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## 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)

## 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.

(1 review)

## Active Calculus 2.0

Copyright Year: 2017

Contributors: Boelkins, Austin, and Schlicker

Publisher: Grand Valley State University

License: CC BY-NC-SA

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.

(13 reviews)

## Precalculus

Copyright Year: 2016

Contributors: Collingwood, Prince, and Conroy

Publisher: A.T. Still University

License: Free Documentation License (GNU)

Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

No ratings

(0 reviews)

## Introduction to Real Analysis

Copyright Year: 2013

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.

No ratings

(0 reviews)

## Elementary Differential Equations with Boundary Value Problems

Copyright Year: 2013

Contributor: Trench

Publisher: A.T. Still University

License: CC BY-NC-SA

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

(9 reviews)

## Open Data Structures: An Introduction

Copyright Year: 2013

Contributor: Morin

Publisher: Athabasca University Press

License: CC BY-NC-ND

Offered as an introduction to the field of data structures and algorithms, Open Data Structures covers the implementation and analysis of data structures for sequences (lists), queues, priority queues, unordered dictionaries, ordered dictionaries, and graphs. Focusing on a mathematically rigorous approach that is fast, practical, and efficient, Morin clearly and briskly presents instruction along with source code.

(3 reviews)

## Mind, Body, World: Foundations of Cognitive Science

Copyright Year: 2013

Contributor: Dawson

Publisher: Athabasca University Press

License: CC BY-NC-ND

Cognitive science arose in the 1950s when it became apparent that a number of disciplines, including psychology, computer science, linguistics, and philosophy, were fragmenting. Perhaps owing to the field's immediate origins in cybernetics, as well as to the foundational assumption that cognition is information processing, cognitive science initially seemed more unified than psychology. However, as a result of differing interpretations of the foundational assumption and dramatically divergent views of the meaning of the term information processing, three separate schools emerged: classical cognitive science, connectionist cognitive science, and embodied cognitive science.

(7 reviews)

## Concepts of Biology

Copyright Year: 2013

Contributors: Fowler, Roush, and Wise

Publisher: OpenStax

License: CC BY

Concepts of Biology is designed for the introductory biology course for nonmajors taught at most two- and four-year colleges. The scope, sequence, and level of the program are designed to match typical course syllabi in the market. Concepts of Biology includes interesting applications, features a rich art program, and conveys the major themes of biology.

(57 reviews)

## Biology - 2e

Copyright Year: 2018

Contributors: Clark, Choi, and Douglas

Publisher: OpenStax

License: CC BY

Biology 2e is designed to cover the scope and sequence requirements of a typical two-semester biology course for science majors. The text provides comprehensive coverage of foundational research and core biology concepts through an evolutionary lens. Biology includes rich features that engage students in scientific inquiry, highlight careers in the biological sciences, and offer everyday applications. The book also includes various types of practice and homework questions that help students understand—and apply—key concepts.

(69 reviews)