Library Home


Mathematics - Applied

Read more about A Computational Introduction to Number Theory and Algebra

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)

Read more about A Primer of Real Analysis

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)

Read more about Advanced High School Statistics First Edition

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)

Read more about Applied Combinatorics

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.

(1 review)

Read more about Applied Discrete Structures

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)

Read more about Applied Finite Mathematics

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)

Read more about Applied Probability

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)

Read more about Basic Analysis: Introduction to Real Analysis

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)

Read more about Calculo diferencial e integral

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)

Read more about Collaborative Statistics

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)

Read more about Combinatorics Through Guided Discovery

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)

Read more about Introduction to Mathematical Analysis I - Second Edition

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)

Read more about Introduction to Probability

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)

Read more about Introduction to Real Analysis

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)

Read more about Introduction to Statistics

Introduction to Statistics

David Lane, Rice University


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

(5 reviews)

Read more about Introductory Business Statistics

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)

Read more about Introductory Business Statistics

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)

Read more about Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition

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)

Read more about Introductory Statistics

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)

Read more about Introductory Statistics

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)

Read more about Introductory Statistics with Randomization and Simulation First Edition

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)

Read more about Learning Statistics with R: A tutorial for psychology students and other beginners

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)

Read more about Linear Algebra with Applications

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)

Read more about OpenIntro Statistics

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)

Read more about Statistical Inference For Everyone

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)