The art and craft of problem solving:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Wiley
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 334 S. Ill. |
| ISBN: | 0471135712 |
Staff View
MARC
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Record in the Search Index
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| adam_text | THE ART AND CRAFT OF PROBLEM SOLVING PAUL ZEITZ UNIVERSITY OF SAN
FRANCISCO JOHN WILEY & SONS, INC. CONTENTS PART I IN GENERAL 1 CHAPTER 1
WHAT THIS BOOK IS ABOUT AND HOW TO READ IT 1.1 EXERCISES VS.
PROBLEMS 3 1.2 THE THREE LEVELS OF PROBLEM SOLVING 5 A MOUNTAINEERING
ANALOGY 5 FROM MOUNTAINEERING TO MATHEMATICS 6 1.3 A PROBLEM SAMPLER 8
RECREATIONAL PROBLEMS 8 CONTEST PROBLEMS 9 OPEN-ENDED PROBLEMS 11 1.4
HOW TO READ THIS BOOK 13 CHAPTER 2 STRATEGIES FOR INVESTIGATING PROBLEMS
15 2.1 PSYCHOLOGICAL STRATEGIES 16 MENTAL TOUGHNESS: LEARN FROM POLYA S
MOUSE 16 CREATIVITY 19 PROBLEMS AND EXERCISES 25 2.2 STRATEGIES FOR
GETTING STARTED 29 THE FIRST STEP: ORIENTATION 29 I M ORIENTED. NOW
WHAT? 30 PROBLEMS AND EXERCISES 40 2.3 METHODS OF ARGUMENT 44 COMMON
ABBREVIATIONS AND STYLISTIC CONVENTIONS 45 DEDUCTION AND SYMBOLIC LOGIC
46 ARGUMENT BY CONTRADICTION 46 MATHEMATICAL INDUCTION 50 PROBLEMS AND
EXERCISES 55 2.4 OTHER IMPORTANT STRATEGIES 58 DRAW A PICTURE! 59
PICTURES DON T HELP? RECAST THE PROBLEM IN OTHER WAYS! 60 CHANGE YOUR
POINT OF VIEW 64 PROBLEMS AND EXERCISES 65 XIII XIV CONTENTS CHAPTER 3
FUNDAMENTAL TACTICS FOR SOLVING PROBLEMS 68 3.1 SYMMETRY 69 GEOMETRIC
SYMMETRY 70 ALGEBRAIC SYMMETRY 74 PROBLEMS AND EXERCISES 79 3.2 THE
EXTREME PRINCIPLE 82 PROBLEMS AND EXERCISES 91 3.3 THE PIGEONHOLE
PRINCIPLE 92 BASIC PIGEONHOLE 92 INTERMEDIATE PIGEONHOLE 94 ADVANCED
PIGEONHOLE 96 PROBLEMS AND EXERCISES 100 3.4 INVARIANTS 102 PARITY 104
MODULAR ARITHMETIC AND COLORING 110 MONOVARIANTS 112 PROBLEMS AND
EXERCISES 116 CHAPTER 4 THREE IMPORTANT CROSSOVER TACTICS 119 4.1 GRAPH
THEORY 119 CONNECTIVITY AND CYCLES 121 EULERIAN AND HAMILTONIAN PATHS
123 THE TWO MEN OF TIBET 126 PROBLEMS AND EXERCISES 128 4.2 COMPLEX
NUMBERS 131 BASIC OPERATIONS 131 ROOTS OF UNITY 137 SOME APPLICATIONS
138 PROBLEMS AND EXERCISES 141 4.3 GENERATING FUNCTIONS 143 INTRODUCTORY
EXAMPLES 144 RECURRENCE RELATIONS 145 PARTITIONS 146 PROBLEMS AND
EXERCISES 152 CONTENTS XV PART II SPECIFICS 155 CHAPTER 5 ALGEBRA 157
5.1 SETS, NUMBERS, AND FUNCTIONS 157 SETS 157 FUNCTIONS 159 PROBLEMS AND
EXERCISES 160 5.2 ALGEBRAIC MANIPULATION REVISITED 162 THE FACTOR TACTIC
163 MANIPULATING SQUARES 164 SUBSTITUTIONS AND SIMPLIFICATIONS 165
PROBLEMS AND EXERCISES 170 5.3 SUMS AND PRODUCTS 171 NOTATION 171
ARITHMETIC SERIES 172 GEOMETRIC SERIES AND THE TELESCOPE TOOL 173
INFINITE SERIES 175 PROBLEMS AND EXERCISES / 78 5.4 POLYNOMIALS 179
POLYNOMIAL OPERATIONS 180 THE ZEROS OF A POLYNOMIAL 181 PROBLEMS AND
EXERCISES 188 5.5 INEQUALITIES 189 FUNDAMENTAL IDEAS 190 THE AM-GM
INEQUALITY 192 MASSAGE, CAUCHY-SCHWARZ, AND CHEBYSHEV 197 PROBLEMS AND
EXERCISES 202 CHAPTER 6 COMBINATORICS 205 6.1 INTRODUCTION TO COUNTING
205 PERMUTATIONS AND COMBINATIONS 205 COMBINATORIAL ARGUMENTS 208
PASCAL S TRIANGLE AND THE BINOMIAL THEOREM 209 STRATEGIES AND TACTICS OF
COUNTING 212 PROBLEMS AND EXERCISES 212 6.2 PARTITIONS AND BIJECTIONS
213 COUNTING SUBSETS 213 INFORMATION MANAGEMENT 216 BALLS IN URNS AND
OTHER CLASSIC ENCODINGS 220 PROBLEMS AND EXERCISES 222 XVI CONTENTS 6.3
THE PRINCIPLE OF INCLUSION-EXCLUSION 225 COUNT THE COMPLEMENT 225 PIE
WITH SETS 226 PIE WITH INDICATOR FUNCTIONS 230 PROBLEMS AND EXERCISES
232 6.4 RECURRENCE 233 TILING AND THE FIBONACCI RECURRENCE 234 THE
CATALAN RECURRENCE 236 PROBLEMS AND EXERCISES 239 CHAPTER 7 NUMBER
THEORY 243 7.1 PRIMES AND DIVISIBILITY 243 THE FUNDAMENTAL THEOREM OF
ARITHMETIC 243 GCD, LCM, AND THE DIVISION ALGORITHM 245 PROBLEMS AND
EXERCISES 249 7.2 CONGRUENCE 251 WHAT S SO GOOD ABOUT PRIMES? 253
FERMAT S LITTLE THEOREM 253 PROBLEMS AND EXERCISES 255 7.3 NUMBER
THEORETIC FUNCTIONS 257 DIVISOR SUMS 257 PHI AND MU 259 PROBLEMS AND
EXERCISES 261 7.4 DIOPHANTINE EQUATIONS 263 GENERAL STRATEGY AND TACTICS
264 PROBLEMS AND EXERCISES 269 7.5 MISCELLANEOUS INSTRUCTIVE EXAMPLES
271 CAN A POLYNOMIAL ALWAYS OUTPUT PRIMES? 271 IF YOU CAN COUNT IT, IT S
AN INTEGER 273 A COMBINATORIAL PROOF OF FERMAT S LITTLE THEOREM 273 SUMS
OF TWO SQUARES 274 PROBLEMS AND EXERCISES 277 CHAPTER 8 CALCULUS 282 8.1
THE FUNDAMENTAL THEOREM OF CALCULUS 282 8.2 CONVERGENCE AND CONTINUITY
284 CONVERGENCE 285 CONTINUITY 288 UNIFORM CONTINUITY 289 PROBLEMS AND
EXERCISES 290 CONTENTS XVII 8.3 DIFFERENTIATION AND INTEGRATION 294
APPROXIMATION AND CURVE SKETCHING 294 THE MEAN VALUE THEOREM 297 A
USEFUL TOOL 300 INTEGRATION 301 PROBLEMS AND EXERCISES 303 8.4 POWER
SERIES AND EULERIAN MATHEMATICS 305 DON T WORRY! 308 TAYLOR SERIES WITH
REMAINDER 310 EULERIAN MATHEMATICS 312 PROBLEMS AND EXERCISES 315
APPENDIX A HINTS TO SELECTED PROBLEMS 319 REFERENCES 328 INDEX 330
|
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| discipline | Mathematik |
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| spelling | Zeitz, Paul Verfasser aut The art and craft of problem solving Paul Zeitz New York Wiley 1999 XVII, 334 S. Ill. txt rdacontent n rdamedia nc rdacarrier Probleemoplossing gtt Résolution de problème Wiskunde gtt Mathematik aProblem solving Mathematik (DE-588)4037944-9 gnd rswk-swf Problemlösen (DE-588)4076358-4 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematik (DE-588)4037944-9 s Problemlösen (DE-588)4076358-4 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013221479&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zeitz, Paul The art and craft of problem solving Probleemoplossing gtt Résolution de problème Wiskunde gtt Mathematik aProblem solving Mathematik (DE-588)4037944-9 gnd Problemlösen (DE-588)4076358-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4076358-4 (DE-588)4143389-0 |
| title | The art and craft of problem solving |
| title_auth | The art and craft of problem solving |
| title_exact_search | The art and craft of problem solving |
| title_full | The art and craft of problem solving Paul Zeitz |
| title_fullStr | The art and craft of problem solving Paul Zeitz |
| title_full_unstemmed | The art and craft of problem solving Paul Zeitz |
| title_short | The art and craft of problem solving |
| title_sort | the art and craft of problem solving |
| topic | Probleemoplossing gtt Résolution de problème Wiskunde gtt Mathematik aProblem solving Mathematik (DE-588)4037944-9 gnd Problemlösen (DE-588)4076358-4 gnd |
| topic_facet | Probleemoplossing Résolution de problème Wiskunde Mathematik aProblem solving Problemlösen Aufgabensammlung |
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