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

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.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

- Subject:
- Mathematics
- Algebra
- Material Type:
- Textbook
- Author:
- Victor Shoup
- Date Added:
- 01/01/2008

This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Textbook
- Author:
- Jason Schmurr
- Michael Hilgemann
- Thomas Gonzalez
- Date Added:
- 05/10/2020

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- Oscar Levin
- Date Added:
- 12/05/2019

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences).

There are 943 exercises in the book, with answers and hints to selected exercises.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Activity/Lab
- Textbook
- Author:
- Michael Corral
- Date Added:
- 02/01/2021

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: • An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. • An elementary text can’t be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. • An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and defonitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures

- Subject:
- Engineering
- Mathematics
- Material Type:
- Textbook
- Provider:
- Trinity University
- Author:
- William F. Trench
- Date Added:
- 10/28/2014

This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.

All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.

Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.

Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.

- Subject:
- Mathematics
- Material Type:
- Homework/Assignment
- Lecture Notes
- Textbook
- Provider:
- Lyryx Learning
- Author:
- Adapted by Lyryx Learning
- K. Kuttler
- Date Added:
- 02/12/2015

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.

- Subject:
- Mathematics
- Algebra
- Material Type:
- Textbook
- Provider:
- University of Puget Sound
- Author:
- Robert Beezer
- Date Added:
- 12/05/2019

This book presents Euclidean Geometry and was designed for a one-semester course preparing junior and senior level college students to teach high school Geometry. The book could also serve as a text for a junior level Introduction to Proofs course.

- Subject:
- Geometry
- Material Type:
- Textbook
- Provider:
- Ohio University Open Faculty Textbooks
- Author:
- Mark Barsamian
- Date Added:
- 10/21/2020

These notes are intended to provide a brief, noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.

- Subject:
- Engineering
- Mathematics
- Material Type:
- Textbook
- Provider:
- Wytheville Community College
- Author:
- Jason Lachniet
- Date Added:
- 05/12/2018

Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.

- Subject:
- Statistics and Probability
- Material Type:
- Textbook
- Author:
- David Lane
- Date Added:
- 12/05/2019

Bringing a fresh approach to intro statistics, Introductory Statistics with Randomization and Simulation introduces inference faster using randomization and simulation techniques

- Subject:
- Statistics and Probability
- Material Type:
- Activity/Lab
- Full Course
- Textbook
- Provider:
- OpenIntro
- Author:
- Christopher Barr
- David Diez
- Mine Çetinkaya-Runde
- Date Added:
- 12/05/2019

This is a first draft of a free (as in speech, not as in beer, [Sta02]) (although it is free as in beer as well) textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University–Pueblo in the spring semester of 2017.

- Subject:
- Statistics and Probability
- Material Type:
- Textbook
- Author:
- Jonathan A. Poritz
- Date Added:
- 12/05/2019

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.

Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.

The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).

- Subject:
- Algebra
- Material Type:
- Textbook
- Provider:
- Lyryx Learning
- Author:
- W. Keith Nicholson
- Date Added:
- 06/15/2019

A syllabus for MTH 161: Precalculus I, taught within the Virginia Community College System.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Syllabus
- Author:
- Virtual Library of Virginia (VIVA)
- Date Added:
- 05/18/2021

A syllabus for MTH 167: Precalculus with Trigonometry as taught by institutions within the Virginia Community College System.

- Subject:
- Mathematics
- Calculus
- Trigonometry
- Material Type:
- Syllabus
- Author:
- Virtual Library of Virginia (VIVA)
- Date Added:
- 05/18/2021

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 quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- David Lippman
- Date Added:
- 12/02/2021

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 quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Washington State Community Colleges' Math 107.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- David Lippman
- Date Added:
- 05/10/2020

The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics then expressions and equations. The core course is a complete, ready to run, fully online course, featuring 9 topics: Problem solving, voting theory, graph theory, growth models, consumer finance, collecting data, describing data, probability, and historical counting. Additional optional topics are provided. The course materials can easily be used with a face-to-face course.

- Subject:
- Mathematics
- Material Type:
- Assessment
- Full Course
- Reading
- Syllabus
- Provider:
- Washington State Board for Community & Technical Colleges
- Provider Set:
- Open Course Library
- Date Added:
- 12/10/2019

A first one-semester course on differential equations aimed at engineers.

- Subject:
- Engineering
- Calculus
- Material Type:
- Full Course
- Textbook
- Provider:
- University of Illinois at Urbana-Champaign
- Provider Set:
- Individual Authors
- Author:
- Jiri Lebl
- Date Added:
- 12/05/2019

OpenIntro Statistics offers a traditional introduction to statistics at the college level. This textbook is widely used at the college level and offers an exceptional and accessible introduction for students from community colleges to the Ivy League. The textbook has been thoroughly vetted with an estimated 20,000 students using it annually.

- Subject:
- Statistics and Probability
- Material Type:
- Activity/Lab
- Textbook
- Provider:
- OpenIntro
- Author:
- Chris Barr
- David Diez
- Mine Çetinkaya-Rundel
- Date Added:
- 08/19/2019

This is a series of lesson plans based upon the OpenStax Introductory Statistics Textbooks. It contains sections on Sampling and Data, Descriptive Statistics, Probability, Discrete Random Variables, Continuous Random Variables, Distributions, The Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Linear Regression and Correlation. Downloading of the slides will begin as soon as you click "View Resource."

- Subject:
- Mathematics
- Material Type:
- Lecture Notes
- Provider:
- College of Coastal Georgia
- Author:
- German Vargas
- Jamil Mortada
- Jose Lugo
- Laura Lynch
- Syvillia Averett
- Treg Thompson
- Victor Vega
- Date Added:
- 05/20/2016

From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems."

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- CUNY Academic Works
- Provider Set:
- New York City College of Technology
- Author:
- Holly Carley
- Thomas Tradler
- Date Added:
- 09/01/2015

A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.

The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.

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

Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives, and includes worked examples that demonstrate problem-solving approaches in an accessible way.

- Subject:
- Mathematics
- 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:
- 02/20/2014

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

This course will cover families of trigonometric functions, their inverses, properties, graphs, and applications. Additionally we will study trigonometric equations and identities, the laws of sines and cosines, polar coordinates and graphs, parametric equations and elementary vector operations.Login: guest_oclPassword: ocl

- Subject:
- Trigonometry
- Material Type:
- Full Course
- Homework/Assignment
- Lecture Notes
- Lesson Plan
- Reading
- Syllabus
- Provider:
- Washington State Board for Community & Technical Colleges
- Provider Set:
- Open Course Library
- Date Added:
- 10/31/2011

This course will cover families of functions, their properties, graphs and applications. These functions include: polynomial, rational, exponential, logarithmic functions and combinations of these. We will solve related equations and inequalities and conduct data analysis, introductory mathematical modeling and develop competency with a graphing calculator.Login: guest_oclPassword: ocl

- Subject:
- Functions
- Material Type:
- Full Course
- Homework/Assignment
- Lecture Notes
- Lesson Plan
- Reading
- Syllabus
- Provider:
- Washington State Board for Community & Technical Colleges
- Provider Set:
- Open Course Library
- Date Added:
- 10/31/2011

There are four primary focus areas of this course - 1) Relations and Functions, 2) Polynomial and Rational Functions, 3) Exponential and Logarithmic Functions and 4) Systems of equations.

Precalculus 1 (MTH 161) was produced by the Virginia Community College System (VCCS) as an online Open Educational Resources (OER) course in partnership with three Community Colleges: J. Sargeant Reynolds, Tidewater, and John Tyler.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Full Course
- Author:
- Amanda Goldstein
- Ben MacKinnon
- Bethany Wright
- C.J. Bracken
- James Wolfle
- John Morea
- Kenyada McLeod
- Libby Watts
- Lisa Payne
- Lynn Riggs
- Matthew Watts
- Sheri Prupis (Grant Director)
- Date Added:
- 05/17/2021

There are nine focus areas of this course - 1) Relations and Functions, 2) Polynomial and Rational Functions, 3) Exponential and Logarithmic Functions, 4) Systems of equations, 5) Trigonometric Functions, 6) Analytic Trigonometry, 7) Applications of Trigonometry, 8) Conics and 9) Sequences and Series.

Precalculus with Trigonometry (MTH 167) was produced by the Virginia Community College System (VCCS) as an online Open Educational Resources (OER) course in partnership with three Community Colleges: J. Sargeant Reynolds, Tidewater, and John Tyler.

- Subject:
- Mathematics
- Calculus
- Trigonometry
- Material Type:
- Full Course
- Author:
- Amanda Goldstein
- Ben MacKinnon
- Bethany Wright
- C.J. Bracken
- James Wolfle
- John Morea
- Kenyada McLeod
- Libby Watts
- Lisa Payne
- Lynn Riggs
- Matthew Watts
- Sheri Prupis (Grant Director)
- Date Added:
- 05/17/2021

Significant Statistics: An Introduction to Statistics is intended for the one-semester introduction to statistics course for students who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a 'Your Turn' problem that is designed as extra practice for students.

Significant Statistics: An Introduction to Statistics was adapted and original content added by John Morgan Russell. It is adapted from content published by OpenStax Introductory Statistics, OpenIntro Statistics, and Introductory Statistics for the Life and Biomedical Sciences.

- Subject:
- Statistics and Probability
- Material Type:
- Textbook
- Author:
- Adapted John Morgan Russell
- Barbara Illowsky
- Christopher D
- David Diez
- David Harrington
- Julie Vu
- Mine Cetinkaya-rundel
- Susan Dean
- Date Added:
- 01/11/2022

Course material on solving linear first-order differential equations.

- Subject:
- Mathematics
- Material Type:
- Reading
- Provider:
- Ursinus College
- Author:
- Adam Parker
- Date Added:
- 08/15/2020

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

- Subject:
- Mathematics
- Functions
- Numbers and Operations
- Material Type:
- Textbook
- Provider:
- State University of New York
- Provider Set:
- Milne Open Textbooks
- Author:
- Harris Kwong, SUNY Fredonia
- Date Added:
- 11/06/2015

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.

- Subject:
- Statistics and Probability
- Material Type:
- Textbook
- Author:
- Brian Blais
- Date Added:
- 12/05/2019

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.

- Subject:
- Statistics and Probability
- Material Type:
- Textbook
- Author:
- Russel A. Poldrack
- Date Added:
- 12/05/2019

Introductory statistics course developed through the Ohio Department of Higher Education OER Innovation Grant. The course is part of the Ohio Transfer Module and is also named TMM010. For more information about credit transfer between Ohio colleges and universities please visit: www.ohiohighered.org/transfer.Team LeadKameswarrao Casukhela Ohio State University – LimaContent ContributorsEmily Dennett Central Ohio Technical CollegeSara Rollo North Central State CollegeNicholas Shay Central Ohio Technical CollegeChan Siriphokha Clark State Community CollegeLibrarianJoy Gao Ohio Wesleyan UniversityReview TeamAlice Taylor University of Rio GrandeJim Cottrill Ohio Dominican University

- Subject:
- Mathematics
- Statistics and Probability
- Material Type:
- Full Course
- Provider:
- Ohio Open Ed Collaborative
- Date Added:
- 11/05/2020

This set of problems for Linear Algebra in the open-source WeBWorK mathematics platform was created under a Round Eleven Mini-Grant for Ancillary Materials Creation. The problems were created for an implementation of the CC-BY Lyrix open textbook A First Course in Linear Algebra. Also included as an additional file are the selected and modified Lyryx Class Notes for the textbook.

Topics covered include:

Linear Independence

Linear Transformations

Matrix of a Transformation

Isomorphisms

Eigenvalues and Eigenvectors

Diagonalization

Orthogonality

- Subject:
- Algebra
- Material Type:
- Interactive
- Provider:
- University System of Georgia
- Provider Set:
- Galileo Open Learning Materials
- Author:
- Beata Hebda
- Hashim Saber
- Date Added:
- 06/20/2018

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Introductory Statistics. They were created through a Round Eight Textbook Transformation Grant.

- Subject:
- Statistics and Probability
- Material Type:
- Interactive
- Provider:
- University System of Georgia
- Provider Set:
- Galileo Open Learning Materials
- Author:
- Scott Kersey
- Stephen Carden
- Date Added:
- 03/20/2018