![]() We do not make use of these axioms subsequently in the text, but it is valuable for any mathematician to be aware that an axiomatic basis for set theory exists. This section includes a very informal discussion of the Zermelo- Fraenkel Axioms for set theory. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets. 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. 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. ![]() This 3-part work carefully balances Proofs, Fundamentals, and Extras. 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. "Proofs and Fundamentals: A First Course in Abstract Mathematics" 2nd edition 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.
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