1. Basic Ideas
1.0 Introduction
1.1 The Classical Theory
1.2 Separation Theorems
1.3 Approximation
2. Functions
2.1 Defining Function
2.2 Analytic Definition
2.3 Convex Functions
2.4 Exhaustion Functions
3. More on Functions
3.1 Other Characterizations
3.2 Convexity of Finite Order
3.3 Extreme Points
3.4 Support Functions
3.5 Approximation from Below
3.6 Bumping
4. Applications
4.1 Nowhere Differentiable Functions
4.2 The Krein-Milman Theorem
4.3 The Minkowski Sum
4.4 Brunn-Minkowski
5. Sophisticated Ideas
5.1 The Polar of a Set
5.2 Optimization
5.3 Generalizations
5.4 Integral Representation
5.5 The Gamma Function
5.6 Hard Analytic Facts
5.7 Sums and Projections
6. The MiniMax Theorem
6.1 von Neuman’s Theorem
7. Concluding Remarks
Appendix: Technical Tools
Table of Notation
Glossary
Biography
Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He has previously taught at UCLA, Princeton University, and Penn State University. He received his PhD from Princeton University in 1974. Prof. Krantz has directed 20 PhD students and 8 master's students. He has published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize. He is a fellow of the American Mathematical Society.
