Introduction to discrete mathematics with ISETL:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 194 S. graph. Darst. |
| ISBN: | 0387947825 |
Internformat
MARC
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| 100 | 1 | |a Fenton, William E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to discrete mathematics with ISETL |c William E. Fenton ; Ed Dubinsky |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XVI, 194 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Computer science |x Mathematics | |
| 650 | 4 | |a ISETL (Computer program language) | |
| 650 | 4 | |a Mathematics | |
| 650 | 0 | 7 | |a ISETL |0 (DE-588)4205825-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a ISETL |0 (DE-588)4205825-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dubinsky, Ed |e Verfasser |4 aut | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
COMMENTS FOR THE INSTRUCTOR xi
To the Student xiv
1 NUMBERS AND PROGRAMS 1
1.1 The Basics of ISETL 1
Activities 1
Discussion 1
Beginning with ISETL 1
Some Syntax 3
Familiar Sets of Numbers 3
Decimal Representation 5
Binary Representation 5
Sequences 6
Exercises 6
1.2 Divisibility 9
Activities 9
Discussion 12
ISETL funcs—Functions 12
ISETL smaps—Functions 13
Sources of Functions 14
Recursive Functions 15
Modular Arithmetic 15
Prime Numbers 16
Common Divisors 18
Common Multiples 20
Exercises 21
Overview of Chapter 1 24
2 PROPOSITIONAL CALCULUS 27
2.1 Boolean Expressions 27
Activities 27
Discussion 29
Constants and Variables 29
Basic Operations 30
Functions Using Boolean Values 32
Exercises 33
2.2 Implication and Proof 34
Activities 34
Discussion 36
Conditional Statements 36
Variations of Conditional Statements 37
Direct Proof 38
Indirect Proof 38
Proof by Contradiction 39
Exercises 40
Overview of Chapter 2 41
3 SETS AND TUPLES 43
3.1 Defining Sets and Tuples 43
Activities 43
Discussion 46
Sets and their Elements 46
Tuples and their Elements 48
Forming Sets and Tuples 48
Sequences 50
Recursive Sequences 50
Exercises 51
3.2 Operations on Sets 53
Activities 53
Discussion 55
Cardinality 55
Subsets 55
Basic Combinations of Sets 57
De Morgan s Laws 58
Cartesian Products 59
Inclusion Exclusion 59
Exercises 60
3.3 Counting Methods 62
Activities 62
Discussion 64
The Multiplication Principle 64
Permutations 65
Combinations 66
The Pigeonhole Principle 67
Exercises 68
Overview of Chapter 3 70
4 PREDICATE CALCULUS 73
4.1 Quantified Expressions 73
Activities 73
Discussion 76
Existential and Universal Quantifiers 76
Quantifying over Proposition Valued Functions—
Existential 76
Quantifying over Proposition Valued Functions—
Universal 77
Negations 78
Reasoning about Quantified Expressions .... 78
Exercises 79
4.2 Multi Level Quantification 84
Activities 84
Discussion 87
Quantified Statements that Depend on a Variable 87
Two Level Quantification 89
Negating Two Level Quantifications 90
Reasoning about Two Level Quantifications . . 91
Three Level Quantification 92
Exercises 92
Overview of Chapter 4 96
5 RELATIONS AND GRAPHS 97
5.1 Relations and their Graphs 97
Activities 97
Discussion 99
Relations 99
Representing a Relation 100
Properties of Relations 101
More about Graphs 102
Exercises 103
5.2 Equivalence Relations and Graph Theory 106
Activities 106
Discussion 107
Equivalence Relations 107
Types of Graphs 109
Subgraphs 109
Planarity Ill
Exercises Ill
Overview of Chapter 5 114
6 FUNCTIONS 117
6.1 Representing Functions 117
Activities 117
Discussion 120
Constructing Functions 120
Functions as Expressions 122
Functions as Sequences 122
Functions as Tables 123
Functions as Graphs 124
The Process of a Function 125
Two Definitions 126
Exercises 126
6.2 Properties of Functions 129
Activities 129
Discussion 132
Basic Properties 132
One to One Functions 133
Combinations of Functions 135
Inverse Functions 137
Rate of Growth for Functions 138
Exercises 140
Overview of Chapter 6 143
7 MATHEMATICAL INDUCTION 145
7.1 Understanding the Method 145
Activities 145
Discussion 148
Proposition Valued Functions 148
Eventually Constant Proposition Valued Func¬
tions 148
Implication Valued Functions 149
Modus Ponens 150
Coordinating the Steps 151
Exercises 151
7.2 Using Mathematical Induction 153
Activities 153
Discussion 154
Making Induction Proofs 154
The Induction Principle 156
Complete Induction 156
The Binomial theorem 157
Exercises 158
Overview of Chapter 7 160
8 PARTIAL ORDERS 163
Activities 163
Discussion 164
Order on a Set 164
Diagrams of Posets 165
Topological Sorting 166
Sperner s Theorem 167
Exercises 168
Overview of Chapter 8 170
9 INFINITE SETS 173
Discussion 173
Sets of Equal Cardinality 173
Infinite Sets 174
Countable Sets 174
Uncountable Sets 178
Ordering of Infinite Sets 179
Exercises 180
APPENDIX 1: GETTING STARTED WITH ISETL 182
A. Working in the Execution Window 182
B. Working with Files 184
C. Using Directives 185
D. Graphing in ISETL 186
APPENDIX 2: SOME SPECIAL CODE 188
INDEX 191
INDEX OF FREQUENTLY USED SETS AND FUNCTIONS 194
|
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| callnumber-first | Q - Science |
| callnumber-label | QA39 |
| callnumber-raw | QA39.2 |
| callnumber-search | QA39.2 |
| callnumber-sort | QA 239.2 |
| callnumber-subject | QA - Mathematics |
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| dewey-full | 511.3/078 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/078 |
| dewey-search | 511.3/078 |
| dewey-sort | 3511.3 278 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:08Z |
| institution | BVB |
| isbn | 0387947825 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007443125 |
| oclc_num | 34618085 |
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| physical | XVI, 194 S. graph. Darst. |
| publishDate | 1996 |
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| publisher | Springer |
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| spelling | Fenton, William E. Verfasser aut Introduction to discrete mathematics with ISETL William E. Fenton ; Ed Dubinsky New York [u.a.] Springer 1996 XVI, 194 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Informatik Mathematik Computer science Mathematics ISETL (Computer program language) Mathematics ISETL (DE-588)4205825-9 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Diskrete Mathematik (DE-588)4129143-8 s ISETL (DE-588)4205825-9 s DE-604 Dubinsky, Ed Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007443125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fenton, William E. Dubinsky, Ed Introduction to discrete mathematics with ISETL Informatik Mathematik Computer science Mathematics ISETL (Computer program language) Mathematics ISETL (DE-588)4205825-9 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4205825-9 (DE-588)4129143-8 (DE-588)4123623-3 |
| title | Introduction to discrete mathematics with ISETL |
| title_auth | Introduction to discrete mathematics with ISETL |
| title_exact_search | Introduction to discrete mathematics with ISETL |
| title_full | Introduction to discrete mathematics with ISETL William E. Fenton ; Ed Dubinsky |
| title_fullStr | Introduction to discrete mathematics with ISETL William E. Fenton ; Ed Dubinsky |
| title_full_unstemmed | Introduction to discrete mathematics with ISETL William E. Fenton ; Ed Dubinsky |
| title_short | Introduction to discrete mathematics with ISETL |
| title_sort | introduction to discrete mathematics with isetl |
| topic | Informatik Mathematik Computer science Mathematics ISETL (Computer program language) Mathematics ISETL (DE-588)4205825-9 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Informatik Mathematik Computer science Mathematics ISETL (Computer program language) Mathematics ISETL Diskrete Mathematik Lehrbuch |
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