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Proofs and Fundamentals: A First Course in Abstract Mathematics

Proofs and Fundamentals: A First Course in Abstract Mathematics
Catalogue Information
Field name Details
Dewey Class 511.3
Title Proofs and Fundamentals (EB) : A First Course in Abstract Mathematics / by Ethan D. Bloch.
Author Bloch, Ethan D. , 1956-
Other name(s) SpringerLink (Online service)
Edition statement 2nd edition
Publication New York, NY : Springer , 2011.
Physical Details XXVI, 358 pages : online resource.
Series Undergraduate texts in mathematics 0172-6056
ISBN 9781441971272
Summary Note 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. Reviews of the first edition: This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course. âZentralblatt Math 'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the bookâs greatest strength is the authorâs zeal and skill for helping students write mathematics better. âMAA Online:
Contents note Preface to the Second Edition -- Preface to the First Edition -- To the Student -- To the Instructor -- Part I. Proofs -- 1. Informal Logic -- 2. Strategies for Proofs -- Part II. Fundamentals -- 3. Sets -- 4. Functions -- 5. Relations -- 6. Finite and Infinite Sets -- Part III. Extras -- 7. Selected Topics -- 8. Explorations -- Appendix: Properties of Numbers -- Bibliography -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-1-4419-7127-2
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