Digital library
Textbooks, references and open learning resources.
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HiSetMatematicas
Saul Lopez · Santiago Canyon College
In the contents: HiSet Mathematica (Lopez)
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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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An Introduction to the Electronic Structure of Atoms and Molecules
McMaster University · Richard F. W. Bader
The beginning student of chemistry must have a knowledge of the theory which forms the basis for our understanding of chemistry and he must acquire this knowledge before he has the mathematical background required for a rigorous course of study in quantum mechanics. The present approach is designed to meet this need by stressing the physical or observable aspects of the theory through an extensive use of the electronic charge density.
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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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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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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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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
In the contents: 10: Axiomatic Treatment of \(\mathbb{R, N, Z, Q}\) and \(\mathbb{C}\)
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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
In the contents: 7.03: Physical Assumptions and Mathematical Consequences
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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.
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Differential Calculus for the Life Sciences
Leah Edelstein-Keshet · University of British Columbia
Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this course, 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.
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An Introduction to the Theory of Numbers
Leo Moser · University of Alberta
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers.
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College Algebra (NWTC)
Northeast Wisconsin Technical College · College Algebra (NWTC)
This text covers a comprehensive range of algebraic principles, including equations and inequalities, functions, polynomial and rational functions, exponential and logarithmic functions, and systems of equations and inequalities. It provides a solid foundation in algebra.
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Discrete Stochastic Processes
Robert Gallager · Massachusetts Institute of Technolog
Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This text aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding.
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The Physics of Waves
Howard Georgi · Harvard University
This text will provide you with the concepts and mathematical tools necessary to understand and explain a broad range of vibrations and waves. You will learn that waves come from many interconnected (coupled) objects when they are vibrating together. We will discuss many of these phenomena, along with related topics, including mechanical vibrations and waves, sound waves, electromagnetic waves, optics, and gravitational waves.