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    Read more about Precalculus

    Precalculus

    Copyright Year:

    Contributors: Abramson, Falduto, and Grosss

    Publisher: OpenStax

    License: CC BY

    Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing College Algebra and Algebra and Trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses.

    (7 reviews)

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    Read more about Liberté

    Liberté

    Copyright Year:

    Contributor: Angelo

    Publisher: Gretchen V. Angelo

    License: CC BY-NC-SA

    This French book is aimed at a first-year college student. Its features include:

    (10 reviews)

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    Read more about Linear Algebra

    Linear Algebra

    Copyright Year:

    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 A Computational Introduction to Number Theory and Algebra

    A Computational Introduction to Number Theory and Algebra

    Copyright Year:

    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 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 Active Calculus 2.0

    Active Calculus 2.0

    Copyright Year:

    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)

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    Read more about A Gentle Introduction to the Art of Mathematics

    A Gentle Introduction to the Art of Mathematics

    Copyright Year:

    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)

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    Read more about Precalculus

    Precalculus

    Copyright Year:

    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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    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 Elementary Differential Equations with Boundary Value Problems

    Elementary Differential Equations with Boundary Value Problems

    Copyright Year:

    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)

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