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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.

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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.

(2 reviews)

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.

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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 Business Math: A Step-by-Step Handbook

Business Math: A Step-by-Step Handbook

Jean-Paul Olivier

Business math is the study of mathematics required by the field of business. Business professionals will work with taxes, gross earnings, product prices, and currency exchange; they will be offered loans, lines of credit, mortgages, leases, savings bonds, and other financial tools. This textbook covers all of these topics and how these financial tools can maximize their earnings and minimize their costs. It also discusses how to execute smart monetary decisions both personally and for their business.

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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.

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