40 Mathematics
General
A Gentle Introduction to the Art of Mathematics
Joe Fields (Southern Connecticut State University)
2023
GNU Free Documentation Licence
This text covers several topics in the foundations of mathematics (logic, sets, relations, functions and cardinality) and introduces the reader to many techniques of mathematical proof (direct, indirect, contradiction, contrapositive, mathematical induction, combinatorial proofs and magic). There are amusing quotations at the start of each chapter.
Format: PDF
Mathematical Reasoning: Writing and Proof
Ted Sundstrom (Grand Valley State University)
2014
Licence: CC BY-NC-SA
This textbook is designed for the first course in a mathematics curriculum that introduces students to the processes of constructing and writing proofs. It focuses on the formal development of mathematics.
Format: PDF
Proofs and Concepts: The Fundamentals of Abstract Mathematics
Dave Witte Morris and Joy Morris (University of Lethbridge)
2013
Licence: CC BY-NC-SA
This textbook has been created and used at the University of Lethbridge. It provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics.
Format: LaTeX and PDF
Technical Mathematics 2e
Morgan Chase
2024
Licence: CC BY-NC-SA
This developmental-level mathematics textbook is intended for career-technical students. It is FREE online and costs $17.35 in print plus shipping; don’t get tricked into paying for access! The approach is conversational—inviting rather than intimidating—and many of the examples are drawn from everyday life rather than from the technical trades. Practice assignments are available on the MyOpenMath platform.
Format: Online, PDF, EPUB
Algebra
Abstract Algebra
Tom Judson
2022
GNU Free Documentation Licence
This text is designed to teach the principles and theory of abstract algebra. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Format: Online, PDF, EPUB
Algebra and Trigonometry 2e
Jay Abramson (Arizona State University)
2021
Licence: CC BY
Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
Format: PDF
College Algebra 2e (OpenStax)
Jay Abramson (Arizona State University)
2021
Licence: CC BY
College Algebra 2e provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for