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    Read more about Combinatorics Through Guided Discovery

    Combinatorics Through Guided Discovery

    Copyright Year:

    Contributor: Bogart

    Publisher: Kenneth P. Bogart

    License: Free Documentation License (GNU)

    This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn't get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you've hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.

    (2 reviews)

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    Read more about Introduction to Real Analysis

    Introduction to Real Analysis

    Copyright Year:

    Contributor: Trench

    Publisher: A.T. Still University

    License: CC BY-NC-SA

    This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

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    Read more about Applied Discrete Structures

    Applied Discrete Structures

    Copyright Year:

    Contributors: Doerr and Levasseur

    Publisher: Alan Doerr & Kenneth Levasseur

    License: CC BY-NC-SA

    In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked.

    (3 reviews)

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    Read more about Introductory Statistics

    Introductory Statistics

    Copyright Year:

    Contributors: Shafer and Zhang

    Publisher: Saylor Foundation

    License: CC BY-NC-SA

    In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level.

    (10 reviews)

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    Read more about Basic Analysis: Introduction to Real Analysis

    Basic Analysis: Introduction to Real Analysis

    Copyright Year:

    Contributor: Lebl

    Publisher: Jirí Lebl

    License: CC BY-NC-SA

    This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.

    (3 reviews)

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    Read more about OpenIntro Statistics - Fourth Edition

    OpenIntro Statistics - Fourth Edition

    Copyright Year:

    Contributors: Diez, Barr, and Cetinkaya-Rundel

    Publisher: OpenIntro

    License: CC BY-SA

    OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to applied

    (21 reviews)

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    Read more about Introduction to Probability

    Introduction to Probability

    Copyright Year:

    Contributors: Grinstead and Snell

    Publisher: American Mathematical Society

    License: Free Documentation License (GNU)

    Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continuedto influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting the risks of new medical treatments.

    (6 reviews)

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    Read more about Collaborative Statistics

    Collaborative Statistics

    Copyright Year:

    Contributors: Illowsky and Dean

    Publisher: OpenStax CNX

    License: CC BY

    Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza Collegein Cupertino, California. The textbook was developed over several years and has been used in regularand honors-level classroom settings and in distance learning classes. Courses using this textbook have beenarticulated by the University of California for transfer of credit. The textbook contains full materials forcourse offerings, including expository text, examples, labs, homework, and projects. A Teacher's Guide iscurrently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections willmeet the Section 508 standards for accessibility.

    (18 reviews)

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