# Search Results: Mathematics & Statistics

Victor Shoup, New York University

This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory.

(0 reviews)

Robert A. 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.

(2 reviews)

Ken Kuttler

*Linear Algebra: A First Course* presents an introduction to the fascinating subject of linear algebra. As the title suggests, this text is designed as a first course in linear algebra for students who have a reasonable understanding of basic algebra. Major topics of linear algebra are presented in detail, with proofs of important theorems provided. Connections to additional topics covered in advanced courses are introduced, in an effort to assist those students who are interested in continuing on in linear algebra.

(1 review)

Joseph E. 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.

(1 review)

Thomas W. 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.

(0 reviews)

David Austin, Grand Valley State University

Matt Boelkins, Grand Valley State University

Steve Schlicker, Grand Valley State University

In Active Calculus, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore.

(1 review)

Brian Heinold, Mount Saint Mary’s University

Dimplekumar Chalishajar, Virginia Military Institute

Gregory Hartman, Virginia Military Institute

Troy Siemers, Virginia Military Institute

APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

(0 reviews)

Alan Doerr, University of Massachusetts Lowell

Kenneth Levasseur, University of Massachusetts Lowell

As a general description one could say that discrete mathematics is the mathematics that deals with "separated" or discrete sets of objects rather than with continuous sets such as the real line.

(0 reviews)

Jirí Lebl

This free online textbook (e-book in webspeak) is a one semester course in basic analysis.

(0 reviews)

Dr. Richard Hammack, Virginia Commonwealth Univ.

*Book of Proof* is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

(1 review)

Gilbert Strang, MIT

Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a straightforward introductory calculus textbook available free online to educators and self-learners alike. It is covers single variable and multivariable calculus, including applications.

(0 reviews)

James L. Cornette, Iowa State University

Ralph A. Ackerman, Iowa State University

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus. The book contains data from experiments, but does not require that students do laboratory experiments.

(0 reviews)

James L. Cornette, Iowa State University

Ralph A. Ackerman

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus. The book contains data from experiments, but does not require that students do laboratory experiments.

(0 reviews)

Multiple Authors, Mooculus

This text is based on David Guichard’s open-source calculus text which in turn is a modification and expansion of notes written by Neal Koblitz at the University of Washington.

(0 reviews)

Susan Dean, De Anza College

Dr. Barbara Illowsky, De Anza College

*Collaborative Statistics* was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.

(4 reviews)

Dr. Carl Stitz, Lakeland Community College

Dr. 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.

(7 reviews)

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

Covers chapters 10-11 of Precalculus.

(1 review)

Kenneth P. Bogart

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.

(1 review)

John Redden, College of the Sequoias

*Elementary Algebra*, is an introductory text that focuses on the study of algebra at the beginning stages. It assumes no prior algebraic experience and is intended for any student who needs build a strong algebraic foundation. The book presents real world applications, setting a foundation for students to translate problems described in words into mathematical equations. The book illustrates the steps required to solve equations and interpret the results through the use of exercise sets and practice problems. The book stresses both the importance to solve problems correctly, and to learn to communicate those solutions to others.

(3 reviews)

William F. 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.

(0 reviews)

Denny Burzynski

Wade Ellis

*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.

(0 reviews)

Eugene Boman, The Pennsylvania State University

Robert Rogers, State University of New York

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context.

(1 review)

John Redden, College of the Sequoias

Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines.

(0 reviews)

Dr. Charles M. Grinstead, Swarthmore College

Dr. J. Laurie Snell, Dartmouth College

This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a ?rm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.

(0 reviews)

William F. Trench, Trinity University

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics 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.

(0 reviews)

Douglas S. Shafer, University of North Carolina

Zhiyi Zhang, University of North Carolina

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.

(3 reviews)

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.

(5 reviews)

Dr 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.

(1 review)

Andrew Waldon

David Cherney

Tom Denton

This book is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors.

(0 reviews)

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.

(0 reviews)

David Lippman

*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.

(0 reviews)

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.

(0 reviews)

Jirí Lebl, Oklahoma State University

A one semester first course on differential equations, aimed at engineering students.

(0 reviews)

Christopher D. Barr, Harvard School of Public Health

David M. Diez, Harvard School of Public Health

Mine Cetinkaya-Rundel, Duke University

Our inaugural effort is *OpenIntro Statistics*. First and foremost, *OpenIntro Statistics* 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 Harvard, Princeton, and many other schools. We look forward to expanding the reach of the project and working with teachers from all colleges and schools.

(3 reviews)

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

College Algebra & Trigonometry

(1 review)

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.

(0 reviews)

David Lippman

Melonie Rasmussen

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

(1 review)

David Guichard

The original version of the text was written by David Guichard. The single variable material is a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original. The text also includes some exercises and examples from Elementary Calculus: An Approach Using Infinitesimals, by H. Jerome Keisler under a Creative Commons license. In addition, the chapter on differential equations and the section on numerical integration are largely derived from the corresponding portions of Keisler’s book. Albert Schueller, Barry Balof, and Mike Wills have also contributed additional material..

(0 reviews)

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.

(0 reviews)

Dr 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)