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7th Grade Algebra PDF7thGrade Math Placement Many parents are interested in the process of how incoming 7th graders are placed into Algebra I. More than 400 students enroll in Granite Oaks Middle School from the five feeder elementary
7thGrade Math Algebra Linear Equations (7thMathAlgebraLinearEquat) 1. 5. You are buying a sweater for your mother that is marked down 10%. If the sweater's sale price is $29.00, how much did it cost originally? A. $3.22 B. $25.78 C. $32.22 D. $36.36 6.
Grade 7 Algebra & Functions a. Write as a mathematical expression: 1. 5 less than R 2. One fourth as large as the area, where the area = A 3. 25 more than Z b. Write as a mathematical equation: 1. Y is 3 more than twice the value of X 2.
2 algebra The operationthat reversesthe effect of another 3 transitive An equation of the form f(x)=0 where f is a polynomial 4 algebraic equation A diagram or graph using anumber line to show the distribution ofset data ... 7thGrade Math Vocabulary TEST 1
preparation for taking Transitional Algebra in the eighth grade and Algebra I in the ninth grade. Introduction to Pre-Algebra focuses on essential 7thgrade standards that include order of operations, operations with rational numbers, ...
Honors Algebra 1 is an 8th grade honors course, open to high performing 7th graders. Students must meet both the following criteria to be eligible for this course in 7thgrade. No exceptions. * 1. ... 7thGrade Author: SDUHSD Created Date:
into a more-rigorous 7thgrade (pre-algebra) curriculum and supplements with some of the Algebra standards. In 8th grade, these students take a one-year Algebra course, and take the Algebra CST. The two-year program divides the Algebra
Pre-Algebra - 7thgrade math students will study Pre-Algebra. It is a transitional course designed to move students from the intermediate level of mathematics to the secondary level. This course will help to transform concrete thinking skills into abstract,
him or her for Algebra 1 in 8. th grade. SCIENCE . Life Science is the text we recommend for science. In addition to the regular reading, it is full of hands-on activities and experiments to reinforce the learning. ... 7thGrade Curriculum |
The theory is all there, but it's placed nicely in a context appropriate for a mixed bag of undergrad students by a large number of interesting-but-doable exercises and informative historical notes. Modern applications to computer science, cryptography, etc are all there and can be emphasized (or not) as you see fit.
This is what I'd read if I were you. Last time I checked, the book was annoyingly expensive - but this is the only criticism of it I have. Most students give this book very favorable reviews, too. |
Calculus review
Calculus review
I'm beginning my undergrad education this fall. I took AP Calculus in my junior year of high school. My school didn't offer any math after AP Calc and so I haven't done any calc for over a year. Does anyone know any good websites where I can go to review calculus concepts before I start college?
Calculus review
(Moderator's note: the following 3 posts have been merged from a separate thread -- Redbelly98)
I'm going back to school and I need to know some websites that could give me a good review of calculus 1 and calculus 2. I haven't seen the stuff in two years. I could also use a physics review website too.
Yes, there are plenty. I don't know if you want single variable calculus resources only or if you also want multivariate calculus resources (in some schools calculus is 2 semesters long, so calc 1 is single variable and cacl 2 is multi/vector; whereas in some schools calculus is taught over 3 semesters), so I will list both.
If you want only notes (which might be most time efficient for review purposes), see the sites below. |
This course develops a structured mathematical system employing inductive and deductive reasoning. It includes plane, spatial, coordinate, and transformational geometry. Algebraic methods are used to solve problems involving geometric principles.
This course is designed to enable students to develop geometric knowledge that can be used to solve a variety of real world and mathematical problems. Sufficient exposure will be given to material so students will be able to:
1) Recognize math equations and/or formulas and applications
2) Be able to apply those standards in the area of problem-solving
3) Be prepared to pass standardized tests such as the FCAT
4) Demonstrate proficiency in various areas of geometry |
MERLOT Search - materialType=Open%20Textbook&category=2514&sort.property=overallRating
A search of MERLOT materialsCopyright 1997-2013 MERLOT. All rights reserved.Fri, 24 May 2013 16:44:53 PDTFri, 24 May 2013 16:44:53 PDTMERLOT Search - materialType=Open%20Textbook&category=2514&sort.property=overallRating
4434A First Course in Linear Algebra
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation LicenseAlgebra: Abstract and Concrete
The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme.A Problem Course in Mathematical Logic
A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory.A ProblemText in Advanced Calculus
Advanced Calculus open textbook. Download LaTeX source or PDF. Creative Commons BY-NC-SA.Advanced Algebra II: Activities and Homework
This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of in-class assignments, homework and lesson plans, that work for me and for other people who have tried them. The complete set comprises three separate books that work together:•The Homework and Activities Book contains in-class and homework assignments that are given to the students day-by-day." "•The" target=״_blank״> Concepts Book provides conceptual explanations, and is intended as a reference or review guide for students; it is not used when teaching the class." •The" target=״_blank״> Teacher's Guide provides detailed lesson plans; it is your guide to how the author "envisioned these materials being used when I created them (and how I use them myself) " target=״_blank״> Instructors should note that this book probably contains more information than you will be able to cover in a single school year."Advanced Algebra II: Conceptual Explanations ( and the "Advanced Algebra II: Teacher's Guide" ( collections to make up the entire course.Algebra for College Students, 3rd ed.
" Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior exposure to beginning algebra in either high school or college. This text explains the why's of algebra, rather than simply expecting students to imitate examples.״Please note that this site will try to sell supplements and you must create an account. However, there is no charge for the download of the textbook. As noted on the website, "Free access to the online book. Includes StudyBreak Ads (advertising placed in natural subject breaks)."Algebra I
CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.Analysis
This is a free, online textbook that is also part of an online course. According to the author, "Analysis is the study of limits. Anything in mathematics which has limits in it uses ideas of analysis. Some of the examples which will be important in this course are sequences, infinite series, derivatives of functions, and integrals. As you know from calculus, limits are the basis of understanding integration and differentiation, and, as you also know from calculus, these things are the basis of everything in the world you could ever need to know.״ |
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The content is organised into six main areas that should enable you to find easily whatever topic you are searching for.
There are 3883 pages on the site that show you how to carry out mathematical techniques. You can view interactive graphs and geometrical diagrams, which are designed for use both on an individual computer and on an interactive whiteboard. There are short quizzes, multiple choice tests and matching exercises designed to help your students practise their skills.
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Manage your students' access to the website and monitor their usage. You can check how often any individual student has accessed the site in the last month and you can view a list of dates of their log-ons that goes back months. Any name in bold indicates that on-line assessment marks are available for that person. |
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Developmental Mathematics: The Lial series has helped thousands of students succeed in developmental mathematics through its approachable writing style, supportive pedagogy, varied exercise sets, and complete supplements package. With this new edition, the authors continue to provide students and instructors with the best package for learning and teaching support–a book written with student success as its top priority, now with an emphasis on study skills growth and an expanded instructor supplements package. Whole Numbers; Multiplying and Dividing Fractions; Adding and Subtracting Fractions; Decimals; Ratio and Proportion; Percent; Geometry; Statistics; The Real Number System; Equations, Inequalities, and Applications; Graphs of Linear Equations and Inequalities in Two Variables; Exponents and Polynomials; Factoring and Applications; Rational Expressions and Applications; Systems of Linear Equations and Inequalities; Roots and Radicals; Quadratic Equations For all readers interested in basic math and introductory algebra. «Show less
Developmental Mathematics: The Lial series has helped thousands of students succeed in developmental mathematics through its approachable writing style, supportive pedagogy, varied exercise sets, and complete supplements package. With this new edition, the authors... Show more»
Rent Developmental Mathematics 2nd Edition today, or search our site for other Lial |
In this text, algebra and trigonometry are presented as a study of special classes of functions. In the process, relationships betwen theory and real-world applications are thoroughly explored, bringing the material to life. Suitable for a second-year course, a trigonometry course, or a pre-calculus course. [via]
More editions of Algebra and Trigonometry: Functions and Applications:
classic text has been praised for its high level of mathematical integrity including complete and precise statements of theorems, use of geometric reasoning in applied problems and the diverse range of applications across the sciences. The Fourth Edition features a new open design and has been reorganized to place emphasis on key topics and to deliver an efficient teaching and learning tool for introductory calculus. *Reorganized for efficiency's sake and to place a greater emphasis on key topics *New open design to promote ease of learning for the student *Early introduction of transcendental functions *Emphasis on geometry, especially in applied problems *Precise statements of theorems *Diverse range of applications from all the sciences including physics, chemistry, engineering and social sciences [via]
The first generation of calculus reformers exploited emerging technologies and the theme of multiple representations of functions. These pioneers also demonstrated effective, innovative teaching techniques, including collaborative learning, writing, discovery, and extended problem solving. Calculus: Mathematics and Modeling introduces a second generation of calculus reform, combining the lessons of the first generation with advances in differential equations through the use of discrete dynamical systems. This teaching philosophy requires a computational environment in which students can move smoothly between symbolic, numeric, graphic, and textual contexts. The text requires use of a computer algebra-capable graphing calculator. [via]
* The use of technology in the Dugopolski precalculus series for 1999 is optional. Thus, instructors may choose to offer either a strong technology-oriented course, or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility. College Algebra is designed for students who are pursuing further study in mathematics, but is equally appropriate for those who are not. For those students who plan to study additional mathematics, this text provides the skills, understanding and insights necessary for success in future courses. For students who do not plan to pursue mathematics further, the emphasis on applications and modeling demonstrates the usefulness and applicability of mathematics in today's world. Additionally, the author's focus on problem solving provides numerous opportunities for students to reason and think their way through problems. The mathematics presented here is interesting, useful, and worth studying. One of the author's principal goals in writing this text is to get students to feel the same way. [via]
A revolutionary text that requires no special advanced training on the instructor's part, and which needs no supplementary manuals to use. The text's "calculus-as-a-foreign-language" approach, using immersion, reading, and writing, promotes mathematical literacy and comprehension. Highly accessible and diverse "conversations" allow the text to be customized for business, science, pre-health, humanities, social science, or mathematics majors, and for classes at any level. [via]
Powerful database systems running on all platforms from PCs to mainframes are vital for the success of modern companies and institutions. This book will enable users to design database systems that are flexible and efficient, following a proven methodology for both logical and physical database design. Highlights of the book include * A step-by-step methodology for logical database design, integrating the Entity Relationship Model with normalization, and showing how to map this on to a physical implementation * A realistic case study integrated throughout the book, illustrating all stages in the development process * Extensive treatment of formal and de facto standards, including SQL, QBE and the ODMG standard for object databases * A clear introduction to implementation and management aspects, including concurrency and recovery control, security and integrity * Comprehensive chapters on distributed and object-oriented databases, including a preview of SQL3 The practical, hands-on approach will benefit students in computing, information systems, engineering and business, while its industrial-strength methodology can be followed by systems analysts/designers, systems or application programmers, and database adm inistrators. All three authors have experience of database design in industry, and now apply this in their teaching and research at the University of Paisley in Scotland. Thomas Connolly has significant industrial experience and was a designer of RAPPORT, the world's first commercial portable DBMS, and of the LIFESPAN configuration management tool -- a winner of the British Design Award. Carolyn Begg specializes in the application of database systems in the medical domain, while Anne Strachan focuses on problems associated with large diverse data sets in organizations. 0201422778B04062001 [via]
More editions of Database Systems: A Practical Approach to Design, Implementation and Management:
Digital Image Processing is a third generation book that builds on two highly successful earlier editions and the authors' twenty years of academic and industrial experience in image processing. The book provides an introduction to basic concepts and methodologies for image processing and develops the foundation for further study in this diverse and rapidly evolving field. The topics covered range from enhancement and restoration to image encoding, segmentation, description, recognition, and interpretation. These topics are illustrated by numerous computer-processed images. [via]
This is a new edition of a successful introduction to discrete mathematics for computer scientists, updated and reorganised to be more appropriate for the modern day undergraduate audience. Discrete mathematics forms the theoretical basis for computer science and this text combines a rigorous approach to mathematical concepts with strong motivation of these techniques via practical examples.
Broad and up-to-date coverage of the principles and practice in the fast moving area of Distributed Systems.
Distributed Systems provides students of computer science and engineering with the skills they will need to design and maintain software for distributed applications. It will also be invaluable to software engineers and systems designers wishing to understand new and future developments in the field.
From mobile phones to the Internet, our lives depend increasingly on distributed systems linking computers and other devices together in a seamless and transparent way. The fifth edition of this best-selling text continues to provide a comprehensive source of material on the principles and practice of distributed computer systems and the exciting new developments based on them, using a wealth of modern case studies to illustrate their design and development. The depth of coverage will enable readers to evaluate existing distributed systems and design new ones.
For courses in Engineering Graphics and Design.Engineering By Design introduces students to a broad range of important design topics. The engineering design process provides the skeletal structure for the text, around which is wrapped numerous cases that illustrate both successes and failures in engineering design. The text provides a balance of qualitative presentation of engineering practices that can be understood by students with little technical knowledge and a more quantitative approach in which substantive analytical techniques are used to develop and evaluate proposed engineering solutions. This flexibility means that the text can be used in a wide variety of courses.To assist instructors with the delivery of text material, a set of instructor support tools are available to adopters of the text via a website. [via]
Written for those C/C++ developers who want to deepen their programming knowledge, Essential C++ provides a short, effective tutorial to some of the most important features of the C++ language, including lessons on generic programming and templates.
Compression is the key in this admirably concise text.
The author explains C++ from the very beginning with basic syntax and language features and always uses some of the best features of today's Standard C++. Perhaps the best thing here is the integration of "generic programming" (meaning the STL library of reusable templates and algorithms for data collections like vectors, linked lists, and maps, which are built into any current C++ compiler).
By focusing on these key features, this tutorial demonstrates C++ in an up-to-the-minute style. (These "advanced" features can help simplify C++ programming from the very beginning.) This tutorial moves quickly, and by the end of the book, the author covers the basics of successful object-oriented design with C++ classes, generic programming, templates, and exception handling. Short examples are the rule here, and each chapter includes exercises for self-study (with solutions provided at the end of the book).
C++ is a very rich and very complicated programming language. Essential C++ cuts to the chase and gives the working programmer a tour of the latest and greatest language features in a compact format. As a quick-start guide to today's C++, this title complements the author's much more massive tutorial, C++ Primer. For anyone who knows a little C/C++ and wants to learn more, especially the newest features of Standard C++, this book certainly deserves a closer look. --Richard Dragan
A completely revised edition of this accessible guide to LATEX document preparation, bringing it up to date with the latest releases and Web ad PC based developments. A Guide to LATEX covers the basics as well as advanced LATEX topics and contains numerous practical examples and handy tips for avoiding problems. It covers the latest LATEX extensions and has been completely updated to cover latest releases and upgrades. The book explains the LATEX macro package for the TEX text formatting program, presenting a complete description for beginners, going on to more advanced and specialized features. Files for LATEX processing contain the actual text plus markup and programming command, al as ASCII text, something tat makes them portable to every computer system. The LATEX/TEX program processes these files to produce high-quality typeset results, especially for complicated mathematics. LATEX offers the user all the features of any text processing system: automatic section formatting, numbering of sections, figures, tables and equations, table of contents, lists of figures and tables, cross-referencing to the numbers, bibliography, keyword index, colour, inclusion of illustrations.All of these are demonstrated to the reader via examples and exercises through a structure that takes him or her from the simplest beginnings to the more complicated refinements. [via]
More editions of A Guide to Latex: Document Preparation for Beginners and Advanced Users: Introduction practical reference guides students and practicing programmers who need to develop Linux applications or port applications from other platforms. Linux is fundamentally similar to UNIX, so much of the book covers ground familiar to UNIX programmers; but the book consistently addresses topics from a Linux point of view. The aim throughout is to present such detailed information on the Linux operating system-especially, on the development environment, and on the interface both to the kernel and to the core system libraries-as is required to take full advantage of Linux. If you are already a proficient UNIX programmer, the book will greatly facilitate your transition to Linux. If you can program in C, but know neither UNIX nor Linux, reading this book in its entirety and working with its numerous examples will give you a solid introduction to Linux programming. Finally, if you are already a Linux programmer, the book's clear treatment of advanced and confusing topics will surely make your programming tasks easier. text has been revised to make more use of MATLAB integration, and features a new chapter on digital controls. Whilst maintaining its real-world perspectives and practical applications, this edition also features: expanded and updated coverage of state space topics; tutorial instruction on using MATLAB in controls and designated MATLAB problems; and a wider variety of applications in examples and problems. This text is intended for students taking courses in electrical and mechanical engineering. [via]PCI System Architecture is a detailed and comprehensive guide to the Peripheral Component Interconnect (PCI) Bus Specification, Intel's technology for fast communication between peripheral devices and the computer processor. This new edition has been thoroughly updated, reorganized, and expanded to cover the PCI Local Bus Specification version 2.2 and other recent developments, including the new PCI Hot-Plug Specification, changes to the PCI-to-PCI Bridge Architecture Specification, revisions to the PCI Bus Power Management Interface Specification, and the new features of the PCI BIOS Specification. This book provides clear and concise explanations of the relationship of PCI to the rest of the system and PCI fundamentals, including commands, read and write transfers, memory and I/O addressing, error handling, interrupts, and configuration transactions and registers. In addition, you will find specific information on such key topics as: *Hot-Plug Specification *Power management *CompactPCI *The 64-bit PCI Extension *66 MHz PCI Implementation *Expansion ROMs *PCI-to-PCI Bridge and the PCI BIOS *Add-in cards and connectors *Bus arbitration *Reflected-wave switching *Early transaction end *Fast back-to-back and stepping Changes from PCI 2.1 to PCI 2.2 and changes from PCI-to-PCI Bridge Specification 1.0 to 1.1 are visibly highlighted throughout the book so that those familiar with the previous versions can quickly get a handle on new features and functions. Anyone who designs or tests hardware or software involving the PCI bus will find PCI System Architecture, Fourth Edition a valuable resource for understanding and working with this important technology. The PC System Architecture Series is a crisply written and comprehensive set of guides to the most important PC hardware standards. Each title explains from a programmers perspective the architecture, features, and operations of systems built using one particular type of chip or hardware specification. [via]
Click for author interviews and demos of four SimpleGUI examples. Object-Oriented Programming This book presents a careful balance between traditional problem-solving techniques and object-oriented design. Embracing the object-oriented paradigm, the authors introduce objects early (Chapter 2) and use them throughout, introducing features as needed in a gentle manner. Chapters 4 - 7 focus on the traditional data and control structures, using objects as needed. Chapter 8 provides a more in-depth study of object-oriented design, providing detailed coverage of visibility, polymorphism, and inheritance. Applications and Applets Focusing on applications early, the book supports user interaction by providing a package called simpleIO. Applets are first introduced in Chapter 4 where the authors use them in an optional section on graphics to introduce the AWT and its features for drawing simple graphical patterns. They are studied extensively in Chapters 9 and 10 where the intricacies of the AWT, programming for the web, and GUI programming are covered.Graphical User Interfaces (GUIs) Starting in Chapter 2, the authors integrate a GUI library that allows students to better understand concepts through visualization and have some fun. GUI concepts are always presented in the context of good problem solving and program development. Optional sections on graphics appear starting in Chapter 4, again to spur student interest and keep them motivated. Proven Software Development Process The book conveys the relationship between good problem-solving skills and effective software development by consistently applying a proven software development method that has been adapted to the object-oriented paradigm. Helpful Learning Features The authors employ several features to enhance the usefulness of this book as a teaching tool. These include syntax displays, program style displays, end-of-section exercises, examples, case studies, error discussions, and chapter reviews. Also, interviews with famous computer scientists provide glimpses into various careers in computer science. 0201357437B04062001 [via]
This best-selling text now includes coverage of the AP string class and apvectors. As with the original, this book stresses problem-solving techniques, while introducing students to object-oriented concepts early. The system-defined string and stream classes and a user-defined money class are used to reinforce the importance of data modeling in programming. The vector version contains all of the classic learning features readers have come to know and trust in authors Frank Friedman and Elliot Koffman. These features include case studies, program style sections, syntax display boxes, end-of-section exercises, common-error sections, chapter reviews, quick-check exercises, and programming projects. High school teachers: If you are interested in using this text for your Advanced Placement Computer Science course, please send your name and address to [email protected] for more information. This book will come bundled with Addison-Wesley's Review for the Computer Science AP Exam in C++. High Schools ordering this book should use the following ISBN: 0-201-35761-5. 0201357569B04062001 [via] |
I've been frustrated lately reading definitions of algebra along the lines of this:
Look: the mere usage of variables or symbols does not immediately indicate algebra. Compare two ways of writing the Celsius to Farenheit formula: vs. "Multiply by 9, then divide by 5, then add 32." Mere calculation is going on. This is arithmetic.
In arithmetic you reason (calculate) with numbers; in algebra you reason (logically) about numbers.
Taking the Celsius to Farenheit formula, and using reasoning to transform it into a Farenheit to Celsius formula –
– now that is algebra. However, the symbols are not required.
To get from Celsius to Farenheit, you multiply by 9, then divide by 5, then add 32. To get from Celsius to Farenheit, you need to do the inverse operations in reverse order. Hence, you subtract 32, multiply by 5, then divide 9.
As Keith Devlin points out, people were using algebra for 3,000 years before symbolic notation.* The two are not equivalent.
Symbolic notation is a massive convenience and once learned it should be used. However, there are good reasons that students in the process of learning should use the real definition of algebra, not the artificial one defined by symbols.
1. You can reason using algebra with words.
The Celsius / Farenheit conversion already given is an example. Most students naturally understand the logic where reversing "add 5″ requires "subtract 5″ and reversing "add 5 then multiply 6″ requires "divide 6 then subtract 5″. Moreover, in this fashion students tend to understand the logic of inverses, not just the mechanics behind a raw procedure.
The students afraid of mathematics tend to like words. It is a comfortable segue for them.
2. You can do algebra without variables.
As practice, it is extremely helpful to perform algebra — that is, reason about arithmetic, not just do arithmetic — with no variables at all. I see many textbooks that introduce the distributive property like this:
Students can linger on pure numbers for a while, thinking intuitively and using geometric models. The rush to variables seems to occur because of the feeling that without variables it isn't algebra yet. Google is wrong. Variables are not algebra.
3. You can do algebra with alternate representations.
Elementary teachers are familiar with the question mark substitution
5 + ? = 8
which gives the start of sensing (as John Derbyshire puts it) "a simple turn of thought from the declarative to the interrogative". However, the question mark is still a symbolic representation.
Rather bolder steps can be made with algebra-as-geometry (for example, tape diagrams, which are now fairly standard in elementary school but usually forgotten by the time high school algebra rolls around):
It is bizarre that something as simple as a definition can restrict thinking, but after reading many textbooks I'm starting to be convinced it is the main obstacle to opening new frontiers in the explanation of algebra.
* He seems to be excluding Diophantus' Arithmetica from the 3rd century. However, the symbolic notation therein wasn't really picked up until the 16th century, so his claim still holds.
5 Responses
I agree with you, and I think the same can be said for much of mathematics. For example, which when I Google 'mathematics', it returns the definition, "(1) The abstract science of number, quantity, and space. (2)The mathematical aspects of something: 'the mathematics of general relativity' ".
I'm pretty sure that defining math as a science kind defeats the purpose of mathematics. Maybe if the "experiment" is the proof, then yeah. But if the experiment is mere observation where if we see enough examples we can conclude that its true. Plus this definition leaves out what's probably the most important part of mathematics and that's that its based on logic and reason. Most students in a set theory class don't do much counting until they get to set cardinality and operations on sets, but there's a lot of math going on before that.
Sometimes it seems like the mere usage of symbols not only does not immediately indicate algebra, but is an indication of that a lack of algebraic thinking is about to take place. That formality often seems to create a barrier to the logical thinking that we all are capable of.
If you google "proof without words" there are many examples of ideas that can be expressed nicely with diagrams. It would be good to see more problems (and solutions) that were less about language and more about math.
No pressure! All posting is anonymous and it will get edited. Although if debate makes you anxious this might be a good one to sit out and watch- we've had some good conversations about slope and solving equations! I'll add the word to our vocab list just to see what happens. |
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This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large Numbers and Three-Series Theorem are proved by martingale techniques. A proof of the Central Limit Theorem is also given. The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints.
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"Williams, who writes as though he were reading the reader's mind, does a brilliant job of leaving it all in. And well that he does, since the bridge from basic probability theory to measure theoretic probability can be difficult crossing. Indeed, so lively is the development from scratch of the needed measure theory, that students of real analysis, even those with no special interest in probability, should take note." D.V. Feldman, |
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A helpful introduction is available, with an overview of specific MATLAB functions commonly used by engineering students. |
Linear Algebra With Application Alt. Edition - 8th edition
Summary: Introductory courses in Linear Algebra can be taught in a variety of ways and the order of topics offered may vary based on the needs of the students. Linear Algebra with Applications, Alternate Eighth Edition provides instructors with an additional presentation of course material. In this edition earlier chapters cover systems of linear equations, matrices, and determinants. The more abstract material on vector spaces starts later, in Chapter 4, with the introduction of the vector s...show morepace R(n). This leads directly into general vector spaces and linear transformations. This alternate edition is especially appropriate for students preparing to apply linear equations and matrices in their own fields.Clear, concise, and comprehensive--the Alternate Eighth Edition continues to educate and enlighten students, leading to a mastery of the matehmatics and an understainding of how to apply it. ...show less
2012 Hardcover New Book New and in stock. 10/23/201214496795 |
Develop student understanding with the Discovering Math series. This 2-pack addresses various aspects of problem solving, including representation of quantities and patterns, mathematical modeling, algorithms, language and symbolism, and logic and proof. |
Friendly Introduction to Number Theory nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers.Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a new chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms. Pro... MOREvides a new chapter that introduces the theory of continued fractions. Includes a new chapter on "Continued Fractions, Square Roots and Pellrs"s Equation." Contains additional historical material, including material on Pellrs"s equation and the Chinese Remainder Theorem.A useful reference for mathematics teachers. For courses in Elementary Number Theory for math majors, for mathematics education students, and for Computer Science students. This introductory undergraduate text is designed to entice a wide variety of majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. the writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results. |
Course Offerings
Mathematics Courses
Math 130. Basic Math – Algebra and Trigonometry. 3(1). This course sis designed to help reinforce algebraic and trigonometric skills necessary for success in the technical core. Basic graphing, algebraic manipulation, and trigonometric calculations are covered. This course may be used as an Academy option to fulfill graduation requirements. This course does not fulfill any major's requirements. Final Exam. Prereq: Can only be enrolled in the course by recommendation of the Department of Mathematical Sciences. Sem hrs: 3 fall.
Math 141.Calculus I. 3 (1). The study of differential calculus. Topics include functions and their applications to physical systems; limits and continuity; vectors and vector arithmetic; a formal treatment of derivatives; numeric estimation of derivatives at a point; basic differentiation formulas for elementary functions; product, quotient, and chain rules; implicit differentiation; and mathematical and physical applications of the derivative, to include extrema, concavity, and optimization. Significant emphasis is placed on using technology to solve and investigate mathematical problems. Final exam. Sem hrs: 3 fall or spring.
Math 142. Calculus II. 3(1). A study of integral calculus with a focus on the Fundamental Theorems and their application. Topics include: estimating area under a curve, antiderivatives, numeric integration methods, antiderivative formulas for the elementary functions, integration by substitution, parts and tables, improper integrals, differential equations, exponential growth and decay, an introduction to Taylor Series, and mathematical and physical applications of the Fundamental Theorems. Physical applications include area and volume problems and the concept of work. Final exam. Prereq: Math 141. Sem hrs: 3 fall or spring.
Math 152. Advanced Placed Calculus II. 3(1). A more intense study of integral calculus for advanced-placed fourth-class cadets. Content is similar to Math 142, with the addition of an introduction to polar coordinates, vector arithmetic, and complex arithmetic. Additional emphasis is placed on the mathematical and physical applications in preparation for cadets interested in pursuing a technical major or minor. Final exam. Prereq: For fourth-class cadets--qualifying performance on DFMS placement exams; for third-class cadets, Department Head approval. Sem hrs: 3 fall.
Math 243. Calculus III. 3(1). Multivariate calculus, including vector functions, partial differentiation, directional derivatives, line integrals, and multiple integration. Maxima and minima in multiple dimensions and the method of Lagrange Multipliers. Solid analytical geometry to include lines, planes, and surfaces in 3-space. Designed for cadets who indicate an interest in a technical major. Final exam. Prereq: C or better in Math 142 or advanced-placement through DFMS exams. Waiver authority is Deputy Head for Academics. Sem hrs: 3 fall or spring.
Math 300. Introduction to Statistics. 3(1). Topics include descriptive statistics, emphasizing graphical displays; basic probability and probability distributions; sampling distribution of the mean and the Central Limit Theorem; statistical inference including confidence intervals and hypothesis testing; correlation; and regression. Math 300 is designed primarily for majors in the Social Sciences and Humanities. It emphasizes the elements of statistical thinking, focuses on concepts, automates most computations, and has less mathematical rigor than Math 356. Final exam. Prereq: Math 142/152 or department permission. Sem hrs: 3 fall or spring.
Math 310. Mathematical Modeling. 3(1). An introductory course in mathematical modeling. Students model various aspects of real-world situations chosen from Air Force applications and from across academic disciplines, including military sciences, operations research, economics, management, and life sciences. Topics include: the modeling process, graphical models, proportionality, model fitting, optimization, and dynamical systems. Several class periods are devoted to in-class work on small projects. Math 310 is not appropriate for Math or OR majors. Final exam. Prereq: Completion of core math. Sem hrs: 3 spring.
Math 320. Foundations of Mathematics. 3(1). Course emphasizes exploration, conjecture, methods of proof, ability to read, write, speak, and think in mathematical terms. Includes an introduction to the theory of sets, relations, and functions. Topics from algebra, analysis, or discrete mathematics may be introduced. A cadet cannot receive credit for both Math 320 and Math 340. Final exam or final project. Prereq: Completed Math 142/152 with a 'C' or better. Wavier authority is the Deputy Head for Academics. Sem hrs: 3 fall or spring.
Math 356. Probability and Statistics for Engineers and Scientists. 3(1). Topics include classical discrete and continuous probability distributions; generalized univariate and bivariate distributions with associated joint, conditional, and marginal distributions; expectations of random variables; Central Limit Theorem with applications in confidence intervals and hypothesis testing; regression; and analysis of variance. This course is a core substitute for Math 300. Credit will not be given for both Math 300 and Math 356, not for both Math 356 and Math 377. Designed for cadets in engineering, science, or other technical disciplines. Math majors and Operations Research majors should take the Math 377/378 sequence. Final Exam. Prereq: Math 142/152. Sem hrs: 3 fall or spring.
Math 359. Design and Analysis of Experiments. 3(1). An introduction to the philosophy of experimentation and the study of statistical designs. The course requires a knowledge of statistics at the Math 300 level. Topics include analysis of variance for K treatments, various two- and three-level designs, interactions, unbalanced designs, and regression analysis. A valuable course for all science and engineering majors. Final project. Prereq: Math 300, Math 356 or Math 378. Sem hrs: 3 spring.
Math 360. Linear Algebra. 3(1). A first course in linear algebra focusing on Euclidean vector spaces and their bases. Using matrices to represent linear transformation, and to solve systems of equations, is a central theme. Emphasizes theoretical foundations (computational aspects are covered in Math 344). A cadet cannot receive credit for both Math 344 and Math 360. Final exam or final project. Prereq/Coreq: Math 320 or department permission. Sem hrs: 3 fall.
Math 366. Real Analysis I. 3(1). A theoretical study of functions of one variable focused on proving results related to concepts first introduced in differential and integral calculus. This course is an essential prerequisite for graduate work in mathematical analysis, differential equations, optimization, and numerical analysis. Final exam or final project. Prereq: Math 360 or department permission. Sem hrs: 3 spring.
Math 370. Introduction to Point-Set Topology. 3(1). Review of set theory; topology on the real line and on the real plane; metric spaces; abstract topological spaces with emphasis on bases; connectedness and compactness. Other topics such as quotient spaces and the separation axioms may be included. A valuable course for all math majors in the graduate school option. Final exam. Prereq: Math 320. Sem hrs: 3 spring of even years.
Math 372. Introduction to Number Theory. 3(1). Basic facts about integers, the Euclidean algorithm, prime numbers, congruencies and modular arithmetic, perfect numbers and the Legendre symbol will be covered and used as tools for the proof of quadratic reciprocity. Special topics such as public key cryptography and the Riemann Zeta function will be covered as time allows. Final exam. Prereq: Math 320 Sem hrs: 3 spring of odd years.
Math 378. Advanced Statistics. 3(1). Topics include point and interval estimation, properties of point estimators, sample inferential statistics with confidence intervals, hypothesis testing, ANOVA, linear regression, design and analysis of experiments, and nonparametric statistics. This course is a core substitute for Math 300 but has much more rigor and depth. Credit will not be given for both Math 300 and Math 378. Final exam. Prereq: Math 377. Sem hrs: 3 spring.
Math 421. Mathematics Capstone II. 3(1). The second semester of the mathematics capstone experience. Students will compete work on their independent research project and produce a thesis to present their findings. Final project. Prereq: C1C standing in the Mathematics major. Sem hrs: 3 spring.
Math 443. Numerical Analysis of differential Equations. 3(1). An intermediate numerical analysis course with an emphasis on solving differential equations. Specific topics include solving linear and nonlinear systems; solutions of initial value problems via Runge-Kutta, Taylor, and multistep methods; convergence and stability; and solutions of boundary value problems. Other topics typically include approximating eigenvalues and eigenvectors and numerically solving partial differential equations. The approach is a balance between the theoretical and applied perspectives with some computer programming required. Final exam or final report. Prereq: Math 346 and one of Math 342 or Physics 356, or department permission. Sem hrs: 3 spring of even-numbered years.
Operations Research Courses
These courses are offered in one of the following departments: Department of Computer Science (DFCS), Department of Economics and Geography (DFEG), Department of Management (DFM), and Department of Mathematical Sciences (DFMS)
Ops Rsch 310. Systems Analysis. 3(1). This course provides an introduction to rigorous quantitative modeling methods that have broad application. The course focuses on the mathematics of the models, the computer implementation of the models, and the application of these models to practical decision-making scenarios. By demonstrating the application of these techniques to problems in a wide range of disciplines, the course is relevant to technical and non-technical majors at USAFA. The course consists of six distinct blocks: decision analysis and utility theory, linear and nonlinear optimization, project management, queuing theory, simulation, and the systems approach to engineering and decision-making. Administered by the Department of Management. Instruction provided by inter-departmental Operations Research faculty. Final exam. Prereq: Comp Sci 110, Math 142. Sem hrs: 3 Fall and Spring.
Ops Rsch 405. First-Class Seminar. 0(1). A course for First-Class Operations Research majors that provides for presentation of cadet and faculty research; guest lectures; field trips; seminars on career and graduate school opportunities for scientific analysts in the Air Force; goal setting exercises; and applications of Operations Research. The class meets once each week. Open only to First-Class Operations Research majors. Pass/Fail. No final exam. Prereq: C1C standing. Sem hrs: 0 fall.
Ops Rsch 411. Topics in Mathematical Programming. 3(1). Topics include linear programming (with sensitivity analysis and applications) and non-linear programming. Both the theory and the computer implementation of these techniques are addressed. Administered by the Department of Mathematical Sciences. Final exam. Prereq: Math 343 or Math 360; and either Ops Rsch 310 or department permission. Sem hrs: 3 fall.
Ops Rsch 419. Case Studies in Operations Research.1.5(1) . The study of methodologies associated with business and operations management. A case-based course intended to provide the proper foundation needed to conduct effective analyses supporting a variety of scenarios. Students will evaluate various cases, develop plans for and conduct analyses, and create effective written and oral presentations. Final Project or Exam. Sem hrs: 1.5 fall. |
The Math Gateway mathgateway.maa.org
In 2004 the National Science Foundation awarded the Mathematical Association of America a Pathways Grant as part of the National STEM (STEM is NSF-speak for Science, Technology, Engineering, and Mathematics) Digital Library (NSDL) Program. This four-year grant is supporting the creation of a portal, The Math Gateway, for undergraduate mathematics materials within NSDL. This project is bringing together collections with significant mathematical content and services of particular importance to the delivery and use of mathematics on the Web.
The Math Gateway project is an outgrowth of the Mathematical Sciences Conference Group on Digital Educational Resources. This group of individuals with an interest in online mathematics has met each year for the past four years at MAA headquarters. Many of the organizations represented at these meetings will participate in the Math Gateway. The initial participating organizations/collections are listed below.
Math Forum
( The Math Forum is one of the oldest online resources in mathematics with a particular emphasis on K-12 mathematics.
iLumina
( The iLumina site, hosted at the University of North Carolina at Wilmington, is one of the oldest collections in the NSDL.
CAUSE
( The Consortium for the Advancement of Undergraduate Statistics Education is a project of the American Statistical Association.
Demos with Positive Impact
( This project is managed by Lila Roberts of Georgia College and State University and Dave Hill of Temple University. The site provides teachers with demos and accompanying information on how these demos might be used.
National Curve Bank
( This site, directed by Shirley Gray at Cal State Los Angeles, has a wide range of online mathematical resources including an audio file of Tom Lehrer singing New Math.
Virtual Laboratories in Probability and Statistics
( site was developed by Kyle Siegrist at the University of Alabama at Huntsville.
Ethnomathematics Digital Library
( The Ethnomathematics Digital Library is a project of Pacific Resources for Education and Learning. The Library has links to relevant websites worldwide.
Duke Connected Curriculum Project
( This site has online materials for lab activities for undergraduate mathematics courses from precalculus through linear algebra, differential equations, and engineering mathematics. Lang Moore and David Smith edit the site.
webODE Project
This project is just getting underway under the direction of Paul Blanchard at Boston University.
Eduworks
( The MAA and MathDL are cooperating with Geoff Collier and Robby Robson of Eduworks on their NSDL project to improve interoperability and reusability.
WeBWork
( WeBWork, founded by Arnie Pizer and Mike Gage of Rochester University, is one of the most useful online homework systems for mathematics. MathDL will provide some services for WeBWork.
NSDL Middle School Portal
( The NSDL Middle School Portal, a project created by the Eisenhower National Clearinghouse, is an online resource for middle school science and math teachers.
College Board
( At their AP Central site the College Board has a wealth of resources directed toward AP high school teachers. The Math Gateway would link to their resources for calculus and statistics. |
02110Requirements
Prerequisites
Successful completion of two years of algebra and one year of geometry.
Materials to be ordered via the DLD
Description
Precalculus is a course that combines reviews of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. The first semester includes linear, quadratic, exponential, logarithmic, radical, polynomial, and rational functions; systems of equations; and conic sections. The second semester covers trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers.
Within each Precalculus lesson, students are supplied with a post-study "Checkup" activity, providing them the opportunity to hone their computational skills by working through a low-stakes problem set before moving on to a formal assessment. Unit-level Precalculus assessments include a computer-scored test and a scaffolded, teacher-scored test.
The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards. |
\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2012b.00686}
\itemau{\v Zilkov\'a, Katar\'\i na}
\itemti{Convex quadrilaterals and their properties in the training of teachers for primary education.}
\itemso{Acta Didact. Univ. Comen., Math., No. 11, 73-84 (2011).}
\itemab
Summary: The article describes the problems involved in the math training of teachers for primary education. The topic involves the correct identification of convex polygons with focus on convex quadrilaterals and on the development of the skills required to sort them on the basis of their properties. The article lists the potential sources of problems and the options available to eliminate these through various modelling techniques.
\itemrv{~}
\itemcc{G29 G49 B50 C32}
\itemut{quadrilaterals; polygons; identification; classification; plane geometry; primary teacher education; tests; educational research}
\itemli{}
\end |
In my opinion, one of the most important concepts to discuss in a liberal arts math course is the notion of mathematical proof—what it is, why mathematicians put so much emphasis on it, whether it is overrated, and how the concept has evolved over time. There are several ways to approach this subject.
Give examples of proofs. This MO question as well as this one provide some nice examples. I'd also recommend the MAA series of books on Proofs Without Words.
Discuss the role of computers and experiment in mathematics. Jonathan Borwein has co-authored several books on experimental mathematics, e.g,. The Computer as Crucible. Though much of the mathematical content may be too advanced, the introductions to these books are extremely lucid and valuable.
Discuss the foundations of mathematics. My top recommendation in this category would be Torkel Franzen's Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. Again, some sections of the book may be too technical, but there are plenty of extremely well-written and valuable non-technical sections.
Even among the educated public, one frequently encounters people who have no concept of how unique mathematical proof is, who think that computers have put mathematicians out of business, and who have heard just enough about Gödel's Theorem to be dangerous. The above readings should go a long way towards dispelling these common misconceptions. |
Maths Year 9
Year 9 is the start of the GCSE programme of study and in Mathematics we continue to build on the work completed in Year 7 and 8. We change our focus from National Curriculum levels to GCSE Grades. Our aim is to provide a seamless transition from KS3 to KS4, and therefore we continue to work using a 'spiral' approach to the learning of the subject. This means that we break the areas of the curriculum down into chunks,and spread them out throughout the course of study with the aim of providing an increasing level of difficulty at the correct pace for the group, as well as developing the links between the different areas as we go. This continues throughout year 10 and 11.
Areas studied
Number & Problem Solving
Algebra
Geometry & Measures
Data Handling/Statistics
Top sets in year 9 and 10 will cover material from the GCSE Statistics course which they will take as an additional GCSE with the aim of completion at the end of Year 10.
Skills
During GCSE Mathematics students will be taught skills that enable them to function in other subjects and in everyday life. We continue to develop the numeracy skills taught in Years 7 and 8 but also develop the more abstract concepts required for GCSE. In particular, students will be taught how to present and analyse data accurately, they will be shown how to calculate percentages quickly and efficiently in their heads, and also how and when it is appropriate to use their calculators. They will study and learn how to convert between widely used measures including metric and imperial measures, and they will also learn how to problem solve, and how to present their findings in a meaningful way. They will also learn to use algebra and geometry to generalize, and to solve problems. The skills learnt during GCSE Mathematics prepare students for life after Year 11, and for those pupils that wish to continue studying the subject post-16 and take A level Mathematics, their GCSE studies will have prepared them for the rigours, as well as the beauty, of the subject.
Setting
Students are set according to their potential, based on prior results in tests and teacher assessments. We are combining both types of assessment to provide a rounded view of individual student understanding so that they are placed in the group that will best meet their Mathematical needs. They are also set challenging yet achievable targets based upon their KS2 results and in conjunction with their last exam result. Students will be in classes of no more than 30 students, and in lower ability groups, sometimes less than 15 per class. There will be opportunities throughout the year for pupils to move groups, according to their progress. Teachers will discuss movements at Mathematics Faculty meetings and decide if a move is in the best interest of the student.
Homework
Students will be set one piece of homework a week. Homework may be from the MyMaths website, which is marked automatically and immediately online, with a written piece of work at least once a fortnight. Both pieces will be designed to extend or consolidate class work, or will be revision work. Students should get written feedback from their teacher on their homework once a fortnight. In year 11, students will be given past papers to complete in the Spring term in preparation for their GCSE exam.
Assessment & Reporting
Students are assessed using a variety of methods with homework and class work being an important part of this. They will have a formal exam at the end of Year 9 and Year 10, to look at progress from previous years. There will also be interim reports throughout the year, as well as an annual full report according to the whole school timetable. Parents can contact class teachers at any time to get an update on their daughter's progress.
How parents can help
Ensuring that students come equipped to their lessons – students will need their own geometry set and a calculator for both class work and homework
Checking that students are completing homework tasks to the best of their ability, and encouraging them to seek support in plenty of time if they are struggling
Giving opportunities to work out how much change you should get in a shop, or to estimate shopping bills – it's a good mental Maths workout!
In Year 11, students are given a MathsWatch revision CD Rom – please encourage them to use it and ask them to show you how it works, its just like having a private tutor at home, but for free!
All pupils have access to MyMaths – they can revise or study independently at any time to complement their studies. It has a GCSE Statistics section too.
Most importantly, be positive about Mathematics at home – students that hear positive things about the subject at home are more likely to develop a positive attitude to it themselves! |
MathDork Tutorials
are the fastest way
to learn the
basic principles
of Algebra.
These lessons
jump into your brain!
They are based on
10 years of
private tutoring
experience.
24 MathDork Lessons - Here's What you get
Algebra Doesn't have to be so serious!!
Properties of Real Numbers
Commutative Property
See how the word "commutative" contains the word "commute?" This lesson illustrates why, when you move numbers around, they still add up to the same number, or multiply to give the same result. A funny alien theme.
Associative Property
Questions about the difference between commutative and associative? Clear it up in just a few minutes. And get the tool for remembering it forever! Theme: MathDork talks to girls at a party.
Distributive Property
Distribute means "multiply out over parentheses." See several examples of how this works.
Golden Rule
Golden Rule of Algebra
The trappings of ancient Egypt lead you through the Golden Rule of Algebra. Do Unto One Side of the Equation What You Do Unto the Other.
Order
Order of Operations
Animations illustrate how to simplify the messiest arithmetic expressions using the Order of Operations. You'll want to view this one a few times, and then you'll be ready to tackle any one of these. Theme: Please Excuse My Dear Aunt Sally.
Absolute
Absolute Value
What's the deal with those "bar" things? Many students of all ages have questions about absolute value. Here you will find an animated explanation that you will see nowhere else! View this lesson, and not only will you have the concept down pat, but working with signed numbers will make a lot more sense.
Signed Numbers
Signed Numbers – Basic Concepts
Covers the basics. How to simplify numbers with several signs in front of them, and a visual tool for remembering. Ever wonder why two negatives multiplied together make a positive? Here is the real explanation—and it makes sense!
Signed Numbers – Addition
How to add signed numbers (and subtract – since subtraction is adding the opposite). Game show theme using $$ examples.
Exponents
Exponents – Introduction
"MathDork" and "Mimi" answer the questions that most students ask about raising a number to a power. What is an exponent? How do you raise a number to a power?
Exponents – Multiplying and Dividing
No need to memorize "rules" for multiplying and dividing with exponents. With this animated explanation, you will know what to do.
Exponents – Power to a Power
Does raising a number to a power, and then to a power again make you feel powerless? A simple animated explanation that you will remember every time!
Working with Variables
Working With Variables – Identifying Like Terms
An endearing squeaky robot breaks down the concept of like terms into easy-to-understand bits and bytes. This interactive lesson works through several examples.
Working With Variables – Combining Like Terms
Our friend the robot teams up with a magnet-toting helicopter to help you identify like terms for simplifying an expression. This lesson is especially visually entertaining.
Working With Variables -- Substitution
An ant, a Chihuahua, and a nascar driver guide you through the substitution process. This topic, which some students find confusing, is actually quite simple. You will see!
Solving Equations
Solving Equations – Basics
Help MathDork buy some junk food. This interactive lesson demonstrates how to set up a basic equation.
Solving Equations – Solving With Plus and Minus
A panoply of strange characters illustrates the basics of word problems, and how to solve very basic equations.
Solving Equations – Solving With Multiplication and Division
A crazy caveman theme will make you smile, as you see examples worked out on a cave wall.
Solving Equations – Solving With Multiple Steps
Mini-Dorks (A little creepy if you ask us) show you how to solve 2- and 3-step equations. We recommended viewing this lesson multiple times, until you almost know the steps by heart.
Factoring
Factoring Numbers
This is the clearest demonstration you'll ever see of how to obtain the prime factorization of an integer. Factoring is kind of fun, and easy to check.
Graphing
Graphing – Basics
We're very proud of this set of four lessons on graphing. You'll find all of your basic graphing questions answered. How do you remember which is the X axis and which is the Y axis? When plotting ordered pairs, do you count the dots or the spaces? What if one of the coordinates is zero? Click the coordinates on the interactive self-quiz. |
Find a King Of Prussia MathAlgebra covers the basics of equation building and terminology. This is generally required as a prerequisite for other math courses and makes up a large percentage of standardized tests like the SAT or GMAT. Algebra 2 builds upon the basic algebra terminology and properties. |
Q&A for Matriculation Physics Semester 2 Updated is a comprehensive question and answer book for students studying Physics in local Matriculation colleges. Written by experienced authors and based on...
Q&A for Matriculation Mathematics Semester 2 Updated is a comprehensive question and answer book for students studying Mathematics in local Matriculation colleges. Written by experienced authors and based... |
3.1 Introduction
This chapter specifies the "presentation" elements of MathML,
which can be used to describe the layout structure of mathematical
notation. It is strongly recommended that one read Section 2.3 on MathML syntax and grammar
before reading Chapter 3. Section 2.3 contains important
information on MathML notations and conventions which are necessary
for understanding some of the material in this chapter.
Presentation elements correspond to the "constructors" of
traditional math notation -- that is, to the basic kinds of symbols
and expression-building structures out of which any particular
piece of traditional math notation is built. They are designed to
be medium-independent, in the sense that there are sensible ways to
render them in audio, as well as in traditional visual media for
math. Because of the importance of traditional visual notation, the
descriptions of which notational constructs the elements represent,
and how they are typically rendered, is often given here in visual
terms. However, the elements have been designed to contain enough
information for good spoken renderings as well, provided the
conventions described herein for their proper use are followed.
Some attributes of these elements may make sense only for visual
media, but most attributes can be treated in an analogous way in
audio as well (for example, by a correspondence between time
duration and horizontal extent).
One major anticipated use of MathML is to describe mathematical
expressions within HTML documents, using multiple MathML
expressions embedded in some manner in an HTML document. Note that
HTML in general describes logical structures such as headings,
paragraphs, etc. but only suggests (i.e. does not require) specific
ways of rendering various logical parts of the document, in order
to allow for medium-dependent rendering and for individual
preferences of style; MathML presentation elements are fully
compatible with this philosophy. This specification describes
suggested visual rendering rules in some detail, but a particular
MathML renderer is free to use its own rules as long as its
renderings are intelligible and mathematics.
The presentation elements are meant to express the syntactic
structure of math notation in much the same way as titles,
sections, and paragraphs capture the higher level syntactic
structure of a textual document. Because of this, for example, a
single row of identifiers and operators, such as "x +
a / b", will often be represented not just by one
<mrow> element (which renders as a horizontal row of its
arguments), but by multiple nested <mrow> elements
corresponding to the nested subexpressions of which one
mathematical expression is composed -- in this case,
Similarly, superscripts are attached not just to the preceding
character, but to the full expression constituting their base. This
structure allows for better quality rendering of math, especially
when details of the rendering environment such as display widths
are not known to the document author; it also greatly eases
automatic interpretation of the mathematical structures being
represented.
Certain extended characters, represented by entity references,
are used to name operators or identifiers which in traditional
notation render the same as other symbols, such as
"ⅆ", "ⅇ", or "ⅈ", or
operators which usually render invisibly, such as
"⁢", "⁡", or "⁣". These
are distinct notational symbols or objects, as evidenced by their
distinct spoken renderings and in some cases by their effects on
linebreaking and spacing in visual rendering, and as such should be
represented by the appropriate specific entity references. For
example, the expression represented visually as "f(x)" would
usually be spoken in English "f of x" rather than just "f x"; this
is expressible in MathML by the use of the "⁡"
operator after the "f", which (in this case) can be aurally
rendered as "of".
The complete list of MathML entities is described in Chapter
6.
3.1.2 Terminology Used In This
Chapter
The MathML specification uses a number of technical terms to
describe MathML-specific rules and conventions. The most notatble
example is the attribute value notations and conventions describe
in Section 2.3.3 (See also the
brief description of XML terminology in Section 2.3.1.)
The remainder of this section introduces MathML-specific
terminology and conventions used in this chapter.
The presentation elements are divided into two classes.
Token elements represent individual symbols, names, numbers,
labels, etc. and can have only characters and entity references (or
the vertical alignment element <malignmark/>) as
content. Layout schemata build expressions out of parts
and which can have only elements as content (except for whitespace,
which they ignore). There are also a few empty elements used only
in conjunction with certain layout schemata.
All individual "symbols" in a mathematical expression should be
represented by MathML token elements. The primary MathML token
element types are identifiers (e.g. variables or function names),
numbers, and operators (including fences, such as parentheses, and
separators, such as commas). There are also token elements for
representing text or whitespace which has more aesthetic than
mathematical significance, and for representing "string literals"
for compatibility with computer algebra systems. Note that although
a token element represents a single meaningful "symbol" (name,
number, label, mathematical symbol, etc.), such symbols may be
comprised of more than one character. For example sin
and 24 are represented by the single tokens
<mi>sin</mi> and
<mn>24</mn> respectively.
In traditional mathematical notation, expressions are
recursively constructed out of smaller expressions, and ultimately
out of single symbols, with the parts grouped and positioned using
one of a small set of notational structures, which can be thought
of as "expression constructors". In MathML, expressions are
constructed in the same way, with the layout schemata playing the
role of the expression constructors. The layout schemata specify
the way in which subexpressions are built into larger expressions.
The terminology derives from the fact that each layout schema
corresponds to a different way of "laying out" its subexpressions
to form a larger expression in traditional mathematical
typesetting.
Terminology for other classes of elements and their
relationships
The terminology used in this Chapter for special classes of
elements, and for relationships between elements, is as follows:
The presentation elements are the MathML elements defined
in the chapter. These elements are listed in section 3.1.5. The content
elements are the MathML elements defined in chapter 4. The
content elements are listed in
section 4.4.
A MathML expression is a single instance of any of the
presentation elements with the exception of the empty elements
<none/> or <mprescripts/>, or is a single
instance of any of the content elements which are allowed as
content of presentation elements (listed in section 5.2.2). A
subexpression of an expression E is any MathML
expression which is part of the content of E, whether
directly or indirectly, i.e. whether it is a "child"
of E or not.
A child of a layout schema is also called an argument
of that element. Token elements have no arguments, by definition,
even though they can contain the <malignmark/>
element; this means that a <malignmark/> element in a
token is not an argument, whereas in a layout schema it is one.
As a consequence of the above definitions, the content of a
layout schema consists exactly of a sequence of zero or more
nonoverlapping elements which are its arguments (possibly with
intervening whitespace, which is ignored in MathML). Note that an
argument is almost always a subexpression; the only exceptions are
the empty elements <none/> and
<mprescripts/> which are allowed only as special
arguments of the <mmultiscripts> element, but are not
subexpressions because they are not MathML expressions as defined
above.
Descriptions of presentation elements
Each MathML presentation element is described below in detail.
The description starts with the information needed by authors of
MathML (or of programs which generate MathML). The intended use of
each element is described, along with the argument syntax it
accepts. (There is also a table of argument count requirements and
argument roles in Section
3.1.3.) The valid attributes, along with their permissible and
default values, are listed, and the effect of each attribute is
discussed.
For certain elements, further information of interest mainly to
those implementing MathML renderers is given in a subsection. This
includes many details of one suggested set of rendering rules which
can be used to render MathML expressions in a manner reminiscent of
traditional visual notation.
3.1.3 Required Arguments
Many of the elements described herein require a specific number
of arguments (always 1, 2, or 3). Recall that MathML uses the term
argument to describe a child
element with additional MathML-specific requirements, usually
related to which position it occupies in its parent.
In the detailed descriptions of element syntax given below, the
number of required arguments is implicitly indicated by giving
names for the arguments at various positions. The descriptions,
interpreted according to the convention just stated, fully specify
the allowed numbers of arguments for every element defined in this
Chapter. A few elements have additional requirements on the number
or type of arguments, which are described with the individual
element. For example, some elements accept sequences of 0 or more
arguments -- that is, they are allowed to occur with no arguments
at all.
Note that MathML elements encoding rendered space do
count as arguments of the elements they appear in. See Section
3.2.6 for a discussion of the proper use of such spacelike elements.
The elements listed in the following table as requiring exactly
1 argument (<msqrt>, <mstyle>,
<merror>, <mpadded>,
<mphantom>, and <mtd>) actually accept any
number of arguments, but if the number of arguments is 0, or is
more than 1, they treat their contents as a single "inferred
<mrow>" formed from all their arguments.
For example,
<mtd>
</mtd>
is treated as if it were
<mtd>
<mrow>
</mrow>
</mtd>
and
<msqrt>
<mo> - </mo>
<mn> 1 </mn>
</msqrt>
is treated as if it were
<msqrt>
<mrow>
<mo> -
</mo>
<mn> 1
</mn>
</mrow>
</msqrt>
This feature allows MathML data not to contain (and its authors
to leave out) many <mrow> elements which would
otherwise be necessary.
In the descriptions in this Chapter of the above-listed
elements' rendering behaviors, their content can be assumed to
consist of exactly one expression, which may be an
<mrow> element formed from their arguments in this
manner. However, their argument counts are shown in the following
table as exactly 1, since they are most naturally understood as
acting on a single expression.
Table of argument requirements
For convenience, here is a table of each element's argument
count requirements, and the roles of individual arguments when
these are distinguished. Recall that a required argument count of 1
may indicate an
inferred <mrow>.
3.1.4 Elements with Special
Behaviors
Certain MathML presentation elements exhibit special behaviors
in certain contexts. Such special behaviors are discussed in the
detailed element descriptions below. However, for convenience, some
of the most important classes of special behavior are listed
here.
Certain elements are considered spacelike; these are defined in
Section 3.2.6. This definition affects some of the suggested rendering
rules for <mo> elements (Section 3.2.4).
Certain elements (e.g., <msup>) are able to
embellish operators which are their first argument. These elements
are listed in Section 3.2.4, which precisely defines an "embellished
operator" and explains how this affects the suggested rendering
rules for stretchy operators.
Certain elements treat their arguments as the arguments of an
"inferred
<mrow>" if they are not given exactly one argument,
as explained in Section 3.1.3.
The <mtable> element can infer <mtr>s
around its arguments, and the <mtr> element can infer
<mtd>s, as explained in the sections about those
elements. |
LEARNING AND APPLYING ALGEBRA
100 Algebra Workouts and Practical Teaching Tips by Tony G.
Williams. Teaching and Learning C., 2008. For Grades 6-8. These warm-ups are
designed to capture students' interest in algebra and provides reinforcement of
algebra skills. Included are such workouts as Algebraic Sudoku, Deal or No Deal,
The Fractionator, The Chair Challenge, Tricks of the Trade, World Currency,
Factoring Carnival, and 93 more. The workouts all support current algebra
curricula and are designed to take 3-10 minutes at the beginning of class.
Topics covered include equations, games, linear equations, system of equations,
polynomials, logic, factoring, pre-geometry, radials, PSAT preparation,
quadratic equations, and more. Answers are provided. 112 pages. BTH-5466
. $11.66-D
Algebra 1 by Sara Freeman. Milliken, 2002. Part of the Math
Reproducibles Series. This easy-to-use workbook will engage your students and
motivate their interest in algebra while reinforcing the major algebra concepts.
A variety of puzzles, mazes, and games will challenge students to think
creatively as they sharpen their algebra skills. A special assessment section is
also included to help prepare students for standardized tests. I recommend this
as a reproducible supplement to an algebra text or workbook. Answers are
provided. For grades 6-8. 48 pages. BTH-4750. $7.17-D
Algebra 2by Sara Freeman. Milliken, 2002. Part of the Math
Reproducibles Series. This easy-to-use workbook is sure to motivate your
students and engage their interest in algebra while reinforcing the major
algebra concepts. A variety of puzzles, mazes, and games will challenge students
to think creatively as they sharpen their algebra skills. A special assessment
section is also included to help prepare students for standardized tests. I
recommend this as a reproducible supplement to an text, not as a stand-alone
Algebra 2 text. Answers are provided. 48 pages. For grades 7-9. BTH-4751.
$7.17-D
Algebra
Demystified: A Self-Teaching Guideby Rhonda Huettenmueller. McGraw
Hill, 2003. This book provides clear and concise explanations of algebra's
trickiest topics, detailed examples and solutions, and special attention
to word problems and other difficulties. It covers fractions, variables,
decimals, negative numbers, exponents and roots, factoring, linear equations,
linear applications, linear inequalities, quadratic equations, and quadratic
applications. Also included are an Appendix, a Final Review, and an Index. 441
pages. Has remainder mark and possible bent corner. BTH-3971 .
$7.93-B
Algebra Puzzlers by Theresa Kan McKell. Good Apple, 1998. For grades
9-12. This collection of challenging and engaging puzzles will work with
students at all algebra skill levels. They can be used as warm-ups, homework, or
even entire math lessons. 112 pages. BTH-5302. $13.49-D
Algebra Puzzles: Build Pre-Algebra and Algebra Skills through Puzzles and
Problems by Hank Garcia. Creative Teaching Press, 2006. This book
uses games, puzzles, and other problem-solving activities to give
students fresh, new ways of exploring learned concepts. While reviewing
essential concepts and vocabulary for pre-algebra and algebra, the book helps
students visualize and think more deeply about these abstract ideas. Key algebra
terms are defined so that students can master the vocabulary they need. The
perfect antidote to algebra anxiety. 80 pages. BTH-5468. $12.59-D
Algebra the Easy Way, Third Edition, by
Douglas Downing. This algebra text is in the form of a fantasy novel where the characters
solve practical problems by using algebra. Includes hundreds of problems with solutions
with more than 100 drawings and diagrams. Paperback / 334 Pages / 7 13/16 x 10 7/8 / 1996.
Cat. #BAR-93933. $12.56-D
Applied Math Series
(from Garlic Press): These show students in the upper grades how various mathematics
disciplines can be used to solve everyday problems. Titles are listed below.
8.96-D each. Prices can change at any time. Follow links below for most accurate
pricing and to check availability or buy on line. If title is out of stock
there, you can email me to see when it should be in or go ahead and use
information here for purchase orders.
Applying Algebra: Helps students
apply algebra to daily activities. Answers included. BTH-77. $9.86-D Basic Equations:
49 pages of instruction and problems to help students understand linear
equations. Emphasis is placed on translating simple algebra and geometry
concepts into the mathematical statements needed to solve everyday problems.
Covers equations and number relationship, solving basic linear equations, word
problems, and formulas. Each topic has step-by-step explanations, examples, and
applications. Answers are provided.BTH-79. $9.86-D Metrics at Work: Provides 81 pages of instruction and problems
to help learn and apply the metric system to daily activities and commerce. Covers
conversions between the SI Metrics and the English System of measurement, square and
volume measurements, temperature measurements, SI Metrics and percents. Answers
to problems provided.BTH-80. $9.86-D Solving Word Problems:
Provides a consistent and logical strategy for solving any word problem. It is
meant to be used by teacher and students at all levels from beginning algebra on
through differential calculus. Covers defining qualities, reducing the number of
variables, and setting and solving equations, There are applications to algebra,
trigonometry, and calculus. 125 pages, including answers. BTH-78. $9.86-D
Building
a Teen Center: An Integrated Algebra Projectby
Mary Ann Christina. A Key Curriculum Publication with blackline activity masters
for grades 6-10. This is a concept to completion project in which students work
in teams to conceive of, design, and build a model of a recreational center for
teenagers. As students learn algebraic concepts, they will apply them as they
build their teen center project. As the project grows, so will student
enthusiasm for learning the concepts and skills they need to complete it. The
project may be done completely or in part, spread throughout the year or
concentrated into a few weeks. It is compatible with any algebra, geometry, or
integrated curriculum, and is especially compatible with block scheduling. 178
pages. BTH-730. $17.96Graphic
Algebra by Gary Asp, John Dowsey, Kaye Stacey and David Tynan. A Key
Curriculum book, quality paper, punched for three-hole notebook. This book of engaging blackline masters provides activities for algebra
students to use with the graphing calculators and graphing software-technology which is
rapidly becoming commonplace in the high school math classroom. Creating graphs is no
longer a time consuming task for students, which leaves them more time to use graphs to
study the properties of functions. Graphic Algebra helps develop
new insights into algebra by providing easy-to-use lessons in which students graph and
study functions using any graphing calculator or computer software for graphing.
The book helps students use graphs to solve
problems set in real-world contexts; to link different representations in order to move
easily between tables of values, algebraic expressions, and graphs; to develop
understanding of different types of functions and their properties; to learn concepts and
skills needed for graphing on a calculator or a computer; and to explore transformations
of functions.
This book grew out of a research project
conducted at the University of Melbourne, Australia. Graphic Algebra
was designed to be used in a variety of ways to supplement and complement the teaching of
algebra. Some problems can be used to introduce new ideas; others offer a novel way to
review familiar ideas in a new context. The book is a perfect supplement for any
curriculum involving algebra. The materials assume that students have a basic familiarity
with algebraic notation and the Cartesian plane. Other prerequisite knowledge is noted for
each chapter. Teachers can select short or long sequences of work designed for students at
various levels. The book contains reproducible blackline masters, as well as teaching
suggestions for using graphing calculators in algebra, extensive teacher notes, and
appendices with specific instructions for the Texas Instruments TI-82 and TI-83,
Hewlett-Packard® HP-38G, and Casio® CFX-9850G graphing
calculators. Grades 8-11 . Cat. BTH-731. $16.16-D
A
Graphing Matter: Activities for Easing into Algebra
by Mark Illingworth, Key Curriculum, 2004. Ease your middle school, prealgebra
and algebra students into algebra with fun and real-world applications of
variables and relationships that will make them laugh as they graph. The
activities in this book will engage the students in problems and experiments in
which variables represent quantities they can see and measure. These informal
explorations of graphs and equations provide a bridge between the concrete and
the abstract and help build a foundation for more formal operations students
will later meet in their study of algebra.
There are problems
in these five areas: line plots, looking for patterns, linear graphs, nonlinear
graphs, and graphs from equations. Among other things, students will examine Dr.
Olivio's Hairy Eyeball Theory, how water gets colder as it gets deeper, how long
it takes to recite tongue twisters, how the mass of a Petri dish of alcohol
changes as the alcohol burns away, and more -- 26 investigations in all.
There is plenty of resource and lesson plan material to assist teachers,
complete answers to problems, and an appendix of reproducible worksheets and
graph papers for student use. 188 pages plus another seven in the appendix and
some with graph paper to reproduce. BTH-4986. Please click title link for
current price, availability, and cover art. If I'm out of stock, I can order it
for you.
Hands On Pre-Algebra Grades 6-8 by Susan Dean. Instructional Fair /
Frank Schaffer, 2007. This a great supplement for grades 6-8. It is full of
activities which can be adapted for varying levels of difficulty. Many
activities are self-guided with questions for additional exploration. You will
find a variety of pre-algebra puzzles, games and other activities which will
help students to understand and enjoy math. 80 pages. BTH-5303. $9.89-D
The
Pattern and Function Connection by Brad S.
Fulton and Bill Lombard. 2001. The 11 progressively paced activities, which
include blackline-master worksheets and homework pages, introduce students in
pre-algebra and algebra to the fundamental concept of function and its multiple
representations. Students recognize, graph, analyze, and solve algebraic
functions, transitioning from concrete to abstract. Full teacher notes and
solutions are provided, as well as an alignment to the NCTM Principles and
Standards. 161 pages. Punched to fit three-hole binder. BTH-4987. Please click title link for current price,
availability, and cover art. If I'm out of stock, I can order it for you.
Painless Algebra, by Lynette
long. Published by Barron's. This book guides the apprehensive student painlessly
through the steps of working out algebra problems. It begins with integers, progresses to
simple equations with one variable, and then leads into a clear explanation of
inequalities, systems of equations, exponents, and roots and radicals. When all this is
understood, the student graduates to the mastery of quadratic equations. All along the way
are fun-to-solve "brain tickler" problems (answers provided). This book will
help middle and high school students who are having trouble in their
algebra courses. BTH-104. $8.06-D
Power Practice Pre-Algebra by Wendy Osterman, Creative Teaching
Press, 2004. For grades 5-8. Books in this series contain over 100 ready-to-use
activity pages to provide skill practice for students. These books supplement
and extend any curriculum and can be used for independent class work or
homework. Answers are provided. This book correlates to the NCTM Standards.
Topics include factors and multiples; decimals; rational numbers; percents;
polynomials; square roots; and solving equations. 128 pages. BTH-5467
Saxon Algebra ½ Homeschool Kit: This
includes the student textbook, a tests booklet, and an answer key booklet. this
course covers all the topics normally taught in prealgebra, and also some topics
from geometry and discrete mathematics. It represents the culmination of the
study of prealgebra mathematics from review of arithmetic operations to
evaluation and simplification of algebraic expressions, word problems involving
algebraic concepts, and classification of geometric figures and solids. 3rd
Edition. 137 lessons. Saxon-499X. BTH-4585. $58.50-D
Saxon Algebra I
Homeschool
Kit: This kit contains everything you need to teach first year algebra at
home -- a textbook, an answer key for homework, and tests with answers. This
course includes five instructional components: introduction of the new
increment, examples with complete solutions, practice of the increment, daily
problem sets, and cumulative assessments. This course covers all topics normally
introduced in first year algebra. these topics range from algebra-based
real-world problems to functions and graphics -- from algebraic proofs to
statistics and probability. 3rd edition. 120 lessons. Saxon-1230. BTH-4582.
$61.50-D
Saxon Homeschool Teacher, Algebra 1 Lesson and Test CDs for Third Edition,
2008. This is the only official video supplement to the Saxon Math Homeschool
program. It supplements, not replaces, the student textbook. Contains over 130
hours of Algebra 1 content, including instruction for every part of every
lesson, as well as complete solutions for every example problem, practice
problem, problem set, and test problem. The user-friendly CD format offers
students helpful navigation tools within a customized player and is compatible
with both Windows and Mac. Contains 6 CDs. BTH-4614. $80.99-D
Saxon Algebra 2 Homeschool Kit, 2nd4584. $58.05-D
Saxon Algebra 2 Homeschool Kit,
3rd Edition
BTH-4584. $60.30-D
Saxon Algebra 2 Homeschool Kit
with Solutions Manual,
3rd4615. $89.10-D
Saxon
Advanced Mathematics: An Incremental Development, Homeschool Kit, Second
Edition, by John Saxon Jr., 2003. Advanced Mathematics fully
integrates topics for algebra, geometry, trigonometry, discrete mathematics, and
mathematical analysis. Word problems are developed throughout the problem sets
and become progressively more elaborate. With this practice, high-school level
students will be able to solve challenging problems such as rate problems and
work problems involving abstract quantities. Conceptually oriented problems that
help prepare students for college entrance exams (such as the ACT and SAT) are
included in the problem sets. Set includes the hardcover student textbook with
125 lessons, proofs and index, answers to all problems in book, 748 pages, and a
Homeschool Packet with test forms and answers to all problem sets in text and
for the 31 tests in packet. BTH-4612 . $64.80-D
Straight Forward Series, Math
Large Editions: by Garlic Press. This series presents the basic facts of the subjects
covered in each book. There is an assessment test at the beginning of each book. This
helps you determine what your student needs to learn. Then there is instruction (about
one-half page per lesson on the average) in a basic concept or skill. This is followed by
exercises which allow the student to practice the skill taught. At the end of the book is
a final test to see if the students have mastered the skills. These books are
reproducible. $8.96 each
Visual
Approach to Functions by Frances Van Dyke. This series of visual
exercises introduces all of the standard
functions and applications students encounter in algebra. Lessons
consisting of blackline masters and teacher notes and answers are organized into
six chapters, each with optional activities that use graphing calculators and
motion detectors. The six chapter titles are Distance as a Function of Time,
Value as a Function of Time, Exponential Growth and Decay, Investments, Height
of a Projectile, and Quadratic Applications. 170 pages. BTH-5095. (Follow link
for availability and current price.)
Working With Numbers: Algebra, by
James Shea. Steck-Vaughn. For Middle School, Junior High, and High School levels. Pretests
and Mastery Tests help place and access students. 208 pages, grades 8-12.
BTH-146.
$19.22--D
Teacher's Guide, BTH-149, $9.59-D
The Write Tool to
Teach Algebra by Virginia Gray, Key Curriculum Press. This activities in
this book are designed to break down student resistance to mathematics with
writing exercises that entertain while they promote critical thinking skills.
This friendly, non-intimidating approach will encourage even your most reluctant
writers to express themselves . The books contains specific class instructions,
writing activities, reproducible teacher's aids, and assessment suggestions.
This is a valuable resource for those who wish to address the NCTM Standards'
emphasis on communication in mathematics classrooms. 104 pages. BTH-3101.
$13.46 |
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The smart way to learn Microsoft Office?one step at a time! The second edition of this popular book features new and expanded content. In addition to covering familiar Microsoft Office applications such as Microsoft Office Access? 2007, Excel® 2007, Outlook® 2007, PowerPoint® 2007, and Word 2007?you now also get coverage of Microsoft Office Publisher... more... instructions. Includes Workshops MCAS Exam Prep More than 500 Essential... more... |
Find a Greenbrae Algebra 1My work there has been aimed at creating new techniques that can move any learner, regardless of sensory preference or learning style (auditory, language, tactile, visual) to subject mastery. More advanced algebra involves quadratic equations, radicals and curvilinear functions. Without a sold base, it's tough stuff |
This course is designed forstudents who need to understand basic arithmetic operations (add, subtract, multiply, and divide) on whole numbers, fractions, and decimals. Students taking this course will study percent problems and other basic math topics.
Mathematical Literacy:
This course addresses mathematical literacy by developing students that can communicate effectively in mathematics and apply those skills learned to real-world applications. This course will focus on the relationships between mathematics in the classroom and to everyday life. Mathematical literacy will develop mathematical understanding by incorporating the use of various web based resources, simulating real world interactions with money and finances, and CAHSEE mathematics exit exam readiness. Various related resources will be presented and utilized to develop mathematically literate students.
This standard course is designed to help students prepare for Algebra 1.
Students taking this course should have basic arithmetic skills but may need some review. Topics covered in this course will include number sense, integers, equations, inequalities, exponents, ratios, graphing, spatial thinking, measurement, geometry, patterns and functions, statistics and probability, logic, and beginning algebra concepts. Algebraic concepts are connected to arithmetic skills to build a foundation necessary for success in algebra 1. Please visit the website of the California State Board of Education for a list of applicable standards. Go to:
A wide variety of instructional techniques will be used, including teacher direct-instruction, small group collaborative learning, and inquiry/lab activities.
Algebra A
Algebra 1 is a course in Algebra. Algebra A covers the first of the course. The course introduces the and methods of algebra. Algebra 1 will include the study of integers and variables, constants, mathematical symbols and and equations. This course is the first part of mathematics.
Algebra B :
Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
This is the second half or Algebra 1 focusing mainly on quadratics with some review of the first half of Algebra 1.
Algebra I
This course introduces the language and methods of algebra. Included in this course are solving and graphing linear equations and inequalities; solving equations of two variables through graphic and algebraic methods; working with irrational numbers; reasoning and logic; and applying algebraic methods into practical situations. Students will be actively engaged using concrete and virtual materials and appropriate technologies such as graphing calculators and computer software. Problem solving is integrated throughout the different components of the curriculum.
Ge are emphasized. Students will be actively engaged using concrete and virtual materials and appropriate technologies such as graphing calculators and computer software. Problem solving is integrated throughout the different components of the curriculum.
Honors Ge emphasized. Topics are treated in depth and alternative assessments are added to the traditional tests. Students will be actively engaged using concrete and virtual materials and appropriate technologies such as graphing calculators and computer software. Problem solving is integrated throughout the different components of the curriculum.
Algebra 2:
Algebra 2 is a course designed to challenge students in their applications of various algebraic techniques. The course expands on the basic algebraic concepts involved in solving equations and inequalities, factoring polynomials, graphs, exponents, and solving
quadratic equations. In addition, it examines quadratic, logarithmic, and exponential
Honors Algebra 2:
Honors Algebra 2 is a course designed to challenge students in their applications of various algebraic techniques. The course expands on the basic algebraic concepts involved in solving equations and inequalities, factoring polynomials, graphs, exponents, and solving quadratic equations. In addition, it examines quadratic, logarithmic, and exponential functions, the application of functions to real world problems, conic sections, probability, trigonometric functions, and complex numbers.
Honors Algebra 2 is an accelerated course designed to develop deductive reasoning and organized logical thinking patterns. The honors class will provide students with a challenging, in-depth study of intermediate algebra..
College Readiness
This course is designed with the specific needs of high school students to prepare them for college-level mathematics courses. There is both Algebra and Trigonometry in this course. As we progress through the course we will work with linear, quadratic, and higher-degree polynomial functions: the absolute value and piecewise linear functions; the greatest integer function and other step functions; square root functions, rational functions, exponential and logarithmic functions: and trigonometric and inverse trigonometric functions. Graphing is also emphasized so that students become proficient in both drawing and interpreting graphs.
Honors Pre-Calculus
The goal of this course is to help the student cover the algebraic, exponential, logarithmic and trigonometric function and their graphs, as well as analytic geometry in preparation for the course in calculus. The prerequisite for this course is successful completion of Algebra II.
AP Calculus
This course will be presented with the same level of depth and rigor as a entry level college and university courses. This course is in preparation of the advanced placement examination in the subject. This course will cover subjects such as limits of functions, continuity of functions, derivatives, integrals, L'Hospital's rule and many others. Calculus is a widely applied area of mathematics and involves a beautiful intrinsic theory. Students mastering this content will be exposed to both aspects of the subject. |
Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning.The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special attention is paid to the topic approach and mathematics across the curriculum. The assessment of mathematical attainment is also dealt with thoroughly.Teachers will find this book an invaluable companion in their day-to-day teaching. less |
Author's Description
Math Center Level 2 - Math software for students
Math software for students studying precalculus and calculus. Can be interesting for teachers teaching calculus. Math Center Level 2 consists of a Scientific Calculator, a Graphing Calculator 2D Numeric, a Graphing Calculator 2D Parametric, and a Graphing Calculator 2D Polar. The Scientific Calculator works in scientific mode. All numbers in internal calculations are treated in scientific format, like 1.23456789012345E+2 for 123.456789012345. You also can use scientific notation in formulas. If you get result NaN, like in ln(-1), that means that the function is not defined for given argument. Otherwise Scientific Calculator is similar to Simple Calculators. There are options to save and print calculation history, to change font, and standard editing options. Graphing Calculator 2D Numeric is a further development of Graphing Calculator2D from Math Center Level 1. It has extended functionality: hyperbolic functions are added. There are also added new capabilities which allow calculating series, product series, Permutations, Combinations, Newton Binomial Coefficients, and Gauss Binomial Coefficients . Graphing Calculator 2D Numeric has capability to build graphs for first and second derivatives, definite integral (area under curve) and length integral (length of curve). Since these calculations are done numerically, not symbolically, the calculator is called Numeric. Graphing Calculator 2D Parametric is a generalization of Graphing Calculator 2D Numeric. Now x and y are functions on parameter ?. If you are typing formula using keyboard, then you can use "tau" for ? . Since all calculations are done twice, for x and y, there was some sacrificing of precision in order to keep speed of calculations. So, although it is possible to build the same graph of y=f(x) in parametric calculator using x=?, y=f(?), the Graphing Calculator 2D Numeric will build it with greater precision. Graphing Calculator 2D Polar is a specialization of Graphing Calculator 2D Numeric.
Math Center Level 2 1.0.0.7 is licensed as Shareware for the Windows operating system / platform. Math Center LevelMath Center Level 2 Tvalx. Please be aware that we do NOT provide Math Center Level 2 cracks, serial numbers, registration codes or any forms of pirated software downloads. |
Unprecedented Differentiation
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Designed to engage, inspire, and motivate learners, the program rewards effort at every step, Think Through Math deepens students' understanding of critical mathematical concepts, improves higher-order thinking and problem-solving skills, and readies students for Algebra and beyond. |
user
is given homework problems for
topics 1A, 1B, 1C, 1D then proceeds to =>
user
is given homework problems for
topics 2A, 2B, 2C, 2D then proceeds to =>
user
is given homework problems for
topics 3A, 3B, 3C, 3D then proceeds to =>
THE
ENSYS R-I-M-S PROBLEM-SOLVING METHOD TO LEARN ENGINEERING
STUDENT-CENTRIC
MODEL
The
ENSYS problem-solving method is oriented towards ABSORBING
INFORMATION by the STUDENT
requires
more time to allow the student to grasp and apply concepts, ideal
for student comprehension and retention
most
time is devoted to absorbing information by the student and to help
the student understand the material
TOPIC
1
we
demonstrate step-by-step how to solve a problem for topic 1A
the
user hand-solves a
problem for topic 1A
we
discuss the solution of the
problem for topic 1A
we
demonstrate step-by-step how to solve a problem for topic 1B
the
user hand-solves a
problem for topic 1B
we
discuss the solution of the
problem for topic 1B
we
demonstrate step-by-step how to solve a problem for topic 1C
the
user hand-solves a
problem for topic 1C
we
discuss the solution of the
problem for topic 1C
we
demonstrate step-by-step how to solve a problem for topic 1D
the
user hand-solves a
problem for topic 1D
we
discuss the solution of the
problem for topic 1D
TOPIC
2
we
demonstrate step-by-step how to solve a problem for topic 2A
the
user hand-solves a
problem for topic 2A
we
discuss the solution of the
problem for topic 2A
we
demonstrate step-by-step how to solve a problem for topic 2B
the
user hand-solves a
problem for topic 2B
we
discuss the solution of the
problem for topic 2B
we
demonstrate step-by-step how to solve a problem for topic 2C
the
user hand-solves a
problem for topic 2C
we
discuss the solution of the
problem for topic 2C
we
demonstrate step-by-step how to solve a problem for topic 2D
the
user hand-solves a
problem for topic 2D
we
discuss the solution of the
problem for topic 2D
TOPIC
3
we
demonstrate step-by-step how to solve a problem for topic 3A
the
user hand-solves a
problem for topic 3A
we
discuss the solution of the
problem for topic 3A
we
demonstrate step-by-step how to solve a problem for topic 3B
the
user hand-solves a
problem for topic 3B
we
discuss the solution of the
problem for topic 3B
we
demonstrate step-by-step how to solve a problem for topic 3C
the
user hand-solves a
problem for topic 3C
we
discuss the solution of the
problem for topic 3C
we
demonstrate step-by-step how to solve a problem for topic 3D
the
user hand-solves a
problem for topic 3D
we
discuss the solution of the
problem for topic 3D
ALL
RIGHTS RESERVED
The ENSYS
R-I-M-S and S-I-M-S
problem-solving Eit-Fe, Pe Mechanical, Pe Electrical, Pe Civil - Exam
Review-Methods are the invention and
intellectual property of ENSYS
These Exam Review-Methods have been pioneered, developed and tested with
thousands of engineers since 1990
These Exam Review-Methods are proprietary, copyrighted, trademarked and
patented
Any implementation, modification, alteration or application of these
Exam Review-Methods without permission of ENSYS are a violation of federal
law
Any implementation, modification, alteration, application or deployment of
these Exam Review-Methods require licensing by ENSYS |
Specification
Aims
To give an introduction to Lebesgue measure on the set of real numbers R
and the concept of measure in general, indicating its
role in the theory of integration. To introduce fractal
sets in R and Rn and the
concept of Hausdorff
dimension, concentrating on simple examples.
Brief Description of the unit
A standard approach to integration on the real line, formalised by
Riemann, is based on partitioning the domain into smaller intervals.
(This theory was described in MATH20101 but is not a prerequisite
for the course.) This approach works in many situations but there
are simple examples for which it fails. In 1902, H. Lebesgue
produced a better theory in which the key idea is to extend the
notion of length from intervals to more complicated subsets of
R. This started an area of mathematics it its own right,
called Measure Theory. Most generally, this is about how one may
sensibly assign a size to members of a collection of sets.
An interesting class of sets in R and higher dimensions
are called fractals. These often exhibit self-similarity and
are complicated by not too complicated to study. In fact, they
give examples of complicated sets to which the Lebesgue theory
assigns zero measure and the key idea of Hausdorff dimension
gives a more delicate way of quantifying their size.
This course will appeal to students who have enjoyed MATH20101
or MATH20111 and MATH20122. It will be useful to student taking
probability course courses in years three and four since the
ideas of measure theory have a central role in probability
theory.
Learning Outcomes
On successful completion of this course unit students will
understand how Lebesgue measure on R is constructed,
understand the general concept of measure,
understand how measures may be used to construct integrals,
understand the notion of Hausdorff dimension of sets in
Rn,
calculate Hausdorff dimension for Cantor sets and other self-similar
examples. |
Welcome to Algebra 1B, the second year of our two
year Algebra 1 program.† Algebra 1B will
consist of both an extensive review of Algebra 1A, and in-depth coverage of
those California Algebra 1 standards not covered in 1A.
Itís important that both
parents and students understand that Algebra 1 can be a rigorous, demanding,
and sometimes very difficult course.† Practice
is crucial and successful students complete their homework.† If a
student is struggling with the tests in Algebra 1, they are often either
neglecting or struggling with their homework.† For that reason, parents are strongly
encouraged to check their studentís homework daily.† Their daily assignments and links to homework
help sites can be found in my weekly lesson plans on my teacher page on the
school website, specifically If a student needs tutoring, Iím available during
their class-time, before school, after school, and during 9th
period.† I strongly encourage students
who are having difficulty to take advantage of this service.† We will also be covering the previous dayís
most challenging problems at the beginning of each class.
The Semester grades are
weighted at 40% per quarter and 20% for the final exam.
I encourage parents to
contact me with any questions or concerns.†
The best way to reach me is by
e-mail at [email protected].† You can also reach me by telephone at
667-2292 extension 243 or you can generally find me in my classroom, Room 9,
before and after school.
Procedures
and Rules for Room 9 Classes
vWhen you
enter the room, be seated and immediately begin the
warm-up questions projected on the overhead.
vStudents will not be allowed to leave the classroom
without their hallpass.† Please produce your hallpass
when requesting to leave.
vCell phones can never be seen or used in Room 9.† If they are seen or heard, or if there is a
suspicion they are being used, they will be taken away.† They can be picked up in the office at the
end of the day.
vMP3 players (ipods), can
never be used during the lesson portion of your math class, nor can they be
used during tests.† Occasionally, with
permission only, students will be allowed to use these devices during seatwork.
vDaily homework assignments will be due at
the beginning of the next class period.†
Late assignments will be accepted until a cut-off day near the end of
each quarter and will be graded at approximately 75%.
vThe
heading on each assignment will be at the top of the page as illustrated in the
following example: |
GCSE Mathematics Revision and Practice: Higher Student Book
This book has been created for the new GCSE specification for first examination in 2010. The book is targeted at the Higher tier GCSE, and it ...Show synopsisThis book has been created for the new GCSE specification for first examination in 2010. The book is targeted at the Higher tier GCSE, and it comprises units organised clearly by topic. Each unit offers: - Summary of objectives at the start so it is clear what students need to know - Clear explanations with examples showing the key techniques - Plenty of practice with clearly differentiated questions pitched at an appropriate level - Summaries and past exam questions to help students gain responsibility for their learning - Functional maths and problem-solving highlighted throughout |
Project Description
The
main thrust of the grant program is to improve student mathematics
scores on standardized tests. The grant project will enrich the
academic program of students by enhancing the mathematics curriculum
with the exploration of mathematical modeling, data analysis,
statistics, forming conjectures, establishing justifications,
and other problem-solving topics by integrating hand-held technology,
specifically, graphing calculators with computer connectivity.
Students will discover mathematics with the TI-73 graphing calculator
as they work through a series of investigations that are designed
to spark their curiosity and make them want to discover the mystery
of why, and to motivate them to want to probe into some important
mathematical concepts. All of the math concepts that will be
addressed are indicated across the strands in the Core Curriculum
Content Standards. The interesting problems and investigations
that students will explore will enable them to gain a deeper
understanding of mathematical concepts that will help them better
approach the more routine problems that are on the standardized
tests. |
Description
Goldstein's BriefCalculus and Its Applications, Twelfth Edition is a comprehensive print and online program for students majoring in business, economics, life science, or social sciences. Without sacrificing mathematical integrity, the book clearly presents the concepts with a large quantity of exceptional, in-depth exercises. The authors' proven formula–pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of exercises–has proven to be tremendously successful with both students and instructors. The textbook is supported by a wide array of supplements as well as MyMathLab® and MathXL®, the most widely adopted and acclaimed online homework and assessment system on the market.
This text is designed for a one-semester course in applied calculus.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
0. Functions
0.1 Functions and Their Graphs
0.2 Some Important Functions
0.3 The Algebra of Functions
0.4 Zeros of Functions–The Quadratic Formula and Factoring
0.5 Exponents and Power Functions
0.6 Functions and Graphs in Applications
1. The Derivative
1.1 The Slope of a Straight Line
1.2 The Slope of a Curve at a Point
1.3 The Derivative
1.4 Limits and the Derivative
1.5 Differentiability and Continuity
1.6 Some Rules for Differentiation
1.7 More About Derivatives
1.8 The Derivative as a Rate of Change
2. Applications of the Derivative
2.1 Describing Graphs of Functions
2.2 The First and Second Derivative Rules
2.3 The First and Second Derivative Tests and Curve Sketching
2.4 Curve Sketching (Conclusion)
2.5 Optimization Problems
2.6 Further Optimization Problems
2.7 Applications of Derivatives to Business and Economics
3. Techniques of Differentiation
3.1 The Product and Quotient Rules
3.2 The Chain Rule and the General Power Rule
3.3 Implicit Differentiation and Related Rates
4. Logarithm Functions
4.1 Exponential Functions
4.2 The Exponential Function ex
4.3 Differentiation of Exponential Functions
4.4 The Natural Logarithm Function
4.5 The Derivative of ln x
4.6 Properties of the Natural Logarithm Function
5. Applications of the Exponential and Natural Logarithm Functions
5.1 Exponential Growth and Decay
5.2 Compound Interest
5.3 Applications of the Natural Logarithm Function to Economics
5.4 Further Exponential Models
6. The Definite Integral
6.1 Antidifferentiation
6.2 Areas and Riemann Sums
6.3 Definite Integrals and the Fundamental Theorem
6.4 Areas in the xy-Plane
6.5 Applications of the Definite Integral
7. Functions of Several Variables
7.1 Examples of Functions of Several Variables
7.2 Partial Derivatives
7.3 Maxima and Minima of Functions of Several Variables
7.4 Lagrange Multipliers and Constrained Optimization
7.5 The Method of Least Squares
7.6 Double Integrals
8. The Trigonometric Functions
8.1 Radian Measure of Angles
8.2 The Sine and the Cosine
8.3 Differentiation and Integration of sin t and cos t
8.4 The Tangent and Other Trigonometric Functions
9. Techniques of Integration
9.1 Integration by Substitution
9.2 Integration by Parts
9.3 Evaluation of Definite Integrals
9.4 Approximation of Definite Integrals
9.5 Some Applications of the Integral
9.6 Improper |
Publisher's Comments
This book provides a review of high school level mathematics and is designed as a self-study aid. Chapters cover number operations, variables, extreme numbers, measurements, algebra, beginning statistics, probability, geometry, graphs, intro trigonometry, vectors, exponentials and logarithms, and si... |
Graphing Quadratic Equations (Overhead Transparencies begins with a brief discussion of the flight of a model rocket, and it is this topic that propels the class through the procedure of graphing quadratic equations.
Graphing guides are included for your students' convenience during independent practice. They work best when they are assigned problems that can be graphed within range of the axes provided. A teacher's guide is provided for your convenience as well.
Word Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
273 13 years of teaching experience in both middle school and high school classrooms. I have taught in public, private, charter, and alternative school settings. My specialty is mathematics, but most of my experiences have involved the teaching of several subjects such as English, history, science, and government. |
Sažetak
(ne postoji na srpskom)
We show how a computer algebra system in MATHEMATICA can be used in several elementary courses in mathematics for students. We have also developed an application in programming language DELPHI for testing students in MATHEMATICA. |
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take noteevin Cassel was awarded the 2002 Alfred Noble Prize for his paper, "A Comparison of Navier-Stokes Solutions with the Theoretical Description of Unsteady Separation," published in the Philosophical Transactions of the Royal Society of London
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Software Engineering: A Practitioner's Approach, 6/eChapter 12 User Interface Designcopyright 1996, 2001, 2005R.S. Pressman & Associates, Inc. For University Use Only May be reproduced ONLY for student use at the university level when used in c |
Mathematics
Applied Algebra
Applied Algebra is intended as an introduction to Algebra I and includes the topics of expression and integers, solving one step equations and inequalities, decimals and equations, factors, fractions and exponents, operations with fractions, ratios, proportions and percents, solving equations and inequalities, linear functions and graphing, spatial thinking, area and volume, right triangles in algebra, date analysis an probability, nonlinear functions and polynomials.
Algebra II/Trigonometry
This course deals with operations and equations, graphing linear equations, solving systems of linear equations (graphically and elimination of variables) products, factoring, solving quadratic equations, graphic conic sections, and rational number calculations. The trig portion of this course deals with an introduction to the six trig functions solving triangles, radian measure, graphing the trig functions, and solving fundamental identities using the six trigonometric functions.
Geometry
A course offered to students in grades 11 and 12, geometry deals with problems involving two dimensional aspects of a line, angles, rectangles, triangles, and circles. Through these problems the deductive method is also studied.
Calculus
Calculus is an advanced level math course open to juniors and seniors with extensive math background. This course deals with functions, limits, differentiation, integration, maximum and minimum values of a function, methods of differentiation, trigonometric, logarithmic and exponential functions as well as applications of calculus. |
diving into Algebra, it is a good idea to know how to recognize and work with polynomials. Learn the vocabulary associated with polynomials and how to write and simplify expressions. Includes: practice test, examples, and teacher's guide.
Notes:
Age group: 7th grade - adult.
Downloadable video file.
Title from title screen (viewed on July 15, 2010 |
The School is composed by five set of lectures, designed to introduce young researchers to the more recent advances on geometric and algebraic approaches for integer programming. Each set of lectures will be about six hours long. They will provide the background, introduce the theme, describe the state-of-the-art, and suggest practical exercises. The organizers will try to provide a relaxed atmosphere with enough time for discussion.
Integer programming is a field of optimization with recognized scientific and economical relevance. The usual approach to solve integer programming problems is to use linear programming within a branch-and-bound or branch-and-cut framework, using whenever possible polyhedral results about the set of feasible solutions. Alternative algebraic and geometric approaches have recently emerged that show great promise. In particular, polynomial algorithms for solving integer programs in fixed dimension have recently been developed. This is a hot topic of international research, and the School will be an opportunity to bring up-to-date knowledge to young researchers. |
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Math 2312: Precalculus
As suggested by the catalog description (below), this course focuses on algebra and trigonometry concepts underpinning calculus. Topics include data analysis, functions, graphs, limits, trigonometry, exponential & logarithmic functions, other functions, and math modeling. For detailed information and policies, please the Read the Full Syllabus.
A more rapid treatment of the material in MATH 1314 and MATH 1316, this course is designed for students who wish a review of the above material, or who are very well prepared. Functions, graphs, trigonometry, and analytic geometry.
Class Posts
Instructions for the Final Exam The final exam counts for 25% of your course grade. The exam has 12 exercises (100 points) and must be completed during 8-10:30 on 12/13/11. You may use a calculator with factory-shipped programs, 1 side of a 8.5 by 11 inch page written in your own handwriting, a provided reference sheet,…
The main topic of the second test in precalculus was trigonometry. See the Exam 2 Study Guide for detailed information. Download the Test Math 2312 - Exam 2 - Trigonometry Extra Credit Opportunity You can earn a transformed grade of $(\mbox{original grade})^{0.7}(100)^{0.3}$ by printing a blank copy of the Exam and turning in a full set of…
This is one of two exams while combine to count for 30% of your grade. The exam has 8 exercises for 100 points and must be completed during class on 11/10/11. The exam has two parts – You may only use a writing utensil on Part 1. For Part 2, you will be provided a reference…
This in-class activity is designed to introduce trig identities by defining the complex exponential function according to Euler's Formula. Results in a fairly straight forward proof of the angle sum formulas for sine and cosine. Trigonometry and the Complex Plane (PDF) Trigonometry and the Complex Plane (DOCX)
Available in Two Formats Reference Guide for Basic Trigonometry (DOCX) Reference Guide for Basic Trigonometry (PDF) Used in-class and potentially useful to anyone who may need a refresher on any of the following: Calculating sine, cosine, tangent, cosecant, secant, cotangent for an angle in a right triangle. Calculating sine, cosine, tangent, cosecant, secant, or cotangent…
This activity is walks you through the steps to perform sine regression for a randomly generated data set using the TI-84. Step 1: Get a TI-84 Graphing Calculator (or similar). Don't have one? If you use Windows, you can download the attached Emulator (ZIP file), extract the Zip folder, and run the Wabbitemu.exe file. Load the…
The following little form produces randomized wave data using javascript. The purpose is to provide example data for someone learning to fit sine and cosine curves to oscillating data. Stop Sitting Around and Go Get You Some Data Press the "Get Data" button to generate some random oscillating data. Then copy and paste into a…
The first precalculus exam was based on functions and graphs. Download the Test and Answer Key Blank Copy of Exam 1 - Functions and Graphs Answer Key - Math 2312 - Exam 1 - Functions and Graphs What's on the Test? The main concepts on the test include reasoning about the following. Challenging topics are…
Exam 1 is scheduled for class time on Tuesday, October 4th. The exam cannot be made up if missed. Review time is set aside for class on Thursday 9/29, and you're encouraged to work on the problems with your mentor. Download the Exam 1 Study Guide |
Description
This book examines a wide array of current computer-graphics methods. Aimed at readers familiar with computer graphics and looking for a mathematically easy presentation of geometric modeling, it may be used in a classroom setting or as a general reference. |
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.
This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below:
Equivalent mathematical notation using standard text found on a keyboard
A variety of applications and word problems included in most exercise sets
Clearly enumerated steps found in context within carefully chosen examples
Video examples available, in context, within the online version of the textbook
Robust and diverse exercise sets with discussion board questions
Key words and key takeaways summarizing each section
This text employs an early-and-often approach to real-world applications, laying the foundation for students to translate problems described in words into mathematical equations. It also clearly lays out the steps required to build the skills needed to solve these equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. In addition to embedded video examples and other online learning resources, the importance of practice with pencil and paper is stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.
Flat World Knowledge is the only publisher today willing to put in the resources that it takes to produce a quality, peer-reviewed textbook and allow it to be published under a Creative Commons license. They have the system that implements the customizable, affordable, and open textbook of the twenty-first century. In fact, this textbook was specifically designed and written to fully maximize the potential of the Flat World Knowledge system. I feel that my partnership with Flat World Knowledge has produced a truly fine example in Elementary Algebra, which demonstrates what is possible in the future of publishing. |
computer files ready to use
Click on any of the following links to download the file you are interested in using.
Choose "Save file to disk" if you want to put it on your desktop for temporary
use or keep it on your hard drive for future reference. You can also right-click
and choose "Save Target As..."
This Mathematica notebook is a palette you can
use to quickly graph a function. You can choose which options you want to include in your
code. It also has options for graphing multiple functions. Very easy to use!
The first is a short, simple program for creating
graphs with instructions
included. The second has a few programs for creating graphs of multiple functions and
graphs with legends and/or grid lines. I recommend playing with Graph Template 1
first. The third file allows you to adjust the
fonts of the labels and the colors of the grid lines too (including nice
values for trigonometry).
Graph one or two inequalities with shading. This Mathematica notebook
give you control over shading colors, solid and dashed lines, grid lines,
tick marks, axis labels, and graph title including fonts and colors. You can
also copy-and-paste graphs into other computer programs to make tests,
worksheets, or notes.
This Mathematica file lets you easily generate polar graphs
on a polar grid. Directions for inserting graphs into Word files are
also included. Try Tracing
a Polar Graph to create animations that draw the graphs.
Use this Mathematica notebook to
illustrate converting a point in rectangular coordinates to polar
coordinates. Copy-and-paste your diagrams into worksheets or tests.
(Note: There are some extra frills
with this one since I was using it to learn some new things.)
Ready to use for classroom demonstration. Two programs
for graphing "y = a cos[b(x - c)] + d." All
you need to do is decide which a, b, c, and d values
you want to see. It is easy to switch "cos" to "sin" or any other trig
function, if desired. The second program lets you animate the graph as any of the
parameters change between the values you set. Includes x-axis labels with p !
This Mathematica notebook is designed more for teachers than for
students. Generate problems quickly for students to solve systems of
equations problems by graphing, substitution, or linear combination. You
control the solution and the y-intercepts.
This lesson demonstrates the difference between
exponential and factorial growth. The lesson uses tables, graphs, and scientific notation.
It also includes directions for using Microsoft Word to answer the guide
questions throughout the lesson. This works for a classroom demonstration, computer lab
activity, or independent study. (Mathematica notebook file)
How do a cone and a plane really make an ellipse? What about
hyperbolas and parabolas? This Mathematica notebook allows you
to adjust the angle of a plane as it intersects a cone to see the curves
that can be generated. Also, see the Conic Sections Gallery below and the Blank
Conic Sections Diagrams.
This Mathematica notebook is a list
of 3D graphics that you can rotate and zoom to see these surface
intersections more clearly. Great for classroom demonstrations or for
students to explore. (Or check out the Interactive
HTML Version or the Still
HTML Version.)
Create figures generated by rotating a region about a
horizontal line. You can specify the region using two functions and you can also pick the
axis of rotation. This is great for illustrating disk- and washer-method problems. It's
very easy to use.
Choose your own region to rotate about the y-axis
and see it formed by a series of cylinders. This program nicely illustrates the shell
method for finding volumes. Instructions are also included for a simple animation.
This file is a catalog of several different
three-dimensional figures created with a given base and a given cross sectional shape.
Also, the four programs I wrote to generate these figures are available to download.
You
can create your own!Create solids with square,
equilateral triangle, semicircle, or rectangle cross sections. 3D Web Graphics!
Directions and links on Interactive
Graphics page.
This Mathematica notebook is a palette to help
you graph curves in three dimensions using parametric equations. It also includes several
options for working with 3D graphs. (Designed for a lesson with Calculus D.)
This program is set up for graphing quadric
surfaces such as the example:
+ = 1. Instructions are included. Be sure to read the hints at the bottom in
case your results don't come out as you expected. Or check out this simple Mathematica
notebook with interactive
examples of each quadric surface.
This PDF file is a lesson designed to show you how to work with series in
Mathematica and to improve your understanding of infinite series. To
download the example code for the third part, click here.
To easily compare the graph of a sequence and the corresponding series, use SequenceSeriesPlot.
Create slope fields
with this Mathematica notebook. Draw curves passing through initial
points and curves corresponding to fixed values of C. Other options
are also included. It explicitly solves the differential equation. For some
functions, there will be errors.
Notebook with Only Slope Fields.
Limits - Illustrations with Geometer's Sketchpad
For each of the four cases below, you can
interactively illustrate the formal definitions of limits. (Also, check
out the Worksheet
and the single file containing
all four sketches.)
This PDF file contains Mathematica code for drawing vector fields
in two and three dimensions. It also guides the user through graphing a
surface and its level curves with its gradient field. The four-dimensional
equivalent is also included.
Curvature is a measure of how tightly a curve is turning. This Mathematica
notebook allows you to type your own 2-dimensional function and select
the point where you want to see the circle whose curvature matches the
curve at that point. Thanks to Whitney Buchanan (TP '03) for
inspiring and helping with this one!
Here is a
calendar just for TPHS and LCCHS
teachers and students. You can
see the entire semester for a class on one page. White means you meet that day, gray means
you don't. Great for planning, notes, and reference.(Updated:
August 11, 2012)
Assignment Sheets
Here are some blank assignment sheets students can use
to keep track of their work for a single class or for a week. Print
one page for each class or each week. Find the one that works best for
you.
It's not a "To Do List," it's
a "To Do Matrix"! This one page has helped keep me organized
for years. Slightly altered versions also work well for organizing
activities in class and appointments with students. To download the PDF version, click
here.
Blank Graph Paper
Six blank graphs per page ready to use for class activities and
homework. Polar
Graphs(Now with 4 different styles!) or Rectangular
Graphs (PDF files)
3D Graph Paper
Blank axes for 3D
graphing created by a student. (Thanks, Austin Landow!)(If the Word
version doesn't open, try right-click and "Save Target
As...")
Are you frustrated with scissors and tape to
cut-and-paste graphs into your tests, quizzes, and worksheets? Download this file and you
can electronically resize, cut, copy, and paste blank and numbered graphs into any
document you're working on. Very handy!
One page with a blank parabola, ellipse, and
hyperbola. Each one shows the directrix, center, foci, and vertices
without any numerical values or labels. Have students fill it in a study
guide, insert the diagrams into
tests and worksheets, or print
a copy on a transparency to use during classroom demonstrations.
(Note: It works well for labels, but the scale is slightly off for
comparing focus, curve, and directrix measurements. Look for updates
soon.) |
Find a Menlo, GAAlgebra is essentially arithmetic with some of the numbers replaced by letters or variables. Initially, algebra referred to equation solving, but now it encompasses the language of algebra and the patterns of reasoning. The rules of algebra are basically the same as the rules for arithmetic. |
Specification
Aims
To introduce students to set theory and its role in mathematics.
Brief Description of the unit
Set theory began to develop in the late 19th century, and now is important in several areas of mathematics. This is a first course on the ideas developed since then. Although Axiomatic Set Theory is mentioned in the course, the material is developed informally, not from a set of axioms.
Learning Outcomes
On successful completion of the course unit students will be able to demonstrate facility with the notions of elementary set theory. |
Word Problems? NO PROBLEM! Now anyone, even those whose palms begin to sweat at the first sight of math problems that begin "A train left the station going 65 mph..." can overcome anxiety and learn to solve word problems. In Math Word Pro
McGraw -Hill's Top 50 Math Skills For GED Success
Editorial review
Written for the millions of students each year who struggle with the math portion of the GED, McGraw-Hill's Top 50 Math Skills for GED Success helps learners focus on the 50 key skills crucial for acing the test. From making an appropriat
College Algebra: A Graphing Approach
Editorial review
This text is a presentation of the fundamentals of college algebra. It is designed to provide a solid foundation for students who will apply the mathematics in a variety of disciplines as well as for students who will continue into calcul
Elementary Algebra I
Editorial review
This book contains selected chapters from Essential Mathematics with Applications, 2/e by Lawrence A. Trivieri
Student SMART CD-Rom Windows for use with Intermediate Algebra
Editorial review
Provides a self-paced, text-specific tutorial to help student review concepts and also provides unlimited problem-solving practice. Contains video clips on the CD-ROM to illustrate concepts and reinforce real-world applications. Each chap |
CMATH for Borland C++ (Win32) Desciption:
CMATH for Borland C/C++ makes fast complex-number math functions (cartesian and polar) available in three precisions. This comprehensive library was written in Assembler for superior speed and accuracy. All functions may be called from C or C++.
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CMATH is a comprehensive library for complex-number arithmetics and mathematics.
The following features make CMATH an ideal replacement for other available complex class libraries:
CMATH is a comprehensive library for complex-number arithmetics and mathematics.
The following features make CMATH an ideal replacement for other available complex class libraries:
1. High-performance implementation in machine code leads to |
Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological… |
TI-83/84 Applications
These are all of my TI-83/84 programs I wrote in high school. Feel free do download and distribute them calculator to calculator.
Read More
Mathematica Applicatio...
Here are some games,programs, and code snippets for my favorite new mathematical programming language. Sorry TI-Basic, you just don't cut it anymore.
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What's My Stage ...
What's My Stage On? is the only feis information app for your iPhone or iPad. View everything you need to know about the feis in one location. Complete with stage schedules, competition lists, school lists, and dancer lists. It even has the printed version of the program if there is one. It is like the Worlds program book on your...
Read More
TI-83/84 Applications
Posted by Marxon13 on Aug 17, 20111
Mathematica Applications
Posted by Marxon13 on Dec 5, 20112
What's My Stage On?
A Minkowski Diagram is a space-time plot for events that have a relative velocity that is a significant fraction of the speed of light. It takes the effects of Special Relativity and puts them into a easily understood form. I created a Mathematica function to draw and plot events on a Minkowski Diagram. It can draw the graph, add grid lines, plot points, add spacial/time reference lines, and show when a space time event is observed in either frame. Its quite easy to use, and example is in the notebook on how to use the function.
This is the first version of my 2-D platformer game Portal for Mathemetica. It's a bit slow, be patient, I'm working on making it faster.
To Play: Download and open the notebook and evaluate all of the cells. The game will be at the bottom of the notebook. Use the buttons, or enable the keyboard (Controlls: move: A/D portals: #'s 1-9 on your keypad)
his program will give you all the information of any quadratic equation. Just enter the equasion in any form, and it will give all of the necessary information about the graph. It will also show the work that teachers want on paper.
This unit circle will be the last one you will ever need. Enter in any angle value, in degrees or radians, and it will give you the values of its (x,y) coordinate. Or enter in a x or y coordinate, and get the possible angles. It also graphs the angle as it solves them. |
High School Math
High school math is the mid level of the math curriculum. Students prepare themselves for colleges at high school.
This the time which asks parents and educator to be very careful about the teenager students.
The main topics in the high school math include Mastering the order of operations involving fractions, exposnets and paranthesis. Kids should be able to do operation with fractions such as how to multiply fractions.
Understaing and apply the basic algebraic concepts such as algebraic expressions, polynomials, equations such as linear equations and quadratic equations.
Introduction to tringonomentry and application of tringonometric ratios in othe areas of math.
Coordinate geometry including lines, circels and conics. Application of lines such as slopes in daily life situations or in physics. Finding area of a circle from its radius or finding area and volume of solids.
Mensuration such as finding the surface area and volume of simple three dimensional shapes and composite figures. |
MATH205 Geometry
This unit has two distinct sections which represent two of the basic aspects of geometry: Euclidean and analytic. In the Euclidean section lines, polygons and circles are considered as well as Euclidean constructions, giving a rationale for each one. Major theorems on concurrence and collinearity follow, together with some 3-dimensional geometry including polyhedral. Suitable geometry software packages will be introduced to support the study of this unit. The analytic geometry section will consider the link between geometry and the algebraic representation of such curves as the conic sections. |
Specification
Aims
This module aims to engage students with the applications of mathematical methods to current questions in biology.
Brief Description of the unit
The life sciences are arguably the greatest scientific adventure of the age. Over the last few decades a series of
revolutions in experimental technique have made it possible to ask very detailed questions about how life works, ranging
from the smallest, sub-cellular scales up through the organisation of tissues and the functioning of the brain
and, on the very largest scales, the evolution of species and ecosystems. Mathematics has so far played a small, but
honourable part in this development, especially by providing simple models designed to illuminate principles and test
broad hypotheses.
The mathematics required for biology is not generally all that hard or deep (though there are exceptions: some of the
most exciting recent work in phylogenetics requires tools from algebraic geometry), but as the sketches above suggest
the range of tools is extremely broad. The point is that modern mathematical biology is genuinely applied maths: its
techniques are chosen to suit the biological problems, not the traditional disciplinary subdivisions. Although some
previous acquaintance with graph theory and probability would be helpful, this course is meant to be self-contained
and will only assume knowledge of differential equations.
Learning Outcomes
The main aim of this course is to see how mathematical ideas, techniques and habits of rigour can contribute to the understanding of questions about living things.
Read scientific papers that emphasize the application of mathematical ideas to biology.
Future topics requiring this course unit
No Fourth Year option requires this unit.
Syllabus
The course falls into two parts: for the first six weeks it is concerned mainly with standard ODE and PDE models and will rely strongly on the first volume of J. Murray's Mathematical Biology. The main topics will be:
• Population models & questions of ecological and evolutionary stability
These topics are normally treated with ODEs or, when one wants to include spatial organisation, PDEs. This area is a good introduction to the "illustrative model" school of mathematical biology.
• Models of chemical reaction networks
The ODE models used here are formally very similar to those used for interacting populations, but the emphasis on chemical reactions prepares the way for the more detailed models of cellular signal
The latter part of the course is more directly connected to current questions in biology and the lectures will, in part, be designed to help the students read scientific papers, though some of the material is also covered in Uri Alon's book (see below).
• Pattern selection and development of body plan
This topic forms a bridge between the textbook study and the research literature. We will begin by reading a famous old paper, Alan Turing's The Chemical Basis of Morphogenesis, and then look at the sorts of things that modern work—both experimental and theoretical—has to say about related questions. The main tools here are, again, differential equations.
• Analysis of regulatory networks
This topic follows naturally from Turing's work and begins to bring in some new mathematical methods and ideas, especially from graph theory and probability. This is mathematical biology at its closest to experimental data (see the online materials for a more detailed list of topics and links to articles).
• Probabilistic simulation of chemical reaction networks
The study of genetic regulation naturally prompts the question "Is it sensible to use ODE-based models when there are only a very few reactants?'' The last few lectures in the course are devoted to addressing this issue via stochastic simulations.
Textbooks
I studied the following—more or less mathematically-minded—books while preparing the course.
Terry A. Brown, Genomes 3 (Garland Science, 2007). ISBN 0-8153-4138-5
The previous edition, Genomes 2, is available online from the National Center for Biotechnology Information (NCBI) Bookshelf, a service of the U.S.A's National Institutes of Health (NIH). |
103. Introductory Algebra: Three hours An algebra course to help prepare a student for Intermediate Algebra (MAT 105). Topics include operations with rational numbers, exponents, simplifying algebraic expressions, and solving equations. Does not count toward the 128 hours needed for graduation, except for Elementary Education majors.
105. Intermediate Algebra: Three hours Prerequisite: MAT103 or satisfactory placement test score. An algebra course to help prepare a student for MAT 108, Introduction to Mathematics, or MAT 111, Pre-Calculus Algebra. Topics include simplifying algebraic expressions, factoring, and solving linear and quadratic equations. Does not count toward the mathematics requirement for a B. S. degree except for Elementary Education majors.
108. Introduction to Mathematics: Three hours Prerequisite: MAT105 or satisfactory placement test scores. A problem solving approach to the introduction of areas such as sets, geometry, probability, measurement, statistics, and consumer mathematics.
111. Precalculus Algebra: Three hours Prerequisite: MAT 105 or satisfactory placement test score. A brief study of numbers followed by a study of solving equations (linear, quadratic, radical, systems, etc.) as well as of inequalities, exponents, and logarithms.
121. Precalculus Trigonometry: Three hours Prerequisite: MAT 111 or consent of the instructor A relatively complete course in trigonometry followed by basic analytic and geometric properties of algebraic and trigonometric functions.
151. Calculus I: Three hours Prerequisite: MAT 111, MAT 121 or consent of the instructor Differentiation of algebraic and trigonometric functions with applications.
301. Foundations of Mathematics: Three hours Prerequisite: MAT 251 An introduction to the techniques and background necessary for abstract mathematical reasoning. Topics covered are elementary theory of logic, direct and indirect techniques of proofs involving the use of logic, elementary set theory, topics from analysis, and algebraic structures.
303. Introduction to Higher Geometry: Three hours Prerequisite: MAT 161 Fundamental concepts of geometry with emphasis given to logical development from basic assumptions.
361. Differential Equations: Three hours Prerequisite: MAT 261 or concurrent enrollment A study of first order and linear second order differential equations with applications. An introduction to linear nth order differential equations.
401. Introduction to Real Analysis: Three hours Prerequisite: MAT 251 and MAT 301 An advanced treatment of limits, continuity, sequences and series of functions, and differentiation. Emphasis is on proofs.
403. Introduction to Abstract Algebra: Three hours Prerequisite: MAT 251 and MAT 301 Introduction to algebraic structures, with an emphasis on groups.
411412413414449, 450. Independent Study: Three hours per course Prerequisite: Approval of the Department Head and Academic Dean Tutorial courses designed to meet particular needs of the students.
471, 472. Internship: Three to Six hours Prerequisite: Approval of the Department Head and Academic Dean An educational experience where the student is exposed, through actual observations and participation to the various aspects of a work situation. |
RELATED LINKS
Math Maneuvers
These Math Maneuvers take time and effort, but they work!
Read BEFORE class marking words, concepts, and examples that are not clear. Read with a pencil, paper, and calculator working out the examples in the reading. Check your progress on these with the solutions provided in the text.
Arrive to class EARLY with your text, pencil, notes, and calculator ready to go.
PARTICIPATE in class by actively taking notes, marking questions in lecture notes, and asking questions from the reading done before class.
Do homework problems AS SOON AS POSSIBLE after class. Some students like to RE-READ the text after class before beginning the homework. Get your lecture questions answered by the instructor (look for office hours on syllabus), a math specialist in the Learning Center, or a classmate.
CHECK ANSWERS to all homework, preferably every two or three problems. If you practice wrong, you may learn wrong, and you will need to unlearn the wrong way and learn the right way.
Find a STUDY PARTNER. When you are stuck, it may help to try to work with someone else. Even if you feel you are giving more help than you are getting, you will find that an excellent way to learn is by teaching others.
Work in the ACADEMIC RESOURCE CENTER in order to access the solution manuals, the math specialists, and other students.
Work during DROP-IN HOMEWORK HELP offered at special times in the Academic Resource Center.
KEEP UP with reading and homework DAILY. Math is sequential. Getting behind, even one day, tends to snowball downhill.
GETTING STUCK is to be expected. Don't get frustrated. Mark the problem, move on, and take the initiative to get help from a classmate, math specialist, or your instructor. Look at it as an opportunity to learn something new.
Cramming for math EXAMS seldom works. If you have kept up with homework, marking and getting your questions answered as you go, you should almost be ready for the exam. Set aside several hours to do a mixture of problems to be covered on the exam. Be sure to check answers to insure you are practicing correctly. |
Topology: An Introduction (working title), in
use in my current topology class. We begin with the
epsilon-delta definition of continuity from Calculus I and
develop topology as a collection of sufficient abstractions
which allow us to understand continuity, compactness,
connectedness, etc. in more abstract settings. The text is
appropriate for students who have had one semester of calculus
and an introduction to proofs.
Basic Statistics with Calculus Enhancement, in
preparation. Initial chapters in use in my current basic
statistics class. We present measures of center,
variation, random variables, normal distributions, binomial
distributions, and ANOVA. The first part of each chapter
is ideal for students with only a college algebra background;
the latter part of each chapter discusses and derives the
results rigorously and is ideal for students who have had the
usual three-semester calculus sequence. |
More About
This Textbook
Overview
This text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off — it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful 8, 2007
A great start for students reaching out for math
This book was extremely well written. I was pleased to see several isolated (but important) topics developed in a coherent logical manner. Depending on what mathematical field you decide to go into, this book has at least one chapter of advanced abstractions that you will use. For example: Congruences are used heavily in Number Theory and numerical analysis, Relations and Sets are useful in nearly every field of mathematics, and of course, they have a chapter 'Introduction to Groups' which can be used as a spring board for abstract algebra. Most important, this book prepares students for what advanced mathematics really is: Proofs. For those of you who dream of getting a Ph.D. in mathematics, this book represents the 'make-or-break' class for math majors. And due to the well-written style, it makes that jump oh so easy.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
Math for Strategists
Abstract
Great strategists rely heavily on numbers as they go about their work. Offers an overview of the high- and low-brow quantitative tools that students encounter during the Strategy course. The class explores high-brow tools in detail; the focus here is on low-brow calculations. Such calculations come up often in class but because they seem so simple, they get little airtime or explanation. From past class experience, roughly 20% of the students in each section come into the course with the intuition and experience to do these simple calculations themselves. The other 80% understand the calculations after they see them and grasp their value, but don't spot the opportunities to do the math themselves, before class |
Functions Modeling Change
Challenging yet accessible text from the Harvard Consortium prepares students for calculus
The As multiple representations encourage students to reflect on the material, each function is presented symbolically, numerically, graphically, and verbally (the Rule of Four).Exceptional Problems: Examples and problems based on real data help students create mathematical models to help them understand their world. An appropriate number of drill problems are included to assist students in learning techniques. The problems are varied and some are more challenging. Most cannot be done by following a template in the text.
Allows for a broad range of teaching styles. This text is flexible enough for use in large lecture halls, small classes, or in group or lab settings.
Focuses on fewer topics than iscustomary, but each topic is treated in greater depth. Only those topics essential to the study of calculus are included.
Reflects the spirit of the standards established by the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC), and meets the recommendations of the National Council of Teachers of Mathematics (NCTM).
Assumes technology has a place in modern mathematics. This text takes full advantage of technology when appropriate, although no specific technology is emphasised. It is important for students to learn how and when to use technology as a tool, as well as its limitations. However the focus of the text is on conceptual understanding not technology.
The Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally.
The Instructor's Manual contains teaching tips, calculator programs, some overhead transparency masters, and test questions arranged according to section. The Instructor's Manual includes identification of technology oriented problems and new syllabi. |
Mission Statement
The Math Lab seeks to develop student's ability to understand and apply mathematical principles and knowledge through tutoring, resources, and programs, which are offered in a relaxing, friendly atmosphere.
About Math Lab
FALL/SPRING
SUMMER
Monday - Thursday 8 am to 9 pm
Friday 8 am to 5 pm
Saturday 10 am to 3 pm
Monday - Thursday 9 am to 7 pm
Friday 9 am to 5 pm
Saturday 10 am to 2 pm
The UVU Math Lab is a drop-in study space dedicated to helping students develop their mathematical abilities. The Math Lab is a great place to work on math homework, so tutors can answer any questions as they arise. Additionally, students are encouraged to discuss homework exercises with fellow students. The Math Lab seeks to maintain a relaxed and friendly atmosphere in order to reduce student anxiety about learning mathematics.
Tutors work with students to help them learn. This takes time and requires active participation from the student. Tutors will not simply give answers or do homework problems for the students – which does not facilitate learning. Instead, tutors coach students through their exercises. Our goal is to increase each student's ability to understand and apply mathematical principles and knowledge.
Note:
Tutors cannot assist students on problems from take-home exams or make-up assignments which earn test credit. Tutors can assist with similar problems from the text.
Students check in and out at the front desk using a UV ID.
Our group study room can be reserved for larger groups
The Math Lab has 10 computers available for students to complete computer-based homework assignments with software such as MyMathLab, WileyPlus, and PHStat. |
This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.
Fernando Q. Gouvêa was born in São Paulo, Brazil and educated at the Universidade de São Paulo and at Harvard University, where he got his Ph.D. with a thesis on p-adic modular forms and Galois representations. He taught at the Universidade de São Paulo (in Brazil) and at Queen's University (in Canada) before settling at Colby College (in Maine), where he is now the Carter Professor of Mathematics. Gouvêa has written several books: Arithmetic of p-adic Modular Forms, p-adic Numbers: An Introduction, Arithmetic of Diagonal Hypersurfaces over Finite Fields (with Noriko Yui), Math through the Ages: A Gentle History for Teachers and Others (with William P. Berlinghoff), and Pathways from the Past I and II (also with Berlinghoff).
Gouvêa was editor of MAA Focus, the newsletter of the Mathematical Association of America, from 1999 to 2010. He is currently editor of MAA Reviews, an online book review service, and of the Carus Mathematical Monographs book series. |
The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathemati [more]
The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geom.[less] |
Riverdeep Mighty Math Astro Algebra Lab Pack
Product #: 1731
Company: Riverdeep Grades/Ages: Ages 12-15 Platform: PC/MAC
Astro Algebra teaches the concepts and problem-solving skills necessary to learn basic algebra. Students learn how to graph functions, translate word problems into solvable equations, and represent algebraic expressions using the Edmark® Virtual Manipulatives®. Hundreds of problems in over 90 space missions provide students with a solid foundation for success in algebra and beyond. |
Higher Engineering Mathematics. Edition No. 6
Elsevier Science and Technology, April 2010, Pages: 752
John Bird's approach, based on numerous worked examples and interactive problems, is ideal for students from a wide range of academic backgrounds, and can be worked through at the student's own pace. Basic mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for a range of university degree modules, foundation degrees, and HNC/D units.
Now in its sixth edition, Higher Engineering Mathematics is an established textbook that has helped many thousands of students to gain exam success. It has been updated to maximise the book's suitability for first year engineering degree students and those following foundation degrees. This book also caters specifically for the engineering mathematics units of the Higher National Engineering schemes from Edexcel. As such it includes the core unit, Analytical Methods for Engineers, and two specialist units, Further Analytical Methods for Engineers and Engineering Mathematics, both of which are common to the electrical/electronic engineering and mechanical engineering pathways. For ease of reference a mapping grid is included that shows precisely which topics are required for the learning outcomes of each unit.
The book is supported by a suite of free web downloads: . Introductory-level algebra: To enable students to revise the basic algebra needed for engineering courses - available at . Instructor's Manual: Featuring full worked solutions and mark schemes for all of the assignments in the book and the remedial algebra assignment - available at (for lecturers only) . Extensive Solutions Manual: 640 pages featuring worked solutions for 1,000 of the further problems and exercises in the book - available on (for lecturers only)
. Unique in introducing higher mathematical concepts from an engineering perspective, ensuring that readers understand what they need to do in order to turn theory into practice . Fully mapped to BTEC Higher National Engineering and Foundation Degree unit specifications . Free instructor's manual available online - contains worked solutions and a suggested mark scheme
Preface Algebra Partial fractions Logarithms Exponential functions Hyperbolic functions Arithmetic and geometric progressions The binomial series Maclaurin's series Solving equations by iterative methods Binary octal and hexadecimal Introduction to trigonometry Cartesian and polar co-ordinates The circle and its properties Trigonometric waveforms Trigonometric identities and equations The relationship between trigonometric and hyperbolic functions Compound angles Functions and their curves Irregular areas volumes and mean values of waveforms Complex numbers De Moivre's theorem The theory of matrices and determinants The solution of simultaneous equations by matrices and determinants Vectors Methods of adding alternating waveforms Scalar and vector products Methods of differentiation Some applications of differentiation Differentiation of parametric equations Differentiation of implicit functions Logarithmic differentiation Differentiation of hyperbolic functions Differentiation of inverse trigonometric and hyperbolic functions Partial differentiation Total differential rates of change and small changes Maxima minima and saddle points for functions of two variables Standard integration Some applications of integration Integration using algebraic substitutions Integration using trigonometric and hyperbolic substitutions Integration using partial fractions The t = __substitution Integration by parts Reduction formulae Numerical integration Solution of first order differential equations by separation of variables Homogeneous first order differential equations Linear first order differential equations Numerical methods for first order differential equations Second order differential equations of the form __ Second order differential equations of the form __ Power series methods of solving ordinary differential equations An introduction to partial differential equations Presentation of statistical data Measures of central tendency and dispersion Probability The binomial and Poisson distributions The normal distribution Linear correlation Linear regression Introduction to Laplace transforms Properties of Laplace transforms Inverse Laplace transforms The solution of differential equations using Laplace transforms The solution of simultaneous differential equations using Laplace transforms Fourier series for periodic functions of period 2p Fourier series for a non-periodic function over range 2p Even and odd functions and half-range Fourier series Fourier series over any range A numerical method of harmonic analysis The complex or exponential form of a Fourier series Essential formulae Index |
1428335242
9781428335240
1111803692
9781111803698 instructions, diagrams, charts, and examples that facilitate the problem-solving process while reinforcing key concepts. The presentation builds from the basics of whole-number operations to cover percentages, linear measurement, ratios, and the use of more advanced formulas. With a special section on graphs, scale reading of test meters, and invoices found in the workplace, this text is tailor-made for students in any automotive course of study! «Show less... Show more»
Rent Practical Problems in Mathematics 7th Edition today, or search our site for other Sformo |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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9/1/2008Chapter ObjectivesPart 1 Chapter 2MATLAB Fundamentals Learning how real and complex numbers are assigned to variables. Learning how vectors and matrices are assigned values using simple assignment, the color operator, and the linspace and logs
Chapter ObjectivesLinear Regression Familiarizing yourself with some basic descriptivestatistics and the normal distribution. Knowing how to compute the slope and intercept ofa best fit straight line with linear regression. Knowing how to compute an
Silvana Ilie - MTH510 Lecture Notes1LU FactorizationPROBLEM: Find the solution of the following system of linear equations:Ax = bwhere A is an n n matrix, x and b are n 1 (column vectors).NOTE: Gaussian elimination used in Chapter 9 to nd solutions
Chapter ObjectivesGeneral LinearLeast-Squares andNonlinear Regression Knowing how to implement polynomial regression. Understanding how the general linear least-squaresmodel can be solved with MATLAB using either thenormal equations or left divisio
MTH 501/510Assignment # 1Fall 2011DUE (at the beginning of your Lab): the week of October 31. Recall that a oating-point number can be expressed as(1)s (1 + f ) 2ewhere s, f and e are binary numbers. Recall that s is the sign indicator, f the mantis
MTH 501/510Assignment # 2Fall 2011DUE (at the beginning of your Lab): the week of October 171. Determine the root of2f (x) = 2ex 1(a) using Newtons method (by hand) with x0 = 1 until you have at least 3 signicantgures. As part of your answer, incl
MTH 501/510Assignment # 4Fall 2011DUE the week of November 28 (at the beginning of your Lab)1. Consider the following data points:xf (x)-1202104426170(a) Use a Table for Divided-Dierences (by hand) to construct the Newton interpolatingpo
IND 300Introduction to ManagementWinter 2012Ch M3IND 300 INTRODUCTION TO MANAGEMENT1History of Canadian Union Movement This section will address: Distinct Canadian characteristics. Early Canadian unionism.The union movement in Canada has a rich
IND 300Introduction to ManagementWinter 2012Ch M4IND 300 INTRODUCTION TO MANAGEMENT1The Structure of Canadian Unions This section will address: Introduction. The local union. Regional, national, and international unions. Labour councils. Provi
IND 300Introduction to ManagementWinter 2012Ch M2IND 300 INTRODUCTION TO MANAGEMENT1Theories of Industrial Relations This section will address: The origin of unions. Theories of union origins. Functions of unions. The future of unions.Source:
IND 300Introduction to ManagementWinter 2012Ch M7IND 300 INTRODUCTION TO MANAGEMENT1Defining and Commencing Collective Bargaining This section will address: The effects of certification. The framework for collective bargaining. Preparing for col
District veterinarians workingenvironment in and around the carLinda RoseKTH, School of Technology and HealthOutline Make a description of the project and its results Give an overview of some methods Have workshop where you students suggestsolutio
IND 712: TERM PROJECT: Investigating Human Factors in the WorkplaceWinter 2011Groups of 3-4 Assignment by Prof.Learning Objectives:- Learn to plan and conduct and HF evaluation of a work system- Developing group work & project management skills- Gai
How is Site recruitment going?IND 712 Business Case for HF Arguments FOR allowing a studentgroup to do an HF improvement project? Arguments Against?Copyright (c) 2012 P. Neumann, BSc, MSc, LicEng, PhD, LEL, Eur.Erg This teaching material is not for
Navigational Objective+PhantomProfitSynergyHuman Factors+WastePerformanceUnmeasuredGains?OKIt helps to think of this before you rebuild your barn doorsSo how do you get the water out at the end of the shift?
Excerpt from Forthcoming Paper: Rose, L., Orrenius, U.E. and Neumann, W.P., Working Paper. Work environment and the bottom line Survey of tools relating work environment to business results. in Human Factors and Ergonomics in Manufacturing & Service Indus |
SO WHAT ACTUALLY GOES ON IN JUNIOR HIGH MATH?
May 10, 2013
SO WHAT ACTUALLY GOES ON IN JUNIOR HIGH MATH?
Hopefully some fun and excitement where junior high students can discover that math isn't all that bad. Definitely some learning! With the change to College and Career Readiness Standards (Common Core), there will be some changes to the math curriculum, but most of what has been covered the past couple of years will still apply.
What is the difference between pre-algebra and algebra? In pre-algebra, the goal is to strengthen concepts from 7th grade math and to introduce students to algebraic concepts. When it comes to state assessments, all 8th graders take the same test, whether they take pre-algebra or algebra. In pre-algebra, we cover the same concepts that are covered in algebra – just not at the same depth or the same pace. |
CMATH for DelphiCMATH is a comprehensive library for complex-number arithmetics and mathematics, both in cartesian and in polar coordinates. This Delphi version includess the same functionality as CMATH for C++ or the complex class libraries of C++ compilers, plus many additions. All functions may be called either with overloaded function names (e.g., exp, sin ), or with type-specific function names (like cf_exp, cd_sin). Superior speed, accuracy and safety are achieved through the implementation in Assembly language. All CMATH functions are optimized for current processors, but will run on computers down to 486DX. This version is for Delphi |
This introduction to real analysis is based on a series of lectures by the author at Tohoku University. The text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; distribution theory; the classical theory of the Fourier transform and Fourier series; and wavelet theory.
Features:
The core subjects of real analysis.
The fundamentals for students who are interested in harmonic analysis, probability or partial differential equations.
This volume would be a suitable textbook for an advanced undergraduate or first year graduate course in analysis.
"The author has done a fine job in presenting the material selected for this book. The reader is exposed to a variety of real analysis concepts, methods, and techniques. The value of Igari's book lies in this exposition; it combines, contrasts, and reveals those concepts that are vital for a future deeper study of real analysis and its applications. The presentation of the material is clear and precise; well-chosen examples and exercises help the student to master the subject matter at hand ... highly recommend this textbook to anyone who is interested in learning about the fundamentals of real and functional analysis, distribution and Fourier theory, and their applications to wavelet theory."
-- Mathematical Reviews
"The book is a nice and compact introduction to Real Analysis. The material has been selected with a good taste and presented in a clear form. Each chapter is supplied with a list of problems, the solutions to which are presented at the end of the book. The bibliography reflects recent developments and contains the titles of the best books in the area." |
Costs
Special Notes
State Course Code
02054
Requirements
Prerequisites
Pre-Algebra, Algebra IA calculator with exponent capabilities; if students do not have one, they should check the accessories on their computerThe purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics in a year long algebra course. Topics included are real numbers, simplifying real number expressions with and without variables, solving linear equations and inequalities, solving quadratic equations, graphing linear and quadratic equations, polynomials, factoring, linear patterns, linear systems of equality and inequality, simple matrices, sequences, and radicals. Assessments within the course include multiple-choice, short-answer, or extended response questions. Also included in this course are self-check quizzes, audio tutorials, and interactive games. |
Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment. They are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography, physics, and engineering. This is a graduate-level textbook to introduce these phenomena by modeling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized with many figures. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differntial equations, complex variable and the elements of fluid mechanics. The book is aimed at graduate students, but is very useful for specialists in other fields.
An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a ...
This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and ...
Organized around problem solving, this book gently introduces the reader to computational simulation of biomedical transport processes, bridging fundamental theory with real-world applications. Using ...
Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex ... |
CS 3656 Numerical Computation
Spring 2011
This course is a one semester general
introduction to modern methods for numerical computation.
Numerical computation is an essential part of both computer
science and applied mathematics.
It has been a driving force behind advances in computer architecture
and in mathmatical theory.
As computing power increases, in engineering and science
guesswork and experiment are being replaced by numerical
modelling and control, a trend making these techniques more
and more widely used.
In the course we will first consider the lowest level and look at
how a computer represents numbers and carries out arithmetic and the
implications of this for practical computation.
Then we will cover the implementation and analysis of a variety of
computer techniques for solving some important mathematical problems
with wide applications.
In some cases students will implement algorithms from scratch; in others they
will use available numerical software.
There will be homework assignments
about once a week, usually consisting
of problems to solve or programming.
You may discuss homework orally among yourselves, but what you hand in should
represent your own work.
I will accept late homework up to 5 days
but will count off about 20 % for each day late.
If programming is assigned, you should turn in a listing of the program
and the output produced by the program.
For most programming assignments, you may use any reasonable computer to
which you have access, or we will provide you with a login on a
university machine.
There will be a midterm and a final exam.
The course grade will be weighted approximately 20-30% on weekly assignments
and 70-80 % on exams.
Assignments will be handed out in class and be available on this web page.
Supplemental information on assignments may be sent by email.
The essential prerequisites are programming ability in a language
such as C or C++ ; linear algebra,
and two semesters of calculus.
The main topics to be covered are: |
*******Text Available 6/25/2004!********** Steven Chapra's new text, Applied Numerical Methods with MATLAB for Engineers and Scientists, is written for engineers and scientists who want to learn numerical problem solving. Aimed at numerical methods users rather than developers, the text employs problems rather than mathematics to motivate readers. Guided by Chapra's proven student-oriented pedagogy, including chapter objectives, worked examples, and student-friendly problems, the reader builds a strong working knowledge of numerical problem solving while moving progressively through the text.
Customer Reviews:
Great Book
By Joseph "Joseph" - January 15, 2005
This is a well-written book that provides a nice, concise introduction to numerical methods. As with other books by this author, it is very student friendly and should be particularly useful for people, like myself, who use it for self-study. I was not familiar with MATLAB prior to using the book. This book made it relatively easy for me to pick up the fundamentals and then implement numerical solutions. As a computer scientist, I also liked the emphasis placed on the development of M-files. My only criticism is that I wish the book covered more material. I hope that the author expands it in future editions.
A good book to help you code numerical methods in MATLAB
By Srikumar Sandeep - February 11, 2009
I use this book. It is very short, but well written. If you want to learn numerical methods - Use Burden & Faires. But this book is for the end - user of the MATLAB numerical methods. It also gives some background info on these methods.
not for beginners
By magumbo - March 6, 2005
I had to buy this book for my class. This book doesn't instruct how to input equations. Not enough example answer codes for each problem. Less visual and tedious to follow all words.
This book provides advice and tools to effectively introduce, design, and deliver assessment or development centers in an organization. A "how to" manual, it runs through every aspect of running an ...
Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous ...
This rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. It covers basic econometric methods and addresses the creative process of model ... |
Casio FX-9860 GII programmable graphical calculator
It has several modes from making basic calculations to drawing graphs, creating tables and solving equations
The Casio FX-9860GII is a graphical calculator aimed at mathematics students from post-GCSE level upwards.
It has several modes from making basic calculations to drawing graphs, creating tables and solving equations.
This breadth can be intimidating but the quick-start guide offers helpful step-by-step examples for the most commonly used features, and there are more extensive user guides available online for more technical procedures.
Perhaps the biggest plus for the FX-9860 GII is its suitability for exams. Since it's capable only of numerical integration and differentiation, not the symbolic solving that other calculator models can do, it is permitted in exams, making it a good choice for maths students.
Looks-wise, it's similar to other graphing calculators and though it was heavier than other models it wasn't too bulky. It comes with a USB cable that connects it to the computer for copying program files and images.
We found navigating the various menus and settings quite time-consuming, with a lot of manual reference required. Ironically though, the biggest potential pitfall for students is the amount of things it can do, which could encourage dependency.
For more advanced uses it can be fully programmed using Casio's own programming language.
While it's not perfect, the FX-9860 GII is an obvious choice for those seeking a more powerful calculator and is a very useful learning tool indeed |
When students participate in an actively engaging environment, both cognitively and physically, they perceive themselves as makers, not just receivers of knowledge." - Mary Ann Davies and Michael Wavering
The Grade K – Calculus BC program strives to meet the academic needs of each student to produce mathematically astute individuals capable of incorporating critical thinking skills and multiple approaches to problem solving.
The curriculum is designed to foster a stimulating learning environment through the use of investigative, hands-on activities, diversified experiences, and current technologies. This program will offer all students a strong foundation for understanding concepts and opportunities to engage in the language of mathematics, which are vertically and horizontally aligned. Connecting strands will spiral throughout the grades K to Calculus BC .
The goals of this program are to develop an appreciation for and a positive attitude toward mathematics, to encourage further mathematical study, and to instill in students the responsibility for learning. As a result, students will be able to acquire the tools needed to become productive members of society with expanded career opportunities. Required Courses:
Grade
Course
Length
9 th – 12 th
Algebra 1
2 Semesters
9 th – 10 th
Geometry
2 Semesters
9 th – 10 th
Geometry Pre-AP *
2 Semesters
11 th – 12 th
Math Models with Applications **
2 Semesters
10 th – 12 th
Algebra 2
2 Semesters
10 th – 12 th
Algebra 2 Pre-AP *
2 Semesters
* May be substituted for regular level of that course.
Elective Courses Offered:
Grade
Course
Length
12 th
Pre College Math
2 Semesters
11 th – 12 th
Pre Calculus
2 Semesters
11 th – 12 th
Pre Calculus Pre-AP
2 Semesters
12 th
AB Calculus AP
2 Semesters
12 th
BC Calculus AP
2 Semesters
11 th – 12 th
Statistics AP
2 Semesters
12 th
Dual Credit College Algebra
1 Semester
12 th
Dual Credit Finite Math
1 Semester
Special Education Math:
Grade
Course
Length
9th – 12th
Algebra 1 Co -Teach
2 Semesters
9th – 12th
Algebra 1 SE
2 Semesters
10th – 12th
Math Models with Applications Co – Teach
2 Semesters
10th – 12th
Math Models with Applications SE
2 Semesters
10th – 12th
Geometry Co –Teach
2 Semesters
10th – 12th
Geometry SE
2 Semesters
Grading Policy:
The grading policy of the Mathematics Department follows the district standard:
Daily Grades .....40%
Major Grades ....60% (May include test, projects, portfolios, research papers, and other assessments.) |
Introduction to Probability with Texas Hold'em Examples illustrates both standard and advanced probability topics using the popular poker game of Texas Hold'em, rather than the typical balls in urns. The author uses students' natural interest in poker to teach important concepts in probability. …
Based on the authors' lecture notes, Introduction to the Theory of Statistical Inference presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book …
An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species …
Based on a highly popular, well-established course taught by the authors, Stochastic Processes: An Introduction, Second Edition discusses the modeling and analysis of random experiments using the theory of probability. It focuses on the way in which the results or outcomes of experiments vary and …
Updated to conform to Mathematica® 7.0, Introduction to Probability with Mathematica®, Second Edition continues to show students how to easily create simulations from templates and solve problems using Mathematica. It provides a real understanding of probabilistic modeling and the analysis of data …
This book covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems and contains an entire chapter devoted to complex measures, … |
Pre-Calculus 40S
Ready for a little math review?
Here's how it works:
No one is allowed to sit alone! Make sure you have at least one other person at the computer next to you.
You'll need some paper, a pencil, and an eraser. Try to avoid using your calculator as much as possible. Actually, you should try discussing the problem with your neighbour(s) before you pick up your calculator.
There are at least 10 multiple choice questions you must answer in each section. Read the question and click on what you belive to be the best answer.
If you get it wrong you'll also be given a hint as to what you did wrong. Think about what the computer tells you. You should recheck your calculations before making another choice.
You can ask for the teacher's help only if you ask the people sitting next to you for help first. |
Math 10
Statistics
Introduction to data analysis making use of graphical and numerical techniques. Topics covered include randomness, data collection, data presentation methods, discrete and continuous distributions and hypothesis testing. The course introduces applications in engineering, business, economics, medicine, education, the sciences, and other related fields. The use of technology will be required in certain applications.
Text: Collaborative Statistics, 2nd ed. by Illowsky and Dean
This text is available for purchase in hard copy at the De Anza College Bookstore or for free downloading at: You may download the text for free onto your computer and print out the pages you want. (Note: If you plan on printing the entire book, it is less expensive to purchase the hard copy at the Bookstore.) |
Synopsis
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks.
Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases.
The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject.
Presents the mathematical foundations of numerical analysis
Explains the mathematical details behind simulation software
Introduces many advanced concepts in modern analysis
Self-contained and mathematically rigorous
Contains problems and solutions in each chapter
Excellent follow-up course to Principles of Mathematical Analysis by Rudin |
Book Description: The premier book for alleviating math anxiety, Using and Understanding Mathematics helps readers develop the ability to reason with quantitative information, so they can be successful in using math in the rapidly changing work environment. It covers principles of reasoning, statistical reason, numbers in the real world, probability, and discrete mathematics. These topics are all presented in the context of real world situations from the social sciences, environmental issues, politics, economics, personal finance, art, and music. |
Mathematics of Finance Get Reviews, prices and save money on
Mathematics of Finance
An introduction to the study of financial mathematics in its own right or as a supplement to a business finance text, the second edition of this Australian text has been thoroughly revised and updated. It assumes minimal prerequisite knowledge.
An introduction to the study of financial mathematics in its own right or as a supplement to a business finance text, the second edition of this Australian text has been thoroughly revised & updated. It assumes minimal prerequisite knowledge Mathematics of Finance.
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£40.96Principles of Finance with Excel Ch. 1 Introduction to finance 3Ch. 2 Business organization & taxes 11Ch. 3 An accounting primer 29Ch. 4 Cash management with Excel 53Ch. 5 The time value of money 75Ch. 6 What does it cost? : applications of the time value of money 128Ch.
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Management of Finance A practical introduction to business finance for the non-specialist, this text covers: the format & interpretation of financial statements; costing, budgeting & project appraisal; & raising finance & the business plan. It also contains...
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Handbook of Finance (v. 3) Volume III Valuation, Financial Modeling, & Quantitative Tools contains the most comprehensive coverage of the analytical tools, risk measurement methods, & valuation techniques currently used in the field of finance. It details a variety of...
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Introduction To The Mathematics Of Finance Presents an elementary introduction to probability & mathematical finance. This book details discrete derivative pricing models, culminating in a derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein |
Features
Provides information in an accessible, easy to comprehend, self-study format
Facilitates the reader's understanding of the material and mastery of basic math
Presents information in a style that has been thoroughly tested and has proven successful
Summary
Accurately calculating medication dosages is a critical element in pharmaceutical care that directly affects optimal patient outcomes. Unfortunately, medication dosage errors happen in pharmacies, in hospitals, or even at home or in homecare settings everyday. In extreme cases, even minor dosage errors can have dire consequences. Careful calculations are essential to providing optimal medical and pharmaceutical care.
Essential Math and Calculations for Pharmacy Technicians fills the need for a basic reference that students and professionals can use to help them understand and perform accurate calculations. Organized in a natural progression from the basic to the complex, the book includes:
Roman and Arabic Numerals
Fractions and decimals
Ratios, proportions, and percentages
Systems of measurement including household conversions
Interpretation of medication orders
Isotonicity, pH, buffers, and reconstitutions
Intravenous flow rates
Insulin and Heparin products
Pediatric dosage
Business math
Packed with numerous solved examples and practice problems, the book presents the math in a step-by-step style that allows readers to quickly grasp concepts. The authors explain the fundamentals simply and clearly and include ample practice problems that help readers become proficient. The focus on critical thinking, real-life problem scenarios, and the self-test format make Essential Math and Calculations for Pharmacy Technicians an indispensable learning tool.
Table of Contents
Working with Roman and Arabic Numerals Using Fractions and Decimals in Pharmacy Math Using Ratios, Proportions and Percentages in Dosage Calculations Applying Systems of Measurements Interpreting Medication Orders Identifying Prescription Errors and Omissions Working with Liquid Dosage Forms Working with Solid Dosage Forms Adjusting Isotonicity Working with Buffer and Ionization Values Dealing with Reconstitutions Determining Milliequivalent Strengths Calculating Caloric Values Determining IV Flow Rates Working with Insulin and Heparin Products Appendices: A: Working with Temperature Conversions B: Working with Capsule Dosage Forms C: Dealing with Pediatric Dosages D: Understanding Essential Business Math
Editorial Reviews
"Calculations are explained in great detail in a logical fashion. The formulas are helpful and explained in several ways. The information is presented so that verification for accuracy is easily done. … Information provided in this text is more complete and detailed than in other math textbooks. I recommend this volume as a textbook or as a supplemental course book. Students could also benefit from Essential Math as a reference book. It should be a very valuable addition to their pharmacy technician library." - Ray Vellenga, Journal of Pharmacy Technology |
Table of Contents
1. Variables, Real Numbers, and Mathematical Models
1.1 Introduction to Algebra: Variables and Mathematical Models
1.2 Fractions in Algebra
1.3 The Real Numbers
1.4 Basic Rules of Algebra
Mid-Chapter Check Point Section 1.1–Section 1.4
1.5 Addition of Real Numbers
1.6 Subtraction of Real Numbers
1.7 Multiplication and Division of Real Numbers
1.8 Exponents and Order of Operations
Chapter 1 Group Project
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
2. Linear Equations and Inequalities in One Variable
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Solving Linear Equations
2.4 Formulas and Percents
Mid-Chapter Check Point Section 2.1–Section 2.4
2.5 An Introduction to Problem Solving
2.6 Problem Solving in Geometry
2.7 Solving Linear Inequalities
Chapter 2 Group Project
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Exercises (Chapters 1–2)
3. Linear Equations in Two Variables
3.1 Graphing Linear Equations in Two Variables
3.2 Graphing Linear Equations Using Intercepts
3.3 Slope
3.4 The Slope-Intercept Form of the Equation of a Line
Mid-Chapter Check Point Section 3.1–Section 3.4
3.5 The Point-Slope Form of the Equation of a Line
Chapter 3 Group Project
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Cumulative Review Exercises (Chapters 1–3)
4. Systems of Linear Equations
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by the Substitution Method
4.3 Solving Systems of Linear Equations by the Addition Method
Mid-Chapter Check Point Section 4.1–Section 4.3
4.4 Problem Solving Using Systems of Equations
4.5 Systems of Linear Equations in Three Variables
Chapter 4 Group Project
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Cumulative Review Exercises (Chapters 1–4)
5. Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.2 Multiplying Polynomials
5.3 Special Products
5.4 Polynomials in Several Variables
Mid-Chapter Check Point Section 5.1–Section 5.4
5.5 Dividing Polynomials
5.6 Long Division of Polynomials; Synthetic Division
5.7 Negative Exponents and Scientific Notation
Chapter 5 Group Project
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Cumulative Review Exercises (Chapters 1–5)
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring By Grouping
6.2 Factoring Trinomials Whose Leading Coefficient Is 1
6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1
Mid-Chapter Check Point Section 6.1–Section 6.3
6.4 Factoring Special Forms
6.5 A General Factoring Strategy
6.6 Solving Quadratic Equations By Factoring
Chapter 6 Group Project
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Cumulative Review Exercises (Chapters 1–6)
7. Rational Expressions
7.1 Rational Expressions and Their Simplification
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with the Same Denominator
7.4 Adding and Subtracting Rational Expressions with Different Denominators
Mid-Chapter Check Point Section 7.1–Section 7.4
7.5 Complex Rational Expressions
7.6 Solving Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Modeling Using Variation
Chapter 7 Group Project
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises (Chapters 1–7)
8. Basics of Functions
8.1 Introduction to Functions
8.2 Graphs of Functions
8.3 The Algebra of Functions
Mid-Chapter Check Point Section 8.1–Section 8.3
8.4 Composite and Inverse Functions
Chapter 8 Group Project
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises (Chapters 1–8)
9. Inequalities and Problem Solving
9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications
9.2 Compound Inequalities
9.3 Equations and Inequalities Involving Absolute Value
Mid-Chapter Check Point Section 9.1–Section 9.3
9.4 Linear Inequalities in Two Variables
Chapter 9 Group Project
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Cumulative Review Exercises (Chapters 1–9)
10. Radicals, Radical Functions, and Rational Exponents
10.1 Radical Expressions and Functions
10.2 Rational Exponents
10.3 Multiplying and Simplifying Radical Expressions
10.4 Adding, Subtracting, and Dividing Radical Expressions
Mid-Chapter Check Point Section 10.1–Section 10.4
10.5 Multiplying with More Than One Term and Rationalizing Denominators
10.6 Radical Equations
10.7 Complex Numbers
Chapter 10 Group Project
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Cumulative Review Exercises (Chapters 1–10)
11. Quadratic Equations and Functions
11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formulas
11.2 The Quadratic Formula
11.3 Quadratic Functions and Their Graphs
Mid-Chapter Check Point Section 11.1–Section 11.3
11.4 Equations Quadratic in Form
11.5 Polynomial and Rational Inequalities
Chapter 11 Group Project
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Test
Cumulative Review Exercises (Chapters 1–11)
12. Exponential and Logarithmic Functions
12.1 Exponential Functions
12.2 Logarithmic Functions
12.3 Properties of Logarithms
Mid-Chapter Check Point Section 12.1–Section 12.3
12.4 Exponential and Logarithmic Equations
12.5 Exponential Growth and Decay; Modeling Data
Chapter 12 Group Project
Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Test
Cumulative Review Exercises (Chapters 1–12)
13. Conic Sections and Systems of Nonlinear Equations
13.1 The Circle
13.2 The Ellipse
13.3 The Hyperbola
Mid-Chapter Check Point Section 13.1–Section 13.3
13.4 The Parabola; Identifying Conic Sections
13.5 Systems of Nonlinear Equations in Two Variables
Chapter 13 Group Project
Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Test
Cumulative Review Exercises (Chapters 1–13)
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences and Summation Notation
14.2 Arithmetic Sequences
14.3 Geometric Sequences and Series
Mid-Chapter Check Point Section 14.1–Section 14.3
14.4 The Binomial Theorem
Chapter 14 Group Project
Chapter 14 Summary
Chapter 14 Review Exercises
Chapter 14 Test
Cumulative Review Exercises (Chapters 1–14)
Appendices
A. Mean, Median, and Mode
B. Matrix Solutions to Linear Systems
C. Determinants and Cramer's Rule
D. Where Did That Come From? Selected Proof |
Product Synopsis
This textbook makes use of the popular computer program MATLAB as the major computer tool to study mechanics of composite materials. It is written specifically for students in engineering and materials science, examining step-by-step solutions of composite material mechanics problems using MATLAB. Each of the 12 chapters is well structured and includes a summary of the basic equations, MATLAB functions used in the chapter, solved examples and problems for students to solve. The main emphasis of Mechanics of Composite Materials with MATLAB is on learning the composite material mechanics computations and on understanding the underlying concepts. The solutions to most of the given problems appear in an appendix at the end of |
Mathematics and Statistics - NCEA Level 1
Qualifications:
• NCEA Level 1.
• You will need at least 10 credits at Level 1 Mathematics to qualify for the NCEA Level 1 Certificate.
• You will need at least 10 numeracy credits at Level 1 or higher to gain University Entrance.
• You will need 14 credits at Merit or above for a subject endorsement. (at least 3 internal and 3 external credits).
Students will be required to have a graphical calculator (These can be purchased through the school).
Entry:
• You have achieved Level 5B or better in all strands of the Year 10 Mathematics course.
• Graphics Calculator (recommended) or a Scientific Calculator.
Information:
• This course can lead onto the MAT201 AND MAS201 courses (see entry requirements below).
• This course is the basis for students wishing to continue studies in Mathematics to NCEA Level 2 and 3. It includes a variety of internal and external assessments. |
Studying to learn is different from studying for grades. Popular study techniques
often fail to produce adequate long-term learning.
Most students spend a majority of their study time on four activities:
highlight the text
read through the examples
try the exercises
copy solutions from the answer book
These activities involve no real commitment. Passive activities such as highlighting, reading, and
copying have little long-term benefits, and trying the exercises before copying solutions is only
minimally active. This kind of study leads to the common complaint, "I 'understood' everything,
but I didn't do well on the test."
People learn mathematics best by doing mathematics and then reflecting on what
they have done.
The words "doing" and "reflecting" imply activity on the part of the learner, rather than passivity.
DOING MATHEMATICS
"Doing" mathematics means reading and working problems actively.
Active reading is done as much with the hand as the eyes. Neatly list key
definitions, ideas, and results for each topic. Stop frequently to work out details and
to rework text examples.
Writing up a few exercises neatly is just as important as doing a lot of exercises.
When you don't understand something, work to frame a specific question. Then
seek help.
Active reading and careful writing of exercise solutions takes a long time, but it is what teachers
do when they prepare to teach a course for the first time, and it is a crucial learning activity.
REFLECTING ON WHAT HAS BEEN DONE
After learning a body of material, prepare a careful summary, as though you were
going to teach the material to others.
We never really know that we understand something until we have successfully written it down or
explained it to others. Often we think we understand an idea, but we find our written or spoken
explanation inadequate. The search for a better way to say something can lead to a better
understanding. |
MATH 1323 - Quantitative Reasoning
This course is designed for curricula where quantitative reasoning is required. The course content includes critical thinking skills, arithmetic and algebra concepts, statistical concepts, financial concepts, as well as numerical systems and applications. A graphing calculator is required. |
Book Description: Whether you're new to algebra or just looking for a refresher, Algebra Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with algebra essentials, this extensive guide covers all vital algebra skills, including combining like terms, solving quadratic equations, polynomials, and beyond. This proven study aid is completely revised with updated lessons and exercises that give students and workers alike the algebra skills they need to succeed. Algebra Success in 20 Minutes a Day also includes: Hundreds of practice exercises, including word problems Application of algebra skills to real-world (and real-work) problems A diagnostic pretest to help pinpoint strengths and weaknesses Targeted lessons with crucial, step-by-step practice in solving algebra problems A helpful posttest to measure progress after the lessons Glossary, additional resources, and tips for preparing for important standardized or certification tests
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Combinatorial And Computational Mathematics:
"Combinatorial and Computational Mathematics serves as an introduction to the current state of knowledge in various areas like Formal Languages, Applications of Fuzzy Set Theory, Combinatorial Problems, Fluid Mechanics, ect."--BOOK JACKET. |
The program called JKGRAPH is a Microsoft WINDOWS program for graphing and
analyzing graphs of various kinds of functions that students are likely to
encounter in a math class. It is also a useful tool for teachers to create
graphs that can be imported into WINDOWS word processing documents. The
math level ranges from precalculus through the first year of calculus. An
overview of the program's capabilities is included in this file following the
descriptions of the distributed files.
THE DISTRIBUTED FILES
=====================
The following describe the contents of the file JKGRAPH.ZIP which contains
the distribution files for the program named JKGRAPH.
Filename Description
----------- --------------------------------------------------------------
JKGRAPH.EXE This is the executable file that is the JKGRAPH program.
JKGRAPH.HLP This is the WINDOWS on-line help file for JKGRAPH.
JKGRAPH.ICO This is the icon file for the JKGRAPH program.
JKGTUT .WRI This is a tutorial file in Microsoft WRITE format.
HELP .TXT This is the text file you are now reading.
You should at least read the document file JKGTUT.WRI before running the
JKGRAPH program for the first time. In fact, it is best to simply print
the file JKGTUT.WRI so you can read from the paper copy while you view the
output on your computer screen. JKGTUT.WRI is a tutorial file that takes
you through the beginning steps of using the program. It is especially
useful for first-time users of the program. JKGTUT.WRI is in the Microsoft
WRITE format which is the word processor that accompanies WINDOWS 3.1. If
you have WINDOWS 95 you can also print this document using the program called
WORDPAD that replaces Microsoft WRITE. In fact, you should be able to import
the file JKGTUT.WRI into any word processor that imports Microsoft WRITE
files. Microsoft WORD for WINDOWS can also import this file.
Another source of information is the WINDOWS on-line help file for JKGRAPH.
This help file contains an overview of the program as well as detailed
sections on all the menu items and all the dialog boxes. It also has a list
of special topics.
JKGRAPH Version 1.0 is a fully functioning program except for the features
using WINDOWS Metafiles because Microsoft has changed the Metafile format to
a new format that is in WINDOWS 95 called Enhanced Metafiles. As soon as
this file format is fully supported in Borland's DELPHI compiler a newer
version of JKGRAPH will be released. The new version may not be available
until early 1996, but at least you can expect that enhanced metafiles will
be supported at some time in the future. The next version will probably also
be specifically written for WINDOWS 95.
JKGRAPH OVERVIEW
================
The program called JKGRAPH is used to graph and analyze 2-dimensional
function curves. By a function curve we mean any graph that can be made
using standard rectangular functions or polar function curves or any other
curve given in a parametric form. Thus we use the term function as a synonym
for any 2D curve that can be described using piecewise continuous formulas.
Curves such as ellipses, hyperbolas and cardioids may not be functions
according to the strict mathematical definition of a function. We allow an
x-coordinate to determine more than one y-coordinate. The next few paragraphs
outline the operations you can perform on various function curves and serve
as a summary of the capabilities of the JKGRAPH program.
JKGRAPH uses four distinct function groups which include standard rectangular
functions in the form Y=F(X), polar functions in the form R=F(@), parametric
functions in the form X=F(T) and Y=G(T), and polar parametrized functions in
the form R=F(T) and @=G(T). Note that we use the variable T for time in
parametric formulas. We also use the special character @ to represent any
angle associated with polar coordinates. Think of using @ for angles because
this is the ASCII character symbol that comes closest to matching any of the
Greek letters alpha, or phi, or theta that would normally be used to denote
angles.
The graphics features of JKGRAPH are quite general. You can view any
rectangular portion of the XY-plane and you can easily perform zooming
operations. You can control individual graph curve attributes which include
colors and line thickness. You can also select from among 8 different
background grids which include combinations of the standard XY-axes,
polar-coordinate axes, and an XY-lattice line-grid. All the background
elements may be scaled and colored to change their appearance. You can also
select colors for any filled region, including the entire graph background.
You can copy any graph to the clipboard in a color bitmap format in which you
specify both the size of the graph in inches and the resolution in terms of
the number of pixels per inch. Thus JKGRAPH can be used to make color graphs
that can be imported into other Windows applications. In particular, JKGRAPH
makes it a breeze to create graphs and other tables that can be incorporated
into the scientific word processor called EXP. This is one of the major
reasons why the author of JKGRAPH decided to write the program.
Within each function group you can work with two independent curves or you
can link the two curves and then perform special operations such as finding
points of intersection or integrating to find the area between two curves.
Once a curve (or curves) have been entered you can analyze the curves.
JKGRAPH provides four trace modes with the names Coordinate Trace Mode, Graph
Trace Mode, Tangent Line Trace Mode, and Normal Line Trace Mode. In each
mode you can drag the mouse cursor across the screen and dynamically see
graphic elements and other information related to the trace position.
JKGRAPH can also perform special animated actions on function curves.
Included are operations for automatically finding maxima and minima points on
a curve or automatically finding multiple intersection points between two
curves. These features operate on all four function groups including polar
and parametrized curves.
For ordinary Y=F(X) function curves you can apply either Newtons Method or
the Method of Successive Bisections to find the x-intercepts. Both of these
methods can show an animated action and can create tables of values that are
generated during the processes. The table information is easily copied to
the Windows clipboard
You can also apply several integration techniques to any curve. For
rectangular functions there are 11 different integration techniques which
include lower, upper and midpoint Riemann sums, the Trapezoid Rule, Simpson's
Rule, Gaussian Quadrature, the Romberg Algorithm, arc length and surface area
and volumes using either disks or washers or cylindrical shells. For polar
and parametric function types you can calculate areas and arc length.
JKGRAPH can also automatically graph the derivative or inverse of any
function curve. |
Math 6
(1 credit) Explores basic math concepts and their applications. Students will increase their skill with decimals, fractions, percents, and ratios. The course provides tools for problem solving and includes an introduction to algebra and geometry. Among the topics studied are discrete math and probability, surface area, equations, statistics, and data analysis. (36 lessons and submissions, 4 exams)
What People are Saying
"With EdOptions you just have a lot of possibilities" - Jacqui Clay, Educator (AZ) |
Beginning Algebra, 6th Edition
Description
Elayn Martin-Gay's developmental math program is based on her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her textbooks and print and media resources (available separately). With this revision, the Martin-Gay program has been enhanced with a new MyMathLab design (access kit available separately) that encourages students to use the text, video resources, and Student Organizer as an integrated learning system.
Table of Contents
1. Review of Real Numbers
1.1 Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Fractions and Mixed Numbers
1.4 Exponents, Order of Operations, Variable Expressions and Equations |
MATLAB for Engineers, 3e, is ideal for Freshman or Introductory courses in Engineering and Computer Science. With a hands-on approach and focus on problem solving, this introduction to the powerful MATLAB computing language is designed for students with only a basic college algebra background. Numerous examples are drawn from a range of engineering disciplines, demonstrating MATLAB's applications to a broad variety of problems. This book is included in Prentice Hall's ESource series. ESource allows professors to select the content appropriate for their freshman/first-year engineering course. Professors can adopt the published manuals as is or use ESource's website to view and select the chapters they need, in the sequence they want. The option to add their own material or copyrighted material from other publishers also exists.
You can earn a 5% commission by selling MATLAB for Engineers |
Role in Curriculum
First developmental-level math course for students who were not exempted from CUNY proficiency and failed both parts I and II of the COMPASS placement exam used to assess CUNY proficiency. MTH 020 with similar learning goals, is for students who have passed at least one part of the COMPASS placement exam. Students successfully passing both the COMPASS and the course content have similar options as those passing MTH 020.
Learning Goals and Assessment Plans
Learning Goal
Assessment
The student will understand lines, including solving linear equations, the concept of slope, the point-slope formula, and graphing of linesThe student will be familiar with applications involving percents, ratios and proportions.
Students will establish CUNY proficiency
The percentage of students passing each part of the COMPASS exam will be tracked |
Purpose
of the course
This course discusses both theoretical and
practical aspects of
numerical interpolation and approximation. Such techniques form the
core of Numerical Analysis and are the basis for solution of many
important problems. We review the relevant mathematical theory and show
how it can be used to construct practical algorithms. These
algorithms are implemented and tested in matlab.
Our focus is on applications to numerical differentiation and
integration of functions. However, we also review certain related
special topics such as Galerkin and wavelet approximation theory. |
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