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Open Textbooks for Mathematics

Active Calculus 2.0 by Matthew Boelkins; David Austin; Steven SchlickerISBN: 9781974206841
Publication Date: 2017
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 34 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. (From the publisher)

Algebra and Trigonometry by Jay AbramsonISBN: 9781947172104
Publication Date: 2015
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. (From the publisher)





Calculus Volume 1 by Gilbert Strang; Edwin "Jed" HermanISBN: 9781947172135
Publication Date: 2016
Calculus is designed for the typical two or threesemester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.
Please note that this title is published under a CC BYNCSA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license. (From the publisher)

Calculus Volume 2 by Gilbert Strang; Edwin "Jed" HermanISBN: 9781947172142
Publication Date: 2016
Calculus is designed for the typical two or threesemester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates..
Please note that this title is published under a CC BYNCSA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license. (From the publisher)

Calculus Volume 3 by Gilbert Strang; Edwin "Jed" HermanISBN: 9781947172166
Publication Date: 2016
Calculus is designed for the typical two or threesemester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and secondorder differential equations.
Please note that this title is published under a CC BYNCSA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license. (From the publisher)

College Algebra by Jay AbramsonISBN: 9781947172128
Publication Date: 2015
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. (From the publisher)



Combinatorics Through Guided Discovery by Kenneth Bogart; Mitchel Keller (Editor); Oscar Levin (Editor); Kent Morrison (Editor)Publication Date: 2004
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 consist 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.Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on.This book is released under an open source licence and is available in electronic form for free at http://bogart.openmathbooks.org/.

A First Course in Linear Algebra, Version 3.50 by Robert A. BeezerPublication Date: 20121201
An introduction to the basic concepts of linear algebra, along with an introduction to the techniques of formal mathematics. Numerous worked examples and exercises, along with precise statements of definitions and complete proofs of every theorem, make the text ideal for independent study.


Introduction to Mathematical Analysis I  Second Edition by Lafferriere, Beatriz; Gerardo Lafferriere; Nguyen Mau NamPublication Date: 2016
Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The lecture notes contain topics of real analysis usually covered in a 10week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many wellselected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of nondifferentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.
The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years.
In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).

Introduction to the Modeling and Analysis of Complex Systems by Sayama, HirokiISBN: 9781942341062
Publication Date: 2015
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many realworld systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technicallyoriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discretetime models, continuoustime models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agentbased models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.


Introductory Business Statistics by Alexander Holmes; Barbara Illowsky; Susan DeanISBN: 9781947172463
Publication Date: 2017
Introductory Business Statistics is designed to meet the scope and sequence requirements of the onesemester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and realworld experiences.

Introductory Statistics by Barbara Illowsky; Susan DeanISBN: 9781947172050
Publication Date: 20130919
Introductory Statistics follows scope and sequence requirements of a onesemester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs. (From the publisher)


Precalculus by Jay AbramsonISBN: 9781947172067
Publication Date: 20141023
Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one or twosemester collegelevel precalculus course. The content is organized by clearlydefined learning objectives and includes worked examples that demonstrate problemsolving approaches in an accessible way. (From the publisher)

Precalculus: An Investigation of Functions, 2nd Edition by David Lippman; Melonie RasmussenPublication Date: 2017
This is a free, open textbook covering a twoquarter precalculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.
The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisted more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.


A Spiral Workbook for Discrete Mathematics by Kwong, HarrisISBN: 9781942341161
Publication Date: 2015
This is a text that covers the standard topics in a sophomorelevel course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Handson exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problemsolving and writing skills.

Tea Time Numerical Analysis Experiences in Mathematics, 2nd Edition by Leon Q. BrinPublication Date: 2016
This textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics. The ultimate goal of Tea Time Numerical Analysis is to be a complete, onesemester, singlepdf, downloadable textbook designed for mathematics classes. (From the publisher)
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