How to solve it: a new aspect of mathematical method
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Ishi Press Internat.
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 253 S. Ill., graph. Darst. |
| ISBN: | 4871878309 9784871878302 |
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Datensatz im Suchindex
| _version_ | 1804143679808471040 |
|---|---|
| adam_text | Contents
From the Preface to the First Printing
v
From the Preface to the Seventh Printing
viii
Preface to the Second Edition
ix
How To Solve It list
xvi
Introduction
xix
PART I. IN THE CLASSROOM
Purpose
1. Helping the student
ι
2.
Questions, recommendations,
mental operations
ι
3.
Generality
2
4.
Common sense
3
5.
Teacher and student. Imitation and practice
3
Main divisions, main questions
6.
Four phases
5
7.
Understanding the problem
б
8.
Example
7
9.
Devising a plan
8
10.
Example
10
11.
Carrying out the plan
12
xi
xii Contents
із.
Example
13
13.
Looking back
14
14.
Example
16
15.
Various approaches
19
16.
The teacher s method of questioning
20
17.
Good questions and bad questions
22
More examples
18.
A problem of construction
19.
A problem to prove
20.
A rate problem
PART II. HOW TO SOLVE IT
A dialogue
33
PART III. SHORT DICTIONARY
OF HEURISTIC
Analogy
Auxiliary elements
Auxiliary problem
Bolzano
Bright idea
Can you check the result?
Can you derive the result diSerently?
Can you use the result?
Carrying out
Contents xiii
Condition
72
Contradictory!
73
Corollary
73
Could you derive something useful from the data?
73
Could you restate the problem?!
75
Decomposing and recombining
75
Definition
85
Descartes
92
Determination, hope, success
93
Diagnosis
94
Did you use all the data?
95
Do you know a related problem?
98
Draw a figuref
99
Examine your guess
99
Figures
103
Generalization
108
Have you seen it before?
110
Here is a problem related to yours
and solved before
110
Heuristic
112
Heuristic reasoning
113
If you cannot solve the proposed problem
114
Induction and mathematical induction
114
Inventor s paradox
121
Is it possible to satisfy the condition?
122
Leibnitz
123
Lemma
123
f
Contains only cross-references.
xiv Contents
Look at the unknown
123
Modern heuristic
129
Notation
134
Pappus
141
Pedantry and mastery
148
Practical problems
49
Problems to find, problems to prove
154
Progress and achievement
157
Puzzles
160
Reductio
ad absurdum
and indirect proof
16г
Redundantf
171
Routine problem
171
Rules of discovery
172
Rules of style
172
Rules of teaching
173
Separate the various parts of the condition
173
Setting up equations
174
Signs of progress
i78
Specialization
190
Subconscious work
197
Symmetry
199
Terms, old and new
200
Test by dimension
202
The future mathematician
205
The intelligent problem-solver
206
The intelligent reader
207
The traditional mathematics professor
208
t
Contains only cross-references.
Contents xv
Variation
of the problem
209
What is the unknown?
214
Why proofs?
215
Wisdom of proverbs
221
Working backwards
225
PART IV. PROBLEMS, HINTS,
SOLUTIONS
Problems
234
Hints
238
Solutions
242
|
| any_adam_object | 1 |
| author | Pólya, George 1887-1985 |
| author_GND | (DE-588)118825321 |
| author_facet | Pólya, George 1887-1985 |
| author_role | aut |
| author_sort | Pólya, George 1887-1985 |
| author_variant | g p gp |
| building | Verbundindex |
| bvnumber | BV036956566 |
| classification_rvk | SN 100 |
| ctrlnum | (OCoLC)706968824 (DE-599)BVBBV036956566 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV036956566 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:51:30Z |
| institution | BVB |
| isbn | 4871878309 9784871878302 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020871530 |
| oclc_num | 706968824 |
| open_access_boolean | |
| owner | DE-1047 DE-473 DE-BY-UBG DE-703 |
| owner_facet | DE-1047 DE-473 DE-BY-UBG DE-703 |
| physical | XXI, 253 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Ishi Press Internat. |
| record_format | marc |
| spelling | Pólya, George 1887-1985 Verfasser (DE-588)118825321 aut How to solve it a new aspect of mathematical method G. Polya New York [u.a.] Ishi Press Internat. 2009 XXI, 253 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Problemlösen (DE-588)4076358-4 gnd rswk-swf Aufgabe (DE-588)4126116-1 gnd rswk-swf Lösung Mathematik (DE-588)4120678-2 gnd rswk-swf Denken (DE-588)4011450-8 gnd rswk-swf Lösung Chemie (DE-588)4036159-7 gnd rswk-swf Methode (DE-588)4038971-6 gnd rswk-swf Unterrichtsmethode (DE-588)4078637-7 gnd rswk-swf Mathematisches Problem (DE-588)4114530-6 gnd rswk-swf Mathematik (DE-588)4037944-9 s Aufgabe (DE-588)4126116-1 s Problemlösen (DE-588)4076358-4 s 1\p DE-604 Lösung Mathematik (DE-588)4120678-2 s 2\p DE-604 Denken (DE-588)4011450-8 s 3\p DE-604 Mathematisches Problem (DE-588)4114530-6 s Lösung Chemie (DE-588)4036159-7 s 4\p DE-604 Methode (DE-588)4038971-6 s 5\p DE-604 Mathematikunterricht (DE-588)4037949-8 s 6\p DE-604 Unterrichtsmethode (DE-588)4078637-7 s 7\p DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020871530&sequence=000002&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pólya, George 1887-1985 How to solve it a new aspect of mathematical method Mathematikunterricht (DE-588)4037949-8 gnd Mathematik (DE-588)4037944-9 gnd Problemlösen (DE-588)4076358-4 gnd Aufgabe (DE-588)4126116-1 gnd Lösung Mathematik (DE-588)4120678-2 gnd Denken (DE-588)4011450-8 gnd Lösung Chemie (DE-588)4036159-7 gnd Methode (DE-588)4038971-6 gnd Unterrichtsmethode (DE-588)4078637-7 gnd Mathematisches Problem (DE-588)4114530-6 gnd |
| subject_GND | (DE-588)4037949-8 (DE-588)4037944-9 (DE-588)4076358-4 (DE-588)4126116-1 (DE-588)4120678-2 (DE-588)4011450-8 (DE-588)4036159-7 (DE-588)4038971-6 (DE-588)4078637-7 (DE-588)4114530-6 |
| title | How to solve it a new aspect of mathematical method |
| title_auth | How to solve it a new aspect of mathematical method |
| title_exact_search | How to solve it a new aspect of mathematical method |
| title_full | How to solve it a new aspect of mathematical method G. Polya |
| title_fullStr | How to solve it a new aspect of mathematical method G. Polya |
| title_full_unstemmed | How to solve it a new aspect of mathematical method G. Polya |
| title_short | How to solve it |
| title_sort | how to solve it a new aspect of mathematical method |
| title_sub | a new aspect of mathematical method |
| topic | Mathematikunterricht (DE-588)4037949-8 gnd Mathematik (DE-588)4037944-9 gnd Problemlösen (DE-588)4076358-4 gnd Aufgabe (DE-588)4126116-1 gnd Lösung Mathematik (DE-588)4120678-2 gnd Denken (DE-588)4011450-8 gnd Lösung Chemie (DE-588)4036159-7 gnd Methode (DE-588)4038971-6 gnd Unterrichtsmethode (DE-588)4078637-7 gnd Mathematisches Problem (DE-588)4114530-6 gnd |
| topic_facet | Mathematikunterricht Mathematik Problemlösen Aufgabe Lösung Mathematik Denken Lösung Chemie Methode Unterrichtsmethode Mathematisches Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020871530&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT polyageorge howtosolveitanewaspectofmathematicalmethod |