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.

Contemporary Mathematics is designed to meet the scope and sequence requirements for …

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.

A Cool, Brisk Walk Through Discrete Mathematics, an innovative and non-traditional approach …

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.

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate …

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.

This textbook covers calculus of a single variable, suitable for a year-long …

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.

Elementary Differential Equations with Boundary Value Problems is written for students in …

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

This text, originally by K. Kuttler, has been redesigned by the Lyryx …

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.

A First Course in Linear Algebra is an introductory textbook aimed at …

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.

This book presents Euclidean Geometry and was designed for a one-semester course …

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.

These notes are intended to provide a brief, noncomprehensive introduction to GNU …

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.

This is an introduction to probability theory, designed for self-study. It covers …

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.

Introduction to Statistics is a resource for learning and teaching introductory statistics. …

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.

Bringing a fresh approach to intro statistics, Introductory Statistics with Randomization and …

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

This is a first draft of a free (as in speech, not …

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.

An e-book (PDF) that integrates the materials for the Spring 2017 offering …

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.

After being traditionally published for many years, this formidable text by W. …

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).

Linear Transformations on Vector Spaces serves primarily as a textbook for undergraduate …

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.

Math in Society is a free, open textbook. This book is a …

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.

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