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Mathematics (Faculty Reviewed)

Course materials in this collection have been mapped to high enrollment Mathematics courses at select Virginia higher education institutions and reviewed by Virginia faculty. All faculty reviewed OER will include a seal of approval in the item record. Scroll through Course Alignments to see what courses and institutions the materials may be suitable for use in the classroom.

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Contemporary Mathematics
Unrestricted Use
CC BY
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Contemporary Mathematics is designed to meet the scope and sequence requirements for a liberal arts mathematics course. This resource provides stand-alone sections with a focus on showing relevance in the features as well as the examples, exercises, and exposition. Contemporary Mathematics integrates technology applications, projects, and highlights a diverse group of contributors to mathematics, statistics, and related fields.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Donna Kirk
Date Added:
09/23/2024
A Cool Brisk Walk Through Discrete Mathematics
Conditional Remix & Share Permitted
CC BY-SA
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0.0 stars

A Cool, Brisk Walk Through Discrete Mathematics, an innovative and non-traditional approach to learning Discrete Math, is available for low cost from Blurb or via free download.

Subject:
Mathematics
Material Type:
Textbook
Author:
Stephen Davies
Date Added:
11/18/2021
Dalton State College APEX Calculus
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

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

Subject:
Calculus
Mathematics
Material Type:
Textbook
Author:
Jason Schmurr
Michael Hilgemann
Thomas Gonzalez
Date Added:
05/10/2020
Discrete Mathematics: An Open Introduction
Conditional Remix & Share Permitted
CC BY-SA
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0.0 stars

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
Elementary Calculus
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0.0 stars

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:
Calculus
Mathematics
Material Type:
Activity/Lab
Textbook
Author:
Michael Corral
Date Added:
02/01/2021
Elementary Differential Equations with Boundary Value Problems
Unrestricted Use
CC BY
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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:
Applied Science
Engineering
Mathematics
Material Type:
Textbook
Provider:
Trinity University
Author:
William F. Trench
Date Added:
10/28/2014
A First Course in Linear Algebra
Unrestricted Use
CC BY
Rating
0.0 stars

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
Read the Fine Print
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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:
Algebra
Mathematics
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Robert Beezer
Date Added:
12/05/2019
Introduction to Axiomatic Geometry
Only Sharing Permitted
CC BY-NC-ND
Rating
0.0 stars

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
Mathematics
Material Type:
Textbook
Provider:
Ohio University Open Faculty Textbooks
Author:
Mark Barsamian
Date Added:
10/21/2020
Introduction to GNU Octave: A Brief Tutorial for Linear Algebra and Calculus Students
Conditional Remix & Share Permitted
CC BY-SA
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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:
Applied Science
Engineering
Mathematics
Material Type:
Textbook
Provider:
Wytheville Community College
Author:
Jason Lachniet
Date Added:
05/12/2018
Introduction to Probability
Conditional Remix & Share Permitted
CC BY-SA
Rating
0.0 stars

This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious. This gives the subject of probability a special interest.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
John R. Baxter
Date Added:
07/09/2024
Introduction to Statistics
Read the Fine Print
Educational Use
Rating
0.0 stars

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:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
David Lane
Date Added:
12/05/2019
Introductory Statistics with Randomization and Simulation
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0.0 stars

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

Subject:
Mathematics
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
Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics
Conditional Remix & Share Permitted
CC BY-SA
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0.0 stars

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:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
Jonathan A. Poritz
Date Added:
12/05/2019
Linear Algebra: Foundations to Frontiers
Rating
0.0 stars

An e-book (PDF) that integrates the materials for the Spring 2017 offering of LAFF, including 270+ short videos, answers to exercises, browser-based activities, and programming exercises in M-script (the programming language of MATLAB). This artifact encompasses a full undergraduate introductory course on linear algebra and is used at the primary resource for such a course at UT-Austin.

Subject:
Applied Science
Computer Science
Material Type:
Activity/Lab
Homework/Assignment
Textbook
Author:
Pierce M. van de Geijn
Robert A. van de Geijn
Margaret E. Myers
Date Added:
02/15/2022
Linear Algebra with Applications
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

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
Mathematics
Material Type:
Textbook
Provider:
Lyryx Learning
Author:
W. Keith Nicholson
Date Added:
06/15/2019
Linear Transformations on Vector Spaces: An Introduction to Linear Algebra
Unrestricted Use
CC BY
Rating
0.0 stars

Linear Transformations on Vector Spaces serves primarily as a textbook for undergraduate Linear Algebra courses. While standard Linear Algebra books begin by focusing on solving systems of linear equations and associated procedural skills, our book begins by developing a conceptual framework for the topic using the central objects, vector spaces and linear transformations. It covers the same concepts, skills, and, applications as conventional texts in a one-semester course, but students walk away with a much richer and more useful mastery of the topics. The book is structured to facilitate the implementation of the flipped classroom. The text features a continuous narrative to illuminate the big picture of the material and is written to help students develop their textbook reading skills. Also, there are “Explorations” scattered throughout each section; these are quick first examples intended for students to complete while reading before class meetings. Additional materials include section overview homework assignments and worksheets that can be used for in-class practice.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
PALNI Press
Author:
Amber Russell
Scott Kaschner
Date Added:
09/01/2023
MTH 161: Precalculus I
Unrestricted Use
CC BY
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A syllabus for MTH 161: Precalculus I, taught within the Virginia Community College System.

Subject:
Calculus
Mathematics
Material Type:
Syllabus
Author:
Virtual Library of Virginia (VIVA)
Date Added:
05/18/2021
Math in Society
Unrestricted Use
CC BY
Rating
0.0 stars

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