How to think like a mathematician: a companion to undergraduate mathematics
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
[2009]
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | xi, 265 Seiten Illustrationen |
ISBN: | 9780521895460 9780521719780 |
Internformat
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Datensatz im Suchindex
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adam_text |
Titel: How to think like a mathematician
Autor: Houston, Kevin
Jahr: 2009
Contents
Preface Page ix
I Study skills for mathematicians 1
1 Sets and functions 3
2 Reading mathematics 14
3 Writing mathematics I 21
4 Writing mathematics II 35
5 How to solve problems 41
II How to think logically 51
6 Making a statement 53
7 Implications 63
8 Finer points concerning implications 69
9 Converse and equivalence 75
10 Quantifiers - For all and There exists 80
11 Complexity and negation of quantifiers 84
12 Examples and counterexamples 90
13 Summary of logic 96
III Definitions, theorems and proofs 97
14 Definitions, theorems and proofs 99
15 How to read a definition 103
16 How to read a theorem 109
17 Proof 116
18 How to read a proof 119
19 A study of Pythagoras' Theorem 126
IV Techniques of proof 137
20 Techniques of proof I: Direct method 139
21 Some common mistakes 149
22 Techniques of proof II: Proof by cases 155
23 Techniques of proof HI: Contradiction 161
24 Techniques of proof IV: Induction 166
viii Contents
25 More sophisticated induction techniques 175
26 Techniques of proof V: Contrapositive method 180
V Mathematics that all good mathematicians need 185
27 Divisors 187
28 The Euclidean Algorithm 196
29 Modular arithmetic 208
30 Injective, surjective, bijective - and a bit about infinity 218
31 Equivalence relations 230
VI Closing remarks 241
32 Putting it all together 243
33 Generalization and specialization 248
34 True understanding 252
35 The biggest secret 255
Appendices 257
A Greek alphabet 257
B Commonly used symbols and notation 258
C How to prove that. 260
Index 263 |
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isbn | 9780521895460 9780521719780 |
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spelling | Houston, Kevin 1968- (DE-588)137824874 aut How to think like a mathematician a companion to undergraduate mathematics Kevin Houston Cambridge [u.a.] Cambridge University Press [2009] © 2009 xi, 265 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematik Mathematics Mathematikstudium (DE-588)4037947-4 gnd rswk-swf (DE-588)4048476-2 Ratgeber gnd-content Mathematikstudium (DE-588)4037947-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018962940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Houston, Kevin 1968- How to think like a mathematician a companion to undergraduate mathematics Mathematik Mathematics Mathematikstudium (DE-588)4037947-4 gnd |
subject_GND | (DE-588)4037947-4 (DE-588)4048476-2 |
title | How to think like a mathematician a companion to undergraduate mathematics |
title_auth | How to think like a mathematician a companion to undergraduate mathematics |
title_exact_search | How to think like a mathematician a companion to undergraduate mathematics |
title_full | How to think like a mathematician a companion to undergraduate mathematics Kevin Houston |
title_fullStr | How to think like a mathematician a companion to undergraduate mathematics Kevin Houston |
title_full_unstemmed | How to think like a mathematician a companion to undergraduate mathematics Kevin Houston |
title_short | How to think like a mathematician |
title_sort | how to think like a mathematician a companion to undergraduate mathematics |
title_sub | a companion to undergraduate mathematics |
topic | Mathematik Mathematics Mathematikstudium (DE-588)4037947-4 gnd |
topic_facet | Mathematik Mathematics Mathematikstudium Ratgeber |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018962940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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