# Pure Textbooks

#### Filters

## Mathematical Reasoning: Writing and Proof

Contributor: Sundstrom

Publisher: Independent

License: CC BY-NC-SA

This textbook is designed for the first course in the college mathematics curriculum that introduces students to the process of constructing and writing proofs.

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## Calculus I

Contributors: Marsden and Weinstein

Publisher: Independent

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems.

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## Calculus II

Contributors: Marsden and Weinstein

Publisher: Independent

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems.

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## Calculus III

Contributors: Marsden and Weinstein

Publisher: Independent

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems.

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## Elements of Abstract and Linear Algebra

Contributor: Connell

Publisher: Independent

This book is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. The first three or four chapters can stand alone as a one semester course in abstract algebra. However they are structured to provide the background for the chapter on linear algebra. Chapter 2 is the most difficult part of the book because groups are written in additive and multiplicative notation, and the concept of coset is confusing at first. After Chapter 2 the book gets easier as you go along. Indeed, after the first four chapters, the linear algebra follows easily. Finishing the chapter on linear algebra gives a basic one year undergraduate course in abstract algebra. Chapter 6 continues the material to complete a first year graduate course. Classes with little background can do the first three chapters in the first semester, and chapters 4 and 5 in the second semester. More advanced classes can do four chapters the first semester and chapters 5 and 6 the second semester. As bare as the first four chapters are, you still have to truck right along to finish them in one semester.

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## Algebra: Abstract and Concrete

Contributor: Goodman

Publisher: Independent

This text provides a thorough introduction to “modern” or “abstract” algebra at a level suitable for upper-level undergraduates and beginning graduate students.

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## Elementary Number Theory: Primes, Congruences, and Secrets

Contributor: Stein

Publisher: Independent

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergrad- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington.

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## A First Course in Complex Analysis

Copyright Year: 2014

Contributors: Beck, Marchesi, Pixton, and Sabalka

Publisher: Independent

These are the lecture notes of a one-semester undergraduate course which we have taught several times at Binghamton University (SUNY) and San Francisco State University. For many of our students, complex analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated “from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.

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## Single Variable Calculus I: Early Transcendentals

Contributor: Guichard

Publisher: Independent

License: CC BY-NC-SA

The emphasis in this course is on problems—doing calculations and story problems. To master problem solving one needs a tremendous amount of practice doing problems. The more problems you do the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to them. You will learn quickly and effectively if you devote some time to doing problems every day. Typically the most difficult problems are story problems, since they require some effort before you can begin calculating. Here are some pointers for doing story problems:

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## Arithmetic - Number Sense and Variable Expressions

Copyright Year: 2012

Contributor: Patel

Publisher: Independent

License: CC BY-NC-SA

Arithmetic - Number Sense and Variable Expressionsprovides a comprehensive introduction of basic arithmetic.

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