Techniques of problem solving / Steven G. Krantz.

CONTENIDO
CHAPTER 1: Basic Concepts
Introductory Remarks 1
A First Problem 3
How to Count 14
The Use of Induction 20
Problems of Logic 30
Issues of Parity 35
Exercises 43
CHAPTER 2: A Deeper Look at Geometry
Classical Planar Geometry 49
Analytic Geometry 71
Miscellaneous and Exotic Geometry Problems 81
Solid Geometry 103
Exercises 121
CHAPTER 3: Problems Involving Counting
Elementary Problems in Probability 129
More Sophisticated Problems in Probability 139
More on Counting 155
The Classical Marriage Problem and Related Ideas 163
Exercises 167
CHAPTER 4: Problems of Logic
Straight Logic 177
Games 183
Tracing Routes, and Learning from Parity 191
Mysterious Arithmetic Problems 201
Surprises 214
Exercises 219
CHAPTER 5: Recreational Math
Magic Squares and Related Ideas 235
Problems Involving Weighings 246
Exercises 257
CHAPTER 6: Algebra and Analysis
A Little Algebra 263
Inequalities 271
Trigonometry and Related Ideas 279
Exercises 286
CHAPTER 7: A Miscellany
Crossing the River and Similar Exercises 295
Things That Are Impossible 299
Exercises 309
CHAPTER 8: Real Life
Introductory Remarks 315
Everyday Objects 315
Some Case Studies 336
Statistics 341
Exercises 347
Bibliography 361