PROBLEM SOLVING
EFFECTIVE METHODS FOR HIGH SCHOOL AND UNIVERSITY STUDENTS - HOW TO BECOME BETTER PROBLEM SOLVERS (A USEFUL APPLICATION OF ARISTOTLE'S LOGIC, A NEW ASPECT)
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«How to become a better problem solver». After a long time of teaching mathematics, and while trying to find an answer to the above question, I came to the conclusion that we have difficulties not only with the problems we deal with but also with our own mind and our way of thinking.
Unjustified phobias, indecision in generating ideas, mind blockage, loops in thought: all these obstacles intermingle and do not allow us to give our best effort. The presence of these difficulties is not only related to mathematical problems but is also so common to other fields where problems do appear in a daily basis of our life.
Here we shall present two methods that help people to generate more ideas for the solution of problems.
In this book you can read some comments, concerning the initial form of the methods, made by professors who have worked on problem solving. You can also read comments for the final form of the methods, as they will be presented here, applying Aristotle's categories.

I An introduction – Methods
1. Method A
1.1 Method A
1.2 A more dynamic form of the method
1.3 Note 1
1.4 A very dynamic scheme of Method A
1.5 An extension of Categories:
1.6 More applications of Method A
1.7 Word, problems
1.8 Some more problems
2. Method B
2.1 Method B – How to get out of loops
2.2 How to develop a computer program to solve problems
2.3 More applications – problems for mathematical competitions
II Special Techniques for certain kinds of problems
1 Grouping Problems
1.1 Grouping problems on percentages
1.2 Compound problems on percentages
1.3 Ratio and proportion
1.4 For High School
1.5 Four useful theorems
1.6 Formulas
1.6.1 Pascal’s triangle – Powers of binomials
1.7 Absolute value and Inequalities
1.8 Geometry and Formulas
1.8.1 A summary of geometric formulas
1.8.2 Geometry Examples
1.9 Linear Functions
1.10 Quadratic functions
1.11 How to find limits – 2 mnemonic rules
1.12 Exponential and Logarithmic function
1.12.1 Logarithms
1.13 Trigonometry
1.14 Analytic and Coordinate Geometry
1.15 Sequences
1.16 Complex Numbers
1.17 Vectors
1.18 Matrices
1.19 Statistics
1.20 Probability 
III Computers and Problem solving using Plato’s ideas
1 Problem solving and Artificial intelligence
1.1 Example of Plato’s Idea
1.2 Problem solving and computers – Artificial intelligence
1.3 Artificial intelligence and Problem 1
1.4 The method and problem 2
1.5 The methods in short notes
1.6 A very interesting and different problem
1.7 Epilogue
1.8 Comments regarding Kalomitsines’ ideas