# Mathematics

## A Computational Introduction to Number Theory and Algebra

Victor Shoup, New York University

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)

## A First Course in Linear Algebra

Robert Beezer, University of Puget Sound

*A First Course in Linear Algebra* is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.

(9 reviews)

## A First Course in Linear Algebra

Ken Kuttler, Brigham Young University

This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.

(6 reviews)

## A Gentle Introduction to the Art of Mathematics

Joseph Fields, Southern Connecticut State University

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.

(1 review)

## A Primer of Real Analysis

Dan Sloughter, Furman University

This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.

No ratings

(0 reviews)

## Abstract Algebra: Theory and Applications

Thomas Judson, Stephen F. Austin State University

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

(3 reviews)

## Active Calculus 2.0

Matt Boelkins, Grand Valley State University

David Austin, Grand Valley State University

Steve Schlicker, Grand Valley State University

*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.

(8 reviews)

## Active Calculus Multivariable

Steve Schlicker, Grand Valley State University

David Austin, Grand Valley State University

Matthew Boelkins, Grand Valley State University

*Active Calculus Multivariable* is the continuation of *Active Calculus *to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, 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; the exercises are few in number and challenging in nature.

No ratings

(0 reviews)

## Advanced High School Statistics First Edition

David Diez, Google/YouTube

Christopher Barr, Varadero Capital

Mine Çetinkaya-Rundel, Duke University

We hope readers will take away three ideas from this book in addition to forming a foundation

(1 review)

## Advanced Problems in Mathematics: Preparing for University

Stephen Siklos, Cambridge University

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.

No ratings

(0 reviews)

## Algebra and Trigonometry

*Algebra and Trigonometry *provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.*Algebra and Trigonometry *guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned.

(9 reviews)

## Algorithms and Data Structures With Applications to Graphics and Geometry

Jurg Nievergelt, ETH Zurich

Klaus Hinrichs, University of Muenster

An introductory coverage of algorithms and data structures with application to graphics and geometry.

(1 review)

## APEX Calculus

Gregory Hartman, Virginia Military Institute

Brian Heinold, Mount St. Mary’s University

Troy Siemers, Virginia Military Institute

Dimplekumar Chalishajar, Virginia Military Institute

Jennifer Bowen, The College of Wooster

This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 13. All three are available separately for free at www.vmi.edu/APEX.

(4 reviews)

## Applied Combinatorics

Mitchel Keller, Washington and Lee University

William Trotter, Georgia Institute of Technology

*Applied Combinatorics *is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics.

(2 reviews)

## Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell

Kenneth Levasseur, University of Massachusetts Lowell

In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked.

(2 reviews)

## Applied Finite Mathematics

Rupinder Sekhon, De Anza College Cupertino

*Applied Finite Mathematics *covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.

(1 review)

## Applied Probability

Paul Pfeiffer, Rice University

This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired.

No ratings

(0 reviews)

## Basic Analysis: Introduction to Real Analysis

Jirí Lebl, Oklahoma State University

This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.

(2 reviews)

## Book of Proof

Richard Hammack, Virginia Commonwealth University

This is a book about how to prove theorems.

(5 reviews)

## Calculo diferencial e integral

Marta Bonacina

Claudia Teti

Alejandra Haidar

Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.

No ratings

(0 reviews)

## Calculus

Gilbert Strang, MIT

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.

(2 reviews)

## Calculus for the Life Sciences: A Modeling Approach Volume 1

James Cornette, Iowa State University

Ralph Ackerman, Iowa State University

Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

No ratings

(0 reviews)

## Calculus for the Life Sciences: A Modeling Approach Volume 2

James Cornette, Iowa State University

Ralph Ackerman

Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

No ratings

(0 reviews)

## Calculus One

Multiple Authors, Mooculus

Calculus is about the very large, the very small, and how things change—the surprise is that something seemingly so abstract ends up explaining the real world.

No ratings

(0 reviews)

## Calculus Volume 1

Gilbert Strang, MIT

Edwin Herman, University of Wisconsin-Stevens Point

*Calculus* is designed for the typical two- or three-semester 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.

(8 reviews)

## Calculus Volume 2

Gilbert Strang, Massachusetts Institute of Technology

*Calculus *is designed for the typical two- or three-semester 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.

No ratings

(0 reviews)

## Calculus Volume 3

Gilbert Strang, Massachusetts Institute of Technology

*Calculus *is designed for the typical two- or three-semester 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 second-order differential equations.

No ratings

(0 reviews)

## Calculus: Early Transcendentals

David Guichard, Whitman College

*Calculus: Early Transcendentals*, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses.

(5 reviews)

## Collaborative Statistics

Barbara Illowsky, De Anza College

Susan Dean, De Anza College

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza Collegein Cupertino, California. The textbook was developed over several years and has been used in regularand honors-level classroom settings and in distance learning classes. Courses using this textbook have beenarticulated by the University of California for transfer of credit. The textbook contains full materials forcourse offerings, including expository text, examples, labs, homework, and projects. A Teacher's Guide iscurrently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections willmeet the Section 508 standards for accessibility.

(14 reviews)

## College Algebra

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

*College Algebra *is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely.

(9 reviews)

## College Algebra

*College Algebra *provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.*College Algebra*guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned.

(8 reviews)

## College Trigonometry

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

Covers chapters 10-11 ofPrecalculus.

(1 review)

## Combinatorics Through Guided Discovery

Kenneth Bogart, Dartmouth College

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)

## Discrete Mathematics: An Open Introduction

Oscar Levin, University of Northern Colorado

*Discrete Mathematics: An Open Introduction *is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

(2 reviews)

## Elementary Algebra

John Redden, College of the Sequoias

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.

(9 reviews)

## Elementary Algebra

Wade Ellis, West Valley Community College

Denny Burzynski, College of Southern Nevada

*Elementary Algebra* is a work text that covers the traditional topics studied in a modern elementary algebra course. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative skills.Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.

(1 review)

## Elementary Algebra

Lynn Marecek, Santa Ana College

MaryAnne Anthony-Smith, Santa Ana College

*Elementary Algebra* is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

No ratings

(0 reviews)

## Elementary College Geometry

Henry Africk, New York City College of Technology

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.

No ratings

(0 reviews)

## Elementary Differential Equations with Boundary Value Problems

William Trench, Trinity University

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

(2 reviews)

## Euclidean plane and its relatives

Anton Petrunin, Penn State

This book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.

(2 reviews)

## Fundamentals of Mathematics

Denny Burzynski, College of Southern Nevada

Wade Ellis, West Valley Community College

*Fundamentals of Mathematics* is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who:

(6 reviews)

## How We Got from There to Here: A Story of Real Analysis

Robert Rogers, State University of New York

Eugene Boman, The Pennsylvania State University

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

(2 reviews)

## Intermediate Algebra

John Redden, College of the Sequoias

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines.

(1 review)

## Intermediate Algebra

Lynn Marecek, Santa Ana College

Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester Intermediate algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

(1 review)

## Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students

Jason Lachniet, Wytheville Community College

This guide is heavy on linear algebra and makes a good supplement to a linear algebra textbook. But, it is assumed that any college student studying linear algebra will also be studying calculus and differential equations, maybe statistics. Therefore it makes sense to apply the Octave skills learned for linear algebra to these subjects as well. Chapters 3 and 5 have several applications to calculus, differential equations, and statistics. The overarching objective is to enhance our understanding of calculus and linear algebra using Octave as a tool for computations. For the most part, we will not address issues of accuracy and round-off error in machine arithmetic. For more details about numerical issues, refer to [1], which also contains many useful Octave examples.

No ratings

(0 reviews)

## Introduction to Mathematical Analysis I - Second Edition

Beatriz Lafferriere, Portland State University

Gerardo Lafferriere, Portland State University

Mau Nam Nguyen, Portland State University

Our goal with this textbook 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.

No ratings

(0 reviews)

## Introduction to Probability

Charles Grinstead, Swarthmore College

J. Laurie Snell, Dartmouth College

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continuedto influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting the risks of new medical treatments.

(5 reviews)

## Introduction to Real Analysis

William Trench, Trinity University

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)

## Introduction to Statistics

David Lane, Rice University

*Introduction to Statistics* is a resource for learning and teaching introductory statistics.

(5 reviews)

## Introductory Business Statistics

Thomas Tiemann, Elon University

The book "*Introductory Business Statistics*" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."

(2 reviews)

## Introductory Business Statistics

Lex Holmes, University of Oklahoma

Barbara Illowsky, De Anza College

Susan Dean, De Anza College

*Introductory Business Statistics* is designed to meet the scope and sequence requirements of the one-semester 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 real-world experiences.

(2 reviews)

## Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition

Mohammad Mahbobi, Thompson Rivers University

Thomas Tiemann, Elon University

*Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition *is an adaptation of Thomas K. Tiemann's book, *Introductory Business Statistics*. This new edition still contains the basic ideas behind statistics, such as populations, samples, the difference between data and information, and sampling distributions as well as information on descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. New topics include the chi-square test and categorical variables, null and alternative hypotheses for the test of independence, simple linear regression model, least squares method, coefficient of determination, confidence interval for the average of the dependent variable, and prediction interval for a specific value of the dependent variable.

(1 review)

## Introductory Statistics

Douglas Shafer, University of North Carolina

Zhiyi Zhang, University of North Carolina

In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level.

(8 reviews)

## Introductory Statistics

Multiple Authors, Openstax College

*Introductory Statistics* follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labs.

(15 reviews)

## Introductory Statistics with Randomization and Simulation First Edition

David Diez, Google/YouTube

Christopher Barr, Varadero Capital

Mine Çetinkaya-Rundel, Duke University

We hope readers will take away three ideas from this book in addition to forming a foundation of statistical thinking and methods.

(1 review)

## Learning Statistics with R: A tutorial for psychology students and other beginners

Danielle Navarro, University of New South Wales

*Learning Statistics with R* covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book.

No ratings

(0 reviews)

## Linear Algebra

Jim Hefferon, Saint Michael's College

This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges.

(3 reviews)

## Linear Algebra

David Cherney, UC Davis

Tom Denton, The Fields Institute and York University

Andrew Waldon, UC Davis

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)

## Linear Algebra with Applications

W. Keith Nicholson, University of Calgary

After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today's students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.

No ratings

(0 reviews)

## Linear Algebra, Theory And Applications

Kenneth Kuttler, Bringham Young University

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however.

(1 review)

## Linear Regression Using R: An Introduction to Data Modeling

David Lilja, University of Minnesota

*Linear Regression Using R: An Introduction to Data Modeling* presents one of the fundamental data modeling techniques in an informal tutorial style. Learn how to predict system outputs from measured data using a detailed step-by-step process to develop, train, and test reliable regression models. Key modeling and programming concepts are intuitively described using the R programming language. All of the necessary resources are freely available online.

(2 reviews)

## Math in Society

David Lippman, Pierce College

Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).

(5 reviews)

## Mathematical Reasoning: Writing and Proof, Version 2.1

Ted Sundstrom, Grand Valley State University

*Mathematical Reasoning: Writing and Proof*is designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students:

(1 review)

## My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition)

Jonathan Cornick, Queensborough Community College

Michael Guy, Queensborough Community College

Karan Puri

*My Math GPS: Elementary Algebra Guided Problem Solving* is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.

No ratings

(0 reviews)

## Notes on Diffy Qs: Differential Equations for Engineers

Jirí Lebl, Oklahoma State University

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.

(4 reviews)

## Open Logic Project

Richard Zach, University of Calgary

Andrew Arana, University of Paris

Jeremy Avigad, Carnegie Mellon University

Walter Dean, University of Warwick

Gillian Russell, University of North Carolina

Nicole Wyatt, University of Calgary

Audrey Yap, University of Victoria

The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous.

(1 review)

## OpenIntro Statistics

David Diez, Harvard School of Public Health

Christopher Barr, Harvard School of Public Health

Mine Cetinkaya-Rundel, Duke University

*OpenIntro Statistics 3rd Edition* strives to be a complete introductory textbook of the highest caliber. Its core derives from the classic notions of statistics education and is extended by recent innovations. The textbook meets high quality standards and has been used at Princeton, Vanderbilt, UMass Amherst, and many other schools. We look forward to expanding the reach of the project and working with teachers from all colleges and schools. The chapters of this book are as follows:

(11 reviews)

## Ordinary Differential Equations

Stephen Wiggins, University of Bristol

This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take.

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(0 reviews)

## Prealgebra

Multiple Authors, Openstax College

*Prealgebra *is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on. The organization makes it easy to adapt the book to suit a variety of course syllabi.

(12 reviews)

## Precalculus

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.

(1 review)

## Precalculus

Multiple Authors, Openstax College

*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.

(3 reviews)

## Precalculus

Thomas Tradler, NYC College of Technology

Holly Carley, NYC College of Technology

These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems.

This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses are revisited under this new function theoretic point of view. However, in order to keep this text as self contained as possible we always recall all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions with the function viewpoint. Throughout, we will always place particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the TI-84 calculator as mentioned above. These are in fact the topics of the first four (of the five) parts of this precalculus course.

In the fifth and last part of the book, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a discussion of the algebra of complex numbers (in particular complex numbers in polar form), the 2-dimensional real vector space R 2 sequences and series with focus on the arithmetic and geometric series (which are again examples of functions, though this is not emphasized), and finally the generalized binomial theorem.

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(0 reviews)

## Precalculus: An Investigation of Functions

David Lippman, Pierce College

Melonie Rasmussen, Pierce College

*Precalculus: An Investigation of Functions* is a free, open textbook covering a two-quarter pre-calculus 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.

(3 reviews)

## Proofs and Concepts: The Fundamentals of Abstract Mathematics

Dave Morris, University of Lethbridge

Joy Morris, University of Lethbridge

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.

(3 reviews)

## Spiral Workbook for Discrete Mathematics

Harris Kwong, State University of New York (SUNY) Fredonia

This is a text that covers the standard topics in a sophomore-level 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. Hands-on 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' problem-solving and writing skills.

(2 reviews)

## Statistical Inference For Everyone

Brian Blais, Bryant University

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.

(1 review)

## Trigonometry

Ted Sundstrom, Grand Valley State University

Steven Schlicker, Grand Valley State University

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.

(1 review)

## Vector Calculus

Michael Corral, Schoolcraft College

This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

No ratings

(0 reviews)

## Whitman Calculus

David Guichard, Whitman College

An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available.

(6 reviews)

## Yet Another Calculus Text

Dan Sloughter, Furman University

I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals.

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(0 reviews)