# Mathematics Textbooks

## 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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## Technical Mathematics

Contributor: Chase

Publisher: Oregon State University

This developmental-level mathematics textbook is intended for career-technical students.

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## 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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## Math in Society: Mathematics for liberal arts majors

Contributor: Lee

Publisher: Portland Community College Math Department

We dedicate this book to our students. May you have greater ease in paying for college and grow your proficiency and confidence in math.

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## First Semester in Numerical Analysis with Python

Contributor: Liu

Publisher: Auraria Institutional Repository

The book is based on “First semester in Numerical Analysis with Julia”, written by Giray Ökten. The contents of the original book are retained, while all the algorithms are implemented in Python (Version 3.8.0). Python is an open source (under OSI), interpreted, general-purpose programming language that has a large number of users around the world. Python is ranked the third in August 2020 by the TIOBE programming community index, a measure of popularity of programming languages, and is the top-ranked interpreted language. We hope this book will better serve readers who are interested in a first course in Numerical Analysis, but are more familiar with Python for the implementation of the algorithms.

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## 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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## 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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## 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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## 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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## Introduction to Game Theory: a Discovery Approach

Contributor: Nordstrom

Publisher: Jennifer Firkins Nordstrom

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in each of these sections are intended to serve as essay prompts for writing assignments.

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