Digital library
Textbooks, references and open learning resources.
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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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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.
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Linear Algebra with Applications
W. Keith Nicholson · University of Calgary
In the contents: 12.C: Mathematical Induction · 1.00: Exercises for Mathematical Induction
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Combinatorics and Graph Theory
David Guichard · Whitman College
Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics.Graph theory is concerned with various types of networks, or really models of networks called graphs. These are not the graphs of analytic geometry, but what are often described as "points connected by lines''.
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Differential Equations and Linear Algebra
Anup Lamichhane · Oho Northern University
In this book, you will learn key techniques for solving differential equations that arise in science and engineering applications. You will also build a strong foundation in linear algebra concepts that support these methods.
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An Inquiry-Based Approach to Abstract Algebra
Dana Ernst · Northern Arizona University
In the contents: 9.02: A.2- Fancy Mathematical Terms · 9.03: A.3- Definitions in Mathematics
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Fundamentals of Matrix Algebra
Gregory Hartman · Virginia Military Institute
This text deals with matrix algebra, as opposed to linear algebra. Without arguing semantics, I view matrix algebra as a subset of linear algebra, focused primarily on basic concepts and solution techniques. There is little formal development of theory and abstract concepts are avoided. This is akin to the master carpenter teaching his apprentice how to use a hammer, saw and plane before teaching how to make a cabinet.
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Corequisite Precalculus
Katherine Skelton · Highline College
This course includes, but not limited to piece-wise, composite, inverse, polynomial, rational, exponential, and logarithmic functions. Also discussed are properties of functions, their relationship to equations and inequalities, as well as applications, and circles.
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Calculus Made Easy
Silvanus P. Thompson · City and Guilds Technical College
Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject. Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.
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Manchester University Physical Chemistry I (CHEM 341)
Kathy Davis · Manchester University
Textbook for CHEM 341 at Manchester University (Physical Chemistry I). Foundations of quantum mechanics for describing atomic structure, molecular motion and chemical bonding, with specific applications to spectroscopy and chemical reactivity. Prerequisite(s): CHEM 113 (General Chemistry II), MATH 122 (Calculus II).
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College Algebra for Liberal Arts and Humanities
Leif Jordan · College of the Desert
A College Level Algebra text designed for students in the Liberal Arts and Humanities. Topics include: Linear, Quadratic, Rational, Exponential and Logarithmic Equations, Inequalities, Graphs and Functions with applications in business, the arts and social sciences. Conic sections, sequences, series, the binomial theorem and some mathematical history are also included.
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Early Childhood Education: STEM (NWTC)
Vicki Tanck · Northeast Wisconsin Technical College
In the contents: 05: Early Math Experiences · 5.01: Importance of Early Childhood Mathematics and Developing Number Sense
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Introduction to Matrix Algebra
Autar Kaw · University of South Florida
This book is an extended primer for undergraduate Matrix Algebra. The book is either to be used as a refresher material for students who have already taken a course in Matrix Algebra or as a just-in-time tool if the burden of teaching Matrix Algebra has been distributed to several courses.
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First-Semester Abstract Algebra: A Structural Approach
Jessica K. Sklar · Pacific Lutheran University
This text is specifically designed to suit a single-semester introductory abstract course, rather than to be a comprehensive reference source.