Dear All,
Included is a message to the Group from Ken Friedman that seems to have been caught up in the system.
Keith russell
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
From: Ken Friedman <[log in to unmask]<mailto:[log in to unmask]>>
Date: 6 May 2014 21:21:38 AEST
To: PHD-DESIGN PHD-DESIGN <[log in to unmask]<mailto:[log in to unmask]>>
Subject: How to Solve It
Dear All,
On Sunday, I announced the availability of a PDF copy of How to Solve It, George Polya's classic book on problem-solving and heuristics. You will find the PDF on my Academia page in the "Teaching Documents" section at:
https://swinburne.academia.edu/KenFriedman
This is a limited opportunity - the book will come down at the end of Monday, May 5.
To give you a sense of this book, here is the table of contents:
PART I. IN THE CLASSROOM
Purpose
1. Helping the student
2. Questions, recommendations,
mental operations
3· Generality
4· Common sense
5· Teacher and student. Imitation and practice
Main divisions~ main questions
6. Four phases
7· Understanding the problem
8. Example
9. Devising a plan
1o. Example
11. Carrying out the plan
12. Example
13. Looking back
14. Example
15. Various approaches
16. The teacher's method of questioning
17. Good questions and bad questions
More examples
18. A problem of construction
19. A problem to prove
20. A rate problem
PART II. HOW TO SOLVE IT
A dialogue
PART III. SHORT DICTIONARY OF HEURISTIC
Analogy
Auxiliary elements
Auxiliary problem
Balzano
Bright idea
Can you check the result?
Can you derive the result differently?
Can you use the result?
Carrying out
Condition
Contradictory
Corollary
Contents
Could you derive something useful from the data?
Could you restate the problem?
Decomposing and recombining
Definition
Descartes
Determination, hope, success
Diagnosis
Did you use all the data?
Do you know a related problem?
Draw a figure
Examine your guess
Figures
Generalization
Have you seen it before?
Here is a problem related to yours and solved before
Heuristic
Heuristic reasoning
If you cannot solve the proposed problem
Induction and mathematical induction
Inventor's paradox
Is it possible to satisfy the condition?
Leibnitz
Lemma
Look at the unknown
Modern heuristic
Notation
Pappus
Pedantry and mastery
Practical problems
Contents
Problems to find, problems to prove
Progress and achievement
Puzzles
Reductio ad absurdum and indirect proof
Redundant
Routine problem
Rules of discovery
Rules of style
Rules of teaching
Separate the various parts of the condition
Setting up equations
Signs of progress
Specialization
Subconscious work
Symmetry
Terms, old and new
Test by dimension
The future mathematician
The intelligent problem-solver
The intelligent reader
The traditional mathematics professor
Variation of the problem
What is the unknown?
Why proofs?
Wisdom of proverbs
Working backwards
PART IV. PROBLEMS, HINTS, SOLUTIONS
Problems
Hints
Solutions
While Polya was a mathematician, many of these techniques and heuristics apply across most fields. Anyone who solves problems for a living will find value in this book.
Yours,
Ken
Ken Friedman, PhD, DSc (hc), FDRS | University Distinguished Professor | Swinburne University of Technology | Melbourne, Australia | University email [log in to unmask]<mailto:[log in to unmask]> | Private email [log in to unmask]<mailto:[log in to unmask]> | Mobile +61 404 830 462 | Academia Pagehttp://swinburne.academia.edu/KenFriedman
Guest Professor | College of Design and Innovation | Tongji University | Shanghai, China ||| Adjunct Professor | School of Creative Arts | James Cook University | Townsville, Australia
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References
Polya, G. 1973 [1957]. How to Solve It. A New Aspect of Mathematical Method. Second edition. Princeton, New Jersey: Princeton University Press.
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