Mathematics/Physics - Affordable Course Material (ACM) - Finding Guide - Research Guides at Saint Francis University

Textbooks

Mathematics Resources

American Institute of Mathematics (AIM) - Approved Open Textbooks
This site provides a list of open textbooks approved for use by the American Institute of Mathematics.
Mathematics for the Liberal Arts
This course was originally developed for the Open Course Library project. The text used is Math in Society, edited by David Lippman, Pierce College. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.

Algebra

OpenStax Prealgebra
Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on. The organization makes it easy to adapt the book to suit a variety of course syllabi.
OpenStax Algebra and Trigonometry
Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.
OpenStax Elementary Algebra
Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles.
OpenStax Intermediate Algebra
Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles.
Beginning & Intermediate Algebra
Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. Topics covered include: pre-algebra review, solving linear equations, graphing linear equations, inequalities, systems of linear equations, polynomials, factoring, rational expressions and equations, radicals, quadratics, and functions including exponential, logarithmic and trigonometric.
A First Course in Linear Algebra
This text, originally by Ken 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.
Linear Algebra with Applications
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.

Calculus

OpenStax Precalculus
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.
OpenStax Calculus
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. Volume 1 covers functions, limits, derivatives, and integration.
Contemporary Calculus I
This is a textbook for differential calculus with explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author.
Applied Calculus
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.
Active Calculus Multivariable
In Active Calculus Multivariable, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore.
Community Calculus
An early transcendentals book covering single variable calculus, infinite series, and multivariable calculus.
Calculus: Early Transcendentals
This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses. To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions.
Differential Calculus for the Life Sciences
In this textbook, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates. While many of the examples have a biological flavour, the level of biology needed to understand those examples is kept at a minimum.

Other Open Textbooks

Proofs and Concepts: The Fundamentals of Abstract Mathematics
This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates.
Elementary Differential Equations with Boundary Value Problems
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.
A Gentle Introduction to the Art of Mathematics
A Gentle Introduction to the Art of Mathematics (GIAM for short) is a textbook for a "transitions" course. Transitions courses (also known as "foundations" or "intro to proofs" courses) are typically taken after the Calculus sequence and before upper-division coursework in the mathematics major. Their purpose is to acclimatize the student to some of the culture and terminology of mathematics and to begin developing in them a proficiency at reading and writing mathematical proofs.
Spiral Workbook for Discrete Mathematics
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.
Combinatorics Through Guided Discovery
This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially, but not exclusively, on the part of combinatorics that mathematicians refer to as "counting." The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Above all, this book is dedicated to the principle that doing mathematics is fun.
Combinatorics: Enumeration, Graph Theory, and Design Theory
Combinatorics provides an introduction to enumeration, graph theory, and design theory. It is aimed at upper-level undergraduate students and the exercises expect some mathematical sophistication, including a reasonable ability to construct proofs. The text is designed to be used in an undergraduate course, but could be suitable for independent study by a student with some mathematical background and understanding of proofs.

Physics
- OpenStax University Physics (Vol. 1)
  
  University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics.
- OpenStax College Physics
  
  College Physics meets standard scope and sequence requirements for a two-semester introductory algebra-based physics course. The text is grounded in real-world examples to help students grasp fundamental physics concepts. It requires knowledge of algebra and some trigonometry, but not calculus.
- Introduction to Electricity, Magnetism, and Circuits
  
  This textbook emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigour inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
- Simple Nature
  
  This is a calculus-based physics textbook meant for the type of freshman survey course taken by engineering and physical science majors, or for AP Physics C. It uses a nontraditional order of topics, with energy coming before force.
- Light & Matter
  
  This is an introductory text intended for a one-year introductory course of the type typically taken by biology majors, or for AP Physics 1 and 2. Algebra and trig are used, and there are optional calculus-based sections.
- OpenStax College Physics (Pressbooks edition)
  
  College Physics is organized such that topics are introduced conceptually with a steady progression to precise definitions and analytical applications. The analytical aspect (problem solving) is tied back to the conceptual before moving on to another topic. Each introductory chapter, for example, opens with an engaging photograph relevant to the subject of the chapter and interesting applications that are easy for most students to visualize.
- PhET Interactive Simulations
  
  Includes “interactive simulations for science and math.” Can be useful for mathematics, physics, engineering, and other subjects.
- MIT Mathlets
  The MIT Mathlets constitute a suite of carefully designed and highly interactive Javascript applets designed to enhance selected university level STEM classes.

Course Materials

My Open Math

MyOpenMath runs on the open source, IMathAS platform, providing free hosted use of this platform in support of free.

PhET Interactive Simulations
Includes “interactive simulations for science and math.” Can be useful for mathematics, physics, engineering, and other subjects.
MIT Mathlets
The MIT Mathlets constitute a suite of carefully designed and highly interactive Javascript applets designed to enhance selected university level STEM classes.
MyOpenMath
Are you an instructor who wants to adopt an open textbook, who feels online interactive homework is valuable, but doesn't want their students to have to pay an additional fee? Then read more about using MyOpenMath in the classroom.
Sage
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.
Grasple
An online platform for instructors to collaboratively create and share open exercises and lessons for Math and Statistics. Includes interactive exercises for Prealgebra, Calculus, Linear Algebra, and Statistics.
Lumen Online Homework Manager
Designed by educators, Lumen Online Homework Manager (OHM) draws from thousands of interactive assessment questions to help students master math and other quantitative skills.

MIT Mathlets
The MIT Mathlets constitute a suite of carefully designed and highly interactive Javascript applets designed to enhance selected university level STEM classes.

GeoGebra
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.

Desmos
Desmos includes multiple tools for use in mathematics courses, including the HTML5 Desmos graphing calculator, which millions of students around the world use for free, including students who are blind or visually-impaired. They also provide teaching activities and an activity builder for instructors using the platform.

Math Insight
The Math Insight web site is a collection of pages and applets designed to shed light on concepts underlying a few topics in mathematics. The focus is on qualitative description rather than getting all technical details precise.

CoCalc
A spinoff from the open source Sagemath, Co Calc offers a platform-specific edition of Jupyter notebooks with real-time collaboration, chat, and precise edit-history, an extensive Python stack, and additional resources for users. To integrate into a course, this requires a payment of ~$5 per student.

Open Courses

Lumen Learning: Finite Math

"This course covers precalculus topics including linear, polynomial, rational, exponential, and logarithmic functions and also finite math topics including linear programming, finance, sets, and probability, with emphasis towards business application examples as appropriate. This course includes complete text, videos, homework, and quizzes, along with a weekly “show your work” assignment for hand grading." Used in MAT120.
Lumen Learning: Statistics Using Technology

"Based on the open textbook, Statistics Using Technology by Kathryn Kozak, this statistics course adapted by David Straayer includes pdf and Microsoft Word formatted textbook, videos, powerpoint slides, worksheets, and online assessments." Used in MAT161.

New!

Technical Mathematics

This developmental-level mathematics textbook is intended for career-technical students.

Affordable Course Material (ACM) - Finding Guide: Mathematics/Physics