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Proofs and fundamentals: a first course in abstract mathematics

By: Bloch, Ethan D.
Publisher: New York Springer 2013Edition: 2nd.Description: xxiv, 359 p.ISBN: 9781461428107.Subject(s): Proof theory | Combinatorial analysis | Symbolic and mathematicalDDC classification: 511.3 Summary: This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis. This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. http://www.springer.com/in/book/9781441971265
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Slot 1353 (0 Floor, East Wing) Non-fiction 511.3 B5P7 (Browse shelf) Available 194959

Table of Contents

Part I. Proofs.
1. Informal logic --
2. Strategies for proofs --

Part II. Fundamentals.
3. Sets --
4. Functions --
5. Relations --
6. Finite sets and infinite sets --

Part III. Extras.
7. Selected topics --
8. Explorations.

This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis.

This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations.

A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised.


http://www.springer.com/in/book/9781441971265

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