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Open Educational Resources (OER)

OER @ Hunter

Hunter College | MATH 101

Hunter College | MATH 101 Algebra for College Students

From the About Page:

"This is a custom designed OER course for Hunter College’s Math 101 – Algebra for College Students – course, remixed by Dr. Tatyana Khodorovskiy, from Lumen’s OER materials.

This course presents topics including solving and graphing linear equations, inequalities, systems of linear equations, functions, polynomials, factoring, rational expressions and equations, radical expressions and equations, quadratic functions and graphing parabolas, composite and inverse functions, exponentials and logarithms, graphing techniques, and applications. This OER text is interactive, aligned with OER videos, and complete assessments, this title is a great low-cost alternative to traditional publisher materials."

The MATH 101 Algebra for College Students Courseware includes:

  • Online Homework Management System (OHM) | [A $25 pre student fee is required for platform support]
  • Instructional Videos and Module/Chapter Summaries
  • Instructor Resources

Textbooks

Book of Proof

Book of Proof
3e
by Richard Hammack, Virginia Commonwealth University

From the Preface to the Third Edition:
"My goal in writing this book has been to create a very inexpensive high-quality textbook. The book can be downloaded from my web page in PDF format for free, and the print version costs considerably less than comparable traditional textbooks. In this third edition, Chapter 3 (on counting) has been expanded, and a new chapter on calculus proofs has been added. New examples and exercises have been added throughout. My decisions regarding revisions have been guided by both the Amazon reviews and emails from readers, and I am grateful for all comments.

This core of this book is an expansion and refinement of lecture notes I developed while teaching proofs courses over the past 18 years at Virginia Commonwealth University (a large state university) and Randolph-Macon College (a small liberal arts college). I found the needs of these two audiences to be nearly identical, and I wrote this book for them. But I am mindful of a larger audience. I believe this book is suitable for almost any undergraduate mathematics program."
A Friendly Introduction to Mathematical Logic

Open SUNY Textbooks:
A Friendly Introduction to Mathematical Logic
2e

From the Abstract:
"At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition’s treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel’s First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises."
 
College Algebra

OpenStax
College Algebra

From the Description:
"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 they’ve learned."
Peer Reviews
Abstract Algebra: Theory and Applications

Abstract Algebra: Theory and Applications

From the MAA Review:
"Of all the prospective texts I looked at from the standpoint of these requirements, Thomas Judson’s Abstract Algebra: Theory and Applications (AATA) was the best. (The fact that it was free was an added bonus.) The level was non-threatening, and the order and presentation of topics seemed perfect for what I was looking for. The “Preliminaries” chapter begins with several pointers on reading and writing proofs — vital background knowledge that most a abstract algebra books take for granted. Next, the book covers sets and equivalence relations in a way that bridges from familiar material to a more abstract setting. In the chapters dealing with groups, there are entire sections devoted to the integers mod n, symmetries, and complex numbers. Some practical topics such as ISBN and UPC codes are well-covered in the exercises; while others such as cryptography (the discussion of RSA is a bit brief) and algebraic coding (group codes, linear codes, and polynomial codes) are treated in well-placed optional chapters.
...one of the greatest strengths of [the] AATA: [it is] full customizability. All of the LaTeX code is freely available online. My graduate student Justin Hill and I took Judson’s source material and in a single semester developed a book that was precisely suited to the background and interests of our particularly students. This turns on its head the conventional model of textbook development, which requires slow evolution of lecture notes over the course of several semesters."
MAA Review
 
Modeling, Functions, and Graphs: Algebra for College Students

Modeling, Functions, and Graphs: Algebra for College Students

From the Preface:
"Mathematics, as we all know, is the language of science, and fluency in algebraic skills has always been necessary for anyone aspiring to disciplines based on calculus. But in the information age, increasingly sophisticated mathematical methods are used in all fields of knowledge, from archaeology to zoology. Consequently, there is a new focus on the courses before calculus. The availability of calculators and computers allows students to tackle complex problems involving real data, but requires more attention to analysis and interpretation of results. All students, not just those headed for science and engineering, should develop a mathematical viewpoint, including critical thinking, problem-solving strategies, and estimation, in addition to computational skills. Modeling, Functions and Graphs employs a variety of applications to motivate mathematical thinking."
Authored by Katherine Yoshiwara,
Professors of Mathematics, Los Angeles Pierce College, Retired
My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition)

My Math GPS: Elementary Algebra Guided Problem Solving
(2016 Edition)

From the Abstract:
"My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors."
  • OpenStax
    Introductory Statistics

    From the Summary:
    "Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs. "

  • Community Calculus

    From the MAA review of this book:
    "The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don’t like calculus books to go on and on.
    The book covers the standard material in a calculus course for science and engineering. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule. The single variable material is contained in eleven chapters beginning with analytic geometry and ending with sequences and series. The multivariable material consists of five chapters and includes with the vector calculus of in two and three dimensions through the divergence theorem. The book ends with a final chapter on differential equations.
    There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Also available are WeBWorK problem sets keyed to the sections of the text. Some students and instructors may want to use something like a Schaum’s outline for additional problems. "

  • Calculus

    From the Text:
    "This is the free digital calculus text by David R. Guichard and others. It was submitted to the Free Digital Textbook Initiative in California and will remain unchanged for at least two years.
    The book is in use at Whitman College and is occasionally updated to correcterrors and add new material. The latest versions may be found by going to http://www.whitman.edu/mathematics/california_calculus/"

  • Geometry with an Introduction to Cosmic Topology

    From the Text:
    "Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.
    The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe. More about the text can be found in the Preface.
    Previously published in 2009, the author has made this updated and revised 2018 Edition freely available, thanks in large part to the PreTeXt Project.
    Read the MAA Review"

  • An Introduction to Combinatorics and Graph Theory

    From the Text:
    "Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics. As the name suggests, however, it is broader than this: it is about combining things. Questions that arise include counting problems: “How many ways can these elements be combined?” But there are other questions, such as whether a certain combination is possible, or what combination is the “best” in some sense. We will see all of these, though counting plays a particularly large role."

  • Introduction to Probability

    From the American Institute of Mathematics:
    "This book of about 500 pages has become a classic because of its engaging style, interesting examples, historical notes, pedagogical use of computer simulations, and more than 600 exercises. Thanks to the American Mathematical Society the book is freely available...[the ]text [is] for a first course in probability assuming some understanding of calculus [and] is open source and can be freely distributed and printed."

Courseware

OpenLab | College Algebra and Trigonometry

OpenLab | College Algebra and Trigonometry

City Tech's OER College Algebra and Trigonometry Course Site includes:

OERs Created by Brooklyn College

Mathematics OERs | CUNY Brooklyn College Mathematics Department

These OER resources and course sites were created by CUNY Brooklyn College Mathematics Department faculty members for use in a number of courses, including:

OpenIntro | Statistics, 3rd Edition

OpenIntro | Statistics, 3rd Edition

From the About Page:

"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.

OpenIntro Statistics is a high-end [courseware] ready for use in the classroom, and it offers extra benefits, including:

  • Instructor Resources Including: Lecture Slides, Sample Exams, and Sample Course Syllabuses
  • Companion Data Sets
  • Labs based on freely available R and RStudio
  • Short videos for each section of some chapters
  • Technical Support"

OpenIntro Statistics is approved by the American Institute of Mathematics.

Mooculus

Mooculus

Created by faculty and staff at Ohio State University, the Mooculus course "is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course is based around doing practice problems."

The Mooculus OER courseware includes:

Journals

Annals of Mathematics

The Annals of Mathematics

From the About Page:
"The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study."
Journal of Mathematical Sciences

Journal of Mathematical Sciences

From the Description:
"Journal of Mathematical Sciences provides English translations from outstanding Russian-and Ukrainian-language publications of authoritative reports on current mathematical advances. Articles cover a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, boundary value problems, linear operators, and number and function theory. See the Aims & Scope for information on the Russian-and Ukrainian-language publications covered by the Journal of Mathematical Sciences.

The journal is a valuable resource for pure and applied mathematicians, statisticians, systems theorists and analysts, and information scientists."
 

Media: Podcasts, Videos, Interactives, Software

Oxford University The Secrets of Mathematics Podcast

Oxford University
The Secrets of Mathematics Podcast

From the Description:
"A series of talks and lectures from Oxford Mathematicians exploring the power and beauty of their subject. These talks would appeal to anyone interested in mathematics and its ever-growing range of applications from medicine to economics and beyond."
PhET Math Simulations

PhET
Math Simulations

From the PhET Homepage:
"Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder creates free interactive math and science simulations. PhET sims are based on extensive education research and engage students through an intuitive, game-like environment where students learn through exploration and discovery."
MyOpenMath

MyOpenMath

From the About Page:
"MyOpenMath is a free, open source, online course management system for mathematics and other quantitative fields. MyOpenMath's primary emphasis is to facilitate the creation and implementation of online homework and assessment, although it also supports content delivery on a limited basis.

MyOpenMath runs on the open source IMathAS platform, providing free hosted use of this platform in support of free, open textbooks like the ones listed on OpenTextBookStore.com. The intent is to provide classroom use of the platform, without any required cost to students, for schools wanting a managed install of the IMathAS platform, and to provide students self-study opportunities.

MyOpenMath.com is operated by the non-profit organization MyOpenMath."
SageMath Open-Source Mathematics Software

SageMath
Open-Source Mathematics Software

From the SageMath Homepage:
"SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers."
Workshops and Seminars

GeoGebra
Free Math Apps

From the About page:
"GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. GeoGebra is a rapidly expanding community of millions of users located in just about every country. GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning worldwide."