Digital library
Textbooks, references and open learning resources.
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An Introduction to Proof via Inquiry-Based Learning
Dana Ernst · Northern Arizona University
This book is intended to be used for a one-semester/quarter introduction to proof course (sometimes referred to as a transition to proof course). The purpose of this book is to introduce the reader to the process of constructing and writing formal and rigorous mathematical proofs. The intended audience is mathematics majors and minors. However, this book is also appropriate for anyone curious about mathematics and writing proofs.
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MAT 1350: Precalculus Part I
Jay Abramson · Prince George's Community College
Algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.
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MAT 206Precalculus
Borough of Manhattan Community College · LibreTexts
OpenStax Precalculus text, modified for MAT 206-1202, Professor Margaret Dean, Mathematics Department, BMCC/CUNY
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Vector Calculus
Michael Corral · Schoolcraft College
The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. The content in this Textmap is complemented by Vector Calculus Modules in the Core and the Vector Calculus (UCD Mat 21D) Libretext.
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Understanding Linear Algebra
David Austin · Grand Valley State University
This book arises from my belief that linear algebra, as presented in a traditional undergraduate curriculum, has for too long lived in the shadow of calculus. Many mathematics programs currently require their students to complete at least three semesters of calculus, but only one semester of linear algebra, which often has two semesters of calculus as a prerequisite.
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Elementary Number Theory
Mike Barrus & W. Edwin Clark · University of Rhode Island
The great Carl Friedrich Gauss once wrote, "Mathematics is the queen of sciences and arithmetic the queen of mathematics." What Gauss called arithmetic, we now call number theory. This text is an extensive update of an original manuscript by Professor W. Edwin Clark (now Emeritus) of the University of South Florida, written in 2002 and made freely available on his website. It is designed for a one-semester undergraduate course and for self study.
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Linear Algebra
David Cherney, Tom Denton, & Andrew Waldron · University of California, Davis
In the contents: 4.01: Addition and Scalar Multiplication in (mathbbRn) · 4.04: Vectors Lists and Functions- (mathbbRS)
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A Primer of Real Analysis
Dan Sloughter · Furman University
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
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Applied Geometric Algebra (Tisza)
László Tisza · Massachusetts Institute of Technology
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These course notes attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools.
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Introduction to Groups and Geometries
David W. Lyons · Lebanon Valley College
This text is two textbooks in one: an introduction to group theory, and an introduction to modern geometries using the Kleinian paradigm. The book can be used for a combined one-semester course in both subjects, or, through supplementary projects, it can be used for a one-semester introduction to group theory or a one-semester introduction to modern geometries.
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Informal Calculus with Applications to Biological and Environmental Sciences
Tyler Seacrest · University of Montana Western
This book is an approachable introduction to calculus with applications to biology and environmental science. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.
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Acoustics
Wikipedia · LibreTexts
Acoustics is the science that studies sound, in particular its production, transmission, and effects. The science of acoustics has many applications which are dependent upon the nature of the sound that is to be produced, transmitted or controlled. In the case of a desirable sound, such as music, the main application of acoustics is to make the music sound as good as possible.
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Computational Physics
Y. D. Chong · Nanyang Technological University
An introductory course in computational physics for upper-level undergraduates. Topics covered include numerical linear algebra, eigenvalue problems, sparse matrix problems, numerical integration and initial-value problems, Fourier transforms, and Monte Carlo simulations. Programming examples are based on Scientific Python.
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Precalculus
Thomas Tradler and Holly Carley · CUNY New York City College of Technology
These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY. Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use.
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College Algebra
Jay Abramson · Arizona State University
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 Algebraoffers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
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Time Scales Analysis
Svetlin G. Georgiev · Sorbonne University
Time scale theory was first initiated by Stefan Hilger in 1988 in his PhD thesis to unify both approaches of dynamic modelling: difference and differential equations. Similar ideas have been used before and go back in the introduction of the Riemann-Stieltjes integral which unifies sums and integrals. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, tim
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Basic Statistics Using R for Crime Analysis
Jaeyong Choi · West Chester University
This text is for those interested in becoming crime analysts, focusing on learning statistics without delving too deeply into mathematics. Moreover, this book emphasizes practical applications by utilizing R for data analysis, ensuring students can develop relevant skills beyond the university. I hope that students can easily follow the instructions in this book and replicate the same outcomes using the provided data. This practical experience will demonstrate the value of statistics and R.
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Yet Another Introductory Number Theory Textbook - Cryptology Emphasis
Jonathan A. Poritz · Colorado State University – Pueblo
In the contents: 1.01: The Well-Ordering Principle and Mathematical Induction
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Applied Linear Algebra and Differential Equations
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
In the contents: 02: I. A Short Mathematical Review
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Introductory Chemistry (Petersen)
Anne Petersen · Introductory Chemistry (Petersen)
This text is designed as an introduction to the experimental science of chemistry. Using mathematical word problems and chemical terms, students will have an overview of inorganic chemistry. This course is suited for those who have no high school chemistry experience. This course serves as preparation for General Chemistry or the first course of a two-semester sequence that satisfies the requirements of allied health programs (e.g. nursing or dental hygiene) that require one year of chemistry.