Proofs and Fundamentals: A First Course in Abstract Mathematics (Repost)

ISBN: 0817641114

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Posted on 2011-03-14. By anonymous.

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Proofs and Fundamentals: A First Course in Abstract Mathematics

Publisher: Birkhäuser Boston | pages: 445 | 2000 | ISBN: 0817641114 | PDF | 14,5 mb

"Proofs and Fundamentals: A First Course in Abstract Mathematics" is designed as a 'transition' course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra, and real analysis.

This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material including sets, functions, and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics, and the Peano Postulates. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and writing are never compromised. The material is presented in the way that mathematicians actually use it; good mathematical taste is preferred to overly clever pedagogy. There is a key section devoted to the proper writing of proofs. The text has over 400 exercises, ranging from straightforward examples to very challenging proofs.

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