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Read more about Combinatorics Through Guided Discovery

Combinatorics Through Guided Discovery

Copyright Year: 2004

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 A Computational Introduction to Number Theory and Algebra

A Computational Introduction to Number Theory and Algebra

Copyright Year: 2009

Contributor: Shoup

Publisher: Cambridge University Press

License: CC BY-NC-ND

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

(3 reviews)

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Read more about Linear Algebra

Linear Algebra

Copyright Year: 2016

Contributors: Cherney, Denton, and Waldon

Publisher: University of California, Davis

License: CC BY-NC-SA

We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.

(2 reviews)

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Read more about Information Systems for Business and Beyond

Information Systems for Business and Beyond

Copyright Year: 2014

Contributors: Bourgeois, Smith, Wang, and Mortati

Publisher: Saylor Foundation

License: CC BY-NC

This book is written as an introductory text, meant for those with little or no experience with computers or information systems. While sometimes the descriptions can get a little bit technical, every effort has been made to convey the information essential to understanding a topic while not getting bogged down in detailed terminology or esoteric discussions.

(18 reviews)

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Read more about Principles of Sociological Inquiry – Qualitative and Quantitative Methods

Principles of Sociological Inquiry – Qualitative and Quantitative Methods

Copyright Year: 2012

Contributor: Blackstone

Publisher: Saylor Foundation

License: CC BY-NC-SA

The author of Principles of Sociological Inquiry: Qualitative and Quantitative Methods, Amy Blackstone, started envisioning this textbook while sitting in her own undergraduate sociology research methods class. She enjoyed the material but wondered about its relevance to her everyday life and future plans (the idea that one day she would be teaching such a class hadn't yet occurred to her).

(28 reviews)

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Read more about Small Business Management in the 21st Century

Small Business Management in the 21st Century

Copyright Year: 2012

Contributors: Cadden and Lueder

Publisher: Saylor Foundation

License: CC BY-NC-SA

Small Business Management in the 21st Century offers a unique perspective and set of capabilities for instructors. The authors designed this book with a “less can be more” approach, and by treating small business management as a practical human activity rather than as an abstract theoretical concept.

(5 reviews)

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Read more about Social Problems: Continuity and Change

Social Problems: Continuity and Change

Copyright Year: 2016

Publisher: Saylor Foundation

License: CC BY-NC-SA

Social Problems: Continuity and Change is a realistic but motivating look at the many issues that are facing our society today. As this book's subtitle, Continuity and Change, implies, social problems are persistent, but they have also improved in the past and can be improved in the present and future, provided that our nation has the wisdom and will to address them.

(43 reviews)

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Read more about The Sustainable Business Case Book

The Sustainable Business Case Book

Copyright Year: 2012

Contributors: Gittell, Magnusson, and Merenda

Publisher: Saylor Foundation

License: CC BY-NC-SA

The issue of sustainability and specifically sustainable business is of increasing interest and importance to students of business and also students in the sciences, government, public policy, planning and other fields. There can be significant benefits from students learning about sustainable business from the rich experiences of business practice.

(4 reviews)

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Read more about Understanding Media and Culture: An Introduction to Mass Communication

Understanding Media and Culture: An Introduction to Mass Communication

Copyright Year: 2016

Publisher: University of Minnesota Libraries Publishing

License: CC BY-NC-SA

According to the author, the world did not need another introductory text in mass communication. But the world did need another kind of introductory text in mass communication, and that is how Understanding Media and Culture: An Introduction to Mass Communication was birthed.

(32 reviews)

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Read more about Programming Fundamentals - A Modular Structured Approach using C++

Programming Fundamentals - A Modular Structured Approach using C++

Copyright Year: 2013

Contributor: Busbee

Publisher: OpenStax CNX

License: CC BY

Programming Fundamentals - A Modular Structured Approach using C++ is written by Kenneth Leroy Busbee, a faculty member at Houston Community College in Houston, Texas. The materials used in this textbook/collection were developed by the author and others as independent modules for publication within the Connexions environment. Programming fundamentals are often divided into three college courses: Modular/Structured, Object Oriented and Data Structures. This textbook/collection covers the first of those three courses.

(8 reviews)

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