Introduction to mathematical proofs: a transition
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Series: | Textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | VIII, 425 S. graph. Darst. |
| ISBN: | 9781420069556 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
νπ
1
Logic
1.1
Statements, Negation, and Compound Statements
...... 2
1.2
Truth Tables and Logical Equivalences
........... 9
1.3
Conditional and Biconditional Statements
......... 21
oq
1.4
Logical Arguments
...................
1.5
Open Statements and Quantifiers
.............
45
1.6
Chapter Review
....................
60
2
Deductive Mathematical Systems and Proofs
69
2.1
Deductive Mathematical Systems
.............
69
on
2.2
Mathematical Proofs
..................
2.2.1
Techniques for Proving the Conditional Statement
Ρ
=>
Q
81
on
2.2.2
Additional Proof Techniques
............
S9
2.2.3
Conjectures, Proofs, and Disproofs
. ......... 100
2.2.3
The System of Rational Numbers and the System of Real ^
Numbers
.....................
119
2.3
Chapter Review
....................
125
3
Set Theory
1
Orí
3.1
Sets and Subsets
....................
133
3.2
Set Operations
.....................
144
3.3
Additional Set Operations
................
3.4
Generalized Set Union and Intersection
..........
159
... 168
3.5
Chapter Review
..............
^
175
4
Relations
..... 175
4.1
Relations
..............
4.2
The Order Relations
<,<,>,>.............
4.3
Reflexive, Symmetric, Transitive, and Equivalence Relations
. . 197
4.4
Equivalence Relations, Equivalence Classes, and Partitions
. . 205
4.5
Chapter Review
...................
VI
5
Functions
219
5.1
Functions
....................... 219
5.2
Onto Functions, One-to-One Functions, and One-to-One
Correspondences
.................... 231
5.3
Inverse of a Function
.................. 240
5.4
Images and Inverse Images of Sets
............. 249
5.5
Chapter Review
.................... 256
6
Mathematical Induction
261
6.1
Mathematical Induction
................. 261
6.2
The Well-Ordering Principle and the Fundamental Theorem of
Arithmetic
....................... 267
7
Cardinalities of Sets
275
7.1
Finite Sets
....................... 276
7.2
Denumerable and Countable Sets
............. 283
7.3
Uncountable Sets
.................... 289
8
Proofs from Real Analysis
297
8.1
Sequences
....................... 297
8.2
Limit Theorems for Sequences
.............. 307
8.3
Monotone Sequences and Subsequences
.......... 313
8.4
Cauchy Sequences
................... 321
9
Proofs from Group Theory
325
9.1
Binary Operations and Algebraic Structures
........ 325
9.2
Groups
........................ 331
9.3
Subgroups and Cyclic Groups
.............. 338
A Reading and Writing Mathematical Proofs
349
Answers to Selected Exercises
357
References
415
Index
417
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| any_adam_object | 1 |
| author | Roberts, Charles E. |
| author_facet | Roberts, Charles E. |
| author_role | aut |
| author_sort | Roberts, Charles E. |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA9 |
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| callnumber-search | QA9.54 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)373482414 (DE-599)BVBBV035649525 |
| dewey-full | 511.36 511.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.36 511.3/6 |
| dewey-search | 511.36 511.3/6 |
| dewey-sort | 3511.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Roberts, Charles E. Verfasser aut Introduction to mathematical proofs a transition Charles E. Roberts Boca Raton [u.a.] CRC Press 2009 VIII, 425 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematics Proof theory Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie (DE-588)4145177-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Beweistheorie (DE-588)4145177-6 s Mathematik (DE-588)4037944-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017704148&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017704148&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Roberts, Charles E. Introduction to mathematical proofs a transition Proof theory Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie (DE-588)4145177-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4037944-9 (DE-588)4151278-9 |
| title | Introduction to mathematical proofs a transition |
| title_auth | Introduction to mathematical proofs a transition |
| title_exact_search | Introduction to mathematical proofs a transition |
| title_full | Introduction to mathematical proofs a transition Charles E. Roberts |
| title_fullStr | Introduction to mathematical proofs a transition Charles E. Roberts |
| title_full_unstemmed | Introduction to mathematical proofs a transition Charles E. Roberts |
| title_short | Introduction to mathematical proofs |
| title_sort | introduction to mathematical proofs a transition |
| title_sub | a transition |
| topic | Proof theory Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie (DE-588)4145177-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Proof theory Textbooks Logic, Symbolic and mathematical Textbooks Beweistheorie Mathematik Einführung |
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