Digital library
Textbooks, references and open learning resources.
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Seven Sketches in Compositionality: An Invitation to Applied Category Theory
Brendan Fong & David I. Spivak · Massachusetts Institute of Technology
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this text, we will give seven sketches on real-world applications of category theory.
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A First Course in Differential Equations for Scientists and Engineers
Russell Herman · University of North Carolina Wilmington
This book is written for an undergraduate course on the introduction to differential equations typically taken by majors in mathematics, the physical sciences, and engineering. In this course we will investigate analytical, graphical, and approximate solutions of differential equations. We will study the theory, methods of solution and applications of ordinary differential equations. This will include common methods of finding solutions, such as using Laplace transform and power series methods.
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Math 223 Calculus 3
LibreTexts
This book considers what happens when we broaden our view of what a function is to include functions that have more than one input, or that produce more than one result, or both. In particular, we consider what it means for such a function to have a limit, and how to differentiate or integrate such functions. In the course of learning these things, we will also encounter many applications of so-called multivariable and vector-valued functions in the natural and social sciences.
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Mathematical Computing with Python
Dennis Hall · Angelo State University
In-progress textbook based on course notes from Angelo State University's Numerical Analysis (Math 4311) course.
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HiSetMatematicas
Saul Lopez · Santiago Canyon College
LibreTexts
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Numerical Methods
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
These notes, taught at the Hong Kong University of Science and Technology with two lecture hours per week, are primarily for non-mathematics majors and were required by several engineering departments.
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Math 222: Calculus II
LibreTexts
Math 222, Calculus II, is the second semester course of the calculus series and is intended as a continuation of the development of single-variable calculus. We will cover the differential calculus of transcendental functions (exponentials, logarithms, inverse trig functions, etc.) as well as continue the integral calculus we began in Math 221, Calculus I. We will introduce techniques of integration such as integration by parts, trigonometric substitution, and partial fraction decompositions.
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An IBL Introduction to Geometries
Mark A. Fitch · University of Alaska Anchorage
This text was designed for an IBL approach to Introduction to Geometries and covers geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and a tiny bit of analytic approaches to geometry and covers both Euclidean (parabolic), hyperbolic, and some projective geometry. Students are expected to have completed a proofs course covering proof techniques, basic set operations, and cardinality as a prerequisite.
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Analytic Geometry and Calculus I (IVC Math 3A OER)
Leonard Lamp, Kenn Huber & Mohamad Youssef · Irvine Valley College
This course covers basic concepts of analytic geometry, limits and continuity; and differentiation and integration of algebraic, trigonometric, exponential, logarithmic and hyperbolic functions. Applications include related rates and optimization problems. L'hospital's rule is studied. Credit may be earned in MATH 3A or 3AH, but not both. C-ID: MATH 210
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Visual Statistics Use R!
Alexey Shipunov · Minot State University
The ignorance of the statistical methods can lead to mistakes and misinterpretations. Unfortunately, understanding of these methods is far from common. Many college majors require a course in probability theory and mathematical statistics, but all many of us remember from these courses is horror and/or frustration at complex mathematical formulas filled with Greek letters, some of them wearing hats.
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Elementary Trigonometry
Michael Corral · Schoolcraft College
This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.
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A First Course in Linear Algebra
Ken Kuttler · Brigham Young University
The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. 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.
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Introductory Statistics STA 2023
Cheban Acharya · Florida Southwestern State College
The Introductory Statistics course/textbook used for STA 2023 at Florida SouthWestern State College, the topics generally follow the standard introductory-statistics sequence. FSW’s STA 2023 is an introductory statistics course, and published course materials emphasize probability, distributions, sampling distributions, confidence intervals, hypothesis testing, and regression/correlation.
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Math 125: Hope College
Katharine Vance · Hope College
This course covers the material typically taught in the first half of a Calculus I course. The calculus material is supplemented by reviewing topics of high school mathematics as needed. The calculus topics are also taught at a slower pace. Topics include function review, limits and continuity, the concept (and definition) of a derivative, and differentiation rules (product rule, quotient rule, chain rule are included).
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Precalculus
Jay Abramson · OpenStax
This precalculus textmap is intended for college-level Precalculus students and is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text.
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Calculus II: Integral Calculus
Doli Bambhania, Neelam R. Shukla & Danny Tran · De Anza College
This second book in a four-part calculus series is designed for both beginners and advanced students, emphasizing a strong conceptual foundation. It explores essential topics such as rates of change and calculating areas and volumes of irregular shapes, with numerous examples and applications across physics, economics, and engineering.
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Elementary Abstract Algebra
W Edwin Clark · University of South Florida
This book is intended for a one semester introduction to abstract algebra. We assume that students have some familiarity with basic set theory linear algebra and calculus. But very little of this nature will be needed To a great extent the course is self contained except for the requirement of a certain amount of mathematical maturity. And hopefully the student's level of mathematical maturity will increase as the course progresses.
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Numerically Solving Ordinary Differential Equations
Stuart Brorson · Northeastern University
The booklet covers basic Euler solvers, Runge-Kutta, and linear multistep methods and discusses explicit vs. implicit methods. It discusses stability and the stability domains of some of the methods and talks about adaptive methods and the concept of stiffness and concluding with a chapter on symplectic methods and why they are important. Beyond the solver algorithms, the book includes many example ODEs and shows their solutions using the methods discussed. Matlab programs accompany the text.
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Complex Variables with Applications
Jeremy Orloff · Massachusetts Institute of Technology
Complex analysis is a basic tool in many mathematical theories. By itself and through some of these theories it also has a great many practical applications. There are a small number of far-reaching theorems that we’ll explore in the first part of the class. Along the way, we’ll touch on some mathematical and engineering applications of these theorems. The last third of the class will be devoted to a deeper look at applications.
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Combinatorics
Joy Morris · University of Lethbridge
Combinatorics is an upper-level introductory course in enumeration, graph theory, and design theory. The text focuses on combinations and arrangements of discrete structures. There are five major branches of combinatorics that we will touch on in this course: enumeration, graph theory, Ramsey Theory, design theory, and coding theory. We will focus on enumeration, graph theory, and design theory, but will briefly introduce the other two topics.