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This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a disti

This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations

“Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to s

This book treats learning a programming language much like learning a spoken language: programming is best learned by immersion. Through building interesting programs and addressing real design issues much earlier than other texts, this title moves beyond the mere syntax and discusses the serious architecture of programs: how delegation and inheritance allow objects to cooperate effectively. The text is filled with programs for realistic applications. These programs are much closer to those the student will encounter in the 'real world' than those in traditional texts. Furthermore, the authors constantly revise the programs as they grow in sophistication so students learn another important aspect of real-world programming: that programs are constantly updated, modified and improved. Finally, in the exercises, the authors encourage students to write programs that interact with programs that they have prepared, and then ask them to write about those programs.