This week we will examine the concept of a function, a fundamental concept underlying all of modern mathematics. You’re undoubtedly already familiar with functions in an intuitive sense: a function is something which, given

an input, produces an output. But you’ve probably never seen the formal definition of a function as it relates to set theory, which is what we’ll look at this week.

# Mathematics (Faculty Reviewed)

Course materials in this collection have been mapped to VCCS Mathematics Transfer Courses and reviewed by Virginia faculty. Filter by Course Alignments to find OER specific to your course.

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.

- Subject:
- Algebra
- Material Type:
- Textbook
- Provider:
- University of Puget Sound
- Author:
- Thomas Judson
- Date Added:
- 01/01/2016

Active Prelude to Calculus is designed as a college-level preparatory text for students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. In particular, the text is intended as an appropriate prerequisite base for students who will go on to study from Active Calculus while also encouraging and promoting an active learning approach. The HTML version of the text includes about 150 anonymous, interactive exercises; static versions of those problems are included in PDF and print. In addition, the text offers about 120 activities designed for student engagement in and out of class.

There are links to interactive Desmos activities, interactive applets, and even some interactive Javascript graphics embedded in the text. These features are best accessed in HTML. In addition, all of the graphics are full-color in the electronic versions. To keep costs low, the bound, print version for sale on Amazon is in black and white.

Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes its importance in calculus. The reader will find that the text requires them to engage actively with the material, to view topics from multiple perspectives, and to develop a deep conceptual understanding of ideas. Many courses at the high school and college level with titles such as college algebra, precalculus, and trigonometry serve other disciplines and prepare students for courses other than calculus. As such, these prerequisite classes frequently contain wide-ranging material that, while mathematically interesting and important, isn't necessary for calculus. Perhaps because of these additional topics, certain ideas that are essential in calculus can be under-emphasized or ignored. In Active Prelude to Calculus, one of our top goals is to keep the focus narrow on the following most important ideas. See more about the motivating forces behind the text in the Our Goals section of the text's preface. Students who will use the text are especially encouraged to read the Students! Read This! section of the preface.

Instructors are strongly encouraged to have their students use the Activities Workbook. This workbook is simply a PDF document that has a single activity per page along with room for students to record their work and thinking. Instructors can provide students with the PDF, have their bookstore or copy center create coursepacks for students to purchase for a small fee, or purchase a bound workbook directly from Amazon. To acquire a PDF copy of the Activities Workbook, please contact the author directly: boelkinm at gvsu dot edu.

Active Prelude to Calculus was first made publicly available in January 2019. The text is free and open-source; the source code can be found on GitHub.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Textbook
- Author:
- Matthew Boelkins
- Date Added:
- 12/02/2021

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

- Subject:
- Algebra
- Trigonometry
- Material Type:
- Textbook
- Provider:
- Rice University
- Provider Set:
- OpenStax College
- Author:
- David Lippman
- Jay Abramson
- Jean-Marie Magnier
- Melonie Rasmussen
- Nicholas Belloit
- Rachael Gross
- Rick Norwood
- Valeree Falduto
- Date Added:
- 01/29/2015

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 Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

- Subject:
- Calculus
- Material Type:
- Full Course
- Textbook
- Provider:
- Lumen Learning
- Provider Set:
- Candela Courseware
- Author:
- Dale Hoffman
- David Lippman
- Shana Calaway
- Date Added:
- 06/13/2019

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.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- Al Doerr
- Ken Levasseurr
- Date Added:
- 01/01/2017

The text covered a comprehensive extent of topics; ranging from introductory topics of linear equations to more advanced topics such as Game Theory.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- About The Contributors
- De Anza College Cupertino
- Rupinder Sekhon
- Date Added:
- 05/10/2020

This is a "first course" in the sense that it presumes no previous course in probability. The units are modules taken from the unpublished text: Paul E. Pfeiffer, ELEMENTS OF APPLIED PROBABILITY, USING MATLAB. The units are numbered as they appear in the text, although of course they may be used in any desired order. For those who wish to use the order of the text, an outline is provided, with indication of which modules contain the material.

- Subject:
- Statistics and Probability
- Material Type:
- Full Course
- Provider:
- Rice University
- Provider Set:
- OpenStax CNX
- Author:
- Paul E. Pfeiffer
- Date Added:
- 09/18/2009

This text is an adaptation of two very excellent open-source textbooks: Active Calculus by Dr. Matt Boelkins and APEX Calculus by Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen. Topics include integrals, volume, arcs, density, physics applications, differential equations, and hyperbolic functions.

Table of Contents:

1. Using Definite Integrals to Find Volume

2. Volume by The Shell Method

3. Arc Length and Surface Area

4. Density, Mass, and Center of Mass

5. Physics Applications: Work, Force, and Pressure

6. An Introduction to Differential Equations

7. Separable differential equations

8. Hyperbolic Functions

This text pulls in portions from Precalculus, Math in Society, and other open textbooks,

and adapts them to have the business focus desired for business precalculus or finite

math course.

Table of Contents:

Chapter 1: Functions and Lines

Chapter 2: Systems of Equations and Matrices

Chapter 3: Linear Programming

Chapter 4: Polynomial and Rational Functions

Chapter 5: Exponential and Logarithmic Functions

Chapter 6: Finance

Chapter 7: Sets

Chapter 8: Probability

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- David Lippman
- Date Added:
- 09/23/2020

The Calculus I course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in February 2019. The course is part of the Ohio Transfer Module and is also named TMM005. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadJim Fowler Ohio State UniversityRita Ralph Columbus State Community CollegeContent ContributorsNela Lakos Ohio State UniversityBart Snapp Ohio State UniversityJames Talamo Ohio State UniversityXiang Yan Edison State Community CollegeLibrarianDaniel Dotson Ohio State University Review TeamThomas Needham Ohio State UniversityCarl Stitz Lakeland Community CollegeSara Rollo North Central State College

- Subject:
- Mathematics
- Calculus
- Material Type:
- Full Course
- Provider:
- Ohio Open Ed Collaborative
- Date Added:
- 11/02/2020

The Calculus II course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in February 2019. The course is part of the Ohio Transfer Module and is also named TMM006. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadJim Fowler Ohio State UniversityRita Ralph Columbus State Community CollegeContent ContributorsNela Lakos Ohio State UniversityBart Snapp Ohio State UniversityJames Talamo Ohio State UniversityXiang Yan Edison State Community CollegeLibrarianDaniel Dotson Ohio State University Review TeamThomas Needham Ohio State UniversityCarl Stitz Lakeland Community CollegeSara Rollo North Central State College

- Subject:
- Mathematics
- Calculus
- Material Type:
- Full Course
- Provider:
- Ohio Open Ed Collaborative
- Date Added:
- 11/02/2020

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

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- Rice University
- Provider Set:
- OpenStax College
- Author:
- Alfred K. Mulzet
- Catherine Abbott
- David McCune
- David Smith
- David Torain
- Edwin “Jed” Herman
- Elaine A. Terry
- Erica M. Rutter
- Gilbert Strang
- Joseph Lakey
- Joyati Debnath
- Julie Levandosky
- Kirsten R. Messer
- Michelle Merriweather
- Nicoleta Virginia Bila
- Sheri J. Boyd
- Valeree Falduto
- William Radulovich
- Date Added:
- 02/01/2016

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.

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- Rice University
- Provider Set:
- OpenStax College
- Author:
- Alfred K. Mulzet
- Catherine Abbott
- David McCune
- David Smith
- David Torain
- Edwin “Jed” Herman
- Elaine A. Terry
- Erica M. Rutter
- Gilbert Strang
- Joseph Lakey
- Joyati Debnath
- Julie Levandosky
- Kirsten R. Messer
- Michelle Merriweather
- Nicoleta Virginia Bila
- Sheri J. Boyd
- Valeree Falduto
- William Radulovich
- Date Added:
- 02/01/2016

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.

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- Rice University
- Provider Set:
- OpenStax College
- Author:
- Alfred K. Mulzet
- Catherine Abbott
- David McCune
- David Smith
- David Torain
- Edwin “Jed” Herman
- Elaine A. Terry
- Erica M. Rutter
- Gilbert Strang
- Joseph Lakey
- Joyati Debnath
- Julie Levandosky
- Kirsten R. Messer
- Michelle Merriweather
- Nicoleta Virginia Bila
- Sheri J. Boyd
- Valeree Falduto
- William Radulovich
- Date Added:
- 02/01/2016

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. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended).

- Subject:
- Algebra
- Material Type:
- Textbook
- Provider:
- Stitz-Zeager Open Source Mathematics
- Author:
- Carl Stitz
- Jeff Zeager
- Date Added:
- 07/15/2011

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what theyve learned.

- Subject:
- Algebra
- Trigonometry
- Material Type:
- Textbook
- Provider:
- Rice University
- Provider Set:
- OpenStax College
- Author:
- David Lippman
- Jay Abramson
- Jean-Marie Magnier
- Melonie Rasmussen
- Nicholas Belloit
- Rachael Gross
- Rick Norwood
- Valeree Falduto
- Date Added:
- 01/29/2015

The College Algebra course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in September 2019. The course is part of the Ohio Transfer Module and is also named TMM001. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadNicholas Shay Central Ohio Technical College (now at Columbus State Community College)Content ContributorsRachida Aboughazi Ohio State UniversityEvelyn Kirschner Columbus State Community CollegeDavid Kish Ohio Dominican UniversityLibrarianDaniel Dotson Ohio State University Review TeamFauna Donahue University of Rio GrandeJared Stadden Kent State University Geauga

- Subject:
- Mathematics
- Algebra
- Material Type:
- Full Course
- Provider:
- Ohio Open Ed Collaborative
- Date Added:
- 11/02/2020

This text was written for a college-level liberal arts math class. It addresses math concepts that most people will encounter as part of their everyday life, including statistics, probability, growth, finance, graph theory, voting systems, fair division, apportionment, and geometric symmetry, and the golden ratio. Each chapter includes a set of homework questions for practice.

- Subject:
- Mathematics
- Material Type:
- Assessment
- Textbook
- Author:
- Jennifer Jameson
- Kathryn Kozak
- Kim Sonier
- Maxie Inigo
- Maya Lanzetta
- Date Added:
- 12/11/2020