Thomas Tymoczko Knihy

Rigorous undergraduate treatment introduces calculus at the basic level, using infinitesimals and concentrating on theory rather than applications. Requires only a solid foundation in high school mathematics. 1. Introduction. 2. Language and Structure. 3. The Hyperreal Numbers. 4. The Hyperreal Line. 5. Continuous Functions. 6. Integral Calculus. 7. Differential Calculus. 8. The Fundamental Theorem. 9. Infinite Sequences and Series. 10. Infinite Polynomials. 11. The Topology of the Real Line. 12. Standard Calculus and Sequences of Functions. Appendixes. Subject Index. Name Index. Numerous figures. 1979 edition.

A revolutionary, introductory text for courses on modern logic. While the basic rudiments of formal and informal logical are all clearly described here, it also focuses students on the real world, where the discipline of logic adds substance and meaning to all kinds of human discourse. Everything from puzzles, paradoxes, and mathematical proofs, to campaign debate excerpts, government regulations, and cartoons are used to show how logic is put to work by philosophers, mathematicians, advertisers, computer scientists, politicians, and others. As the book alternately discusses, instructs, questions, teases, and challenges, readers will find themselves absorbing the fundamentals of the discipline, becoming fluent in the language of logic, understanding how logic works in the real world, and enjoying logic's ability to entertain, surprise, subvert, and enlighten.