Proofs and Fundamentals: A First Course in Abstract Mathematics"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." "The excellent exposition, organization and choice of topics will make this text valuable for classroom use as well as for the general reader who wants to gain a deeper understanding of how modern mathematics is currently practiced by mathematicians." -- Book Jacket. |
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Proofs and Fundamentals: A First Course in Abstract Mathematics Ethan D. Bloch No preview available - 2000 |
Common terms and phrases
A₁ algebraic argument assume axioms bijective map binary operation Chapter codomain complex numbers compute contradiction Corollary countably infinite deduce denote the set discussed equation equivalence relation example exists fact Fibonacci numbers finite sets following theorem formula function f fuzzy greatest lower bound Hasse diagrams Hence holds homomorphism hypothesis identity element implies integers intuitively lattices least upper bound left inverse Lemma Let f Let G logical map f map ƒ mathematical induction mathematicians natural numbers non-empty set notation number systems order homomorphism order isomorphism Peano Postulates poset positive integer possible prime numbers properties Prove Theorem quantifiers rational numbers reader in Exercise real numbers reflexive result right inverse Section 6.1 sequence Show statement subgroup subset Suppose surjective symbols symmetric tion total ordering true truth table Uiel unique verify write