Comprehensive mathematics for computer scientists: 1 Sets and numbers, graphs and algebra, logic and machines, linear geometry
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Universitext
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 383 S. Ill., graph. Darst. |
| ISBN: | 3540368736 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | GUERINO MAZZOLA * GERARD MILMEISTER * JODY WEISSMANN COMPREHENSIVE
MATHEMATICS FOR COMPUTER SCIENTISTS 1 SETS AND NUMBERS, GRAPHS AND
ALGEBRA, LOGIC AND MACHINES, LINEAR GEOMETRY (SECOND EDITION) WITH 118
FIGURES |Y SPRINGER CONTENTS I SETS, NUMBERS, AND GRAPHS 1 1
FUNDAMENTALS*CONCEPTS AND LOGIC 3 1.1 PROPOSITIONAL LOGIC 4 1.2
ARCHITECTURE OF CONCEPTS 8 2 AXIOMATIC SET THEORY 15 2.1 THE AXIOMS 17
2.2 BASIC CONCEPTS AND RESULTS 20 3 BOOLEAN SET ALGEBRA 25 3.1 THE
BOOLEAN ALGEBRA OF SUBSETS 25 4 FUNCTIONS AND RELATIONS 29 4.1 GRAPHS
AND FUNCTIONS 29 4.2 RELATIONS 41 5 ORDINAL AND NATURAL NUMBERS 45 5.1
ORDINAL NUMBERS 45 5.2 NATURAL NUMBERS 50 6 RECURSION THEOREM AND
UNIVERSAL PROPERTIES 55 6.1 RECURSION THEOREM 56 6.2 UNIVERSAL
PROPERTIES 58 6.3 UNIVERSAL PROPERTIES IN RELATIONAL DATABASE THEORY 66
7 NATURAL ARITHMETIC 73 7.1 NATURAL OPERATIONS 73 7.2 EUCLID AND THE
NORMAL FORMS 76 8 INFINITIES 79 8.1 THE DIAGONALIZATION PROCEDURE 79 XII
CONTENTS 9 THE CLASSICAL NUMBER DOMAINS 1, Q, R, AND C 81 9.1 INTEGERS Z
82 9.2 RATIONALS Q 87 9.3 REAL NUMBERS R 90 9.4 COMPLEX NUMBERS C 102 10
CATEGORIES OF GRAPHS 107 10.1 DIRECTED AND UNDIRECTED GRAPHS 108 10.2
MORPHISMS OF DIGRAPHS AND GRAPHS 114 10.3 CYCLES 125 11 CONSTRUCTION OF
GRAPHS 129 12 SOME SPECIAL GRAPHS 137 12.1 N-ARY TREES 137 12.2 MOORE
GRAPHS 139 13 PLANARITY 143 13.1 EULER S FORMULA FOR POLYHEDRA 143 13.2
KURATOWSKI S PLANARITY THEOREM 147 14 FIRST ADVANCED TOPIC 149 14.1
FLOATING POINT ARITHMETIC 149 14.2 EXAMPLE FOR AN ADDITION 154 II
ALGEBRA, FORMAL LOGIC, AND LINEAR GEOMETRY 157 15 MONOIDS, GROUPS,
RINGS, AND FIELDS 159 15.1 MONOIDS 159 15.2 GROUPS 163 15.3 RINGS 171
15.4 FIELDS 177 16 PRIMES 181 16.1 PRIME FACTORIZATION 181 16.2 ROOTS OF
POLYNOMIALS AND INTERPOLATION 186 17 FORMAL PROPOSITIONAL LOGIC 191 17.1
SYNTACTICS: THE LANGUAGE OF FORMAL PROPOSITIONAL LOGIC .. 193 17.2
SEMANTICS: LOGICAL ALGEBRAS 196 17.3 SIGNIFICATION: VALUATIONS 200 17.4
AXIOMATICS 203 CONTENTS XIH 18 FORMAL PREDICATE LOGIC 209 18.1
SYNTACTICS: FIRST-ORDER LANGUAGE 211 18.2 SEMANTICS: Z-STRUCTURES 217
18.3 SIGNIFICATION: MODELS 218 19 LANGUAGES, GRAMMARS, AND AUTOMATA 223
19.1 LANGUAGES 224 19.2 GRAMMARS 229 19.3 AUTOMATA AND ACCEPTORS 243 20
CATEGORIES OF MATRIXES 261 20.1 WHAT MATRIXES ARE 262 20.2 STANDARD
OPERATIONS ON MATRIXES 265 20.3 SQUARE MATRIXES AND THEIR DETERMINANT
271 21 MODULES AND VECTOR SPACES 279 22 LINEAR DEPENDENCE, BASES, AND
DIMENSION 287 22.1 BASES IN VECTOR SPACES 288 22.2 EQUATIONS 295 22.3
AFNNE HOMOMORPHISMS 296 23 ALGORITHMS IN LINEAR ALGEBRA 303 23.1 GAUSS
ELIMINATION 303 23.2 THE LUP DECOMPOSITION 307 24 LINEAR GEOMETRY 311
24.1 EUCLIDEAN VECTOR SPACES 311 24.2 TRIGONOMETRIC FUNCTIONS FROM
TWO-DIMENSIONAL ROTATIONS 320 24.3 GRAM S DETERMINANT AND THE SCHWARZ
INEQUALITY 323 25 EIGENVALUES, THE VECTOR PRODUCT, AND QUATERNIONS 327
25.1 EIGENVALUES AND ROTATIONS 327 25.2 THE VECTOR PRODUCT 331 25.3
QUATERNIONS 333 26 SECOND ADVANCED TOPIC 343 26.1 GALOIS FIELDS 343 26.2
THE REED-SOLOMON (RS) ERROR CORRECTION CODE 349 26.3 THE
RIVEST-SHAMIR-ADLEMAN (RSA) ENCRYPTION ALGORITHM . 353 A FURTHER READING
357 XIV CONTENTS B BIBLIOGRAPHY 359 INDEX 363 VOLUME II IN TOPOLOGY AND
CALCULUS LIMITS AND TOPOLOGY, DIFFERENTIABILITY, INVERSE AND IMPLICIT
FUNC- TIONS, INTEGRATION, FUBINI AND CHANGING VARIABLES, VECTOR FIELDS,
FIXPOINTS, MAIN THEOREM OF ODES IV SELECTED HIGHER SUBJECTS NUMERICS,
PROBABILITY AND STATISTICS, SPLINES, FOURIER, WAVELETS, FRACTALS, NEURAL
NETS, GLOBAL COORDINATES AND MANIFOLDS, CATE- GORIES, LAMBDA CALCULUS
|
| adam_txt |
GUERINO MAZZOLA * GERARD MILMEISTER * JODY WEISSMANN COMPREHENSIVE
MATHEMATICS FOR COMPUTER SCIENTISTS 1 SETS AND NUMBERS, GRAPHS AND
ALGEBRA, LOGIC AND MACHINES, LINEAR GEOMETRY (SECOND EDITION) WITH 118
FIGURES |Y SPRINGER CONTENTS I SETS, NUMBERS, AND GRAPHS 1 1
FUNDAMENTALS*CONCEPTS AND LOGIC 3 1.1 PROPOSITIONAL LOGIC 4 1.2
ARCHITECTURE OF CONCEPTS 8 2 AXIOMATIC SET THEORY 15 2.1 THE AXIOMS 17
2.2 BASIC CONCEPTS AND RESULTS 20 3 BOOLEAN SET ALGEBRA 25 3.1 THE
BOOLEAN ALGEBRA OF SUBSETS 25 4 FUNCTIONS AND RELATIONS 29 4.1 GRAPHS
AND FUNCTIONS 29 4.2 RELATIONS 41 5 ORDINAL AND NATURAL NUMBERS 45 5.1
ORDINAL NUMBERS 45 5.2 NATURAL NUMBERS 50 6 RECURSION THEOREM AND
UNIVERSAL PROPERTIES 55 6.1 RECURSION THEOREM 56 6.2 UNIVERSAL
PROPERTIES 58 6.3 UNIVERSAL PROPERTIES IN RELATIONAL DATABASE THEORY 66
7 NATURAL ARITHMETIC 73 7.1 NATURAL OPERATIONS 73 7.2 EUCLID AND THE
NORMAL FORMS 76 8 INFINITIES 79 8.1 THE DIAGONALIZATION PROCEDURE 79 XII
CONTENTS 9 THE CLASSICAL NUMBER DOMAINS 1, Q, R, AND C 81 9.1 INTEGERS Z
82 9.2 RATIONALS Q 87 9.3 REAL NUMBERS R 90 9.4 COMPLEX NUMBERS C 102 10
CATEGORIES OF GRAPHS 107 10.1 DIRECTED AND UNDIRECTED GRAPHS 108 10.2
MORPHISMS OF DIGRAPHS AND GRAPHS 114 10.3 CYCLES 125 11 CONSTRUCTION OF
GRAPHS 129 12 SOME SPECIAL GRAPHS 137 12.1 N-ARY TREES 137 12.2 MOORE
GRAPHS 139 13 PLANARITY 143 13.1 EULER'S FORMULA FOR POLYHEDRA 143 13.2
KURATOWSKI'S PLANARITY THEOREM 147 14 FIRST ADVANCED TOPIC 149 14.1
FLOATING POINT ARITHMETIC 149 14.2 EXAMPLE FOR AN ADDITION 154 II
ALGEBRA, FORMAL LOGIC, AND LINEAR GEOMETRY 157 15 MONOIDS, GROUPS,
RINGS, AND FIELDS 159 15.1 MONOIDS 159 15.2 GROUPS 163 15.3 RINGS 171
15.4 FIELDS 177 16 PRIMES 181 16.1 PRIME FACTORIZATION 181 16.2 ROOTS OF
POLYNOMIALS AND INTERPOLATION 186 17 FORMAL PROPOSITIONAL LOGIC 191 17.1
SYNTACTICS: THE LANGUAGE OF FORMAL PROPOSITIONAL LOGIC . 193 17.2
SEMANTICS: LOGICAL ALGEBRAS 196 17.3 SIGNIFICATION: VALUATIONS 200 17.4
AXIOMATICS 203 CONTENTS XIH 18 FORMAL PREDICATE LOGIC 209 18.1
SYNTACTICS: FIRST-ORDER LANGUAGE 211 18.2 SEMANTICS: Z-STRUCTURES 217
18.3 SIGNIFICATION: MODELS 218 19 LANGUAGES, GRAMMARS, AND AUTOMATA 223
19.1 LANGUAGES 224 19.2 GRAMMARS 229 19.3 AUTOMATA AND ACCEPTORS 243 20
CATEGORIES OF MATRIXES 261 20.1 WHAT MATRIXES ARE 262 20.2 STANDARD
OPERATIONS ON MATRIXES 265 20.3 SQUARE MATRIXES AND THEIR DETERMINANT
271 21 MODULES AND VECTOR SPACES 279 22 LINEAR DEPENDENCE, BASES, AND
DIMENSION 287 22.1 BASES IN VECTOR SPACES 288 22.2 EQUATIONS 295 22.3
AFNNE HOMOMORPHISMS 296 23 ALGORITHMS IN LINEAR ALGEBRA 303 23.1 GAUSS
ELIMINATION 303 23.2 THE LUP DECOMPOSITION 307 24 LINEAR GEOMETRY 311
24.1 EUCLIDEAN VECTOR SPACES 311 24.2 TRIGONOMETRIC FUNCTIONS FROM
TWO-DIMENSIONAL ROTATIONS 320 24.3 GRAM'S DETERMINANT AND THE SCHWARZ
INEQUALITY 323 25 EIGENVALUES, THE VECTOR PRODUCT, AND QUATERNIONS 327
25.1 EIGENVALUES AND ROTATIONS 327 25.2 THE VECTOR PRODUCT 331 25.3
QUATERNIONS 333 26 SECOND ADVANCED TOPIC 343 26.1 GALOIS FIELDS 343 26.2
THE REED-SOLOMON (RS) ERROR CORRECTION CODE 349 26.3 THE
RIVEST-SHAMIR-ADLEMAN (RSA) ENCRYPTION ALGORITHM . 353 A FURTHER READING
357 XIV CONTENTS B BIBLIOGRAPHY 359 INDEX 363 VOLUME II IN TOPOLOGY AND
CALCULUS LIMITS AND TOPOLOGY, DIFFERENTIABILITY, INVERSE AND IMPLICIT
FUNC- TIONS, INTEGRATION, FUBINI AND CHANGING VARIABLES, VECTOR FIELDS,
FIXPOINTS, MAIN THEOREM OF ODES IV SELECTED HIGHER SUBJECTS NUMERICS,
PROBABILITY AND STATISTICS, SPLINES, FOURIER, WAVELETS, FRACTALS, NEURAL
NETS, GLOBAL COORDINATES AND MANIFOLDS, CATE- GORIES, LAMBDA CALCULUS |
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| author | Mazzola, Guerino 1947- Milmeister, Gérard 1971- Weissmann, Jody |
| author_GND | (DE-588)120861437 (DE-588)1120930758 |
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| building | Verbundindex |
| bvnumber | BV021810678 |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)180939872 (DE-599)BVBBV021810678 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T20:45:10Z |
| institution | BVB |
| isbn | 3540368736 |
| language | English |
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| physical | XIV, 383 S. Ill., graph. Darst. |
| publishDate | 2006 |
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| spelling | Mazzola, Guerino 1947- Verfasser (DE-588)120861437 aut Comprehensive mathematics for computer scientists 1 Sets and numbers, graphs and algebra, logic and machines, linear geometry Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann 2. ed. Berlin [u.a.] Springer 2006 XIV, 383 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Milmeister, Gérard 1971- Verfasser (DE-588)1120930758 aut Weissmann, Jody Verfasser aut (DE-604)BV019431205 1 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015022977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazzola, Guerino 1947- Milmeister, Gérard 1971- Weissmann, Jody Comprehensive mathematics for computer scientists |
| title | Comprehensive mathematics for computer scientists |
| title_auth | Comprehensive mathematics for computer scientists |
| title_exact_search | Comprehensive mathematics for computer scientists |
| title_exact_search_txtP | Comprehensive mathematics for computer scientists |
| title_full | Comprehensive mathematics for computer scientists 1 Sets and numbers, graphs and algebra, logic and machines, linear geometry Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann |
| title_fullStr | Comprehensive mathematics for computer scientists 1 Sets and numbers, graphs and algebra, logic and machines, linear geometry Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann |
| title_full_unstemmed | Comprehensive mathematics for computer scientists 1 Sets and numbers, graphs and algebra, logic and machines, linear geometry Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann |
| title_short | Comprehensive mathematics for computer scientists |
| title_sort | comprehensive mathematics for computer scientists sets and numbers graphs and algebra logic and machines linear geometry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015022977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019431205 |
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