Discrete mathematics using a computer:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 339 S. graph. Darst. |
| ISBN: | 1852330899 |
Internformat
MARC
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| 084 | |a MAT 050f |2 stub | ||
| 084 | |a DAT 500f |2 stub | ||
| 100 | 1 | |a Hall, Cordelia |d 1955- |e Verfasser |0 (DE-588)120908972 |4 aut | |
| 245 | 1 | 0 | |a Discrete mathematics using a computer |c Cordelia Hall and John O'Donnell |
| 264 | 1 | |a London [u.a.] |b Springer |c 2000 | |
| 300 | |a XVIII, 339 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Computer science - Mathematics | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x Data processing | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a HASKELL |0 (DE-588)4318275-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Programmierung |0 (DE-588)4076370-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mengenlehre |0 (DE-588)4074715-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |D s |
| 689 | 0 | 1 | |a HASKELL |0 (DE-588)4318275-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a HASKELL |0 (DE-588)4318275-6 |D s |
| 689 | 1 | 1 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
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| 689 | 2 | 0 | |a Mengenlehre |0 (DE-588)4074715-3 |D s |
| 689 | 2 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a O'Donnell, John |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008766844&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008766844 | |
Datensatz im Suchindex
| _version_ | 1807772870653247488 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
TO
HASKELL
.
1
1.1
OBTAINING
AND
RUNNING
HASKELL
.
2
1.2
EXPRESSIONS
.
4
1.2.1
INTEGER
AND
INT
.
4
1.2.2
RATIONAL
AND
FLOATING
POINT
NUMBERS
.
6
1.2.3
BOOLEANS
.
6
1.2.4
CHARACTERS
.
7
1.2.5
STRINGS
.
8
1.3
BASIC
DATA
STRUCTURES:
TUPLES
AND
LISTS
.
8
1.3.1
TUPLES
.
8
1.3.2
LISTS
.
9
1.3.3
LIST
NOTATION
AND
(:)
.
10
1.3.4
LIST
COMPREHENSIONS
.
10
1.4
FUNCTIONS
.
12
1.4.1
FUNCTION
APPLICATION
.
13
1.4.2
FUNCTION
TYPES
.
13
1.4.3
OPERATORS
AND
FUNCTIONS
.
13
1.4.4
FUNCTION
DEFINITIONS
.
14
1.4.5
PATTERN
MATCHING
.
14
1.4.6
EQUATIONAL
REASONING
.
17
1.4.7
HIGHER
ORDER
FUNCTIONS
.
18
1.5
CONDITIONAL
EXPRESSIONS
.
19
1.6
LOCAL
VARIABLES:
LET
EXPRESSIONS
.
19
1.7
TYPE
VARIABLES
.
20
1.8
COMMON
FUNCTIONS
ON
LISTS
.
21
1.9
DATA
TYPE
DEFINITIONS
.
26
1.10
TYPE
CLASSES
AND
OVERLOADING
.
29
1.11
SUGGESTIONS
FOR
FURTHER
READING
.
31
1.12
REVIEW
EXERCISES
.
31
XIV
CONTENTS
2
PROPOSITIONAL
LOGIC
.
35
2.1
THE
NEED
FOR
FORMALISM
.
37
2.2
THE
BASIC
LOGICAL
OPERATORS
.
38
2.2.1
LOGICAL
AND
(A)
.
39
2.2.2
INCLUSIVE
LOGICAL
OR
(V)
.
40
2.2.3
EXCLUSIVE
LOGICAL
OR
()
.
41
2.2.4
LOGICAL
NOT
(-YY)
.
41
2.2.5
LOGICAL
IMPLICATION
(- )
.
41
2.2.6
LOGICAL
EQUIVALENCE
( - )
.
43
2.3
THE
LANGUAGE
OF
PROPOSITIONAL
LOGIC
.
44
2.3.1
THE
SYNTAX
OF
WELL-FORMED
FORMULAS
.
44
2.3.2
PRECEDENCE
OF
LOGICAL
OPERATORS
.
46
2.3.3
OBJECT
LANGUAGE
AND
META-LANGUAGE
.
46
2.3.4
COMPUTING
WITH
BOOLEAN
EXPRESSIONS
.
47
2.4
TRUTH
TABLES:
SEMANTIC
REASONING
.
48
2.4.1
TRUTH
TABLE
CALCULATIONS
AND
PROOFS
.
48
2.4.2
LIMITATIONS
OF
TRUTH
TABLES
.
49
2.4.3
COMPUTING
TRUTH
TABLES
.
50
2.5
NATURAL
DEDUCTION:
INFERENCE
REASONING
.
50
2.5.1
DEFINITIONS
OF
TRUE,
-
AND
O
.
52
2.5.2
AND
INTRODUCTION
{A/}
.
.
.
54
2.5.3
AND
ELIMINATION
{AE^},
{AE
R
}
.
56
2.5.4
IMPLY
ELIMINATION
{
-
E}
.
57
2.5.5
IMPLY
INTRODUCTION
{
-
1}
.
58
2.5.6
OR
INTRODUCTION
{V/^},
{V/
R
}
.
61
2.5.7
OR
ELIMINATION
{VE}
.
62
2.5.8
IDENTITY
{ID}
.
63
2.5.9
CONTRADICTION
{CTR}
.
63
2.5.10
REDUCTIO
AD
ABSURDUM
{RAA}
.
65
2.5.11
INFERRING
THE
OPERATOR
TRUTH
TABLES
.
66
2.6
PROOF
CHECKING
BY
COMPUTER
.
67
2.6.1
EXAMPLE
OF
PROOF
CHECKING
.
68
2.6.2
REPRESENTATION
OF
WFFS
.
72
2.6.3
REPRESENTING
PROOFS
.
73
2.7
BOOLEAN
ALGEBRA:
EQUATIONS!
REASONING
.
74
2.7.1
THE
LAWS
OF
BOOLEAN
ALGEBRA
.
76
2.7.2
OPERATIONS
WITH
CONSTANTS
.
76
2.7.3
BASIC
PROPERTIES
OF
A
AND
V
.
78
2.7.4
DISTRIBUTIVE
AND
DEMORGAN
'
S
LAWS
.
79
2.7.5
LAWS
ON
NEGATION
.
80
2.7.6
LAWS
ON
IMPLICATION
.
80
2.7.7
EQUIVALENCE
.
81
2.8
LOGIC
IN
COMPUTER
SCIENCE
.
81
2.9
METALOGIC
.
83
CONTENTS
XV
2.10
SUGGESTIONS
FOR
FURTHER
READING
.
84
2.11
REVIEW
EXERCISES
.
86
3
PREDICATE
LOGIC
.
89
3.1
THE
LANGUAGE
OF
PREDICATE
LOGIC
.
89
3.1.1
PREDICATES
.
89
3.1.2
QUANTIFIERS
.
90
3.1.3
EXPANDING
QUANTIFIED
EXPRESSIONS
.
92
3.1.4
THE
SCOPE
OF
VARIABLE
BINDINGS
.
94
3.1.5
TRANSLATING
BETWEEN
ENGLISH
AND
LOGIC
.
95
3.2
COMPUTING
WITH
QUANTIFIERS
.
98
3.3
LOGICAL
INFERENCE
WITH
PREDICATES
.
100
3.3.1
UNIVERSAL
INTRODUCTION
{VI}
.
101
3.3.2
UNIVERSAL
ELIMINATION
{VE}
.
103
3.3.3
EXISTENTIAL
INTRODUCTION
{21}
.
104
3.3.4
EXISTENTIAL
ELIMINATION
{BE}
.
105
3.4
ALGEBRAIC
LAWS
OF
PREDICATE
LOGIC
.
106
3.5
SUGGESTIONS
FOR
FURTHER
READING
.
109
3.6
REVIEW
EXERCISES
.
109
4
SET
THEORY
.
ILL
4.1
NOTATIONS
FOR
DESCRIBING
SETS
.
ILL
4.2
BASIC
OPERATIONS
ON
SETS
.
114
4.2.1
SUBSETS
AND
SET
EQUALITY
.
114
4.2.2
UNION,
INTERSECTION
AND
DIFFERENCE
.
114
4.2.3
COMPLEMENT
AND
POWER
.
116
4.3
FINITE
SETS
WITH
EQUALITY
.
117
4.3.1
COMPUTING
WITH
SETS
.
119
4.4
SET
LAWS
.
122
4.4.1
ASSOCIATIVE
AND
COMMUTATIVE
SET
OPERATIONS
.
123
4.4.2
DISTRIBUTIVE
LAWS
.
124
4.4.3
DEMORGAN
'
S
LAWS
FOR
SETS
.
124
4.5
SUGGESTIONS
FOR
FURTHER
READING
.
125
4.6
REVIEW
EXERCISES
.
125
5
RECURSION
.
129
5.1
RECURSION
OVER
LISTS
.
130
5.2
HIGHER
ORDER
RECURSIVE
FUNCTIONS
.
136
5.3
RECURSION
OVER
TREES
.
139
5.4
PEANO
ARITHMETIC
.
142
5.5
DATA
RECURSION
.
143
5.6
SUGGESTIONS
FOR
FURTHER
READING
.
144
5.7
REVIEW
EXERCISES
.
144
XVI
CONTENTS
6
INDUCTIVELY
DEFINED
SETS
.
147
6.1
THE
IDEA
BEHIND
INDUCTION
.
147
6.1.1
THE
INDUCTION
RULE
.
150
6.2
HOW
TO
DEFINE
A
SET
USING
INDUCTION
.
152
6.2.1
INDUCTIVE
DEFINITION
OF
THE
SET
OF
NATURAL
NUMBERS
.
.
.
153
6.2.2
THE
SET
OF
BINARY
MACHINE
WORDS
.
154
6.3
DEFINING
THE
SET
OF
INTEGERS
.
155
6.3.1
FIRST
ATTEMPT
.
155
6.3.2
SECOND
ATTEMPT
.
156
6.3.3
THIRD
ATTEMPT
.
156
6.3.4
FOURTH
ATTEMPT
.
158
6.3.5
FIFTH
ATTEMPT
.
159
6.4
SUGGESTIONS
FOR
FURTHER
READING
.
159
6.5
REVIEW
EXERCISES
.
159
7
INDUCTION
.
163
7.1
THE
PRINCIPLE
OF
MATHEMATICAL
INDUCTION
.
164
7.2
INDUCTION
ON
NATURAL
NUMBERS
.
165
7.3
INDUCTION
AND
RECURSION
.
168
7.4
INDUCTION
ON
PEANO
NATURALS
.
169
7.5
INDUCTION
ON
LISTS
.
172
7.6
FUNCTIONAL
EQUALITY
.
177
7.7
INDUCTION
ON
TREES
.
179
7.8
PITFALLS
AND
COMMON
MISTAKES
.
181
7.8.1
A
HORSE
OF
ANOTHER
COLOUR
.
181
7.9
LIMITATIONS
OF
INDUCTION
.
181
7.10
SUGGESTIONS
FOR
FURTHER
READING
.
183
7.11
REVIEW
EXERCISES
.
183
8
RELATIONS
.
185
8.1
BINARY
RELATIONS
.
185
8.2
REPRESENTING
RELATIONS
WITH
DIGRAPHS
.
187
8.3
COMPUTING
WITH
BINARY
RELATIONS
.
188
8.4
PROPERTIES
OF
RELATIONS
.
190
8.4.1
REFLEXIVE
RELATIONS
.
190
8.4.2
IRREFLEXIVE
RELATIONS
.
191
8.4.3
SYMMETRIC
RELATIONS
.
193
8.4.4
ANTISYMMETRIC
RELATIONS
.
195
8.4.5
TRANSITIVE
RELATIONS
.
197
8.5
RELATIONAL
COMPOSITION
.
199
8.6
POWERS
OF
RELATIONS
.
202
8.7
CLOSURE
PROPERTIES
OF
RELATIONS
.
207
8.7.1
REFLEXIVE
CLOSURE
.
208
8.7.2
SYMMETRIC
CLOSURE
.
210
8.7.3
TRANSITIVE
CLOSURE
.
211
CONTENTS
XVII
8.8
ORDER
RELATIONS
.
214
8.8.1
PARTIAL
ORDER
.
214
8.8.2
QUASI
ORDER
.
219
8.8.3
LINEAR
ORDER
.
220
8.8.4
WELL
ORDER
.
221
8.8.5
TOPOLOGICAL
SORT
.
222
8.9
EQUIVALENCE
RELATIONS
.
223
8.10
SUGGESTIONS
FOR
FURTHER
READING
.
226
8.11
REVIEW
EXERCISES
.
226
9
FUNCTIONS
.
229
9.1
THE
GRAPH
OF
A
FUNCTION
.
230
9.2
FUNCTIONS
IN
PROGRAMMING
.
233
9.2.1
INDUCTIVELY
DEFINED
FUNCTIONS
.
234
9.2.2
PRIMITIVE
RECURSION
.
235
9.2.3
COMPUTATIONAL
COMPLEXITY
.
236
9.2.4
STATE
.
237
9.3
HIGHER
ORDER
FUNCTIONS
.
238
9.3.1
FUNCTIONS
THAT
TAKE
FUNCTIONS
AS
ARGUMENTS
.
239
9.3.2
FUNCTIONS
THAT
RETURN
FUNCTIONS
.
240
9.3.3
MULTIPLE
ARGUMENTS
AS
TUPLES
.
242
9.3.4
MULTIPLE
RESULTS
AS
A
TUPLE
.
243
9.3.5
MULTIPLE
ARGUMENTS
WITH
HIGHER
ORDER
FUNCTIONS
.
.
.
243
9.4
TOTAL
AND
PARTIAL
FUNCTIONS
.
244
9.5
FUNCTION
COMPOSITION
.
249
9.6
PROPERTIES
OF
FUNCTIONS
.
253
9.6.1
SURJECTIVE
FUNCTIONS
.
253
9.6.2
INJECTIVE
FUNCTIONS
.
255
9.6.3
THE
PIGEONHOLE
PRINCIPLE
.
258
9.7
BIJECTIVE
FUNCTIONS
.
258
9.7.1
PERMUTATIONS
.
259
9.7.2
INVERSE
FUNCTIONS
.
261
9.8
CARDINALITY
OF
SETS
.
261
9.8.1
THE
RATIONAL
NUMBERS
ARE
COUNTABLE
.
264
9.8.2
THE
REAL
NUMBERS
ARE
UNCOUNTABLE
.
264
9.9
SUGGESTIONS
FOR
FURTHER
READING
.
266
9.10
REVIEW
EXERCISES
.
266
10
DISCRETE
MATHEMATICS
IN
CIRCUIT
DESIGN
.
273
10.1
BOOLEAN
LOGIC
GATES
.
274
10.2
FUNCTIONAL
CIRCUIT
SPECIFICATION
.
275
10.2.1
CIRCUIT
SIMULATION
.
276
10.2.2
CIRCUIT
SYNTHESIS
FROM
TRUTH
TABLES
.
277
10.2.3
MULTIPLEXORS
.
280
10.2.4
BIT
ARITHMETIC
.
281
XVIII
CONTENTS
10.2.5
BINARY
REPRESENTATION
.
284
10.3
RIPPLE
CARRY
ADDITION
.
285
10.3.1
CIRCUIT
PATTERNS
.
286
10.3.2
THE
N-BIT
RIPPLE
CARRY
ADDER
.
288
10.3.3
CORRECTNESS
OF
THE
RIPPLE
CARRY
ADDER
.
289
10.3.4
BINARY
COMPARISON
.
290
10.4
SUGGESTIONS
FOR
FURTHER
READING
.
292
10.5
REVIEW
EXERCISES
.
292
A
SOFTWARE
TOOLS
FOR
DISCRETE
MATHEMATICS
.
295
B
RESOURCES
ON
THE
WEB
.
297
C
SOLUTIONS
TO
SELECTED
EXERCISES
.
299
C.L
INTRODUCTION
TO
HASKELL
.
299
C.2
PROPOSITIONAL
LOGIC
.
302
C.3
PREDICATE
LOGIC
.
308
C.4
SET
THEORY
.
310
C.5
RECURSION
.
312
C.6
INDUCTIVELY
DEFINED
SETS
.
316
C.7
INDUCTION
.
318
C.8
RELATIONS
.
323
C.9
FUNCTIONS
.
325
C.10
DISCRETE
MATHEMATICS
IN
CIRCUIT
DESIGN
.
327
BIBLIOGRAPHY
.
331
INDEX
.
333 |
| any_adam_object | 1 |
| author | Hall, Cordelia 1955- O'Donnell, John |
| author_GND | (DE-588)120908972 |
| author_facet | Hall, Cordelia 1955- O'Donnell, John |
| author_role | aut aut |
| author_sort | Hall, Cordelia 1955- |
| author_variant | c h ch j o jo |
| building | Verbundindex |
| bvnumber | BV012879127 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.95 |
| callnumber-search | QA76.95 |
| callnumber-sort | QA 276.95 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| classification_tum | MAT 050f DAT 500f |
| ctrlnum | (OCoLC)41070963 (DE-599)BVBBV012879127 |
| dewey-full | 004.0151 510/.285 |
| dewey-hundreds | 000 - Computer science, information, general works 500 - Natural sciences and mathematics |
| dewey-ones | 004 - Computer science 510 - Mathematics |
| dewey-raw | 004.0151 510/.285 |
| dewey-search | 004.0151 510/.285 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV012879127 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:15:56Z |
| institution | BVB |
| isbn | 1852330899 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008766844 |
| oclc_num | 41070963 |
| open_access_boolean | |
| owner | DE-703 DE-824 DE-859 DE-20 DE-739 DE-898 DE-BY-UBR DE-1028 DE-706 DE-634 DE-188 |
| owner_facet | DE-703 DE-824 DE-859 DE-20 DE-739 DE-898 DE-BY-UBR DE-1028 DE-706 DE-634 DE-188 |
| physical | XVIII, 339 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| spelling | Hall, Cordelia 1955- Verfasser (DE-588)120908972 aut Discrete mathematics using a computer Cordelia Hall and John O'Donnell London [u.a.] Springer 2000 XVIII, 339 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computer science - Mathematics Datenverarbeitung Informatik Mathematik Mathematics Data processing Mathematische Logik (DE-588)4037951-6 gnd rswk-swf HASKELL (DE-588)4318275-6 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 s HASKELL (DE-588)4318275-6 s DE-604 Mathematische Logik (DE-588)4037951-6 s Programmierung (DE-588)4076370-5 s 1\p DE-604 Mengenlehre (DE-588)4074715-3 s 2\p DE-604 O'Donnell, John Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008766844&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hall, Cordelia 1955- O'Donnell, John Discrete mathematics using a computer Computer science - Mathematics Datenverarbeitung Informatik Mathematik Mathematics Data processing Mathematische Logik (DE-588)4037951-6 gnd HASKELL (DE-588)4318275-6 gnd Programmierung (DE-588)4076370-5 gnd Mengenlehre (DE-588)4074715-3 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4318275-6 (DE-588)4076370-5 (DE-588)4074715-3 (DE-588)4129143-8 |
| title | Discrete mathematics using a computer |
| title_auth | Discrete mathematics using a computer |
| title_exact_search | Discrete mathematics using a computer |
| title_full | Discrete mathematics using a computer Cordelia Hall and John O'Donnell |
| title_fullStr | Discrete mathematics using a computer Cordelia Hall and John O'Donnell |
| title_full_unstemmed | Discrete mathematics using a computer Cordelia Hall and John O'Donnell |
| title_short | Discrete mathematics using a computer |
| title_sort | discrete mathematics using a computer |
| topic | Computer science - Mathematics Datenverarbeitung Informatik Mathematik Mathematics Data processing Mathematische Logik (DE-588)4037951-6 gnd HASKELL (DE-588)4318275-6 gnd Programmierung (DE-588)4076370-5 gnd Mengenlehre (DE-588)4074715-3 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Computer science - Mathematics Datenverarbeitung Informatik Mathematik Mathematics Data processing Mathematische Logik HASKELL Programmierung Mengenlehre Diskrete Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008766844&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hallcordelia discretemathematicsusingacomputer AT odonnelljohn discretemathematicsusingacomputer |