An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that text.

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.
Applied Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom’s MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book’s source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book.

Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics.

The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.

To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.

Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

An Instructor's Guide is available to any instructor who uses the text.

Best open source book in Discrete Math. Covers all the subjects in a standard Discrete Math class for mathematics or computer science students and contains sage cells for all subjects. Set Theory, Combinatorics, Logic, Relations, Recursion, Graph Theory, Trees, Algebraic Structures, Boolean Algebras, Automata, etc. Originally published commercially, its original text was peer-reviewed and was adopted for use at several universities throughout the country. Now in its open source version, has the same quality but it is free.

This applied mathematics textbook covers Matrices and Pathways, Statistics and Probability, Finance, Cyclic, Recursive and Fractal Patterns, Vectors, and Design. The approach used is primarily data driven, using numerical and geometrical problem-solving techniques.

The primary learning objective of this textbook is to introduce the reader to the fundamental statistical methods and basic analytical procedures associated with processing data in regard to healthcare research. It is intended that by working through the applications and practice problems, readers should be able to understand and apply some of the methods for developing, implementing, and applying healthcare statistic principles in research.

Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment. The book can be used in conjunction with WeBWork for homework (online) or with the Arithmetic | Algebra Homework handbook (traditional). The content in the book, WeBWork and the homework handbook are also aligned to prepare students for the CUNY Elementary Algebra Final Exam (CEAFE).

Arithmetic | Algebra Homework book is a static version of the WeBWork online homework assignments that accompany the textbook Arithmetic | Algebra for the developmental math courses MAT 0630 and MAT 0650 at New York City College of Technology, CUNY.

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.
The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution.

Christopher Hammond, Professor of Mathematics at Connecticut College, published The Art of Analysis, an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply a special case of integrability, with particular properties that are worth noting. This point of view has implications for the treatment of other topics, particularly continuity and differentiability.

Word Count: 10612

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Chapter 1. Concepts
Chapter 2. Linear Equations
Chapter 3. Graphing
Chapter 4. Linear Systems
Chapter 5. Polynomial Equations
Chapter 6. Factoring Polynomials
Chapter 7. Rational Expressions
Chapter 8. Radicals
Chapter 9. Quadratic Equations

This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.

Short Description:
This book provides a brief introduction to some common ideas in the study of probability. At the University of Minnesota, this material is included in a course on College Algebra designed to give students the basic skills to take an introductory Statistics course. The material itself is basic, and should be within the grasp of students who have successfully completed a high school Algebra I course.

Word Count: 1827

ISBN: 978-1-946135-79-7

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Short Description:
This textbook is aligned with the British Columbia Adult Basic Education learning outcomes for Mathematics: Intermediate Level Algebra. The textbook introduces the fundamental concepts of algebra, geometry, and trigonometry 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.

Long Description:
This textbook is the first part of three texts that are aligned with the British Columbia Adult Basic Education learning outcomes for Mathematics: Intermediate Level Algebra. The textbook focuses on a review of basic arithmetic 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.

Word Count: 42219

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An unintimidating guide to basic hypothesis testing logic for beginners

Word Count: 45834

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This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

This book is used in Reach Higher, Oklahoma's adult degree completion program, for a course called Data Analysis & Interpretation. It provides basic statistics that can be used for organizational data analysis by individuals with managerial professional goals, while also teaching essential skills from Microsoft Excel commonly needed for data analysis. This book uses material from Lumen Learning's Boundless Statistics (Boundless Learning) and Excel for Decision Making from University of Houston Libraries (multiple authors).

This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems. For a more traditional text designed for classroom use, see Fundamentals of Calculus (http://www.lightandmatter.com/fund/). The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.

This is an online textbook for a one semester calculus course aimed at business students.
The material covered is fairly standard: differentiation and integration without trigonometry, partial derivatives and optimization of functions of several variables.
There are several characteristics that differentiate the text from other texts:
Excel is used as the main computational engine throughout the text and the needed Excel skills are taught rather than assumed.
Examples, exercises, and vocabulary are tailored to uses in a business curriculum.
There is a modeling thread throughout the text.
Webwork versions of exercises are available on request.