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The Art of Proof : Basic Training for Deeper Mathematics

Author: Matthias Beck; Ross Geoghegan
Publisher: New York, NY : Matthias Beck and Ross Geoghegan, 2010.
Series: SpringerLink: Springer e-Books; Undergraduate Texts in Mathematics, 0.
Edition/Format:   Computer file : English : Online-ausgView all editions and formats
Summary:

Written to accompany a one- or two-semester course, this text combines rigor and wit to cover a plethora of topics from integers to uncountable sets. It teaches methods such as axiom, theorem, and  Read more...

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Genre/Form: Einführung
Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Matthias Beck; Ross Geoghegan
ISBN: 9781441970237 1441970231 9781441970220 1441970223
OCLC Number: 663863257
Reproduction Notes: Online-Ausg. Berlin [u.a.] Springer, 2010. online-Ressource.
Description: S.
Contents: Preface.- Notes for the Student.- Notes for Instructors.- Part I: The Discrete.- 1 Integers.- 2 Natural Numbers and Induction.- 3 Some Points of Logic.- 4 Recursion.- 5 Underlying Notions in Set Theory.- 6 Equivalence Relations and Modular Arithmetic.- 7 Arithmetic in Base Ten.- Part II: The Continuous.- 8 Real Numbers.- 9 Embedding Z in R.- 10. Limits and Other Consequences of Completeness.- 11 Rational and Irrational Numbers.- 12 Decimal Expansions.- 13 Cardinality.- 14 Final Remarks.- Further Topics.- A Continuity and Uniform Continuity.- B Public-Key Cryptography.- C Complex Numbers.- D Groups and Graphs.- E Generating Functions.- F Cardinal Number and Ordinal Number.- G Remarks on Euclidean Geometry.- List of Symbols.- Index.
Series Title: SpringerLink: Springer e-Books; Undergraduate Texts in Mathematics, 0.
Responsibility: by Matthias Beck, Ross Geoghegan.
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From the reviews:"The Art of Proof is a surprising union of rigor with taste and wit. The authors take a hard-core axiomatic approach, but the writing is never dry. Instead, topics are carefully Read more...

 
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