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Introduction to Discrete Mathematics via Logic and Proof
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with …
Undergraduate Algebra
This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the hnear algebra from the other basic …
Undergraduate Analysis
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with …
Calculus of Several Variables
This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered. The presentation is self-contained, assuming only a …
An Introduction to Complex Function Theory
This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of …
Geometry: Euclid and Beyond
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school …
The Art of Proof
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an …
Complex Analysis
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven …
Rational Points on Elliptic Curves
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, …
Real Mathematical Analysis
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures …
Finite-Dimensional Vector Spaces
“The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a …
Ideals, Varieties, and Algorithms
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of …