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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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