Proofs and fundamentals: a first course in abstract mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 424 S. Ill., graph. Darst. |
| ISBN: | 9780817641115 3764341114 0817641114 |
Internformat
MARC
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| 020 | |a 0817641114 |9 0-8176-4111-4 | ||
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| 100 | 1 | |a Bloch, Ethan D. |d 1956- |e Verfasser |0 (DE-588)143980874 |4 aut | |
| 245 | 1 | 0 | |a Proofs and fundamentals |b a first course in abstract mathematics |c Ethan D. Bloch |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2000 | |
| 300 | |a XX, 424 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Ensembles, Théorie des | |
| 650 | 4 | |a Preuve, Théorie de la | |
| 650 | 4 | |a Proof theory | |
| 650 | 4 | |a Set theory | |
| 650 | 0 | 7 | |a Beweistheorie |0 (DE-588)4145177-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127977056763904 |
|---|---|
| adam_text | Contents
Introduction
ix
To the
Student xiii
To the Instructor
xix
Parti PROOFS
1
1
Informal Logic
3
1.1
Introduction
......................... 3
1.2
Statements
.......................... 4
1.3
Relations Between Statements
............... 18
1.4
Valid Arguments
...................... 31
1.5
Quantifiers
.......................... 41
2
Strategies for Proofs
55
2.1
Mathematical Proofs
—
What They Are and
Why We Need Them
.................... 55
2.2
Direct Proofs
........................ 63
2.3
Proofs by
Contrapositive
and Contradiction
........ 67
2.4
Cases, and If and Only If
.................. 74
2.5
Quantifiers in Theorems
.................. 81
2.6
Writing Mathematics
.................... 93
Partii
FUNDAMENTALS
105
3
Sets
107
3.1
Introduction
......................... 107
3.2
Sets
—
Basic Definitions
.................. 109
3.3
Set Operations
........................ 119
3.4
Indexed Families of Sets
.................. 129
4
Functions
135
4.1
Functions
..........................135
4.2
Image and Inverse Image
.................. 145
4.3
Composition and Inverse Functions
............. 152
4.4
Injectivity, Surjectivity and Bijectivity
........... 161
4.5
Sets of Functions
...................... 170
5
Relations
177
5.1
Relations
.......................... 177
5.2
Congruence
......................... 184
5.3
Equivalence Relations
.................... 191
6
Infinite and Finite Sets
203
6.1
Cardinality of Sets
..................... 203
6.2
Cardinality of the Number Systems
............. 218
6.3
Mathematical Induction
................... 226
6.4
Recursion
.......................... 236
Partili
EXTRAS
249
7
Selected Topics
251
7.1
Binary Operations
...................... 251
7.2
Groups
............................ 258
7.3
Homomorphisms and Isomorphisms
............ 267
7.4
Partially Ordered Sets
.................... 273
7.5
Lattices
........................... 284
7.6
Counting: Products and Sums
................ 294
7.7
Counting: Permutations and Combinations
......... 304
8
Number
Systems
323
8.1
Back to the Beginning
................... 323
8.2
The Natural Numbers
.................... 324
8.3
Further Properties of the Natural Numbers
......... 333
8.4
The Integers
......................... 338
8.5
The Rational Numbers
................... 348
8.6
The Real Numbers and the Complex Numbers
....... 352
8.7
Appendix: Proof of Theorem
8.2.1............. 361
9
Explorations
363
9.1
Introduction
......................... 363
9.2
Greatest Common Divisors
................. 364
9.3
Divisibility Tests
...................... 366
9.4
Real-Valued Functions
................... 367
9.5
Iterations of Functions
................... 368
9.6
Fibonacci Numbers and Lucas Numbers
.......... 369
9.7
Fuzzy Sets
.......................... 371
Appendix: Properties of Numbers
375
Hints for Selected Exercises
379
References
405
Index
413
|
| any_adam_object | 1 |
| author | Bloch, Ethan D. 1956- |
| author_GND | (DE-588)143980874 |
| author_facet | Bloch, Ethan D. 1956- |
| author_role | aut |
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| author_variant | e d b ed edb |
| building | Verbundindex |
| bvnumber | BV013220088 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.54 |
| callnumber-search | QA9.54 |
| callnumber-sort | QA 19.54 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 SK 130 |
| ctrlnum | (OCoLC)43427798 (DE-599)BVBBV013220088 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| id | DE-604.BV013220088 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:41:55Z |
| institution | BVB |
| isbn | 9780817641115 3764341114 0817641114 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009007887 |
| oclc_num | 43427798 |
| open_access_boolean | |
| owner | DE-20 DE-739 DE-29 DE-634 DE-11 |
| owner_facet | DE-20 DE-739 DE-29 DE-634 DE-11 |
| physical | XX, 424 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Bloch, Ethan D. 1956- Verfasser (DE-588)143980874 aut Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch Boston [u.a.] Birkhäuser 2000 XX, 424 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007887&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bloch, Ethan D. 1956- Proofs and fundamentals a first course in abstract mathematics Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4145177-6 |
| title | Proofs and fundamentals a first course in abstract mathematics |
| title_auth | Proofs and fundamentals a first course in abstract mathematics |
| title_exact_search | Proofs and fundamentals a first course in abstract mathematics |
| title_full | Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch |
| title_fullStr | Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch |
| title_full_unstemmed | Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch |
| title_short | Proofs and fundamentals |
| title_sort | proofs and fundamentals a first course in abstract mathematics |
| title_sub | a first course in abstract mathematics |
| topic | Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007887&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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