequences 10.2 Infinite Series 10.3 The Integral Test 10.4 Comparison Tests 10.5 The Ratio and Root Tests 10.6 Alternating Series, Absolute and Conditional Convergence 10.7 Power Series 10.8 Taylor and Maclaurin Series 10.9 Convergence of Taylor Series 10.10 The Binomial Series and Applications of Taylor Series | 677.169 | 1 |
•SETS AND SUBSETS: Equality, Membership, Singleton sets,
The empty set, Venn diagrams, Subsets, Power sets, Number of elements of a power
set, Number of k-element subsets of a set with m elements (Pascal's formula)
•OPERATIONS WITH SETS: Intersection, Union, Difference, Symmetric difference
Unit 3: MAPPING
•MAPPINGS: Mappings from A to B, Mappings from A onto B,
One-to-one mappings, Permutations on a set, The image of an element under a
mapping ("f(x)" notation), Composition of mappings, Arithmetic mappings,
Circular slide rules
•MAGNIFICATION OF MAPPINGS ON LENGTHS: "Stretchers," "Shrinkers," Composites of
stretchers and shrinkers, Addition of lengths, Comparison of lengths
•APPLICATIONS OF MAGNIFICATION MAPPINGS: Photography, Map making, Scale drawing,
Solution of problems on weight, time, and money
•PERCENT MAPPINGS
Unit 4: THE RATIONAL NUMBERS, DECIMALS AND AN
APPLICATION OF RATIONAL NUMBERS
•WHAT IS THE NUMBER π?: Ratio of circumference to diameter
as a fundamental constant of nature, circumference and area of circles
•SOME USES OF π: Volume of a cylinder, Surface area of a cylinder, Role of
William Jones, John Machin, Leonhard Euler, π as first letter of the Greek words
for perimeter and periphery, Pappus' rule for surface area, Pappus' rule for
volume of a solid, solids of rotation
•EARLY HISTORY OF π: Babylonian, Egyptian, Biblical, Greek, Chinese, Hindu
approximations, infinite series and products of ratios of integers that yield π
•COMPUTATION OF π: A Discovery of Archimedes, Pi determined by slicing a
circular disk, Pi determined by interior and exterior regular polygons, Johann
Lambert's role showing π is irrational using continued fractions
•PI MISCELLANY: Buffon Needle Problem, Using Random Numbers to approximate π | 677.169 | 1 |
Thinking Mathematically 2nd Edition
50% OFF
J Mason L Burton & K Stacey
A revamped classic.
How can you develop your powers to think deeply about mathematics? The impeccably credentialled authors believe that when tackling mathematical problems "…being stuck is an honourable state and an essential part of improving thinking." Originally published more than 30 years ago, the text has been updated with 77 fresh problems which intrigue and challenge, suitable for senior secondary students, pre-service teachers and/or undergraduates.
Thought processes and problem solving techniques are examined and explained: specialising and generalising, phases of work, responses to being stuck, conjecturing, justifying and convincing. This is a book to be used, not read. Challenge yourself! | 677.169 | 1 |
Product Media
Product Description
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This solutions manual is part of the Saxon Math Intermediate 5 curriculum series. Answers are arranged by section and lesson, and include complete step-by-step solutions to the Lesson Practice, Written Practice, and Early Finishers questions, as well as the questions and practice items in the Investigations, found together in the Saxon Math Intermediate 5 Textbook.
The Lesson Practice, Written Practice, and Investigations solutions also align with the Adaptations for Saxon Math 5 Workbook, which contains space to work out the problems in the textbook; the same Written Practice questions in the Textbook and Adaptations Workbook are also found in the Written Practice Workbook, along with the Early Finishers questions from the textbook (which are not in the Adaptations Workbook).
This manual does not contain the answers to the Power-Up Workbook, as answers are not currently available. 221 newsprint-like pages, softcover. | 677.169 | 1 |
Algebra+ is a 10-week online course designed for students who have successfully completed high school algebra but who placed into pre-college level mathematics at their local college or university. This course is for refreshing their math skills with a review of pre-college level algebra. After successfully completing this course, the goal would be to retake your college
This course is a review of Basic Arithmetic skills that serve as a prerequisite for placement into and success in pre-college and college-level algebra courses. In this course, primary emphasis will be placed on fundamental operations with whole numbers, fractions, decimals, and integers. Other topics covered include proportions, percentages, representations of data, geometric figures, and measurement. Students who should take this course include: those that have an interest in brushing up on arithmetic skills prior to taking an upcoming placement test or those that have not had math in many years and want to review foundational skills and concepts. This course provides free digital access to all required materials including a student workbook, lesson videos, and online homework practice and assessment. A certificate of completion will be awarded by the instructor to students who complete required activities. The course instructor recommends purchase of a textbook or other course materials. Please see the details below. Required materials: Basic Arithmetic Student Workbook Purchase Info: Hard copy at Lulu.com or access via free digital download. Approximate cost for hard copy: $15
College Algebra Prep will get you ready for College Algebra. We will cover the prerequisite algebra topics, study skills, success skills, and things you need to know about electronic homework systems, to be successful in college algebra. You will supply the drive and commitment to make this a successful course for you.
During this four week course, instructors will learn how to create and teach an exciting new type of developmental math course known as a pathways course. These courses (e.g., Math Literacy for College Students, Quantway
This course is designed for students who will be starting or restarting college within the next year, and for current students who have not completed their general education math requirement. It will provide math refresher materials covering a wide range of mathematical concepts together with information about success in college. Incoming college students are typically placed in college math courses based on placement exam scores. Students often take these placement exams with minimal preparation or after a long break since their last math class. The study materials in the course will help students prepare for placement exams, and higher scores mean fewer required math courses in college. Students who have already taken a placement exam (such as the ACT) can also use these materials to study and then retest, hopefully scoring higher. College students who have started, but not finished their math courses, can also retake a placement exam and possibly skip a math class. The course will also be valuable for anyone who just wants to refresh their math skills. The provided study materials are individualized based on a student's current knowledge. Each student will be provided a customized learning path that maximizes efficiency so that study time is spent where it's needed most. Beyond math content, the course will also provide college success material such as test-taking strategies, new student orientation, and study techniques. All of this material can be accessed separately from the math content so even if a student is already placed highly in math, or has tested out of it completely, the course will provide valuable information to help the student orient to college and to get the most out of the college experience.
Students often encounter grave difficulty in calculus if their algebraic knowledge is insufficient. This course is designed to provide students with algebraic knowledge needed for success in a typical calculus course. We explore a suite of functions used in calculus, including polynomials (with special emphasis on linear and quadratic functions), rational functions, exponential functions, and logarithmic functions. Along the way, basic strategies for solving equations and inequalities are reinforced, as are strategies for interpreting and manipulating a variety of algebraic expressions. Students enrolling in the course are expected to have good number sense and to have taken an intermediate algebra course.
The key learning objectives of this MOOC are:
1. Review, develop, and demonstrate their conceptual understanding and procedural skills with selected fundamental mathematical topics
2. Collaborate with peers to solve problems that arise in mathematics and other contexts
3. Create and use representations to organize, record, and communicate mathematical ideas
4. Reflect on the process of problem solving
5. Justify results using mathematical reasoning
6. Communicate mathematical thinking clearly to peers and to the instructor
The learning objectives and course content align with on?campus versions of this type of course. We are building this MOOC around key concepts and skills in the nationally recognized Common Core State Standards for Mathematics, the ACT College Readiness Standards, and the SAT Skills Insight. Students
successfully completing our MOOC will find their subject matter knowledge to be in alignment with the
"typical" course offered by other U.S. colleges and universities. By using Common Core standards, ACT
College Readiness Standards, and the SAT Skills Insight, we can also begin to develop post?test instruments
that will assess the students' levels of proficiency | 677.169 | 1 |
A First Book in Algebra by Wallace C. Boyden
By Wallace C. Boyden
It is a new printing of the vintage algebra publication by way of Boyden. The publication is appropriate for college students taking a primary direction in algebra. it really is full of approximately 1500 workouts for college kids to perform. themes coated contain notation, operations, factoring, fractions, advanced fractions, fixing equations, and fixing simultaneous equations. solutions to all of the workouts are supplied on the finish of the publication. technological know-how and Religiosity; outdated Clo'; the good Emancipator; The Fourth size; The final Idol; Retrospect; and The Priesthood of technological know-how.
Compiled through a professional crew of accountants, seventy eight Tax assistance For Canadians For Dummies bargains useful tax making plans options. those person counsel provide ordinary recommendation and perception that may shop readers aggravation and cash.
ALGEBRA AND TRIGONOMETRY: actual arithmetic, genuine humans, seventh version, is a perfect pupil and teacher source for classes that require using a graphing calculator. the standard and volume of the workouts, mixed with attention-grabbing purposes and cutting edge assets, make instructing more uncomplicated and aid scholars prevail. | 677.169 | 1 |
I would suggest going through these books in order to get a nice introduction to mathematical thinking, proofs and analysis (which is a revisit of calculus but through the eyes of a mathematician as opposed to someone who might be learning calculus as a tool to solve problems, like an engineer or physicist.)
Try to revisit earlier mathematical content. This is great for two reasons.
(1)Great review of older material. Helps with the eventual GRE. You will find out how much information was not understood the first time.
(2)Since the material is something you are familiar with, you will have easier time reading, and writing proofs of something known.
I learned to read and write proofs from: Reading all of my textbooks throughout my education. Engage the textbook!
I re learned geometry from: Geometry: Moise/Downs, restudied Linear Algebra from Anton( reading, doing, and doing the proofs on my own). I later moved into more advance material.
I cannot stress the trying and doing proofs enough.
The explanation that Moise gives for Existence and Uniqueness is very GOOD. It was something I did not grasp until reading this basic, but good book. | 677.169 | 1 |
The Concise Oxford Dictionary of Mathematics provides jargon-free definitions for over 3,000 of even the most technical mathematical terms. This dictionary covers all commonly encountered terms and concepts from pure and applied mathematics and statistics, such as linear algebra, optimization, nonlinear equations, and differential equations. In addition, there are entries on major mathematicians and topics of more general interest, such as fractals, game theory, and chaos.
The Concise Oxford English Dictionary is the most popular dictionary of its kind and is noted for its clear, concise definitions as well as its comprehensive and authoritative coverage of the vocabulary of the English-speaking world. | 677.169 | 1 |
Reading materials (Freshman undergrad)
Hello!
I'm currently in the summer before my freshman year at a University and I was wondering what books would be "good" to read.
I'm a physics major but I'm also interested in math.
Let me expand, by "good" I mean some book (textbook, etc) that would expand my knowledge of physics beyond non calculus physics and my math knowledge beyond basic calculus.
How about a chemistry book? This knowledge could give you more insight into matter and particles. Not sure what math subject would suit your interest, but mathematical logic is nice to read about if you are into that kinda thing, and there are a few pdf's available online.
PS. I don't know of a good physics book to read, given that you'll be learning physics soon enough anyway.
I would recommend looking into a pop science book rather than a text book if you'd like to do physics over the summer. Something written for an undergraduate or even the layman would be beneficial. For instance, to prepare for quantum mechanics, one of my professors recommended I purchase The Meaning of Quantum Theory by Jim Baggot ($0.75 on Amazon), it helped a lot conceptually and allowed me to ask questions about the theory without having it heavily obscured by mathematics. That said, I wouldn't argue to read that book when not having been introduced to some modern physics such as the Schrodinger equation in 1 and 3 dimensions in square/cubic wells. QED by Feyman has been interesting so far, but the effort he takes to remove the mathematics makes me slightly less interested; it would probably be interesting to read as a recent high school graduate.
Chemistry is something that I would second, I'm currently studying for the PGRE and having looked at previous tests, the mild amount of more chemical/atomic physics is by far my weakest area; however, when I took chemistry years ago I was not a good student. I am actually ordering some physical chemistry and general chemistry texts now from goodwillbooks.com.
If you'd like math books, there are some paperbacks available about famous math problems. I have a text, Dr. Reimann's Zeroes, about the Reimann Hypothesis as well books on the history of math including Zero, e, and in general. Admittedly, I haven't read them yet, but they're on my to-do list! If you insist on a math book, pick up a cheap linear algebra or discrete math text, it probably doesn't matter too much what as the intro texts (in my opinion) are a dime a dozen these days.
You say you're good with calculus, but there is a lot to study. I'm assuming you took AP calculus, did you take AB or BC? Have you looked into vector calculus yet? Dot and cross products are things you should know, and if you still need to learn them, linear algebra and vector calculus go well together when learning them simultaneously. Also, in my experience, students don't really retain Taylor Series well however, they're very important and you should know them backwards and forwards. Same goes with power series expansions in general, it's important to not let yourself be confused by abstract versus obscurity.
Another option is to find a topic that is related to physics, in fact, this is what I would really suggest. You'll have plenty of time to forward yourself in classes, but your unique interests are what will give you an edge over others for projects as well as serve as a guide for where you want to go in physics. Music and music theory highly interests me, including designing sound studios and electronic instrument effects, amps, etc. I have a book called Designing Hi-fi Furniture which covers some history of furniture as well as designing speaker cabinets. If you share this interest, I highly recommend the text. The paperback is dirt cheap and you can even find a .pdf online for free. PMillett (google it) has several old audio/electrical design texts that are in the public domain as .pdfs.
As far as where to buy them, I never get tired of recommending goodwillbooks.com if you don't object to used books and are in The States. Very cheap texts, very cheap shipping costs. It's perfect if you want to have a couple intro linear algebra or calculus or any other intro subject texts on hand without spending $20 a book. Plus, if you get a dud, a lot of the time you're only out a couple dollars per book, nothing really lost there! Other places include alibris.com and betterworldbooks.com . | 677.169 | 1 |
Calculators and computers: Most modern calculators, in particular the TI-83 used in
our calculus courses, are capable of matrix operations, and are very useful in math 309 for
checking homework answers and other problems. However, since these calculators automate
many of the skills that are taught in this course, it was decided that
use of calculators on exams will not be allowed.
Access to a computer
and a mathematical utility program like MATLAB, Maple or Mathematica can be very helpful indeed.
If you are in science or engineering you'll want to learn to use such a program in any
case, but it is not strictly required in this course. It will, however, greatly reduce
the tedium involved in doing matrix algebra problems.
The textbook contains an excellent chapter describing matrix operations in MATLAB,
and the MATLAB program is widely available in computer labs around the campus.
Exams: There will be two in-class exams and a final. Each of the
three exams will count 30% of the grade. The final will be cummulative, with an
emphasis on material covered since exam 2. Exams are closed book and calculators
are not allowed. All exams will be hand-graded and partial credit for
a problem will be awarded when appropriate. The exam schedule is as follows:
exam I
exam II
final
2/17
3/31
5/10 (deadline)
The final will be a take home exam. Precise instructions for taking it will be given
later. Notice that the date given above is the deadline for turning it in.
Homework and take-home problems: There will be (roughly) weekly homework assignments.
The homework problems will be posted on the lesson schedule at least a week in
advance of its due date. They will also be announced in class. Homeworks will not
be accepted past the due date.
Homework problems will be
relatively few in number. It is expected that you will write them clearly and cleanly.
Even if your answer to a particular problem is correct, you may still lose points
for writing it in a sloppy or confusing way. Homework assignments will make 10% of
the grade.
Often, especially early in the
course, problems may amount to performing a matrix operation that can in principle be
done with a calculator without
much understanding of the subject. Make sure to show enough work in those cases so that
we know you did those problems by hand. Of course, you can still use your calculator to
check the answer. This requirement (of solving problems by hand) may be relaxed
as the course progresses and problems become more complex.
In addition to the homework problems, the lesson schedule has a long list of
suggested problems. These will not be collected. You should work on as many of them
as possible to gain practice with the material of each lecture.
The date row in which the problems are listed tells you, approximately, when the corresponding
topic is being discussed. I will be drawing from this list to make exam problems.
(Longer problems may have to be modified to make them doable in the amount of time
available during exams.)
Grades: Your grade will be calculated on the basis of the two exams, final, and
homeworks. Each exam and the final will make 30% of the grade and the homeworks 10%.
The exact grade scale will not be decided till the end of the course.
However, the final letter grade is guaranteed to be no harsher than the following:
Score
Grade is at least (possibly with a + or - attached)
90-100%
A
80-89.99%
B
65-79.99%
C
50-64.99%
D
Below 50%
NCR (F)
(Potentially) useful links: You might find some of these links useful (or not).
They contain lecture notes and texts for linear algebra that can be freely downloaded,
a few historical notes and other resources. I'll add to this list as I find
other interesting Web pages.
In any event, I will not rely on any of this material for the course. If you find
other useful pages, let me know so that I can add to this list. | 677.169 | 1 |
Intermediate Mathematics and Statistics Handbook
Units of Study
In this chapter, Mathematics units are listed, by semester, in numerical
order; then Statistics units are listed, by semester, in numerical order.
Units are designated Mainstream or Advanced. Entry to an Advanced level
unit normally requires a Credit or better in a Mainstream level prerequisite,
or a Pass or better in an Advanced level prerequisite.
Mathematics units are also labelled Applied, or Pure, or both.
Although there is no clear distinction between applied mathematics
and pure mathematics at the intermediate level, this labelling
gives a rough guide as to which senior level units the intermediate
level units are most closely allied with.
The unit code for an intermediate unit of study in the School consists
of MATH or STAT followed by four digits: for example MATH2068 or STAT2011.
The first digit is 1 for junior level units, 2 for intermediate level units,
3 for senior level units. The second digit indicates whether the unit is
mainstream (0 or 1) or advanced (9). In most cases two units which share the
same last two digits are mutually exclusive: for example, MATH2061 may
not be counted with MATH2961. The one exception is that MATH2068
and MATH2968 are not mutually exclusive. Instead MATH2068 and
MATH2988 are mutually exclusive.
Text and reference books are yet to be advised. Except for The Little Blue
Book it is suggested that you do not purchase any books until
recommendations are made by lecturers.
The Little Blue Book is a compact reference book: it contains definitions,
formulas and important results from Junior Mathematics which are used
in Intermediate Units. It is recommended that all students have access to
this book: it is available from the Coop Bookshop.
This unit starts with an investigation of linearity: linear functions, general
principles relating to the solution sets of homogeneous and inhomogeneous
linear equations (including differential equations), linear independence and
the dimension of a linear space. The study of eigenvalues and eigenvectors,
begun in junior level linear algebra, is extended and developed. Linear operators
on two dimensional real space are investigated, paying particular attention
to the geometrical significance of eigenvalues and eigenvectors.
The unit then moves on to topics from vector calculus, including vector-valued
functions
(parametrised curves and surfaces; vector fields; div, grad and curl; gradient
fields and potential functions), line integrals (arc length; work; pathindependent
integrals and conservative fields; flux across a curve), iterated integrals
(double and triple integrals; polar, cylindrical and spherical coordinates; areas,
volumes and mass; Green's Theorem), flux integrals (flow through a surface;
flux integrals through a surface defined by a function of two variables, though
cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem
and Stokes' Theorem.
The unit starts by introducing students to solution techniques of ordinary and
partial differential equations (ODEs and PDEs) relevant to the engineering disciplines:
it provides a basic grounding in these techniques to enable students
to build on the concepts in their subsequent engineering classes. The main
topics are Fourier series, second order ODEs, including inhomogeneous equations
and Laplace transforms, and second order PDEs in rectangular domains
(solution by separation of variables).
We introduce students to several related areas of discrete mathematics, which
serve their interests for further study in pure and applied mathematics, computer
science and engineering. Topics to be covered in the first part of the
unit include recursion and induction, generating functions and recurrences,
combinatorics, asymptotics and analysis of algorithms. Topics covered in the
second part of the unit include Eulerian and Hamiltonian graphs, the theory
of trees (used in the study of data structures), planar graphs, the study of
chromatic polynomials (important in scheduling problems), maximal flows in
networks, matching theory.
MATH2961 Linear Mathematics and Vector Calculus
(6 credit points, Advanced, Pure and AppliedThis unit is an advanced version of MATH2061, with more emphasis on the
underlying concepts and on mathematical rigour. Topics from linear algebra
focus on the theory of vector spaces and linear transformations. The
connection between matrices and linear transformations is studied in detail.
Determinants, introduced in first year, are revised and investigated further, as
are eigenvalues and eigenvectors. The calculus component of the unit includes
local maxima and minima, Lagrange multipliers, the inverse function theorem
and Jacobians. There is an informal treatment of multiple integrals: double integrals,
change of variables, triple integrals, line and surface integrals, Green's
theorem and Stokes' theorem.
MATH2962 Real and Complex Analysis
(6 credit points, Advanced, PureAnalysis is one of the fundamental topics underlying much of mathematics
including differential equations, dynamical systems, differential geometry,
topology and Fourier analysis. Starting off with an axiomatic description of the
real number system, this first course in analysis concentrates on the limiting
behaviour of infinite sequences and series on the real line and the complex
plane. These concepts are then applied to sequences and series of functions,
looking at pointwise
and uniform convergence. Particular attention is given to
power series leading into the theory of analytic functions and complex analysis.
Topics in complex analysis include elementary functions on the complex plane,
the Cauchy integral theorem, Cauchy integral formula, residues and related
topics with applications to real integrals.
MATH2916 Working Seminar A is an introductory course in the analytical solutions of partial differential
equations and boundary value problems. The techniques covered include separation
of variables, Fourier series, Fourier transforms and Laplace transforms.
MATH2068/2988 Number Theory and Cryptography
(6 credit points, Mainstream/Avanced, Pure)
Prerequisites (MATH2068): 6 credit points of Junior Mathematics.
Prerequisites (MATH2988): 9 credit points of Junior Mathematics at the
advanced level or at the mainstream level with credit.
Cryptography is the branch of mathematics that provides the techniques for
confidential exchange of information sent via possibly insecure channels. This
unit introduces the tools from elementary number theory that are needed to
understand the mathematics underlying the most commonly used modern
public key cryptosystems. Topics include the Euclidean Algorithm, Fermat's
Little Theorem, the Chinese Remainder Theorem, Möbius Inversion, the RSA
Cryptosystem, the Elgamal Cryptosystem and the Diffie-Hellman
Protocol. Issues of computational complexity are also discussed.
MATH2070/2970 Optimisation and Financial Mathematics
(6 credit points, Mainstream/Avanced, Applied)
Prerequisites (MATH2070): MATH1011 or MATH1001 or MATH1901 or MATH1906,
and MATH1014 or MATH1002 or MATH1902.
Prerequisites (MATH2970): MATH1901 or MATH1906 or credit in MATH1001,
and MATH1902 or credit MATH1002.
Problems in industry and commerce often involve maximising profits or minimising
costs subject to constraints arising from resource limitations. The first
part of this unit looks at the important class of linear programming problems
and their solution using the simplex algorithm, and the minimisation of functions
of several variables with constraints, including Lagrange multipliers,
Kuhn-Tucker theory and quadratic programming.
The second part of the unit deals with utility theory and modern portfolio theory.
Topics covered include: pricing under the principles of expected return and expected
utility; mean-variance Markowitz portfolio theory, the Capital Asset Pricing Model,
log-optimal portfolios and the Kelly criterion; dynamical programming. Some
understanding of probability theory including distributions and expectations is
required in this part. Theory developed in lectures will be complemented by computer
laboratory sessions using MATLAB. Minimal computing experience will be required.
The course begins with a brief introduction to ordinary differential equations
including variation of parameters and series solution techniques.
The major part of the course deals with partial differential equations and
boundary value problems using Fourier Series, separation of variables, Laplace
and Fourier transforms and other orthogonal expansion procedures. Applications
include the heat equation, Laplace's equation and the wave equation.
The course concludes with a brief introduction to the solution of first order
PDEs using the method of characteristics and deals with applications such as
traffic flow.
This unit provides an introduction to modern abstract algebra, via linear algebra
and group theory. It extends the linear algebra covered in Junior Mathematics
and MATH2961, and proceeds to a classification of linear operators
on finite dimensional spaces. Permutation groups are used to introduce and
motivate the study of abstract group theory. Topics covered include actions of
groups on sets, subgroups, homomorphisms, quotient groups and the classification
of finite abelian groups.
MATH2917 Working Seminar B unit provides an introduction to univariate techniques in data analysis
and the most common statistical distributions that are used to model patterns
of variability. Common discrete random variable models, like the binomial,
Poisson and geometric, and continuous models, including the normal and exponential,
will be studied. The method of moments and maximum likelihood
techniques for fitting statistical distributions to data will be explored. The
unit will have weekly computer classes where candidates will learn to use a
statistical computing package to perform simulations and carry out computer
intensive estimation techniques like the bootstrap method.
STAT2911 Probability and Statistical Models
(6 credit points, Advanced)
Prerequisites: MATH1903 or MATH1907 or credit in MATH1003, and
and MATH1905 or credit in MATH1005 or MATH1015 or ECMT1010.
This unit is essentially an advanced version of STAT2011 with an emphasis on
the mathematical techniques used to manipulate random variables and probability
models. Common random variables including the Poisson, normal,
beta and gamma families are introduced. Probability generating functions
and convolution methods are used to understand the behaviour of sums of
random variables. The method of moments and maximum likelihood techniques
for fitting statistical distributions to data will be explored. The unit will
have weekly computer classes where students will learn to use a statistical
computing package to perform simulations and carry out computer intensive
estimation techniques like the bootstrap method.
The unit provides an introduction to the standard methods of statistical analysis
of data: Tests of hypotheses and confidence intervals, including t-tests,
analysis of variance, regression least
squares and robust methods, power of
tests, nonparametric
tests, nonparametric
smoothing, tests for count data goodness
of fit, contingency tables. Graphical methods and diagnostics are
used throughout with all analyses discussed in the context of computation
with real data using an interactive statistical package.
STAT2912 Statistical Tests (Advanced)
(6 credit points, Advanced)
Prerequisites: MATH1905 or credit in MATH1005 or MATH1015 or ECMT1010.
This unit is essentially an advanced version of STAT2012 with an emphasis
on both methods and the mathematical derivation of these methods: Tests of
hypotheses and confidence intervals, including t-tests,
analysis of variance,
regression least
squares and robust methods, power of tests, nonparametric
methods, nonparametric
smoothing, analysis of count data goodness
of fit,
contingency tables. Graphical methods and diagnostics are used throughout
with all analyses discussed in the context of computation with real data using
an interactive statistical package. | 677.169 | 1 |
Behold, I am now a college Student!
Yes, after several years of mental-retirement, I have decided to go to school. I am entering my first semester for a hopefull Business Administration degree.
I've tried to keep up on current events and reading (as a hobbie) so I'm not expecting too many troubles in keeping-up with my studies in English composition or Western Civilization History (History has always been my favorite subject), I'm afraid Intermediate algebra will kill me...
What the fuck are these 120 buttons on a graphic calculator for? I promptly forgot anything involving fake numbers immediately after class in highschool. Geometry wasn't too bad because it involved shapes and stuff.... Arghh!!!!
Anyway, anybody know any good websites for some immediate help in (re)learning the basics of algebra and scientific calculator useage? Any help would be most appreciatedGarrett, if you foresee problems, find the lowest level math class and start there. There may be a pre-algebra course or something you can start with, it might not be for credit, but it'll help get you up to speed. I knew a lot of people that were continually retaking College Algebra at my school, and considering they weren't understanding it even after taking it a few times I got a hunch they skipped the earlier stuff because it wouldn't count towards anything. Another thing you can do is look for tutoring and math labs and that sort of stuff at your school. | 677.169 | 1 |
Alright check this out I am about to buy my books and they are reccomending a TI-80 Scientific calculator.
I have a TI-30Xa Is there really that much differance that I would need to buy this $135 calculator cause Im new to the college thing and If I buy that and cant use it im liable to throw it at the professor.
So you guys who took MA-109 think this TI30 will do what I need it to do? or should I buy this TI-80???
Any help would be appreciated I dont wanna drop cash on bullcrap i dont need.
Sorry dude, I had to use a TI-Abacus Ok I am not that old, I had a TI-85 through college which it and the TI-80 does graphing and a few other things. I am not sure what all the TI-30xa can do. I am searching for a compare site, but I am not having any luck. Maybe there is no comparson. lol
The upgrade is well worth it.... the graphing part is great. When i went through college I had a TI-86 <--- or 85 one of those and I am so glad i made the purchase. If you are good with programming you can mkae formulas and all that also with it. So to answer your question though, I don't think you can make a comparrison, only because both calculators do totally diff things, and one is deff a lot more high tech then the other.
I also had a TI 86 all through college (major was ME, gradutated in 2001)... it's essential for the graphing capabilities, and being able to store programs (or, what looks like a program but is an equation/thumbrule etc) was good too...
My 1st calculator however was a TI 1, I think, it had glowing wires (orangish glow) with little magnifiying bubbles over each bumber area, and used 2 C batteries...
I have never needed more then a TI-83 in college that has worked for Calc, ALG, Stats. They are simple to use many tutorials on the web to figure anything out. You can find them cheap on Ebay, and sell them for the same price when you are done. If you are going into business a BA-II is a must but buy one from someone fininshing their Finance classes. You can always ask your professors most still use the 83 and whatever the majority is using is the way to go for the simple reason that it is easy to reproduce the calculation. I have watched many stuggle with super fancy calculators trying to figure out how to work a problem out and miss other parts of the class cause of it.
i was always amazed at a math class that wouldnt allow notes but would allow the use of the ti calculators, i mean, seriously wtf you think i'm not going to program formulas and notes into the caluclator
hehe actually my last highschool math class i had a college prof as a teacher and she dumped all her programs into our calculators, that go me all the way through college and then some
was so sweet, course now adays one can simply get one and plug it into the net with the right equipment and probably fare better than i
I couldn't help you here, I always do my math by counting the amount of Meatball subs it would take to solve the equation. I would explain the logic behind this but only me and other fat people would understand. | 677.169 | 1 |
Category: EducationCategory: EducationCategory: Reference
NYSTCE CST Math 004 Includes 21 competencies/skills found on the CST Mathematics test and 125 sample-test questions. This guide, aligned specifically to standards prescribed by the New York Department of Education, covers the sub-areas of Mathematical Reasoning and Communication; Algebra; Trigonometry and Calculus; Measurement and Geometry; Data Analysis, and Probability, Statistics, and Discrete Mathematics.
Category: Study AidsCategory: | 677.169 | 1 |
Mathematics
The mathematics department offers both a major and a minor in mathematics. The major prepares students for graduate studies or employment in a quantitative field. In addition, a student may prepare for teaching high school mathematics by selecting the math-ed option. (Students interested in this option should consult with the department adviser as soon as possible, preferably before the start of classes.) The Departments of Mathematics and Economics offer a joint major.
Program Activities
The department sponsors student chapters of Pi Mu Epsilon (the national mathematics honors society) and MAA (Mathematical Association of America). In addition, the Math Club sponsors meetings on interesting topics in mathematics and career possibilities. There are opportunities for summer research projects.
Majors in biology, chemistry, computer science, economics, general science, natural science, physics, and psychology should consult with their department advisers, as these majors have specific mathematics requirements. Students in the Gabelli School of Business (GSB) take MATH 1108 MATH FOR BUSINESS: FINITE and MATH 1109 MATH FOR BUSINESS: CALCULUS. GSB students interested in a math minor should take MATH 1206 CALCULUS I or MATH 1207 CALCULUS II in place of MATH 1109 MATH FOR BUSINESS: CALCULUS.
Incoming freshmen are placed in mathematics courses based on their standardized test scores and their high school transcript record.
This course does not fulfill the Mathematics reasoning portion of the Curriculum. The course is designed to allow students entry into calculus courses.
MATH 1001. MATH FOR BUSINESS: PRECALCULUS. (3 Credits)
A preparatory course to assist students at GSB to take Math for Business: Calculus. Topics include inequalities; linear, polynomial, rational, exponential, logarithm and inverse functions and their graphs; distance, lengths and area of simple regions. This course does not satisfy the mathematical reasoning core area requirement.
This course covers classic mathematical concepts found in music. Part one of the course considers consonance and dissonance from the perspective of mathematical properties of trigonometric functions. In the second part of the course, we study combinations of pitches and use these combinations to explain the unique sound characteristics of well-known instruments. The final part of the course deals with the tuning of musical scales and describing symmetries that arise in musical composition. Successful students will be able to use mathematics to explain musical sounds from their everyday experience. They will understand the motivations that led to modern tuning systems and be able to contextualize instrumentation and patterns in contemporary music. The material does not assume a background in Calculus or music theory, and the lectures include experimental demonstrations.
Attributes: MANR, MCR.
MATH 1100. FINITE MATHEMATICS. (3 Credits)
Solutions to systems of linear equations, counting techniques including Venn diagrams, permutations, combinations, probability, Bayes theorem, Markov chains. This course is designed to introduce general liberal arts students to the use of mathematics as a tool in the solution of problems that arise in the "real world". Applications will be chosen from areas such as business, economics, and other social and natural sciences. These applications will be based upon mathematical topics chosen from a field called Finite Mathematics. Specific topics to be covered may include Linear Programming, Probability, Statistics, and Finance. The only prerequisites are arithmetic, elementary algebra, and graphing, which students should already be familiar with from previous high school or college courses and/or the Mathematics Workshop. It will be presumed that students possess basic skills in these areas.
Open only to CBA students. Calculus for business majors. Topics include derivatives of polynomial, rational, exponential and logarithm functions. Curve sketching and optimization problems. The definite integral. Applications are drawn from business and economics.
MATH 1198. HONORS BUSINESS MATH. (4 Credits)
Review of Calculus. Solutions of systems of linear equations using matrix algebra. Discrete and continuous probability. Applications to business. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
A continuation of MATH 1203. Topics include derivatives of trigonometric functions, methods of integration and applications, calculus of functions of several variables, Lagrange multipliers. Prerequisite: MATH 1203 or equivalent.
Prerequisite: MTEU 1203.
MATH 1205. APPLIED STATISTICS. (3 Credits)
Course designed for students in fields that emphasize quantitative methods. It includes calculus based preliminary probability material followed by introduction to the basic statistical methods such as estimation, hypothesis testing, correlation and regression analysis. Illustrations are taken from a variety of fields. Practical experience with statistical software. Prerequisite: MATH 1203 or equivalent.
Calculus for science and math majors. Functions, limits, continuity, Intermediate Value Theorem. The derivative and applications, antiderivatives, Riemann sums, definite integrals, the Fundamental Theorem of Calculus. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Attributes: ENVS, MCR.
MATH 1207. CALCULUS II. (4 Credits)
A continuation of MATH 1206. The definite integral, area, volumes, work. Logarithm, inverse functions, techniques of integration, Taylor polynomials. Prerequisite: MATH 1206 or equivalent. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
This course shows how discrete and continuous mathematical models can be built and used to solve problems in many fields. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
In this student-initiated program, the student may earn one additional credit by connecting a service experience to a course with the approval of the professor and the service-learning director.
MATH 2001. DISCRETE MATHEMATICS. (4 Credits)
Topics include elementary logic, set theory, basic counting techniques including generating functions, induction, recurrence. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
The calculus of sequences and series, power series, uniform convergence, vector methods of solid geometry, vector valued functions, functions of several variables, partial derivatives, gradients, Lagrange multipliers. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
This is a continuation of MATH 2004. Topics include vector fields and their derivatives, multiple integrals, line and surface integrals, and the theorems of Gauss, Green and Stokes. Additional topics, as time permits, may cover one or more of the following: differential forms, functions of a complex variable, equations of fluid mechanics, or mean and Gauss curvature.
Topics include systems of linear equations, Real and complex vector spaces, linear independence, dimension, linear transformations, matrix representations, kernel and range, determinants and eigenvalues. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Basic Python programming and scripting and basic algorithms of linear algebra. Students will develope their own Python implementations of these algorithms, which form the basis of many computational methods in the sciences. The course is accessible to students in the physical and social sciences, computer science and math. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Topics include vector spaces over arbitrary fields, triangular form, Jordan canonical form, inner product spaces, coding theory. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Topics include existence and uniqueness theorems for ordinary differential equations, linear differential equations, power series solutions and numerical methods. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Analysis on the real line. Topics include cardinality of sets, limits, continuity, uniform continuity, sequences of numbers and functions, modes of convergence, compact sets and associated theorems. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
MATH 3004. COMPLEX ANALYSIS. (4 Credits)
Topics include complex numbers and mappings, analytic functions, Cauchy-Riemann equations, Cauchy integral theorem, Taylor and Laurent series expansions, residue theory. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Topics include well ordering and induction, unique factorization, modular arithmetic, groups, subgroups, Lagrange's theorem, normality, homomorphisms of groups, permutation groups, simple groups. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Topics include discrete and continuous probability models in one and several variables, expectation and variance, limit theorems, applications. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
MATH 3007. STATISTICS. (4 Credits)
Topics include sampling distributions, estimation, testing hypotheses, analysis of variance, regression and correlation, nonparametric methods, time series. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Topics include divisibility and related concepts, congruencies, quadratic residues, number theoretic functions, additive number theory, some Diophantine equations. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
The market for options, a type of contract in finance, has grown quickly in the past fifty years. In this course we will explore the Nobel Prize-winning Black-Scholes-Merton model for valuing these contracts. We will introduce basic notions of probability (such as Brownian motion) as well as basic notions from finance (such as the No Arbitrage Principle) and use these to derive and solve the Black-Scholes equation. Prerequisite: Math 2004. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Students develop skills in written and oral communication needed to produce scientific articles, monographs and presentations that are accomplised in both form and content. The course covers both the use of LaTeX to produce work that meets the highest standards of design and typography, and the techniques of writing, organization, and scholarly citation needed to ensure that this work accurately embodies, effectively communicates, and professionally documents the author's scientific thought. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Attribute: EP3.
MATH 3012. MATH OF INFINITY. (4 Credits)
Elementary set and function theory. Notion of counting infinite sets, including Hilbert's infinite hotel. Cardinality and infinite cardinals. Cantor's work on infinite sets. Additional topics may include: well-ordered sets and math induction; prime number generators; the Riemann zeta function; logic and meta-mathematics. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
MATH 4001. MATHEMATICAL ETHICS PRACTICUM. (4 Credits)
In this class, which fulfills the Senior Values seminar requirement of the Core Curriculum and serves as a capstone to both the pure and applied tracks of the Mathematics major, students will learn the ethical responsibilities of mathematicians, both as interpreters and as creators of mathematics. The course will combine historical and contemporary case studies with practical training in the skills and disciplines students must master to assume full ownership of their mathematics. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
Attribute: EP4.
MATH 4004. TOPOLOGY. (4 Credits)
Topics include open sets and continuity in metric spaces and topological spaces, subspaces and quotient topologies, compact sets, connected sets. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
MATH 4006. NUMERICAL ANALYSIS. (4 Credits)
Prerequisites: MATH 1700 and MATH 2006. Topics include approximation of functions, interpolation, solution of systems of equations, numerical integration, and solutions to different equations, error analysis. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
This course focuses on the study of Euclidean and Non-Euclidean geometries using both axiomatic and discovery based approaches. We review some of the basics in logic and study some of the proofs presented in Euclid's Elements before focusing on more advanced topics. We may use Geometer's Sketchpad in making discoveries and conjectures. We will study the history of the parallel postulate, the discovery of Non-Euclidean Geometry and the attendant philosophical implications. We will build models and focus on some interesting properties in hyperbolic geometry. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
This course introduces the geometry of curved spaces in many dimensions, which are the basis of subjects such as Einstein's theory of gravitation. Topics include manifolds, tangent spaces, the Gauss map, the shape operator, curvature, and geodesics. Prerequisites: MATH 2004 and MATH 2006. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.
This course is an introduction to the theory of partial differential equations. The course covers first hyperbolic, heat and wave equations, Poisson's equation and harmonic functions. Topics include Poisson's intergral formulas, the method of characteristics, the method of images, maxiumum principles and barriers and series solutions. Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction. | 677.169 | 1 |
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Description
Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics.
Key Features
Covers methodologies in studying emotion in mathematical knowledge
Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition
Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches
Explores the role of anxiety in mathematical learning
Synthesizes unifies the work of multiple sub-disciplines in one place
Readership
Academics/researchers, graduate and undergraduate students specializing in the following disciplines: cognitive psychology; infant cognition; cognitive neuroscience; behavioral genetics; educational psychology; early childhood education; and special education
Table of Contents
PART I
INTRODUCTION: AN OVERVIEW OF THE FIELD
Chapter 1 – An Overview of the Growth and Trends of Current Research on
Details
About the Editor
Ulises Xolocotzin
Ulises Xolocotzin is a faculty member in the Mathematics Education Department at the Centre for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav-IPN). He completed his undergraduate studies in Psychology, and an MSc in Educational Psychology, at the National Autonomous University of Mexico (UNAM). Following this, he obtained a PhD in Psychology at the Learning Sciences Research Institute in the University of Nottingham. After postdoctoral positions at the University of Bristol and Cinvestav, he was a full-time researcher in the Education and University Research Institute (IISUE) at UNAM. His work focuses on the psychology of mathematics education, with a special interest in how emotion relates to cognition during mathematical activity.
Affiliations and Expertise
Institute for Research in Education and University, National Autonomous University of Mexico, Mexico City, Mexico
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Mathematical Studies (Level 3 Certificate)
What's it all about?
This Level 3 Certificate in Mathematical Studies is a new qualification studied over two years which carries the same UCAS points as an AS level. The aim is to consolidate and build on students' mathematical understanding, develop it further and build skills in the application of maths to authentic problems. An excellent course to develop GCSE skills.
This course will enable students to:
- Study a mathematics curriculum that is integrated with other areas of their study, work or interest, leading to the application of mathematics in these areas.
- Develop mathematical modelling, evaluating and reasoning skills
- Solve open-ended problems
- Solve substantial and realistic problems encountered by adults
- Use ICT for developing mathematical understanding and solving problems
- Develop skills in the communication, selection, use and interpretation of their mathematics
- Enjoy mathematics and develop confidence in using mathematics.
Exam and Assessment Information:
AQA Level 3 Certificate Mathematical Studies (1350)
The course is linear with two 90 minute papers sat at the end of the two year course.
Paper 1 assesses:
Analysis of data
Maths for personal finance
Estimation
Paper 2 assesses:
Critical analysis of given data and models including spreadsheets and tabular data
Statistical techniques
To get started:
The Mathematics Studies course is suitable for any student with a grade 4 or above from either Foundation or Higher tier GCSE Mathematics.
What next?
Mathematical Studies will prepare students for the varied contexts they are likely to encounter in vocational and academic study and in future employment and life. As such, Mathematical Studies fosters the ability to think mathematically and to apply mathematical techniques to a variety of unfamiliar situations, questions and issues with confidence. While Mathematical Studies is likely to be particularly valuable for students progressing to higher education courses with a distinct mathematical or statistical element, this qualification will also be valuable for any student aiming for a career in a professional, creative or technical field and supports AS/2 level subjects with a mathematical element, such as Geography, Psychology, Economics and the sciences
Our students say …
"I'm finding it really useful to use maths to solve more real life problems." Jake Michel
As you work your way through the subject pages of the prospectus you will see this symbol. This indicates Mathematical Studies would be a very useful addition to that subject as it will support the statistical or numerical content. | 677.169 | 1 |
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I'm desperately trying to teach IB Math Studies, first year. The IB program itself has no pacing guide, only a vague outline of curriculum which you can read in 30 seconds - so you're basically on your own to develop the curriculum. So you look for books, and there's only two. This is the inferior of two very bad books.
This book is full of short semi-explanations of topics, and then a bunch of exercises which haven't been illuminated in the text. For some odd reason, the topics don't even line up with the vague IB outline of curriculum, so if you have a roadmap, you will spend the year trying to figure out which chapter follows chapter 8 - maybe chapter 2? Worse yet, if you know math, the chapters don't even follow a logical order - they jump all over the place. Additionally, all the answers are in the rear, so the students constantly cheat (naturally).
Somebody got paid way too much money for this load of horse dung. How can I get a job like that? | 677.169 | 1 |
Honors Calculus Advice
Showing 1 to 1 of 1
This is a great course if you love math. If you don't, however, this class might be more than you bargained for. It is an in depth look at math, that you won't find in any of the other elementary math courses. While it is greatly rewarding and eye-opening, you must appreciate mathematics and be prepared to devote time to this class and work.
Course highlights:
The approach to math in this course, to a few proofs in particular (reimann's sums, sterling's theory, etc..) is something you will not find in any other course. We pick apart big theories and proofs part by part, to understand mathematical tools that are often taken for granted.
Hours per week:
6-8 hours
Advice for students:
A sturdy work effort is the key to doing well in this course, stay hooked and motivated! It will be worth it. | 677.169 | 1 |
Algebra
Algebra is a course generally taught between middle school and high school. In its most general form algebra is the study of symbols and the rules for manipulating symbols. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.
Accendo will help students prepare for tests and quizzes and assist with homework assignments to help improve overall understanding. | 677.169 | 1 |
A Catalog of Mathematics Resources on the WWW and the Internet (M. Maheswaran, University of Wisconsin, Marathon County).
Comprehensive links to mathematics sites, organized into categories including pure and applied mathematics. Over 100 links under Activities for College and Pre-college Mathematics, although many are K-12. Other categories offer useful information and materials for college mathematics teachers.
Ted Panitz's Teaching/Learning Website.
Scroll down the page for links to several articles by Panitz and others on using cooperative learning and writing to reduce math anxiety, increase learning, and create a student-centered learning environment in college math courses.
Syllabi and Course Materials in Mathematics
MERLOT Mathematics Portal (Multimedia Educational Resource for Learning and Online Teaching).
The portal for online teaching and learning materials from faculty and educators in higher education around the world.
Journals in Mathematics Education
Quantitative Literacy Across the Curriculum
What Is QL/QR? (Bill Briggs, University of Colorado at Denver).
This page offers definitions of quantitative literacy/reasoning set forth in various publications and describes its importance in contemporary life.
Center for Mathematics and Quantitative Education at Dartmouth College.
Offers links to resources for college and university QL education in a wide variety of disciplines including art, literature, the sciences, and mathematics. Most are downloadable at no cost.
Colleges with QL/QR Programs:
QuIRK, Carleton College's Quantitative Inquiry, Reasoning, and Knowledge Initiative.
The material on this site, designed with grants from FIPSE, NSF, and the Keck Foundation, is intended to help institutions "better prepare students to evaluate and use quantitative evidence in their future roles." The site provides curricular materials for infusing quantitative reasoning throughout the curriculum, assessment, program design, and more.
See also the QuIRK page of links to other quantitative reasoning programs and additional QR teaching resources.
Quantitative Reasoning Across the Curriculum at Hollins University.
Describes their QR Program instituted in 2001 with Basic and Applied requirements. Lists courses that fulfill these requirements. Links to brief descriptions of QL courses in a variety of disciplines.
Mathematics Across the Curriculum at Dartmouth College.
The MATC Project ended in 2000, but this site has their goals, principals, links to MATC courses, and the Evaluation Summary for this five-year project. The resources they compiled are described above with a link to those in higher education.
Assessing Quantitative Literacy
Mathematics Resources for Students
Professor Freedman's Math Help (Camden County College, Blackwood New Jersey).
This site addresses the learning needs in mathematics of the community college adult learner. Useful for both students and teachers, the site offers math tutorials, homework assignments, video snippets on math topics, information about learning styles, and much more. | 677.169 | 1 |
Departments
Special Areas
Algebra II
Course Description:
This course includes a thorough treatment of advanced algebraic concepts provided through the study of functions, "families of functions," equations, inequalities, systems of equations and inequalities, polynomials, rational expressions, complex numbers, matrices, and sequences and series. Emphasis will be placed on practical applications and modeling throughout the course of study. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results will permeate the course. Students will use graphing calculators, computers, and other appropriate technology. Students taking this course will take an end-of-course SOL test in Algebra II. Students must pass both the course and the SOL test to earn a verified credit. | 677.169 | 1 |
Wednesday, December 19, 2012
Alright. Today in class we went over last night's homework and answered any questions that you had (that is if you weren't there or just didn't pay attention). Last night's homework was the first two sides of the packet about graphing Logs. The post below will have what you need. Tonight's homework is to finish the packet. As Anthony FAILED to mention yesterday, Mrs. Prior handed out the Midterm Review Packet that we all know and love. So, if you didn't get one, ask.
Tuesday, December 11, 2012
Monday, December 10, 2012
Essential Questions: What is a composite function? How do we create a composition of two or more functions? What do we know about the domain of composite functions? How do we decompose a function? And 6 more....
Classwork: Today we went over the 10 essential questions that summarize what we have learned so far(Mrs. Prior took a picture of them). Specifically, we spent more time reviewing how to restrict the domain of the original function so that the inverse would be a function.
Homework: Study for the quiz on Wednesday! It would be helpful to review the essential questions, Glencoe homework assignments, and the rule of four packets. Also, all of the notes we have taken during class. Good luck studying!
Thursday, December 6, 2012
December 6, 2012
Today in class we received Contemporary Mathematics in Context textbook (blue). Everyone needs to return the orange books at some point. Then, we worked on Investigations 1 and 2 in the blue book (pg 143-149) and tried answering the essential questions written on the board.
Essential Questions:
What is the definition of inverse function?
What is the relationship between the domains and ranges of inverse functions?
Wednesday, December 5, 2012
Today in class 12/5 we talked about the definition of inverse functions.
We also discussed the factors that have to be true for two functions to
be inverse. We discussed and did practice problems on how to find and
verify/ prove inverse functions. We went over why some functions must
have restrictions put on them in order to find the inverse functions. If
a function doesn't pass the horizontal line test it must have
restrictions on it's domain before the inverse function can be found.
There was no homework tonight.
Yesterday
12/4 in class we went over the homework from Monday and went over how
to decompose functions. We also made a table about what Opposite,
Reciprocal, Additive Inverse, Multiplicative Inverse, and Inverse
functions. We also went over what Identity was. Our homework was in the
Glencoe Precalculus book assignment 3 | 677.169 | 1 |
This textbook for engineering students introduces the commands and graphical tools of MATLAB and their application to performing numerical analysis. The numerical methods include linear algebra, numerical differentiation, successive substitution, Newton iteration, curve fitting to measured data, Eul
"synopsis" may belong to another edition of this title.
From the Publisher:
This book explores using MATLAB for numerical methods and graphic visualization. It offers a complete tutorial of MATLAB, covering numerical methods with MATLAB and advanced three-dimensional graphics with colors.
From the Inside Flap:
Preface This book is intended to introduce numerical analysis and graphic visualization using MATLAB to college students in engineering and science. It can also be a handbook of MATLAB applications to professional engineers and scientists.
With its unique and fascinating capabilities, MATLAB has changed the concept of programming for numerical and mathematical analyses. It has been found difficulty, however, to teach its application in numerical analysis with a text written previously. For this reason, developing a text that fully implements the mathematical and graphic tools of MATLAB in application of numerical analysis became desirable. The following four fundamental elements are integrated in this book: (1) programming in MATLAB, (2) mathematical basics of numerical analysis, (3) application of numerical methods to engineering, scientific, and mathematical problems, and (4) scientific graphics with MATLAB.
The first two chapters are comprehensive tutorials of MATLAB commands and graphic tools. Chapters 3 through 11 cover numerical methods with their implementations with MATLAB. All the numerical methods described are illustrated with applications on MATLAB. Using the lists of the scripts and functions or copying from the diskette (available to readers free from MathWorks), readers can run most examples and figures on their own computers.
Appendices describe special topics, including advanced three-dimensional graphics with colors, motion pictures, image processing, and graphical user interface. This book is based on MATLAB Student Edition 4, or MATLAB Professional Edition 4.1 or higher.
WHAT IS UNIQUE ABOUT MATLAB? MATLAB may be regarded as a programming language like Fortran or C, although describing it in a few words is difficult. Some of its outstanding features for numerical analyses, however, are: pah
An extraordinary feature of numbers in MATLAB is that there is no distinction among real, complex, integer, single, and double. In MATLAB, all these numbers are continuously connected, as they should be. It means that in MATLAB, any variable can take any types of numbers without special declaration in programming. This makes programming faster and more productive. In Fortran, a different subroutine is necessary for each of single, double, real or complex, or integer variable, while in MATLAB there is no need to separate them. The mathematical library in MATLAB makes mathematical analyses easy.
Yet the user can develop additional mathematical routines significantly more easily than in other programming languages because of the continuity between real and complex variables. Among numerous mathematical functions, linear algebra solvers play central roles. Indeed, the whole MATLAB system is founded upon linear algebra solvers.
IMPORTANCE OF GRAPHICS Visual analysis of mathematical analyses helps understand mathematics and makes it enjoyable. Although this advantage has been well known, presenting computed results with computer graphics was not without substantial extra effort. With MATLAB, however, graphic presentations of mathematical material is possible with a few commands. Scientific and even artistic graphic objects can be created on the screen using mathematical expressions. It has been found that MATLAB graphics motivate and even excite students to learn mathematical and numerical methods that could otherwise often be dull. MATLAB graphics is easy and will be great fun for readers. This book also illustrates image processing and production of motion pictures for scientific computing as well as for artistic or hobby material.
COMMAND AND FUNCTION NAMES IN THIS BOOK
The command and function names peculiar to this book all include {stt _} for example {stt rotx_.m}. The functions and commands that do not include the underscore are original from MATLAB.
WILL MATLAB ELIMINATE THE NEED FOR FORTRAN OR C?} The answer is no.
Fortran and C are still important for high-performance computing that requires large memory or long computing time. The speed of MATLAB computation is significantly slower than that with Fortran or C because MATLAB is paying the high price for the nice features.
Learning Fortran or C, however, is not a prerequisite for understanding MATLAB.
REFERENCE BOOKS THAT ARE IMPORTANT TO LEARN MATLAB This book explains many MATLAB commands but is not intended to be a complete guide to MATLAB. Readers interested in further information on MATLAB are advised to read the following literature on MATLAB: *** The MathWorks, The Student Edition of MATLAB, } *** hspace{0.5in} Version 4, User's Guide,} Prentice-Hall 1995 *** MATLAB, Reference Guide, MathWorks, 1992 *** MATLAB, User's Guide, MathWorks, 1992 *** MATLAB, Building a Graphical User Interface, MathWorks, 1993
HOW TO OBTAIN M-FILES DISKETTE All the scripts and functions developed in the present book are included in the diskette available from MathWorks. Please mail the diskette request card inserted at the end of this book. If the request card is missing, MathWorks' address appears on the next page. The diskette includes the following files: *** (1) All M-files listed at the end of chapters. *** (2) All scripts illustrated in the book (except short ones). *** (3) Scripts to plot typical figures in the book. SOLUTION KEYS
Solution keys for the problems at the end of chapters will be included in the M-Files Diskette.
HOW TO OBTAIN MORE INFORMATION ABOUT MATLAB Answers to frequently asked questions and Technical Notes on MATLAB are available directly from MathWorks via ftp. Its Internet address is
ftp.mathworks (144.212.100.10). The FAQ and the Technical Notes can be found in the directories {stt /pub/doc/faq and {stt /pub/tech-support/tech-notes respectively. Pagebreak You may also receive the following information free of charge:
* The MathWorks Newsletter (quarterly publication)
* The MATLAB News Digest (distributed via email)
* Technical Support
Send email to {stt subscribe@mathworks. Include in the email your name, company/university, address, phone number, email address, and license or serial number, which can be found by entering "ver" at the MATLAB prompt. For other communication with MathWorks, their address is: The MathWorks, Inc., 24 Prime Park Way, Natick, MA 01760, Phone: 508-653-1415, Fax: 508-653-2997. LIST OF REVIEWERS This book has been reviewed by: | 677.169 | 1 |
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Math in Minutes (Paperback)
Related Editions
Description
Paul Glendinning is Professor of Applied Mathematics at the University of Manchester. He was founding Head of School for Mathematics at the combined University of Manchester and has published over fifty academic articles and an undergraduate textbook on chaos theory.
Both simple and accessible, Math in Minutes is a visually led introduction to 200 key mathematical concepts. Each concept is described by means of an easy-to-understand illustration and a compact, 200-word explanation. Concepts span all of the key areas of mathematics, including Fundamentals of Mathematics, Sets and Numbers, Geometry, Equations, Limits, Functions and Calculus, Vectors and Algebra, Complex Numbers, Combinatorics, Number Theory, and more.
About the Author
Paul Glendinning is Professor of Applied Mathematics at the University of Manchester. He was a student and a lecturer at Cambridge before moving to a chair at Queen Mary, University of London and then Manchester (UMIST). He was founding Head of School for Mathematics at the combined University of Manchester and has published over fifty academic articles and an undergraduate textbook on chaos theory | 677.169 | 1 |
Differential Equations, Fourth Edition, by Blanchard, Devaney, Hall.
The study of differential equations is a beautiful application of the
ideas and techniques of calculus to our everyday lives. Indeed, it
could be said that calculus was developed mainly so that the
fundamental principles that govern many phenomena could be expressed
in the language of differential equations. Unfortunately, it was
difficult to convey the beauty of the subject in the traditional first
course on differential equations because the number of equations that
can be treated by analytic techniques is very limited. Consequently,
the course tended to focus on technique rather than on concept.
At Boston University, we decided to revise our course, and
we wrote this book to support our efforts.
We now approach our course with
several goals in mind. First, the traditional emphasis on specialized
tricks and techniques for solving differential equations is no longer
appropriate given the technology (laptops, ipads, smart phones, ...) that we
carry around with us everywhere. Second,
many of the most important differential equations are nonlinear, and
numerical and qualitative techniques are more effective than analytic
techniques in this setting. Finally, the differential equations
course is one of the few undergraduate courses where we can
give our students a glimpse of the nature of contemporary mathematical
research.
The Qualitative, Numeric, and Analytic Approaches
Accordingly, this book is a very different from the typical
"cookbook" differential equations text. We have eliminated many of the
specialized techniques for deriving formulas for solutions, and we
have replaced them with topics that focus on the formulation of
differential equations and the interpretation of their solutions. To
obtain an understanding of the solutions, we generally attack a given
equation from three different points of view.
One major approach we adopt is qualitative. We expect students to be
able to visualize differential equations and their solutions in many
geometric ways. For example, we readily use slope fields, graphs of
solutions, vector fields, and solution curves in the phase plane as
tools to gain a better understanding of solutions. We also ask
students to become adept at moving among these geometric
representations and more traditional analytic representations.
Since differential equations are easily studied using a computer,
we also emphasize numerical techniques.
DETools, the
software that accompanies this book, provides students with
ample computational tools to investigate the behavior of solutions
of differential equations both numerically and graphically.
Even if we can find an explicit
formula for a solution, we often work with the equation both
numerically and qualitatively to understand the geometry and the
long-term behavior of solutions. When we can find explicit solutions
easily, we do the calculations. But we
always examine the resulting formulas using
qualitative and numerical points of view as well..
How This Book is Different
There are several specific ways in which this book differs from other
books at this level. First, we incorporate modeling throughout. We
expect students to understand the meaning of the variables and
parameters in a differential equation and to be able to interpret this
meaning in terms of a particular model. Certain models reappear often
as running themes, and they are drawn from a variety of
disciplines so that students with various backgrounds will find
something familiar.
We also advocate a dynamical systems point of view. That is, we are always
concerned with the long-term behavior of solutions of an equation, and
using all of the appropriate approaches outlined above, we ask
students to predict this long-term behavior. In
addition, we emphasize the role of parameters in many of our examples,
and we specifically address the manner in which the behavior of
solutions changes as these parameters vary.
It is our philosophy that using a computer is as natural
and necessary to the study of differential equations as is the use
of paper and pencil. DETools
should make the inclusion of
technology in the course as easy as possible.
This suite of computer programs
illustrates the basic
concepts of differential equations.
Three of these programs are solvers
which allow the student to compute and graph numerical
solutions of both first-order equations and systems of differential equations.
The other 26 tools are demonstrations that allow students and teachers
to investigate in detail specific topics covered in the text.
A number of exercises in the text refer directly to these tools.
DETools is available through CengageBrain.com.
As most texts do, we begin with a chapter on
first-order equations. However,
the only analytic technique we use to find closed-form solutions is separation
of variables until we discuss linear equations at the end of
the chapter. Instead, we emphasize the
meaning of a differential equation and its solutions in terms of its
slope field and the graphs of its solutions. If the differential
equation is autonomous, we also discuss its phase line. This
discussion of the phase line serves as an elementary introduction to
the idea of a phase plane, which plays a fundamental role in
subsequent chapters.
We then move directly from first-order equations to
systems of first-order differential equations. Rather
than consider second-order equations separately, we
convert these equations to first-order systems.
When these equations are viewed as
systems, we are able to use qualitative and numerical techniques
more readily. Of course, we then use the information about these
systems gleaned from these techniques to recover information about the
solutions of the original equation.
We also begin the treatment of systems with a general approach. We do
not immediately restrict our attention to linear systems. Qualitative
and numerical techniques work just as easily on nonlinear systems,
and one can proceed a long way toward understanding solutions
without resorting to algebraic techniques. However, qualitative ideas
do not tell the whole story, and we are led naturally to the idea of
linearization. With this background in the fundamental geometric and
qualitative concepts, we then discuss linear systems in
detail.
Not only do we emphasize the formula for the general solution of
a linear system, but also the geometry of its solution curves
and its relationship to the eigenvalues and eigenvectors of
the system.
While our study of systems requires the minimal use of some linear
algebra, it is definitely not a prerequisite. Because we deal primarily
with two-dimensional systems, we easily develop all of the necessary
algebraic techniques as we proceed.
In the process, we give considerable insight into the geometry
of eigenvectors and eigenvalues.
These topics form the core of our approach. However, there are many
additional topics that one would like to cover in the course.
Consequently, we have included
discussions of
forced second-order equations, nonlinear systems, Laplace transforms,
numerical
methods, and discrete dynamical systems.
In Appendix A, we even have a short discussion of Riccati and Bernoulli
equations,
and Appendix B is an ultra-lite treatment of power series methods.
In Appendix B we take the point of view that power series are
an algebraic way of finding approximate solutions much like numerical
methods. Occasional surprises, such as
Hermite and Legendre polynomials,
are icing on the cake.
Although some of these topics are
quite traditional, we always present them in a manner that is
consistent with the philosophy developed in the first half of
the text.
At the end of each chapter, we have included several ``labs.'' Doing
detailed numerical experimentation and writing reports has been our
most successful modification of our course at Boston
University. Good labs are tough to write and to grade, but we feel
that the benefit to students is extraordinary.
Changes in the Fourth Edition
This revision has been our most extensive since we published the first edition
in 1998. In Chapter 1, the table of contents remains the same. However, many
new exercises have been added, and they often introduce models that are new to
the text. For example, the theta model for the spiking of a neuron appears in
the exercise sets of Section 1.3 (Qualitative Technique: Slope Fields),
Section 1.4 (Numerical Technique: Euler's Method), Section 1.6 (Equilibria and
the Phase Line), and Section 1.7 (Bifurcations). The concept of a time
constant is introduced in Section 1.1 (Modeling via Differential Equations)
and discussed in the context of a blinking light in Section 1.3 (Qualitative
Technique: Slope Fields). The velocity of a freefalling skydiver is discussed
in three exercise sets. In Section 1.1 (Modeling via Differential Equations),
we discuss terminal velocity to illustrate the concept of long-term
behavior. In Section 1.2 (Analytical Technique: Separation of Variables), we
find the general solution of the velocity equation using the method of of
separation of varibles, and in Section 1.4 (Numerical Technique: Euler's
Method), we study these solutions numerically using Euler's method.
Chapter 2 has undergone a complete overhaul. We added a section (Section 2.7)
on the SIR model. We include this topic for two reasons. First, many of our
students had first-hand experience with the H1N1 pandemic in 2009-2010.
Second, many users of the preliminary edition liked the fact that we discussed
nullclines in Chapter 2. Section 2.7 (The SIR Model of an Epidemic) provides
some phase plane analysis without going into the detail that is found in in
our section on nullclines in Chapter 5.
Chapter 2 now has eight sections rather than five. Section 2.1 (Modeling via
Systems) and Section 2.2 (The Geometry of Systems) are essentially
unchanged. Section 2.3 (The Damped Harmonic Oscillator) is a short section in
which the damped harmonic oscillator is introduced. This model is so important
that it deserves a section of its own rather than being buried at the end of a
section as it was in previous editions. The remaining analytic techniques that
we presented in the previous editions can now be found in Section 2.4
(Additional Analytic Methods for Special Systems). The Existence and Uniqueness Theorem for systems along with its consequences has its own
section (Section 2.6), and the consequences of uniqueness are discussed in
more detail. The presentations of Euler's method for systems and Lorenz's
chaotic system are essentially unchanged.
This material is presented in smaller sections to give the instructor more
flexibility to pick and choose topics from Chapter 2. Only Section 2.1
and Section 2.2 are absolute prerequisities for what follows. Chapter 2 has
always been the most difficult one to teach, and now instructors can cover as
many (or as few) sections from Chapter 2 as they see fit.
Pathways Through This Book
There are a number of possible tracks that instructors can follow in
using this book. Chapters 1-3 form the core (with the possible exception of
Section 2.8 and Section 3.8, which cover systems in three dimensions). Most
of the later chapters assume familiarity with this material. Certain sections
such as Section 1.7 (Bifurcations), Section 1.9 (Integrating Factors for
Linear Equations), and Sections 2.4-2.7 can be skipped if some care is taken
in choosing material from subsequent sections. However, the material on phase
lines and phase planes, qualitative analysis, and solutions of linear systems
is central.
A typical track for an engineering-oriented course would follow
Chapters 1-3 (perhaps skipping Sections 1.7, 1.9, 2.4, 2.6, 2.7, and 3.8)
Appendix A (Changing Variables) can be covered at the
end of Chapter 1. These chapters will take roughly two-thirds of a semester.
The final third of the course might cover Sections 4.1-4.3 (Forced,
Second-Order Linear Equations and Resonance), Section 5.1 (Linearization of
Nonlinear Systems), and Chapter 6 (Laplace Transforms). Chapters 4 and 5
are independent of each other and can be covered in either order. In
particular, Section 5.1 on linearization of nonlinear systems near equilibrium
points forms an excellent capstone for the material on linear systems in
Chapter 3. Appendix B (Power Series) goes well after Chapter 4.
Incidentally, it is possible to cover Sections 6.1 and 6.2 (Laplace
Transforms for First-Order Equations) immediately after Chapter 1. As we have
learned from our colleagues in the College of Engineering at Boston
University, some engineering programs teach a circuit theory course that uses
the Laplace transform early in the course. Consequently,
Sections 6.1 and 6.2 are written so that the differential equations course and
such a circuits course could proceed in parallel. However, if possible, we
recommend waiting to cover Chapter 6 entirely until after the material
in Sections 4.1-4.3 has been discussed.
Instructors can substitute material on discrete dynamics (Chapter 8)
for Laplace transforms. A course for students with a strong background in
physics might involve more of Chapter 5, including a treatment of systems that
are Hamiltonian (Section 5.3) and gradient (Section 5.4).
A course geared toward applied mathematics might include a more detailed
discussion of numerical methods (Chapter 7).
Our Website and Ancillaries
Readers and instructors are invited to make extensive use of our
web site
At this site
we have posted an on-line instructor's guide that includes
discussions of how we use the text.
We have sample syllabi
contributed by users at various institutions as well as information about
workshops and seminars dealing with the teaching of differential
equations. Solution Builder, available to instructors who have adopted the
text for class use, creates customized, secure PDF copies of solutions matched
exactly to the the exercises assigned for class.
The website for Solution Builder is
The Student Solutions Manual contains the solutions to all odd-numbered
exercises.
The Boston University Differential Equations Project
This book is a product of the now complete National Science Foundation
Boston University
Differential Equations Project (NSF Grant DUE-9352833) sponsored by the
National Science Foundation and Boston University. The goal of
that project was to rethink the traditional, sophomore-level
differential equations course. We are especially thankful for that
support. | 677.169 | 1 |
Showing 1 to 18 of 18
INTE 290
Lesson 2: Introduction to Computers
What is a computer?
Someone or something that computes. Oxford describes a computer as 1) an
electronic device for storing and processing data, according to instructions given to
it in a variable program or 2)
Topics in Inequalities - Theorems and Techniques
Hojoo Lee
Introduction
Inequalities are useful in all elds of Mathematics. The aim of this problem-oriented book is to present
elementary techniques in the theory of inequalities. The readers will meet clas
Problems in Elementary Number Theory
Peter Vandendriessche
Hojoo Lee
July 11, 2007
God does arithmetic.
C. F. Gauss
Chapter 1
Introduction
The heart of Mathematics is its problems.
Paul Halmos
Number Theory is a beautiful branch of Mathematics. The purpos
a
1
2
b
Preface
This work blends together classic inequality results with brand new problems,
some of which devised only a few days ago. What could be special about it when so
many inequality problem books have already been written? We strongly believe th
Basics of Olympiad Inequalities
Samin Riasat
ii
Introduction
The aim of this note is to acquaint students, who want to participate in mathematical Olympiads, to
Olympiad level inequalities from the basics. Inequalities are used in all elds of mathematics.
Inequalities from 2008 Mathematical Competition
Inequalities from
2008 Mathematical Competition
Editor
Manh Dung Nguyen, Special High School for Gifted Students, Hanoi University of
Science, Vietnam
Vo Thanh Van, Special High School for Gifted Students, | 677.169 | 1 |
Cynthis Young's Algebra & Trigonometry, Fourth Edition will allow students to take the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right, while seamlessly integrating to Young's learning content. Algebra & Trigonometry, Fourth Edition is written in a clear, single voice that speaks to students and mirrors how instructors communicate in lecture. Young's hallmark pedagogy enables students to become independent, successful learners. Varied exercise types and modeling projects keep the learning fresh and motivating. Algebra & Trigonometry 4e continues Young's tradition of fostering a love for succeeding in mathematics. | 677.169 | 1 |
This easy-to-use workbook is full of stimulating activities that will give your students a solid introduction to trigonometry! A variety of puzzles and self-check formats will challenge students to think creatively as they work to build their trigonometric skills. Each page begins with a clear explanation of a featured trigonometric topic, providing extra review and reinforcement. A special assessment section is included at the end of the book to help students prepare for standardized tests. 48 pages. | 677.169 | 1 |
The TI-84 Plus CE has six times the memory of the TI-84 Plus so students can store vivid, full-color graphs, images and data. The lightweight yet durable design also makes the graphingcalculator easier to carry to and from school and activities for... more
Stay mobile, continue learning - Transfer class assignments from handheld to computer (PC and Mac). Complete work outside of school using student software. On the desktop at home or a laptop on the bus, at the library, coffee shop wherever. Visualize in f more
The TI-83 Plus is an easy-to-use graphingcalculator for math and science. Ideal for algebra through pre-calculus, plus powerful statistics and finance features. Offers flash technology to upgrade. Financial functions include TVM, cash flows,... more
Calculator provides advanced graphing for calculus, AP courses and university studies. Permitted for use on many state and standardized tests. Includes official AP calculus review questions on the enclosed product CD. Graphs functions, parametric and... more
This graphingcalculator features touchpad navigation with a full keyboard for simple operation and includes TI-Nspire Student software to help you complete assignments outside of the classroom. The USB port allows flexible connectivity options. more
The TI-84 Plus Silver Edition graphingcalculator comes with a USB cable, plenty of storage and operating memory, and lots of pre-loaded software applications (Apps) -- all to help you gain an academic edge from pre-algebra through calculus, as well as bi more
Perhaps if we'd had this calculator in high school we would have done much better in trigonometry. The TexasInstruments TI-83 is an ideal unit for any math student, combining powerful features for graphing and statistical analysis. The LCD screen... more
The TexasInstruments TI-Nspire CASGraphing Calculator helps educators incorporate CAS (Computer Algebra System) as a tool for students to explore, evaluate and simplify expressions, numeric problems and variables in symbolic form. Educators have the... more
More information about Calculators
Best prices on Texas instruments graphing calculator in Calculators. Check out Bizrate for great deals on popular brands like Connect, Dataproducts and EBS | 677.169 | 1 |
The History of Mathematics: An Introduction
The background of arithmetic: An creation, 7th variation, is written for the only- or two-semester math heritage direction taken via juniors or seniors, and covers the background in the back of the themes regularly coated in an undergraduate math curriculum or in ordinary faculties or excessive colleges. Elegantly written in David Burton's imitable prose, this vintage textual content offers wealthy historic context to the maths that undergrad math and math schooling majors come across on a daily basis. Burton illuminates the folk, tales, and social context at the back of arithmetic' maximum historic advances whereas conserving acceptable specialize in the mathematical strategies themselves. Its wealth of knowledge, mathematical and historic accuracy, and well known presentation make The heritage of arithmetic: An creation, 7th version a precious source that academics and scholars will wish as a part of an everlasting library.
Thought of to be the toughest mathematical difficulties to resolve, notice difficulties proceed to terrify scholars throughout all math disciplines. This new identify on this planet difficulties sequence demystifies those tricky difficulties as soon as and for all via exhibiting even the main math-phobic readers easy, step by step information and strategies.
This approachable textual content experiences discrete items and the relationsips that bind them. It is helping scholars comprehend and follow the ability of discrete math to electronic computers and different smooth purposes. It presents very good guidance for classes in linear algebra, quantity concept, and modern/abstract algebra and for computing device technological know-how classes in info constructions, algorithms, programming languages, compilers, databases, and computation.
Focus inequalities for capabilities of autonomous random variables is a space of likelihood idea that has witnessed an outstanding revolution within the previous couple of many years, and has purposes in a large choice of parts similar to desktop studying, information, discrete arithmetic, and high-dimensional geometry.
Allow us to kingdom this challenge and Ahmes's resolution in sleek phrases, including a couple of clarifying info. instance. give some thought to a bunch, and upload 23 of this quantity to itself. From this sum subtract 1 1 its worth and say what your resolution is. believe the reply was once 10. Then remove 10 three of this 10, giving nine. Then this used to be the quantity first considered. evidence. If the unique quantity was once nine, then 23 is 6, which additional makes 15. Then is five, which on subtraction leaves 10. that's the way you do it. 1 three of 15 right here the scribe used to be rather illustrating the algebraic id n+ 2n three − 1 2n n+ three three − 1 10 n+ 2n three − 1 2n n+ three three =n via an easy instance, to that end utilizing the quantity n = nine.
To turn out Proposition 29, we needs to use the parallel postulate for the 1st time. PROPOSITION 29 A transversal falling on parallel traces makes the exchange inside angles congruent to each other, the corresponding angles congruent, and the sum of the inner angles at the comparable part of the transversal congruent to 2 correct angles. evidence. feel that the traces and angles are categorized as within the determine. We finish instantly that simply because a and b are supplementary angles, a plus b equals correct angles (this is the content material of Proposition 13).
Rhind additionally bought a brief leather-based manuscript, the Egyptian Mathematical leather-based Scroll, even as his papyrus; yet due to its very brittle , it remained unexamined for greater than 60 years. A Key to interpreting: The Rosetta Stone It was once attainable to start the interpretation of the Rhind Papyrus shortly end result of the wisdom won from the Rosetta Stone. discovering this slab of polished black basalt used to be the main major occasion of Napoleon's excursion. It used to be exposed via officials of Napoleon's military close to the Rosetta department of the Nile in 1799, once they have been digging the principles of a castle. | 677.169 | 1 |
MathCast: Algebraic Cheat Sheet 1.0 MathCast: Algebraic Cheat Sheet provides a set of basic math facts that will greatly simplify solving algebraic problems. This app demystifies basic algebraic concepts by using practical examples that can easily be applied in all areas of math including algebra, trig, and calculus. From introductory Algebra to Calculus and everything in between - the basic building blocks presented HERE are sure to make your problem solving simpler, your
Algebraic Calculators 1.0 This app can be used to solve different algebraic calculations such as, 1. Quadratic Equations and 2. Pythagoras Theorem
Function Mystery Machine! 2.0 The Center for Algebraic Thinking introduces the Function Mystery Machine, a simple, yet fun way to practice algebraic functions! Choose a level or go head-to-head with a friend as you try to guess the mystery function with the help of your Algebra Machine! This game supports algebra functions ranging from simple "x + 5" equations to ones such as quadratics and "x+a" for two-player. Function Mystery Machine is recommended for middle school | 677.169 | 1 |
Very good This app is great at factoring. I haven't been able to test it with other problems other than factoring but it does well of explaining and also has little links if you don't understand something mentioned in the explanation. The only difficulty I am having so far is the fact that when I try to take a picture of a problem it says the camera is always out of focus.
Amazing app. This app not only gets the answer to your question, but it explains each step by stating what rule/law it used and writing out each step. This app even explains integration by means of partial fractions step by step, from the complex parts, to how to solve a system of equations. I would recommend this app to anyone studying mathematics!
Excelent My teacher showed me this app and no it is not considered cheating as it explains step by step how to do problems and not only gives the answers. It comes in handy when yu miss a step, forget, or need a quick answer. This app will not disappoint you!
Life Saver I never took precaculus before so me teaching myself was out the question because my teacher didn't really explain so now I get full detailed explanation for each problem. Thank you so much!! | 677.169 | 1 |
Friends Who Are Going
Friends Attending
Friends Attending
Friends Attending
Description
Everybody knows that it's important to take good notes in your maths and statistics lectures, but do you really know how to take notes that really make a difference? It's important to find the method of note taking that best compliments your study habits and the way you think. Perfect maths note taking may be different for you than for others, but some elements are fairly universal. This session goes through some of these universal techniques to enable productive learning. | 677.169 | 1 |
1. Teach mathematics and mathematical thinking at the appropriate levels to enable students.
2. Extend the frontiers of knowledge in pure and applied mathematics.
3. Build a unified and collegial atmosphere in which faculty and students support each other in teaching and learning. | 677.169 | 1 |
The purpose of this course is to provide students a working knowledge of basic operations in Calculus, including differentiation and integration of simple functions. At the end of the course the student should be able to use these techniques to graph functions and solve financial problems involving optimization, growth, and rates of change. Evaluation of the student's mastery of these concepts will be done through written exams.
University "M" Credit:
Successful completion of this course satisfies the BU "M" credit requirement. Students in "M" courses will demonstrate competence in an area such as calculus, symbolic logic, the logic of computers, the logic of deductive and inductive reasoning, or probability and statistical inference.
Prerequisites:
Students must pass the Calculus Screening Test. To be successful in this course a student should be competent in high school algebra. Passing the Screening Test does not certify competence in algebra; not passing it shows insufficient skill. For information on the Screening Test, click here . Students who struggle with the Screening Test should seriously consider taking Binghamton University's Pre-Calculus course, MATH 108.
Attendance:
You are required to attend all classes. In case of illness or other necessary absences, notify your instructor by email. According to Harpur College policy, a student can receive a grade of F for any course for which they have missed 25% or more of its meetings. We reserve the right to invoke this policy.
Academic Honesty:
Academic dishonesty will be dealt with severely. There is precedent for giving an "F" for the course to a student who attempts to advance his/her grade illegally. Dishonesty includes, but is not limited to: copying another student's work, letting someone copy your work, lying to or intentionally misleading an instructor, handing in modified work for additional points, or signing someone else's name to a document.
To eliminate suspicion, only writing/erasing utensils will be permitted on desks during an exam.
Calculators and Other Electronic Devices:
Calculators will not be allowed during any quiz or test. They may be useful for some homework assignments. No particular type is recommended.
Students may not access any electronic devices during a quiz or test. Doing so will be considered cheating regardless of the actual action or intent.
Extra Help Extra help both at the University Tutorial Services (UTS) and in the Calculus Help Rooms in Whitney Hall.
The Calculus Help Rooms in Whitney Hall have a wide range of opening hours. For details see Help Rooms. This site is updated about a week after classes begin each semester.
Course text:
REQUIRED: Math 220 Course Pack, 7th Edition
This is obtainable at the Campus Bookstore. If you have an earlier edition, this is fine, but show check for corrections or other addenda in current edition.
Special Services:
Binghamton University is committed to full and equitable access for all enrolled students. Students requesting accommodations based on a disability must register with Services for Students with Disabilities located in UU-119 (777-2686).
Exams:
Dates for the exams will be announced here and in your classes within the first week of the semester.
There will be three in-class exams, as well as a comprehensive final. The in-class exams take place during regularly scheduled class time, in your usual classroom location.
Make-up exams are not given except in the direst of circumstances (serious student illness or death in the immediate family). If you have an emergency, do everything you can to contact your instructor as soon as possible. DO NOT WAIT until the next class meeting.
The final exam is comprehensive, covering most of the material in the course. Details as to what specific material will be excluded will be provided in advance. The best way to study for the final exams is to understand the problems from the prior exams given in the course.
If you have a university conflict with other final exams (another exam scheduled for the same time, or three exams within a 24-hour period) you are entitled to have one of your exams rescheduled. Of course we would rather that you reschedule your OTHER test, but we do understand that this cannot always be done. If you request a makeup be prepared to stay on campus through all of Exam Week.
Grading:
Course Grades will be awarded as follows:
Total Points Grade
A 900-1000 A- 850-899 B+ 800-849 B 750-799 B- 700-749
C+ 650-699 C 600-649 C- 550-599 D 500-549 F 0-499
Your grade for the course is out of 1000 points. The following scheme is subject to change, but in general, the final exam is worth 300 points (30%), the three in-class exams 200 points each, and class performance 100 points, as determined by your quiz scores, preparedness, and attendance. It is up to the discretion of each instructor to allot these points; each class will hear from the instructor as to how these points are awarded.
An important note about grading:
Instructors do not "give grades." Instructors simply award points based on the work the student produces. Each student's point total happens to correspond to a letter grade at semester's end. Very little (if any) subjectivity is involved in the grading process. Students are responsible for earning the requisite number of points (as detailed above) to earn the grade they desire. | 677.169 | 1 |
Martin Flashman Professor of Mathematics Humboldt State University
Abstact:Winplot
is freeware developed by Richard Parris. This presentation will give an
introduction to using Winplot to illustrate concepts from precalculus through
Calculus III and Differential Equations.
Disclaimer: Any errors in this presentation are those of the presenter and
not the responsibility of Richard Parris- the author and creator of Winplot.
Winplot is a tool primarily to assist in the learning of mathematics and
is freeware.
Starting- Download and unzip:
On-line help: Al Lehnen
has prepared a detailed
guide
to Winplot . | 677.169 | 1 |
In this course you learn everything you need to know to solve problems involving determinants. The course consists of theoretic as well as practice lectures. In the theoretic lectures I explain the statements of important theorems and give easy to understand examples. In practice lectures I go over solutions to exercises.
No preliminary knowledge beyond precalculus is assumed. Anyone who is interested in linear algebra are welcome to take the course.
However, the course is designed primarily for college students. It is great for those who'd like to get prepared ahead of live lectures, and those who need help with homework. You may also use this short course as a review before a college exam.
Like any other tutorial, this course is not a substitute to regular lectures. The goal of this tutorial is to help you learn how to solve problems in linear algebra rather than explain the proofs of theorems. | 677.169 | 1 |
Mathematics
Associate in Science
Mathematics as a discipline helps us understand and validate the world we live
in . As a science, it is the building block of all other sciences. It is used to model
the world around us in diverse arenas such as technology, science, engineering, money,
sports & medicine. As an art, it is used to recognize, study and understand patterns
in poetry, music, painting and architecture. | 677.169 | 1 |
System requirements:
Our users:
The simple interface of Algebrator makes it easy for my son to get right down to solving math problems. Thanks for offering such a useful program. Horace Wagner, MO
I need help with complex numbers and polynomials, but couldn't find a tutor. Someone suggested the Algebrator software. The software is great!, it's like having my own math professor. Thank you! Warren Mills, CA
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A First Course in Abstract Algebra John B. Fraleigh download
What are some examples from real life in which you might use polynomial division?
Why is it important to simplify radical expressions before adding or subtracting?How is adding radical expressions similar to adding polynomial expressions?How is it different? Provide a radical expression for your classmates to simplify. | 677.169 | 1 |
Texas Instruments, the No
TI-Nspire™
What is it about?App Details
Version
4.5.0
Rating
(70)
Size
93Mb
Genre
Education
Last updated
September 19, 2017
Release date
January 25, 2013
More info
App Screenshots
App Store DescriptionONE APP. ALL THE MATH.
Open the door to math mastery with the first-in-class iPad app that delivers comprehensive graphing, data entry and analysis, statistical modeling and calculating functionality.
Make math more meaningful by importing images from the iPad camera or photo library and overlaying graphs and equations on them to illustrate abstract math principles in the real world.*
Visualize crucial connections by observing how equations change — in real time, on one screen — when you touch, grab and interact with shapes, graphs and objects on the screen. | 677.169 | 1 |
Description
For courses in undergraduate Combinatorics for juniors or seniors.This carefully crafted text emphasizes applications and problem solving. It is divided into 4 parts. Part I introduces basic tools of combinatorics, Part II discusses advanced tools, Part III covers the existence problem, and Part IV deals with combinatorial optimization.show more
Review quote
"The writing style is excellent. Roberts' original text has always been one of my favorites and the new edition maintains the same high standards. Roberts and Tesman reads as well as the original, I'm pleased to say. The explanations are detailed enough that the students can follow the arguments readily. The motivating examples are a truly strong point for the text. No other text with which I am familiar comes even close to the number of applications presented here." - John Elwin, San Diego State University "I began using this book last fall in an undergraduate course. I used it because I believe it is one of the best books on the market for the purpose of this class. The text is written clearly throughout. The book is very well suited for a junior/senior course consisting of mathematics and computer science majors." - Joachim Rosentahal, University of Notre Dame "The new material in this reviewed manuscript makes this new edition even stronger than the old text. I love the inclusion of extra material on cryptography and code. The writing style is clear and straightforward. The examples and clarity of explanations are quite good." - Edward Allen, Wake Forest Universityshow more
Rating details
18 ratings
4.05 out of 5 stars
5
39% (7)
4
33% (6)
3
22% (4 | 677.169 | 1 |
Fundamentals of College Mathematics By N.P.Bali, P.N.Gupta, Neeru Shrama
Book Summary:
It discusses logical connectives. propositions, tautology and contradiction including real number systems and complex number systems. The book also deals with real valued functions, different types of functions , and their graphs. At the end, the book describes conic sections and second degree equations.
Audience of the Book :
This well-organised book is meant for the undergraduate students of Mathematics.
Key Features:
The main features of the book are as follows:
1.It fully covers the required syllabus.
2.It has a simple, lucid, easy to understand , and conversational style.
3.Each chapter begins with a clear statement of pertinent definitions, principles and theorems together with illustrative and descriptive material.
4.The development of mathematical concepts in each chapter is logical, and the preparation of each new idea is based on the preceding material. | 677.169 | 1 |
We use the example of solving a quadratic equation to introduce the
concept of round-off error and how to avoid it. We also introduce
simple arithmetic expressions, logical expressions, and the
conditional if...else statement. | 677.169 | 1 |
GeoGebra is dynamic mathematics software designed for all levels of education. It joins arithmetic, geometry, algebra and calculus while offering multiple representations of an object in its graphic, algebraic, and spreadsheet form. Different views that are all dynamically linked.
GeoGebra focuses on manipulating geometrical objects in a dynamic fashion, the core idea is to join geometric, algebraic, and numeric representations in an interactive environment. You can do a lot of different things including constructing objects with points, vectors, lines, conic sections. | 677.169 | 1 |
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this file type before downloading and/or purchasing.
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This lesson focuses on writing "let statements" when modeling real world situations with algebraic expressions. It is an introduction to writing expressions and equations. It includes the lesson plan, a doodle note sheet (designed to engage both hemispheres of students' brains) and an answer key. | 677.169 | 1 |
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples.
Starting from linear inequalities and Fourier-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point algorithm.
"Overall, the author has managed to keep a sound balance between the different approaches to convexity in geometry, analysis, and applied mathematics. The entire presentation is utmost lucid, didactically well-composed, thematically versatile and essentially self-contained. The large number of instructive examples and illustrating figures will certainly help the unexperienced reader grasp the abstract concepts, methods and results, all of which are treated in a mathematically rigorous way. Also, the emphasis on computational, especially algorithmic methods is a particular feature of this fine undergraduate textbook, which will be a great source for students and instructors like-wise ... the book under review is an excellent, rather unique primer on convexity in several branches of mathematics." --Zentralblatt MATH
"Undergraduate Convexity would make an excellent textbook. An instructor might choose to have students present some of the examples while he or she provides commentary, perhaps alternating coaching and lecturing. A course taught from this book could be a good transition into more abstract mathematics, exposing students to general theory then giving them the familiar comfort of more computational exercises. One could also use the book as a warm-up to a more advanced course in optimization." --MAA Review | 677.169 | 1 |
Description
For freshman/sophomore-level courses in Linear Algebra. This book provides an applied introduction to the basic ideas, computational techniques, and applications of linear algebra. The most applied of our basic books in this market, this text has a superb range of problem sets. Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled "Calculus Required.") The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors) and introduce applications of linear algebra in a one-semester course.show more | 677.169 | 1 |
3
Advanced Quantitative Reasoning O Type of class – O Student learning done in groups. A wide range of topics and types of math will be examined most of which you will be fairly familiar with. Analytically based O What will it prepare you for – O AQR "prepares students for a range of future options in non-mathematics-intensive college majors or for entering workforce training programs" O Prereq is Alg 2
4
Statistics / AP Statistics O Type of class – O Not similar to other math classes you have taken, a lot of reading, writing, and analysis of data (compared to other math classes) O What will it prepare you for – O Regular stats will prepare you to do well in college stat classes. O AP Stats will prepare you for the AP exam which, with a high enough score, could place you out of college Stats
5
Calculus / AB Calc / BC Calc O Type of class – O Problem based, individualized, very algebraic O What will it prepare you for – O Calc – To do well in a college calculus class O AB Calc – The AB Calc exam, which could place you out of Calc 1 in college O BC Calc – The BC Calc exam, which could place you out of Calc 1 and Calc 2 in college
6
Difference between AB and BC Calculus O AB Calc O One period (meets every other day) = Calc 1 in college O BC Calc O Two periods (meets every day) = Calc 1 and 2 in college Sophomores in precal can take AB as juniors and BC as seniors.
7
Difference between AB and BC Calculus O Difficulty level is the SAME!!! O Both classes require strong algebraic skills and strong knowledge of trigonometry (unit circle known by heart) O Calculator use is extremely limited. O The primary difference is the amount of material covered. (BC covering three extra units of material)
8
What classes will be required in college if I study….. O Depends on your major O Almost all majors require at least some math courses (core classes that every student must take) O Not all require calculus as that math class O All typically require a statistics class O Which ones require calculus O Any of the Sciences (chem, biology, computer science, environmental science, physics, math) O Business O Engineering
9
Advice… O The best "bang for the buck" is BC Calculus. O If you pass the BC exam you get credit for 2 college classes. At UT for an in state student that is worth ~$2000 and many hours of your time O Everyone in college will need to take some sort of Stats class O Why not take AP Stats and pass the AP exam so you don't have to take the class in college?
10
Advice… O All AP classes are tough! O Some will find Calculus harder while others may find Statistics harder O Typically students in Pre AP Pre Calc are ready for the rigor in either AP Calc or AP Stats O If you are a strong regular pre calc student you are ready O Can't fit BC Calc in your schedule (or you don't want to be in math every day?) O AB Calc is a solid option. O A select group of students from AB will be learning the extra material on their own time to take the BC exam. O But to be clear… AB Calc and AP Stats is not "easier" than BC Calc
11
Advice… O Don't want to take an AP math class at all? O AQR, regular Stats, and regular Calc will all prepare you for college math classes. | 677.169 | 1 |
Division Updates
K-12 Parent-Teacher Day - NO CLASSES
An upcoming Division event, on Friday, November 17th.
Mathematics
Portage Collegiate Institute offers all three streams of mathematics after the completion of Math 10F. Each of the three streams is provided in some detail below as well as advanced placement calculus. It must be noted that a math credit from each grade from S1 to S4 must be attained to graduate from the school.
Final exams in all math courses are mandatory
Transitional Math (MTT10F)
Grade 9 Transitional Mathematics is comprised of a series of units designed to address gaps in students' mathematical understanding as they transition from grade 8 to grade 9 Mathematics. The curriculum for grade 9 Transitional Mathematics allows students to earn an optional credit within Senior Years graduation requirements. Grade 9 Mathematics (Math 10F) will remain as the compulsory core credit for Grade 9 Mathematics.
Timetabling for this new curriculum is a local decision as is determining the students for whom it is appropriate. Some students may require this program while other students will not require Grade 9 Transitional Mathematics in order to transition satisfactorily to Grade 9 Mathematics (10F).
Math 10F (MAT10F)
This course is arranged by topics which will be used to help students become engaged in making connections among concepts and thus make mathematical experiences meaningful. The focus of student learning should be on developing a conceptual and procedural understanding of mathematics. Students' conceptual understanding and procedural understanding must be directly related.
Introduction to Applied and Pre-calculus Mathematics (20S) is intended for students considering post-secondary studies that require a math pre-requisite. This pathway provides students with the mathematical understanding and critical-thinking skills that have been identified for specific post-secondary programs of study. The topics studied form the foundation for topics to be studied later in both Grade 11 Applied Mathematics and Grade 11 Pre-calculus Mathematics. Components of the curriculum are both context driven and algebraic in nature. Students will engage in experiments and activities that include the use of technology, problem solving, mental mathematics, and theoretical mathematics to promote the development of mathematical skills. These experiences will provide opportunities for students to make connections between symbolic mathematical ideas and the world around us.
(20S) is intended for students whose post-secondary planning does not include a focus on mathematics and science-related fields. Essential Mathematics is a one-credit course emphasizing consumer applications, problem solving, decision making, and spatial sense. Students are expected to work both individually and in small groups on mathematical concepts and skills encountered in everyday life in a technological society.
Pre-calculus Mathematics is designed for students who intend to study calculus and related mathematics as part of post-secondary education including fields such as engineering, sciences, medicine, management and agriculture. Pre-Calculus 30S will build on concepts studied in grade 10 Intro to Applied and Pre-Calculus and Pre-Calculus 40S will develop concepts that are needed in Calculus and other university math courses. The course comprises a high-level study of theoretical mathematics and algebra with an emphasis on problem solving and mental mathematics. Students can expect at least an hour of homework each night, with limited class time to complete assignments.
Applied Mathematics is intended for students considering post-secondary studies that do not require a study of theoretical calculus. It is context driven and promotes the learning of numerical and geometrical problem-solving techniques as they relate to the world around us. Grade 11 Applied will build on concepts studied in grade 10 Introduction to Applied and Pre-Calculus to prepare students for Grade 12 Applied Math. Primary goals of Applied Mathematics are to have students develop critical-thinking skills through problem solving and model real-world situations mathematically to make predictions. There will be a strong technology component in the program and students can expect at least an hour of homework each night. Students must note that 30S Applied Mathematics will be a pre-requisite for grade 12 Applied Mathematics.
Calculus 42S is designed to prepare students for the Advanced Placement Calculus AB examination. Pre-Calculus 40S is a prerequisite and this course continues the study of calculus with integration, the fundamental theorem of calculus and application problems. There will be a thorough review of all topics from 41G as well as the material that is new in this semester. The outline for this course is determined by the College Board and is available at their web site or at the AP web site Graphing technology continues to be an integral tool for this course and graphing calculators may be used daily. Students who are successful in completing this course and passing the AP exam will be eligible for credit or advanced standing at many universities in Canada and around the world. | 677.169 | 1 |
> Il giorno 28/ago/2015, alle ore 15:37, Torsten Otto <torsten.otto at hamburg.de> ha scritto:
>> What an interesting topic to discuss!
>>> Am 28.08.2015 um 12:12 schrieb Nicola Gigante <nicola.gigante at gmail.com>:
>>>> Using Haskell (specifically some kind of concepts, e.g. equational reasoning)
>> will also make easier for students to see the connection between math
>> and programming, making them more motivated to learn math as well.
>> Can you elaborate on that? What would you do in class in terms of "equational reasoning"?
>
It depends on the age of the students and the math they already know.
I don't have specific examples of in-class exercises or things like that.
However, the point is that writing Haskell code you can
often come up with shorter or more elegant solutions by
manipulating terms exactly as done in elementary algebra.
Starting from a 10lines function and coming up with
a simple and readable oneliner is fun and rewarding,
and shows one of the possible connections to math,
especially if you can make them reason about types,
in which case the task becomes very similar to theorem
proving than to algebraic manipulations alone.
Another possible connection arise when you teach things
such as the Monoid typeclass.
Even if students have not been exposed to abstract
mathematics, they can still appreciate the usefulness of
abstracting similar operations (addition in this case) to
being able to uniformly reason about apparently different
concepts. Abstraction is the core of mathematics, but is
also a fundamental concept in programming, of course,
so you're implicitly teaching two things at once.
> Regards,
> Torsten
Greetings,
Nicola | 677.169 | 1 |
Algebra 1 Matching Review Activity
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this file type before downloading and/or purchasing.
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Covers linear, exponential, geometric, and arithmetic. Gives students a piece of information about a function or sequence on the left hand side, and equations/functions/sequences on the right hand side. Students match 1 from the right to its appropriate part on the left. Made in word, and made so that you cut in half vertically and you save a bit of paper. Will really make kids think, can take a full class period. Let me know if you have questions or feedback! | 677.169 | 1 |
Foreword by Patrick J. Driscoll
Mathematical modeling is a challenging endeavor whether you are new to the task or have been professionally engaged in it
for many years. Efficiencies are gained with experience, but never at the cost of assuming
a new problem can be solved in the same way with exactly the same ingredients as a previous
one. Time and circumstances affect modeling parameters and assumptions, amplifying some and
negating others. Simply asking a different question about the exact same situation can introduce
intractable elements into a previously well-defined problem.
These facts, among others, mark the participation of MCM teams as extraordinary, no matter what level of award is achieved.
The mere fact that undergraduates are willing to commit a solid block of their own time to
tackle an unfamiliar problem speaks highly of their motivation to learn and develop. Ah,
but the satisfaction of experiencing a model function as intended, and yield significant
results pertaining to a line of inquiry – that is what will bring someone back for more.
Like the one beautiful golf shot on an otherwise unremarkable round.
A writer friend of mine once said that a novel is a bit like achieving mental telepathy in that an author conveys a scene,
an idea, or a plot existing in her mind into the mind of a reader using text or illustrations.
If successful, someone on the other side of the world could read the text and 'see' the imagery
that the author intended to convey. In many ways, teaching mathematics, and mathematical
modeling in particular, is a similar endeavor.
As educators, we use various symbols, diagrams, text, and graphs to present our understanding, our imagery of challenging
concepts to students in the hope that an insight gained from one or more of these approaches
will become a foothold upon which students can construct their own logical understanding.
When students attempt to do this, active learning occurs. When students attain this ownership,
a level of understanding occurs that leads to innovation and creativity in mathematics, science,
and engineering that is not possible to achieve through other means. Pattern matching and
mimicry, while appearing to produce similar results, are deceptively inadequate to the task.
Since the beginning of MCM, we've published a good deal of recommendations and critique concerning what judges consider to
be elements of a proper engagement with mathematical modeling. This advice was primarily
intended for teams and institutions new to mathematical modeling and its nuances, recognizing
both the important role that a faculty advisor plays in preparing teams to compete and the
limited time within which the tasks required by MCM must take place.
Teams participating from institutions with an existing strong commitment to mathematical modeling might use such advice as
simply an editorial check prior to submitting their paper. Regardless, the advice was never
intended to prescribe a lockstep adherence to a process as a recipe for success, but rather
to provide a framework within which MCM teams might initiate their efforts and bring about
a respectable level of completion.
There are some things in life that cannot be rushed, no expedients exist that can accelerate them, and while technologies
and templates exist to augment and enhance processes associated with these activities, understanding
demands time. Mathematical modeling is one of these. And this, we must remember, is what
makes the accomplishments of every MCM team so special. | 677.169 | 1 |
Omtale
GCSE Maths Edexcel Foundation Student Book
Exam Board: EdexcelLevel & Subject: GCSE MathsFirst teaching: September 2015 First exams: June 2017
Endorsed by Edexcel
Collins GCSE Maths 4th edition Foundation Student Book, written by experienced teachers, matches the Edexcel GCSE specification for Foundation tier students, and Collins have entered the Student Book into the Edexcel approval process. This is the ideal resource to help all students fulfil their potential at GCSE Maths.
*Bring awe and wonder with a chapter opener that puts the maths in context*Provide rigorous maths practice with hundreds of high quality questions*Focus on literacy skills with key words per topic*Reason, interpret and communicate mathematically with flagged mathematical reasoning questions (labelled MR and CM)*Solve problems within mathematics and in other contexts with flagged problem-solving questions (labelled PS and EV)*Show step by step working through worked examples (numbered sequentially throughout the chapter)*Help students get to grips with concepts with more diagrams and visual representation*Access answers online, in the Teacher's Pack and in the Collins Connect edition | 677.169 | 1 |
Mathematics: Learning Express Mathematics Review eBook Collection
Learning Express (PrepStep) Math Review eBook Collection
1,001 Problems to Master Algebra, 2nd Edition
Whether you answer all 1,001 questions or skip around to the problems you need to work on, this guide offers practice for standardized tests and in-class assignments that include algebra. Every question includes a detailed answer explanation.
501 Algebra Questions, 3rd Edition
Using a multiple-choice approach that moves from basic to difficult questions, this eBook will teach you concepts and skills in algebra. This eBook covers the full range of algebra concepts, with tips on how to avoid careless mistakes.
Algebra Success in 20 Minutes a Day, 5th Edition
This eBook guides you through all the topics of fundamental algebra you need to know—fractions, coordinate geometry, systems of equations, exponents, polynomials, and word problems—in 20 easy steps. Each step takes just 20 minutes a day.
Express Review Guides: Algebra I
Algebra can be as easy as 1-2-3 with Express Review Guides: Algebra I. This eBook provides targeted lessons that give you the skills you need to make sense of any early algebra problem. With this guidance, you can bring your algebra skills up to speed.
Express Review Guides: Algebra II
Express Review Guides: Algebra II will help you make sense of advanced algebra. This eBook will lead you through functions, graphs, parabolas, tricky equations, inequalities, matrices, roots and radicals, quadratic equations, and the quadratic formula.
Just in Time Algebra
In this eBook, you'll learn the basics of algebra that you need for your next test. You will also learn time-saving study skills and test-taking tips. Topics include equations, coordinate geometry, inequalities, exponents, polynomials, and fractions.
Express Review Guides: Math Word Problems
With targeted lessons that reinforce basic math skills, this eBook is a guide for solving one of the most difficult of math challenges: the word problem. With tips and strategies for translating and solving questions, you'll be a pro in no time.
Math Builder
This eBook is perfect for anyone seeking to quickly and easily gain better math skills. Math Builder contains over 500 problems and answer explanations to help you practice the concepts and skills you need to get ahead.
Math to the Max
This eBook has 1,200 questions to help you improve your math skills. Problems and explanations help you take command of arithmetic, algebra, and geometry. Each topic covered includes an overview of key terms and formulas.
Practical Math Success in 20 Minutes a Day, 5th Edition
Not everyone is good at math, but math literacy is essential for getting ahead in our high-tech world, especially in college and on the job. A refresher on pre-algebra, algebra, and geometry, this eBook covers all the basics.
Calculus Success in 20 Minutes a Day, 2nd Edition
Learn or review the essential calculus skills college students need for important tests and courses. Master key topics, sharpen your test-taking skills, and maximize your time and effort in just 20 minutes a day!
501 Measurement and Conversion Questions
In this eBook, you will learn all about measurement and conversions, including: calculating perimeter, area, volume, and angles; converting from metric to standard units; solving questions dealing with time, currency, weight, and temperature; and more.
Geometry Success in 20 Minutes a Day, 4th Edition
Geometry Success in 20 Minutes a Day provides a course in geometry skills that fits into any busy schedule—and takes just 20 minutes a day.
Just in Time Geometry
If you don't have time to read a math textbook, you'll have time for the quick lessons in this eBook. In ten chapters, you will learn the basics of geometry that you need to know, time-saving study skills, and essential test-taking strategies.
501 Challenging Logic and Reasoning Problems, 2nd Edition
Do you want to improve your reasoning skills, learn to work smarter, and think better? This eBook will help you improve your critical thinking skills at your own pace. As you practice, you'll benefit from seeing full explanations for every question.
Critical Thinking Skills Success, 3rd Edition
Become an effective critical thinker in 20 minutes a day! Learning to think critically will improve your decision-making and problem-solving skills, giving you the tools you need to tackle tough decisions. Use these practical examples to learn quickly.
Reasoning Skills Success in 20 Minutes a Day, 3rd Edition
This eBook provides techniques for developing your critical reasoning skills, and will show you specific techniques of thinking clearly and logically, in an easy 20-step program. Each step takes just 20 minutes a day.
501 Math Word Problems, 3rd Edition
Many important exams use word problems to test math and logic skills. Each chapter covers a different topic: algebra, geometry, fractions, percents, decimals, and more, and questions progress in difficulty.
501 Quantitative Comparison Questions
Standardized tests like the GRE® and SAT* use quantitative comparison questions to assess math skills. This eBook provides targeted practice on these questions to attain higher scores and to help you master this question type. | 677.169 | 1 |
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Performance Task – Systems of Linear Equations – Hit the Slopes: Vail
In the Hit the Slopes Performance Task, students use the prices of lift tickets and ski lessons to write linear equations and solve a system. As marketing executives, they make decisions about the best promotional package to offer during the last week of the ski season.
What's included in this Performance Task:
* Teacher Guide – Get an overview of the Performance Task, including helpful suggestions for use and the Common Core alignment for each activity.
* Level 1 Activity – Laying the foundation. Students start by practicing a core skill matched to a Common Core State standard.
* Level 2 Activity – Adding some complexity. Students integrate a different skill or set of skills from the Level 1 activity.
* Challenge Activity – Bring on the critical thinking! Stretch students to reason with math and data to come to conclusions.
* Finale Activities – Extend the learning. Each activity also includes a finale to extend the math lesson into another subject (usually ELA). | 677.169 | 1 |
Tuesday, July 28, 2009
A Calculator by any other Name Is still a Calculator
A calculator by any other name is still a calculator. Or is it? A lot has changed since the invention of one of the first counting machines, the abacus. The abacus once provided solutions to complex calculations. Then there was Blaise Pascal's invention in 1642, a machine that could be used to add and subtract. Over time newer calculators were and continue to be introduced thus categorized based on functionalities that make them unique from others. For example there are basic calculators, scientific calculators and financial calculators. In addition, there are graphical calculators. Graphical calculators are used quite a bit by both middle school and high school students for use in classes such as geometry, algebra, trigonometry, calculus and physics. Among the list of graphical calculators are a myriad of choices to select from which include the following: TI83, TI84 and the TI-NSprie, HP Calculators, Casio Graphing Calculators, Texas Instruments Graphing Calculators. To truly understand the bells and whistles of each calculator count (plan) on spending a few minutes visiting their websites. | 677.169 | 1 |
Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications.This second edition includes new chapters on labeling and communications networks and small-worlds, as well as expanded beginner's material in the early chapters, including more examples, exercises, hints and solutions to key problems. Many additional changes, improvements, and corrections resulting from classroom use and feedback have been added throughout. With a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites.
Rezensionen ( 0 )
Every Friday we give gifts for the best reviews.
The winner is announced on the pages of ReadRate in social networks. | 677.169 | 1 |
Features Archive
Welcome!
Welcome to the Department of Mathematics and Statistics. We offer a wide variety of undergraduate and graduate degree programs designed for students with diverse career or higher educational goals. Our faculty members maintain active research programs in the fields of combinatorics, algebra, analysis, applied mathematics and applied statistics.
In a nod toward the unity of mathematics, we offer the following question—whose answer requires several of the above fields, as well as geometry:
A collection of small waves are travelling through shallow water and happen to collide. What happens next?
The first half of the above sentence is governed by the famous KdV equations. (Jerry Bona, UIC, spoke at our colloquium about these waves not long ago.)
The second half of the above sentence is governed by cells in the totally positive part of the Grassmannian and plabic graphs. (Dr. Lauve can tell you more about this aspect of the theory of totally positive matrices.)
See our Faculty Research page for a list of local people to ask for more details, or consult the original sources: | 677.169 | 1 |
serves the education community through research and advocacy on behalf of students .. points are set so that the lowest raw score needed to earn an AP Exam score of 5 is Calculus AB plus additional topics, but both courses are intended to be . 6 4 3 2.,,,,,, and their multiples. topic outline for calculus AB. This topic.
Literature Review of papers dealing with student understanding of topics in calculs ant idea of a function has led to much research in student understanding of this topic. for a small, well-defined set of functions whose graphs have linear asymptotes. Most traditional calculus courses offer little opportunity for students to.
Students will be able to set up and solve linear systems/linear inequalities and recognize the appropriate use of technology to enhance those skills, Math 222 - Upon successful completion of Math 222 - Calculus II, a student will be able to: .. Engage in the study or research of a topic that is beyond the regular math.
Set of subjects college calculus 2 technology research topics ideas paper - more
It diffuses out the other end at a predictable rate. An intensive development of the important concepts and methods of abstract mathematics. Students explore power series, Laurent series, and trigonometric series, culminating with an in-depth examination of Fourier series. Recognize the relationship between the confidence interval estimation and tests of hypothesis,. For students in arts and letters.
The: Set of subjects college calculus 2 technology research topics ideas paper
HEATING AND AIR CONDITIONING (HVAC) RESEARCH PAPER COLLEGE SAMPLE
Forensic Science subjects mathematics
Set of subjects college calculus 2 technology research topics ideas paper
124
Audio and Video Production free samples of essay writing
There will be course projects and some usage of computing software. Place a Primal linear programming problem into standard form and use the Simplex Method or Revised Simplex Method to solve it. Aimed at highly engaged math students, Honors Calculus emphasizes the 'why' of mathematics as well as the 'how'. Analyze and interpret statistical data using appropriate probability distributions, e. Contains the study of voting systems and fair division, apportionment using divisor methods, and game theory.
Indeed, much of the fascination of this subject comes from the myriad ways in which arguments squarely in one realm give surprising consequences that fall squarely in a different realm. University of Notre Dame. Also covered are transcendental functions and their inverses, infinite sequences and series, parameterized curves in the plane, and polar coordinates. Null distributions of test statistics will be discussed in the small sample and asymptotic cases, with and without ties. Assess the value of model results discussed in the news and in scientific and mathematical literature. Top 10 Best Favourite Physics Topics | 677.169 | 1 |
The Math Department
The Miller School of Albemarle Mathematics Department is committed to providing an effective quality program to prepare students for college mathematics. At all levels in our curriculum, we encourage the students to approach problems algebraically, graphically, numerically, and verbally. Seeing similarities in the ways to represent different situations is a key step toward abstraction. The role of our teachers is to provide rich problems in a climate that supports mathematical thinking and to equip students with the mathematical tools that will allow development of the expertise they need in making mathematical connections across the curriculum.
Miller School Math Video
3-D modeling by Mr. Macdonald's geometry students featuring the MSA Art Studio and chapel, library, and foyer of Old Main. | 677.169 | 1 |
Important Dates:
The dates for the first two in-class exams will be announced in class,
one week prior to the exams. The material covered is as follows:
Exam I
Chapters 1 & 2
Exam II
Chapters 4 & 5
Exam III
Chapters 7, 8 & part of 6 (if time)
Final
Cumulative.
Note the links at the bottom of this page to old exams.
These are very useful, both to show what I think is important and to show
how much I expect you to accomplish in an hour exam.
Homework problems will not be collected, but they,
together with the problems
on the old exams, cover the skills I expect you to master. You should be able
to do all assigned problems, and should work on them immediately after the
lecture to which they pertain. I'll be happy to go over homework problems
at the beginning of most class sessions.
Please do ask lots of questions. Your questions are a very good indicator of
what you understand. My goal here is to teach you, not to penalize you. The
test for all of us is how you do on the exams. So please make use of the
class and office hours to get my help. I am happy to give it. Remember, if
you have a question, there will be at least 5 others in the class with the
same question. I hope one of you will ask it, because that is how we learn.
Most people learn mathematics more quickly and thoroughly if they discuss it.
Verbalizing a question is often the most important step in solving it. So
please make frequent use of office hours. It is also very useful to get to
know your fellow students and form study groups. | 677.169 | 1 |
Introductory Calculus, Part II
Math 10, "Introductory Calculus, Part II," is the second semester
of the Math 9-10 sequence. It involves learning such topics as:
techniques of integration, inverse trigonometric and logarithmic
functions, infinite series, power series, Taylor's formula, polar
coordinates, and more. The prerequisite for this course is Math 9 or
placement. Math 10 is recommended for all students intending to
concentrate in the sciences or mathematics.
Students raved about Professor [sic] Towse's performancce. He was
reported to be excellent and highly energentic. He presented
difficult concepts in an easily understandable way. Professor Towse
welcomed questions and participation in class. Students found his
class to be relaxing, not intimidating. They even reported that he
had a sense of humor! Even better, he cared about his students.
The workload for this course was reasonable. Students spent
approximately 2-3 hours onthe weekly problem sets.
There wree two exams and a final. All were quite challenging.
Sporadic quizzes were also given out. Secions met once a week. The
majority of reviewers found the sections to be useful. TAs Almeida
and She were said to be helpful in solving the homework problems.
Most of the survey respondents felt that this course was
worthwhile. They feel like they now have a stronger math background.
Others found that it adequately satisfied their requirements.
In conclusion, the reviews for Professor Towse's Math 10 course
rate it a thumbs up. Most anyone interested in taking Math 10 will be
pleased. | 677.169 | 1 |
Designed for high-school scholars and academics with an curiosity in mathematical problem-solving, this stimulating assortment contains greater than three hundred difficulties which are "off the overwhelmed course" — i.e., difficulties that supply a brand new twist to widespread themes that introduce unexpected subject matters. With few exceptions, their answer calls for little greater than a few wisdom of simple algebra, although a splash of ingenuity could help. Readers will locate the following thought-provoking posers regarding equations and inequalities, diophantine equations, quantity concept, quadratic equations, logarithms, mixtures and likelihood, and masses extra. the issues diversity from rather effortless to tough, and plenty of have extensions or adaptations the writer calls "challenges." By learning those nonroutine difficulties, scholars won't basically stimulate and advance problem-solving abilities, they're going to gather useful underpinnings for extra complex paintings in mathematics.
Adobe Photoshop Lightroom used to be designed from the floor up with electronic photographers in brain, providing strong modifying positive factors in a streamlined interface that we could photographers import, type, and arrange group workforce has extra sophisticated the presentation and workouts during the textual content.
The publication extends the highschool curriculum and gives a backdrop for later learn in calculus, sleek algebra, numerical research, and intricate variable thought. workouts introduce many innovations and themes within the thought of equations, equivalent to evolution and factorization of polynomials, answer of equations, interpolation, approximation, and congruences. | 677.169 | 1 |
Study Companion – Got Math Anxiety
You are at the kitchen table and it's 10:00pm. You've raided the junk food cupboard twice, texted seven friends and thought about turning on Netflix.
It's the night before the big math exam and you are anxious. The textbook examples look like a foreign language and you can't understand your teacher's notes. You are at a loss and no matter who much you cram, none of it makes sense. You need help now | 677.169 | 1 |
Visual Math School Edition
Visual Math School Edition is a Education::Mathematics software developed by GraphNow. After our trial and test, the software was found to be official, secure and free. Here is the official description for Visual Math School Edition: Visual Math school edition. Visual Math help users to teach or study mathematics, including algebra, geometry, analytic geometry, solid geometry, calculus, statistics, complex variable function, fractal, curve fitting, probability analysis, linear programming etc. you can download Visual Math School Edition free now. | 677.169 | 1 |
The students know the basics of vector algebra, matrix algebra, differential and integral calculus.
3. Course contents *
Solving problems or issues in an economic or technological context, often involves a little math. Systems of linear equations have to be solved. The matrix algebra taught in this course , can be useful.
To discuss setting up relationships between quantities , for example economics or physics , to recognize and to form new relationships we learn to use differential and integral calculus ( derivatives and integrals ) .
Many quantities in physics are expressed as vectors. To calculate or reason with this quantities, vector algebra is needed.
4 International dimension*
The course has an international dimension.
The lecturer uses course materials in a foreign language
The lecturer teaches the subject of the course mainly as an internationally oriented comparison | 677.169 | 1 |
Listed in the following table are problem sets and solutions. For each problem set, there is also an interactive problem set checker. Students in the class were able to work on the assigned problems in the PDF file, then use the problem set checker to input each answer into a box and find out if the answer was correct or incorrect. Students could use the problem set checker as many times as they wanted to, and they weren't graded on this in any way.
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MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. With more than 2,200 courses available, OCW is delivering on the promise of open sharing of knowledge. Learn more » | 677.169 | 1 |
Math 371: Probability --- Fall 2015
Textbook and Resources:
Homework Assignments:
The dates below are when problems were
assigned. Unless otherwise noted, problems are always due the following Tuesday. Unless otherwise noted, please read the text up through the location of assigned problems. | 677.169 | 1 |
Explanation of Pre-requisites
Ideas from MC144, MC145, MC147 and MC241 are used in the construction of
examples. In particular, the concepts of sets, mappings and
Cartesian products from MC144 and of modular arithmetic and
algebraic structures from MC145 are used extensively. Basic concepts
from matrix algebra are needed from MC147 and (to a lesser extent) MC241.
Course Description
This module provides an introduction to group theory through a combination of abstract theory and specific examples of groups. Group theory can be thought of as the measurement of symmetry, both of geometrical objects and of other structures and this will be a significant theme of the lectures.
Aims
The main aim is to lay down a firm foundation in the basic concepts of the theory ready for development in later (third and fourth year) modules, but it is also intended that this course should be self-contained and lead to its own interesting conclusions.
Objectives
It is intended that the workshops will encourage experimentation with the examples of small groups provided and that the projects will give an opportunity for practice with the presentation of abstract mathematical material.
You will be expected to become familiar with various particular examples of groups and to know how to prove some of the theorems. You should also be able to apply your newly learned knowledge in unfamiliar but similar situations.
Syllabus
The course begins with the general concept of a binary operation and
the various properties that such an operation may enjoy leading to the
definition of a group. These ideas are investigated in greater detail
through use of the computer package ``Exploring Small Groups''. Apart
from those provided by the package, there
is a standard list of examples derived from symmetries of geometrical
shapes, matrices and modular arithmetic. These are used to illustrate
the results and ideas introduced in later chapters.
Topics covered include: subgroups and generators; the lattice of
subgroups; cyclic (sub)groups; the order of an element; cosets
and Lagrange's Theorem; the index equation; conjugation; centre;
class equation; normal subgroups and factor groups; the symmetric and
alternating groups; cycle notation for permutations; conjugate
permutations; the class equation of A5; A5 is simple.
Background:
Details of Assessment
Assessment is based on three components - a one and a half hour examination in
May/June (80%), 4 problem sheets set in alternate weeks (10%) and two computer
assignments (1 short, 1 longer) (10%).
The examination paper will have four questions all carrying the same weight and
full marks will be obtained for correct answers to three. Questions on the paper
will include proofs of elementary results. Familiarity with the examples of groups
met in the course will be expected and you should be able to apply the methods learnt. | 677.169 | 1 |
Mulitple Choice is Boring
Main menu
Post navigation
Simple and Complex Matrices
This series of animations was designed to help student visualize patterns of matrices in a finite mathematics course. Specific topics included addition, subtraction, scalar multiply and product multiply as well as the explanations of the differing types of matrices | 677.169 | 1 |
An Introduction to Proof through Real Analysis
An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis
A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own.
An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems.
• Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects
• Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation
• Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction
• Uses a particular mathematical idea as the focus of each type of proof presented
• Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses
An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time | 677.169 | 1 |
Calculus: Rates of Change and Introduction to Derivatives
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this file type before downloading and/or purchasing.
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This is the first lesson in a thirteen-lesson unit on Differentiation for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus. Every lesson includes
✎ A set of Guided Student Notes
✎ A daily homework assignment
✎ Four forms of a daily homework quiz or exit ticket
✎ Teachers also have the benefit of a fully-editable SMART Board® Lesson for presentation and discussion.
Lesson Objective:
• Estimate average and instantaneous rates of change graphically and numerically
• Interpret distance vs. time graphs
• Explore the concept of local linearity using graphing calculators
• Interpret the meaning of derivative as it relates to real-world scenarios | 677.169 | 1 |
Linear Algebra: A Pure Mathematical Approach(Paperback)
Synopsis
In algebra, an entity is called linear if it can be expressed in terms of addition, and multiplication by a scalar; a linear expression is a sum of scalar multiples of the entities under consideration. Also, an operation is called linear if it preserves addition, and multiplication by a scalar. For example, if A and Bare 2 x 2 real matrices, v is a (row) vector in the real plane, and c is a real number, then v(A + B) = vA + vB and (cv)A = c(vA), that is, the process of applying a matrix to a vector is linear. Linear Algebra is the study of properties and systems which preserve these two operations, and the following pages present the basic theory and results of this important branch of pure mathematics. There are many books on linear algebra in the bookshops and libraries of the world, so why write another? A number of excellent texts were written about fifty years ago (see the bibliography); in the intervening period the 'style' of math- ematical presentation has changed. Also, some of the more modern texts have concentrated on applications both inside and outside mathematics. There is noth- ing wrong with this approach; these books serve a very useful purpose. But linear algebra contains some fine pure mathematics and so a modern text taking the pure mathematician's viewpoint was thought to be worthwhile | 677.169 | 1 |
CBSE Class 12 Maths Paper Analysis
Table of Content
This year, Central Board of Secondary Education conducted its CBSE Class 12 examination on 2nd March 2015. Since Mathematics is considered to be one of the best options to score better and achieve more percentage, hence CBSE Mathematics 12th board examination remains to be crucial for all Science stream candidates.
At askIITians, we help analyze you with CBSE class 12 Maths paper.
KEY HIGHLIGHTS
Difficulty Level:Moderate
Was it a Lengthy Paper ? Yes
Was Tricky Questions Asked ?: There was just one trick questions which was Set I, Question number 11
Out of Syllabus Question:None of the questions were out of syllabus and no errors at all.
Calculus & Vectors & Dimensional Geometry was given much weightage as compared to topics such as Relations of Functions & Algebra
Tips for preparation of calculus portion
Calculus portion is the most important section of class 12 mathematics syllabus. It usually fetches maximum number of questions in CBSE exam. Hence, those who want to outshine in their boards must work hard on this portion. Listed below are some of the expert tips which can prove fruitful in mastering this section:
In order to excel in the calculus portion, it is important to be well-versed with the various formulae including the differentiation and integration of various functions,
Good speed is imperative for a good performance. Since the section is completely based on calculations, so students must practice hard so as to develop a good speed.
Besides knowing the statements of theorems like Rolle's, Lagrange's etc., it is also important to know the applications and interpretation of these theorems.
Do not try to cram the methods; instead try to figure out why a particular method is applied in a particular question.
During the preparation phase, begin with the simple questions followed by moderate and the tough ones.
Prepare your flash cards containing the list of formulae so that you can revise them again and again.
Solve various sample papers and past year papers to get acquainted with the trend of questions asked in the exam.
Practice and a good speed is all what you need to come out with flying colors. Hence, the more you practice, better it is.
While taking the exam, try to attempt the simple questions first. Those involving lengthy calculations must be attempted at the end.
Differential equation is a simple topic which can fetch you some easy scores. So, revise it thoroughly.
While taking the exam, it is quite normal to get stuck in a problem and you might find it difficult to proceed further. If this happens in an exam then it is advised to switch to some other problem.
Tips for mathematics section of CBSE class 12th
Read some of the useful tips and tricks, specially made for the students preparing for CBSE class 12 Examination 2015.
General Tips
The most important thing is to have a positive attitude towards math and try to fall in love with this monster
Hard work is the only key to success. You cannot expect to climb the final step before going through all the steps of the ladder
The basic funda of success in mathematics is practice. One cannot expect to excel in this subject without practicing innumerable questions on various concepts
Take out some time from your busy schedule on daily basis for solving some mathematics questions
Work on your fundamentals and basics. Firm groundwork can help you fetch excellent marks
Mathematics is not meant to be read. After reading a formula try to attempt good number of questions based on it as it will automatically help in its memorization. You won't have to spend extra time on mugging it up
The various formulae should be on your finger-tips including those on derivatives, integrals, sum and product of roots, sum and product of trigonometric functions, various progressions, sequences and series etc.
Simple facts like trace of a matrix equals the sum of roots and the determinant gives the product of roots can help in getting quick answers to the questions of algebra
Be well-versed with the conventional methods of solving problems. Practice sufficient number of questions using these methods first and once you are confident enough you may switch to short-cut methods in order to improve your speed. But be sure that you don't end up committing mistakes by missing steps
Commit as many mistakes as you can during the preparation phase. This will help you in identifying the areas where you might commit errors so that you don't do so on the final day
Jot down all the important formulae and prepare a list for the same. Paste it somewhere near your study table or bed and revise it whenever you see it
Practice good number of problems of square roots and cube roots so that you don't spend too much time on them during exam | 677.169 | 1 |
ward-winning Windows calculator that includes nearly every feature imaginable, including a scrolling tape that automatically recalculates when you edit it. Ziff Davis named Judy's TenKey the Desktop Accessory of the Year!
This is an easy to use Scientific Calculator that incorporates a molar mass calculator, a triangle calculator, vector calculator, shape calculator, kinematic calculator and a statistical calculator. Numerous science data tables are included. | 677.169 | 1 |
Electronic Proceedings of the Twentieth Annual International Conference on Technology in Collegiate Mathematics
San Antonio, Texas, March 6-9, 2008
Paper S075Carl R. Spitznagel
See a cardioid transformed into a circle or limaçon as you drag a slider to change a parameter. Help students understand why a polar rose has the number of petals that it does. With teacher-created demos in Geometer's Sketchpad, presenting ideas such as these is a snap! | 677.169 | 1 |
Second Grade Saxon Math And Ccss
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Mathematics Academy
You are here
July 1 – July 21, 2018
The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students in topics such as:
Discrete Mathematics
Combinatorics (enumerative, algebraic and geometric)
Generating functions and partitions
Graph theory
Probability
Combinational game theory
Algebra and Number Theory
Linear algebra
Prime and factorization algorithms
Congruencies and quadratic reciprocity
Galois theory
Geometry of numbers
Geometry and Topology
Euclidean and non-Euclidean geometries
Geometric transformations
Algebraic geometry
Point-set topology
Knot theory
If you attend a School District of Philadelphia public or charter high school, you may be eligible to attend a Penn Summer Academy free of charge with a Penn Summer Scholarship.
Features
Prerequisite: One year of high school Algebra II/Trigonometry is required for application.
Faculty
Program Director: Avi Barr Avi Barr has worked as a part-time instructor of mathematics at the University of Pennsylvania for 34 years, where he also implemented and taught an online learning course. Avi taught high school math for 43 years, and was department chair for the last ten years. | 677.169 | 1 |
When will I ever use algebra? Why do I need to learn this? Every year, math teachers are asked these same questions by a number of their students. Despite explaining the many ways in which algebra is used by different professionals, algebra is rarely brought to life in the classroom. However, on Tuesday, May 21, 2013, Mark Love, the founder of Engineers Teaching Algebra, visited with MKA Middle School seventh grade math classes to promote STEM (Science, Technology, Engineering and Mathematics) education. In addition to promoting STEM, Love did so much more - he made math come alive.
STEM education is an interdisciplinary approach to learning where rigorous academic concepts are coupled with real-world lessons as students apply science, technology, engineering, and mathematics in contexts that make connections between school, community, work, and the global enterprise enabling the development of STEM literacy and with it the ability to compete in the new economy. (Tsupros, 2009)
Nichole Foster-Hinds, Middle School Math Chair, arranged for students to participate in Engineers Teaching Algebra active, hands-on practical approach to algebra in order to foster and strengthen MKA's curriculum objectives to focus on students' development of mathematical reasoning and problem-solving skills at the same time that it reinforces students' basic computational skills and introduces new mathematical concepts.
As the field trip session began, Love asked students to identify which tool is most useful to an engineer and later explained that it is an eraser. His rationale behind the opening exercise was to inspire students to take risks and to encourage problem-solving. If you don't succeed at first…try again, and as students began to work through a series of formulas to design accurate, safe and efficient traffic patterns, they were reminded by Love that: "Wrong answers are better than no answers at all."
Love, a civil engineer by trade, helped students relate what they knew with what they needed to know. Without using any sophisticated math, Love challenged students to develop a problem-solving plan; he then asked them the fundamental question, "Why did your plan work?" Students did not initially realize that, in using their logic and reasoning skills, they were actually creating their own algorithm for finding the most efficient traffic pattern – they were nascent civil engineers.
After creating the traffic pattern algorithm and receiving some additional information, students were challenged to a tenth grade puzzle resembling the development of a safe and efficient phasing plan for a signalized intersection, whereby optimal efficiency is between 1400 and 1450 vehicles per hour. For Love, such an intricate task necessitates that students be equipped to go back to hands-on, manual arithmetic because technology, calculators and the like, is not always a reliable tool.
With paper and pencil in hand and erasers rapidly wearing away, a great discovery was made, the Engineers Teaching Algebra in-school field trip proved that: "In a world of technology, information and ideas, math is not a subject, it's a necessary language." - Mark Love, Founder, Engineers Teaching Algebra. | 677.169 | 1 |
Lecture 1
Complex Numbers
Denitions.
Let i2 = 1.
i = 1.
Complex numbers are often denoted by z.
Just as R is the set of real numbers, C is the set of complex numbers. If z is a complex
number, z is of the form
z = x + iy C, for some x, y R.
e.g. 3 + 4i i
After completing this chapter you should be able to
add, subtract, multiply and divide complex numbers
nd the modulus and argument of a complex number
show complex numbers on an Argand diagram
solve equations that have complex roots.
Complex
numbers
1
The
Chapter 5
COMPLEX NUMBERS
5.1 Constructing the complex numbers
One way of introducing the field C of complex numbers is via the arithmetic of 2 2 matrices. DEFINITION 5.1.1 A complex number is a matrix of the form x -y y x where x and y are real numbers.
Mathematical Database
COMPLEX NUMBERS
When we are solving quadratic equations with real roots, the roots of the equations exhibit
three cases: two distinct real roots, a double root or no real roots. To accommodate the case of no
real roots, i.e., to prov
MATH2005/ STAT1210
Probability and Statistics for Computer Science
Problem Set 4
Special Random Variable
Section A (Required)
Problem 1
A multiple-choice test consists of 8 questions, each having 4 possible answers.
(a) A student who has done no preparato
MATH2005/ STAT1210
Probability and Statistics for Computer Science
Problem Set 3
Basic Concept of Random Variable
Section A (Required)
Problem 1
It is given that 35%, 25% and 40% of the families have no child, one child and two children
respectively. 5 fa
MATH2005/ STAT1210
Probability and Statistics for Computer Science
Problem Set 2
Advanced Probability Theory
Section A (Required)
Problem 1 (General Addition Rule)
An experiment is carried out to verify a research idea. It is given that the experiment
suc
MATH2005/ STAT1210
Probability and Statistics for Computer Science
Problem Set 1
Introduction to Probability
Section A (Required)
Problem 1
In an experiment, a fair coin is first tossed. If head is shown, a biased coin (loaded 75%
head) will then be tosse
Why we bias MOSFET amplifiers
in the saturation region.
D. W. Parent
When designing an amplifier we usually want
the magnitude of the gain to be at least 2.
Operating in the saturation regime allows for a
magnitude of the common source gain to be greater | 677.169 | 1 |
An ATAR course which must be selected in conjunction with Mathematical Methods. The Specialist course provides opportunities beyond those presented in Methods course, to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively. The course contains topics in functions and calculus that build on and deepen the ideas presented in Methods course. The Specialist course extends understanding of statistics and introduces the topics of vectors, complex numbers and matrices. Unit 1 involves developing mathematical arguments, Euclidean Geometry, vectors and complex numbers. The topic combinations provides techniques that are useful in many areas of mathematics, including probability and algebra. The topic Vectors in the Plane provides perspectives on working in two dimensions.
Unit 2, Matrices provide new perspectives in two dimensional space and Real and Complex Numbers provides a continuation of the study of numbers. The topic Trigonometry contains techniques used in Methods. All topics develop students' abilities to construct mathematical arguments. The technique of proof by the principle of mathematical induction is introduced.
Year 12
Mathematics Specialist
An ATAR course which provides opportunities, beyond those presented in the Mathematics Methods ATAR course, to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively. The Mathematics Specialist ATAR course contains topics in functions and calculus that build on and deepen the ideas presented in the Mathematics Methods ATAR course, as well as demonstrate their application in many areas. This course also extends understanding and knowledge of statistics and introduces the topics of vectors, complex numbers and matrices. The Mathematics Specialist ATAR course is the only ATAR mathematics course that should not be taken as a stand-alone course. | 677.169 | 1 |
I actually write this article to help highschool and college students that are majoring in math. My nephew Marc will be so happy to read this.
When students understand the underlying patterns of algebra, and then learn to extend those patterns, something miraculous occurs. Students learn algebra! It makes sense to them, and they even enjoy it!
Brain research has confirmed that it is through recognition of patterns that the brain learns. Patterns of Algebra takes advantage of that natural learning, and leads students to discover for themselves all the big ideas relating to linear and quadratic functions.
Do you need tools in order to learn Algebra? In my opinion a good algebra book, a great scientific/graphing calculator and of course your brain is enough to master Algebra. If you are interested in purchasing a calculator, please view this What Is The Best Graphing Calculator Today article.
When students discover for themselves the patterns upon which algebra is built, they quickly and easily master linear and quadratic functions. Much of what we call education is based on memorization. And what students are asked to memorize makes little sense to them or to the frustrated teachers who struggle to motivate and encourage their students.
Some teachers want to "teach for understanding," but are not always clear on what it is that students should understand. Patterns of Algebra does away with memorization, choosing instead to introduce students to the patterns which form the foundations of algebra.
Students are lead to discover big ideas, and then to build on those ideas as they progress through their study of algebra. As you work through the material presented here, you will find that concepts are presented when they are needed.
It is what has been called "just in time" learning, as opposed to the more conventional "just in case" learning. When students can use and build on what they learn, their learning accelerates and their motivation is resurrected. | 677.169 | 1 |
The department currently follows the AQA Syllabus A in Mathematics. There
are 3 tiers of entry as follows:
Foundation Grades available D-G Unclassified below this
Intermediate Grades available B-E Unclassified below this
Higher Grades available A *- c Unclassified below this
Four pieces of coursework are required by the department, but more
may be given if necessary, to enable pupils to gain the highest
possible marks. The coursework is worth 20% of the final mark.
There are two final examination papers for Foundation,
Intermediate and Higher of lIf2, 2 and 2 hours duration,
respectively, the first paper in each tier being a non-calculator
paper.
Pupils are expected to have a calculator and drawing equipment.
The Intermediate and Higher level students require a scientific
calculator, which may be purchased through the department, in
August of each year. A basic calculator is adequate for Foundation
level.
During the course pupils will be expected to use computers.
Spreadsheets, data handling, and graphical work may be used to
enhance classroom teaching.
Revision booklets can also be purchased through school, at a cost
of around £2, along with a workbook at £2. These are made
available in Year 10 and Year 11, usually in the autumn term, and
relate to the courses studied.
Most Foundation coursework will be completed at school, but it is
expected that Intermediate and Higher coursework may have to be
completed as homework, individually, arid in line with G.C.S.E.
regulations.
There will be an opportunity for some pupils to take statistics as
an extra GCSE. This involves a heavier workload and is not
suitable for all students. Separate coursework will be needed for
Statistics, but this should also be usable as an element of the
Mathematics coursework, saving time and effort if done well.
All pupils will study G.C.S.E mathematics a11d we expect the
majority to sit the examination. If not, pupils may be entered for
an alternative examination.
It is most important that every student gains a qualification in
Mathematics, before leaving school.
WHOM TO CONTACT FOR FURTHER INFORMATION:
HEAD OF DEPARTMENT
MR COOK | 677.169 | 1 |
Math Tutoring | Blog Style
Category: Calculus AB & BC
Hello everyone! I hope you all had a lovely Spring Break. It still feels like winter here, but since it's April we can just pretend like it's Spring! As my seniors are gearing up for AP tests at the beginning of May I will be including videos of some of the final chapters that they've been studying this past month. The topic today is how to find the volume of a solid by using cross-sections. Both AB and BC Calculus students study this topic so I will include one video for both classes. I've shown the most frequent shapes that Calculus books use for the cross-sections (square, equilateral triangle, circle etc.) Hopefully this will help some of you as you begin reviewing everything this month for the AP exams!!
Hello everyone! I'm super busy this week tutoring my students for their finals (which mostly take place next week). Yesterday I had 13 hours of students, yikes!! I'm going to try to blog everyday this week but am going to keep my posts pretty short in the essence of my time crunch
Here's a video on how and why it's good for my BC Calculus students to know the cylindrical shell method for finding volumes of revolution (in addition to their preferred methods of disks and washers)…
And here's a video explaining how to look at a graph of a derivative and answer questions about the original function. I ALWAYS get a ton of questions on how to do this! My AB Calculus students have been doing this very recently…
One more week and then Winter Break! All of my students have their finals in January so this week is filled with lots of chapter tests and quizzes. I know it's a busy time for all of you…and not just in math!
My AB Calculus students have been studying the relationship between position, velocity and acceleration. They have been working on word problems involving all three which can definitely be confusing. Hopefully this example will help you sort through similar problems. I'm planning on doing another video on this same subject next time too. It's just too much to cover in only one video!
My BC Calculus students recently learned integration by parts. This is a method that helps you take a very difficult integral and rewrite it as a much easier one instead. I've shown two very frequent types of integration by parts…the tabular method where you keep taking the derivative of "u" until you get 0 and a wrap-around problem where you eventually get the same integral that you started with (which doesn't seem like something that would be very helpful, but it is!)
Have a great week! Just keep looking forward to winter break, and I know you can make it!!
If students will hear me out, I usually show them how to factor quadratics that have a leading coefficient by splitting the middle term (instead of using other tricks). I've noticed that it introduces them to the idea that a GCF doesn't only have to be a monomial but that it can be a binomial quantity, which in turn helps them with more difficult factoring in Precalculus and also with simplifying derivatives in Calculus!
This was just an extra post today in addition to my daily posts for you students! See you tomorrow!
Oh wow, it was hard hearing that alarm go off this morning after a relaxing Thanksgiving break! I so much just wanted to rollover and go back to sleep! I did make it here today though, and if we all push through it's only a quick, busy 3 weeks until Winter break
I'm anticipating that my BC Calculus students will be working on solving differential equations by separation of variables this coming week. I've included two examples in my video. If the timing works out properly, I'm planning to do a few word problems using separation of variables next week.
And right before Thanksgiving my AB Calculus students were working on related rates which is where they will be picking back up again today. I've worked through one of the very commonly seen "ladder" problems.
See you tomorrow for Precalculus!
Posts navigation | 677.169 | 1 |
What Happens if We Just Ask Questions?
"The weeklyMathematicalabs that we have in my Calculus 3 class are set up so that some background material (usually a combination of math concepts and newMathematica commands) is presented in the lab handout followed by some situations centered around questions, the answers to which are likely to involve Calculus 3 andMathematica. I saidlikely, notinevitably. There is no rule that says students must use Calculus 3 to answer the question. The only rules are: (1) the entire solution has to be done in aMathematicanotebook, and (2) the solutions have to be clear, convincing, and mathematically correct.
What's been good about this approach is that promotes an ownership mindset of the mathematics in the class. Students get very creative and engaged when they have some say in the proceedings and it's not just parroting what they learned in class. The lab problems are created so that they apply what we've learned in class, but often students will find some creative workaround | 677.169 | 1 |
Math 115 - Section 93: Calculus I Fall 2017
About the webpage.
This is the website for Section 93 of Math 115. The primary
website for the course is here. Please check this website at all times
for any administrative information about the course.
About the course.
We quote from the primary website:
Math 115 presents the concepts of calculus from four points of view: geometric, numerical, algebraic, and verbal.
The emphasis is on concepts and solving problems rather than theory and proof.
In addition to problem solving skills, we expect students to demonstrate marked growth in their reading, writing, and questioning skills.
Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and an introduction to integration. | 677.169 | 1 |
Description
YayMath.org and Study By App, LLC have partnered to create a comprehensive Algebra 1 app. The Yay Math movement and this project are built on an understanding of Algebra's importance, not just for this class, but also for advancing to next levels. The consciousness of this app is in decreasing student anxiety over math, clarifying topics that regularly confuse students in the classroom, and meeting the unique needs of the busy, time-deprived, always on-the-go student.
With this app, students receive 12 audio lessons each of which contains complete step-by-step guides and examples and 25 robust flashcards, constructed in easy to understand, succinct terms. Each lesson also has a 50-question multiple choice test with carefully crafted hints for approaching the problems and complete explanations for incorrect answers. In addition, the app allows students to track performance and time. Those lessons are:
Intro to Algebra
Know your Numbers
Solving Equations
Exponents and Polynomials
Factoring
Factoring to Solve Equations
Graphing Lines
Systems of Equations
Radicals
Percents and Variation
Inequalities, Absolute Value
Completing the Square, Quadratic Formula
What stands out about this app is exactly at the heart of what makes Yay Math special: energy. Informal language, disarming tone, positive approach, thorough step-by-step instructions, and a constant mindfulness of student achievement are the platform from which the content is delivered. Your success is valuable, and it is with that sentiment that this app was made. Best wishes in all your endeavors.
Algebra App development, biography:
This app was developed by Robert Ahdoot, a full-time high school math teacher since 2005, and founder of YayMath.org. The Yay Math video project is a free service dedicated to meeting the growing need for math success in a positive, lively, and confidence-boosting way. Yay Math stands as the only online video lesson series filmed in a live classroom, with real student interaction. It has grown into a global movement, boldly redefining how people perform better in their math coursework.
We appreciate your feedback. For questions or comments please email: jgrady@studybyapp | 677.169 | 1 |
Algebra 1: Unit 1: Lesson 3: Concept 1: Using a Replacement Set to Solve an Equation | 677.169 | 1 |
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For help with side labeling, allow students to reference student made charts from lesson 25.
Lesson 27 (P)
Consider using numbers instead of symbols for Example 1. Consider laminating cut-outs from lesson 21 as they will be used again in this lesson. In Classwork problem, if students are struggling to see the connection, use a right triangle with side lengths 3, 4, and 5 to help make the values of the ratios more apparent.
Lesson 28 (P)
Students will need graphing calculators to work out trigonometry problems. Consider spending a small amount of time during class modeling calculator button pushing. Ensure that all calculators are in degree mode, not radian.
Lesson 29 (P)
For Opening Exercises, consider asking half the class to work on part (a) and the other half to go directly to part (b), and then share results. Alternately, have students work in small groups. Students can work in pairs (or fours to split the work a little more); a student divides the values while the partner finds the tangent values, and they compare their results. Then, the class can debrief as a whole.
Consider having students make a graphic organizer to clearly distinguish between the law of sines and the law of cosines and when to use which one.
Lesson 34 Omit
This lesson is omitted for pacing consideration. In lesson 34 students are exposed to arcsin, arccos, and arctan. Students will be exposed to these concepts formally in Algebra 2 and are not assessed on them in the EOM assessment.
Two extra days this week given to administer assessment, return assessment, and remediation for Module 2.
To see how this content is addressed in earlier grades, see Topic C of Grade 5, Module 4. Upper and lower limits are intentionally used to prepare students for future math learning.
Lesson 2 (E)
Two days are given for this lesson. Consider covering three properties the first day and two the second. As notation is introduced, have students make a chart that includes the name, symbol, and a simple drawing that represents each term. Consider posting a chart in the classroom for students to reference throughout the module.
Lesson 3 (E)
Consider jigsawing questions a-d in the classwork section with two groups and sharing out answers whole group to save time.
Consider keeping a list of notations on the board to help students make quick references as the lesson progresses.
Lesson 5 (E)
Two days are given for this lesson. It is suggested that everything that precedes the Exploratory Challenge is covered on the first day, and the Exploratory Challenge itself is covered on the second day.
Lesson 6 (E)
Use Problem Set for small group stations this week to give students reinforcement practice.
One extra day this week given to return assessment and remediation for Module 3.
Lesson 1 (E)
Consider moving anchor charts to front of room that include; right triangle trigonometry, the Pythagorean theorem, a the distance formula, and the rate formula, they will be needed for lesson. Technology needed to show opening video. | 677.169 | 1 |
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