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Read more about Euclid's Elements Redux

Euclid's Elements Redux

Contributor: Callahan

Publisher: Sample

"Euclid's 'Elements' Redux" is an open textbook on mathematical logic and geometry based on Euclid's "Elements" for use in grades 7-12 and in undergraduate college courses on proof writing.

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Read more about Impact of Materials on Society

Impact of Materials on Society

Contributors: Acord, Jones, and Bryant

Publisher: University of Florida

This textbook supports the Impact of Materials on Society course and teaching materials, developed with the Materials Research Society. The textbook offers an exploration into materials (including ceramics, clay, concrete, glass, metals, and polymers) and the relationship with technologies and social structures. The textbook was developed by an interdisciplinary team from Engineering and Liberal Arts and Sciences, including anthropologists, sociologists, historians, media studies experts, Classicists, and more.

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Read more about Optimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences

Optimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences

Contributors: Belevan, Hamidi, Malhotra, and Yeager

Publisher: Bruno Belevan, Parham Hamidi, Nisha Malhotra, and Elyse Yeager

Optimal, Integral, Likely is a free, open-source textbook intended for UBC’s course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences. It is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Read more about Measure, Integration & Real Analysis

Measure, Integration & Real Analysis

Contributor: Axler

Publisher: Sheldon Axler

This book seeks to provide students with a deep understanding of the definitions, examples, theorems, and proofs related to measure, integration, and real analysis. The content and level of this book fit well with the first-year graduate course on these topics at most American universities. This textbook features a reader-friendly style and format that will appeal to today's students.

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Read more about Elementary Calculus

Elementary Calculus

Contributor: Corral

Publisher: Michael Corral

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences).

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Read more about The Joy of Cryptography

The Joy of Cryptography

Contributor: Rosulek

Publisher: Oregon State University

The pedagogical approach is anchored in formal definitions/proof of security, but in a way that I believe is more accessible than what is "traditional" in crypto. All security definitions are written in a unified and simplified "game-based" style. For an example of what security definitions look like in this style, see the index of security definitions (which will make more sense after reading chapters 2 & 4).

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Read more about Transition to Higher Mathematics: Structure and Proof - Second Edition

Transition to Higher Mathematics: Structure and Proof - Second Edition

Contributors: Dumas and McCarthy

Publisher: Open Scholarship

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.

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Read more about Elementary Abstract Algebra: Examples and Applications

Elementary Abstract Algebra: Examples and Applications

Contributors: Hill and Thron

Publisher: Justin Hill and Chris Thron

This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.

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Read more about A Cool Brisk Walk Through Discrete Mathematics

A Cool Brisk Walk Through Discrete Mathematics

Contributor: Davies

Publisher: University of Mary Washington

A Cool, Brisk Walk Through Discrete Mathematics, an innovative and non-traditional approach to learning Discrete Math, is available for low cost from Blurb or via free download.

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Read more about Multivariable Calculus

Multivariable Calculus

Contributor: Shimamoto

Publisher: Don Shimamoto

This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.

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