Proofs and Fundamentals
A First Course in Abstract Mathematics, Originaltitel:Proofs and Fundementals: A First Course in Abstract Mathematics
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ISBN-13:
9781441971265
Veröffentl:
2011
Erscheinungsdatum:
21.02.2011
Seiten:
359
Autor:
Ethan D. Bloch
Gewicht:
736 g
Format:
239x158x28 mm
Serie:
Undergraduate Texts in Mathematics
Sprache:
Englisch
Beschreibung:
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.
A gentle, friendly style is used, in which motivation and informal discussion play a key role The material is presented in the way that mathematicians actually use it; good mathematical tast is preferred to overly clever pedagogy There is an important section devoted to the proper writing of proofs
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
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