The Art and Craft of Problem Solving, 3rd ed

Paul Zeitz

ISBN: 9788126571840

380 pages

Exclusively distributed by Saraswati Pustakalaya

 

Description

Appealing to everyone from college-level majors to independent learners, The Art and Craft of Problem Solving, 3rd Edition introduces a problem-solving approach to mathematics, as opposed to the traditional exercises approach. The goal of The Art and Craft of Problem Solving is to develop strong problem solving skills, which it achieves by encouraging students to do math rather than just study it. Paul Zeitz draws upon his experience as a coach for the international mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

1 What This Book Is About and How to Read It

1.1 "Exercises" vs. "Problems"  

1.2 The Three Levels of Problem Solving  

1.3 A Problem Sampler

1.4 How to Read This Book

 

2 Strategies for Investigating Problems

2.1 Psychological Strategies

2.2 Strategies for Getting Started

2.3 Methods of Argument

2.4 Other Important Strategies

 

3 Tactics for Solving Problems

3.1 Symmetry

3.2 The Extreme Principle

3.3 The Pigeonhole Principle

3.4 Invariants

 

4 Three Important Crossover Tactics

4.1 Graph Theory

4.2 Complex Numbers

4.3 Generating Functions

4.4 Interlude: A few Mathematical Games

 

5 Algebra

5.1 Sets, Numbers and Functions

5.2 Algebraic Manipulation Revisited

5.3 Sums and Products

5.4 Polynomials

5.5 Inequalities

 

6 Combinatorics

6.1 Introduction to Counting

6.2 Partitions and Bijections

6.3 The Principle of Inclusion-Exclusion

6.4 Recurrence

 

7 Number Theory

7.1 Primes and Divisibility

7.2 Congruence

7.3 Number Theoretic Functions

7.4 Diophantine Equations

7.5 Miscellaneous Instructive Examples

 

8 Geometry for Americans

8.1 Three "Easy" Problems

8.2 Survival Geometry I

8.3 Survival Geometry II

8.4 The Power of Elementary Geometry

8.5 Transformations

 

9 Calculus

9.1 The Fundamental Theorem of Calculus

9.2 Convergence and Continuity

9.3 Differentiation and Integration

9.4 Power Series and Eulerian Mathematics

 

References

Index