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Mind, Body, World: Foundations of Cognitive Science

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.

(6 reviews)

Open Data Structures: An Introduction

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)

Contract Doctrine, Theory & Practice Volume 3

Contributor: Verkerke

Publisher: CALI's eLangdell® Press

License: CC BY-SA

This is Volume 3 in a three volume series written for Contracts Law. Its former title is "Collaborative Teaching Materials for Contracts."

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(0 reviews)

Elementary Differential Equations with Boundary Value Problems

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)

Introduction to Real Analysis

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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(0 reviews)

Precalculus

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:

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(0 reviews)

A Gentle Introduction to the Art of Mathematics

Contributor: Fields

Publisher: A.T. Still University

License: Free Documentation License (GNU)

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.

(2 reviews)

Active Calculus 2.0

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)

Combinatorics Through Guided Discovery

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)

A Computational Introduction to Number Theory and Algebra

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)