Dreams of calculus: perspectives on mathematics education
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 158 S. Ill., graph. Darst. |
| ISBN: | 3540219765 |
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Record in the Search Index
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|---|---|
| adam_text | JOHAN HOFFMAN CLAES JOHNSON ANDERS LOGG DREAMS OF CALCULUS PERSPECTIVES
ON MATHEMATICS EDUCATION FYA SPRINGER CONTENTS I PERSPECTIVES 1 1
INTRODUCTION 3 1.1 THE MATHEMATICS DELEGATION AND ITS MAIN TASK . . . .
3 1.2 CRISIS AND CHANGE OF PARADIGM, OR NOT? 4 1.3 THE BODY&SOUL PROJECT
4 1.4 SAME QUESTIONS IN ALL COUNTRIES 5 1.5 WHY WE WROTE THIS BOOK 5 2
WHAT? HOW? FOR WHOM? WHY? 7 2.1 MATHEMATICS AND THE COMPUTER 7 2.2 PURE
AND COMPUTATIONAL MATHEMATICS 8 2.3 THE BODY&SOUL REFORM PROJECT 11 2.4
DIFFICULTIES OF LEARNING 12 2.5 DIFFICULTIES OF DISCUSSION , 13 2.6
SUMMING UP THE DIFFICULTIES 14 3 A BRIEF HISTORY OF MATHEMATICS
EDUCATION 15 3.1 PROM PYTHAGORAS TO CALCULUS AND LINEAR ALGEBRA ... 15
3.2 FROM VON NEUMANN INTO MODERN SOCIETY 16 3.3 MATHEMATICS EDUCATION
AND THE COMPUTER 17 3.4 THE MULTIPLICATION TABLE 17 3.5 AGAIN: WHAT? 18
X CONTENTS 4 WHAT IS MATHEMATICS? 19 4.1 INTRODUCTION 19 4.2 THE MODERN
WORLD 19 4.3 THE ROLE OF MATHEMATICS 23 4.4 DESIGN AND PRODUCTION OF
CARS 26 4.5 NAVIGATION: FROM STARS TO GPS 26 4.6 MEDICAL TOMOGRAPHY 26
4.7 MOLECULAR DYNAMICS AND MEDICAL DRUG DESIGN . . . . 27 4.8 WEATHER
PREDICTION AND GLOBAL WARMING 28 4.9 ECONOMY: STOCKS AND OPTIONS 28 4.10
THE WORLD OF DIGITAL IMAGE, WORD AND SOUND 29 4.11 LANGUAGES 29 4.12
MATHEMATICS AS THE LANGUAGE OF SCIENCE 30 4.13 THE BASIC AREAS OF
MATHEMATICS 30 4.14 WHAT IS SCIENCE? 31 4.15 MATHEMATICS IS DIFFICULT:
CHOOSE YOUR OWN LEVEL OF AMBITION 32 4.16 SOME PARTS OF MATHEMATICS ARE
EASY 32 4.17 INCREASED/DECREASED IMPORTANCE OF MATHEMATICS ... 33 5
VIRTUAL REALITY AND THE MATRIX 35 5.1 VIRTUAL REALITY 35 5.2 DIGITAL
CAMERAS 36 5.3 MP3 36 5.4 MATRIX AND MARILYN MONROE 36 6 MOUNTAIN
CLIMBING 39 7 SCIENTIFIC REVOLUTIONS 41 7.1 GALILEO AND THE MARKET 41
7.2 THOMAS KUHN AND SCIENTIFIC REVOLUTIONS 42 7.3 SHIFT OF PARADIGM IN
MATHEMATICS? 42 7.4 QUARRELLING MATHEMATICIANS 43 7.5 CHANGE OF
PARADIGM? OR NOT? 43 7.6 TO PROVE OR PROVE NOT 44 7.7 THE ROLE OF TEXT
BOOKS 44 8 EDUCATION IS BASED ON SCIENCE 45 8.1 THE SCIENTIFIC BASIS OF
STANDARD CALCULUS 45 8.2 A NEW SCIENTIFIC BASIS 46 8.3 THE SCIENTIFIC
BASIS OF BODY&SOUL 47 CONTENTS XI 9 THE UNREASONABLE EFFECTIVENESS OF
MATHEMATICS IN THE NATURAL SCIENCES? 49 9.1 NEWTON S MODEL OF
GRAVITATION 50 9.2 LAPLACE S MODEL OF GRAVITATION 51 9.3 MOLECULAR
DYNAMICS 51 9.4 EINSTEIN S LAW OF GRAVITATION 52 9.5 THE NAVIER-STOKES
EQUATIONS FOR FLUID DYNAMICS ... 52 9.6 SCHRODINGER S EQUATION 52 9.7
DISCUSSION OF EFFECTIVENESS 53 9.8 WEATHER PREDICTION 54 10 DO WE LIVE
IN THE BEST OF WORLDS ? 57 11 THE REASONABLE EFFECTIVENESS OF
COMPUTATIONAL MATHEMATICS 59 11.1 THE SOLAR SYSTEM: NEWTON S EQUATIONS
60 11.2 TURBULENCE: NAVIER-STOKES EQUATIONS 61 11.3 SCHRODINGER S
EQUATION 61 11.4 EINSTEIN S EQUATION 62 11.5 COMPARING ANALYTICAL AND
COMPUTATIONAL SOLUTION TECHNIQUES 62 11.6 ALGORITHMIC INFORMATION THEORY
63 11.7 HOW SMART IS AN ELECTRON? 64 11.8 THE HUMAN GENOME PROJECT 65 12
JAZZ/POP/FOLK VS. CLASSICAL MUSIC 67 13 THE RIGHT TO NOT KNOW 69 14 AN
AGENDA 71 14.1 FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 71 14.2 NEW
POSSIBILITIES FOR MATHEMATICS EDUCATION . . . . . 72 II ESSENCE 73 15 A
VERY SHORT CALCULUS COURSE 75 15.1 INTRODUCTION *. 75 15.2 ALGEBRAIC
EQUATIONS 76 15.3 DIFFERENTIAL EQUATIONS 76 15.4 GENERALIZATION 81 15.5
LEIBNIZ TEEN-AGE DREAM 82 15.6 SUMMARY 85 15.7 LEIBNIZ 86 XII CONTENTS
16 THE SOLAR SYSTEM 89 16.1 INTRODUCTION 89 16.2 NEWTON S EQUATION 90
16.3 EINSTEIN S EQUATION 92 16.4 THE SOLAR SYSTEM AS A SYSTEM OF ODES 94
16.5 PREDICTABILITY AND COMPUTABILITY 95 16.6 ADAPTIVE TIME-STEPPING 98
16.7 LIMITS OF COMPUTABILITY AND PREDICTABILITY 99 17 TURBULENCE AND THE
CLAY PRIZE 101 17.1 THE CLAY INSTITUTE $1 MILLION PRIZE 101 17.2 ARE
TURBULENT SOLUTIONS UNIQUE AND SMOOTH? 103 17.3 WELL-POSEDNESS ACCORDING
TO HADAMARD 104 17.4 IS MATHEMATICS A SCIENCE? 105 17.5 A COMPUTATIONAL
APPROACH TO THE PROBLEM 106 17.6 THE NAVIER-STOKES EQUATIONS 109 17.7
THE BASIC ENERGY ESTIMATE FOR THE NAVIER-STOKES EQUATIONS 110 17.8 WEAK
SOLUTIONS ILL 17.9 COMPUTATIONAL SOLUTION ILL 17.10 OUTPUT ERROR
REPRESENTATION 112 17.11 THE DUAL PROBLEM 113 17.12 OUTPUT UNIQUENESS OF
WEAK SOLUTIONS 114 17.13 COMPUTATIONAL RESULTS 115 17.14 CONCLUSION 119
18 DO MATHEMATICIANS QUARREL? 121 18.1 INTRODUCTION 121 18.2 THE
FORMALISTS 124 18.3 THE LOGICISTS AND SET THEORY 124 18.4 THE
CONSTRUCTIVISTS 127 18.5 THE PEANO AXIOM SYSTEM FOR NATURAL NUMBERS . .
. . 129 18.6 REAL NUMBERS 130 18.7 CANTOR VERSUS KRONECKER 131 18.8
DECIDING WHETHER A NUMBER IS RATIONAL OR IRRATIONAL . 132 18.9 THE SET
OF ALL POSSIBLE BOOKS 133 18.10 RECIPES AND GOOD FOOD 134 18.11 THE NEW
MATH IN ELEMENTARY EDUCATION 135 18.12 THE SEARCH FOR RIGOR IN
MATHEMATICS 135 18.13 A NON-CONSTRUCTIVE PROOF 136 18.14 SUMMARY 137
CONTENTS XIII III APPENDIX 141 A COMMENTS ON THE DIRECTIVES OF THE
MATHEMATICS DELEGATION 143 A.I THE DIRECTIVES 143 A.2 COMMENTS 144 A.3 A
SUM UP 145 B PREFACE TO BODY&SOUL 147 C PUBLIC DEBATE 155
|
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| isbn | 3540219765 |
| language | English |
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| physical | XIII, 158 S. Ill., graph. Darst. |
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| spelling | Hoffman, Johan Verfasser aut Dreams of calculus perspectives on mathematics education Johan Hoffman ; Claes Johnson ; Anders Logg Berlin [u.a.] Springer 2004 XIII, 158 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calcul infinitésimal Calculus Computermathematik (DE-588)4788218-9 gnd rswk-swf Computermathematik (DE-588)4788218-9 s DE-604 Johnson, Claes Verfasser aut Logg, Anders 1976- Verfasser (DE-588)1022132792 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012900345&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoffman, Johan Johnson, Claes Logg, Anders 1976- Dreams of calculus perspectives on mathematics education Calcul infinitésimal Calculus Computermathematik (DE-588)4788218-9 gnd |
| subject_GND | (DE-588)4788218-9 |
| title | Dreams of calculus perspectives on mathematics education |
| title_auth | Dreams of calculus perspectives on mathematics education |
| title_exact_search | Dreams of calculus perspectives on mathematics education |
| title_full | Dreams of calculus perspectives on mathematics education Johan Hoffman ; Claes Johnson ; Anders Logg |
| title_fullStr | Dreams of calculus perspectives on mathematics education Johan Hoffman ; Claes Johnson ; Anders Logg |
| title_full_unstemmed | Dreams of calculus perspectives on mathematics education Johan Hoffman ; Claes Johnson ; Anders Logg |
| title_short | Dreams of calculus |
| title_sort | dreams of calculus perspectives on mathematics education |
| title_sub | perspectives on mathematics education |
| topic | Calcul infinitésimal Calculus Computermathematik (DE-588)4788218-9 gnd |
| topic_facet | Calcul infinitésimal Calculus Computermathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012900345&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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