Table of contents:
Basic Logic. Methods of Proof. Set Theory. Axioms of Set Theory, Paradoxes, and Rigor. Number Systems. More on the Real Number System. Examples of Axiomatic Theories. Solutions to Selected Exercises. Bibliography. Index.
The gap between the rote, calculational learning of calculus and ordinary differential equations and the more theoretical learning of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, brought thoroughly up to date, and expanded, more than ever, the second edition of this classic builds the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs.
Basic Logic. Methods of Proof. Set Theory. Axioms of Set Theory, Paradoxes, and Rigor. Number Systems. More on the Real Number System. Examples of Axiomatic Theories. Solutions to Selected Exercises. Bibliography. Index.
The gap between the rote, calculational learning of calculus and ordinary differential equations and the more theoretical learning of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, brought thoroughly up to date, and expanded, more than ever, the second edition of this classic builds the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs.
The great strength of the book overall and of the chapters I read is a very accessible writing style, and extremely good exercises. The mix of discussion of advanced topics alongside the presentation of more elementary material is excellent. This is a product of having a highly accomplished and knowledgeable mathematician writing a textbook intended for not-so-advanced students.--David Walnut, George Washington University