Applications of Continuous Mathematics to Computer Science

This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics.
Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering.

Preface. 1. Algorithm Complexity: Two Simple Examples. 2. Solving General Linear Functional Equations: An Application to Algorithm Complexity. 3. Program Testing: A Problem. 4. Optimal Program Testing. 5. Optimal Choice of a Penalty Function: Simplest Case of Algorithm Design. 6. Solving General Linear Differential Equations with Constant Coefficients: An Application to Constrained Optimization. 7. Simulated Annealing: `Smooth' (Local) Discrete Optimization. 8. Genetic Algorithms: `Non-Smooth' Discrete Optimization. 9. RISC Computer Architecture and Internet Growth: Two Applications of Extrapolation. 10. Systems of Differential Equations and Their Use in Computer-Related Extrapolation Problems. 11. Network Congestion: An Example of Non-Linear Extrapolation. 12. Neural Networks: A General Form of Non-Linear Extrapolation. 13. Expert Systems and the Basics of Fuzzy Logic. 14. Intelligent and Fuzzy Control. 15. Randomness, Chaos, and Fractals. A: Simulated Annealing Revisited. B: Software Cost Estimation. C: Electronic Engineering: How to Describe PN-Junctions. D: Log-Normal Distribution Justified: An Application to Computational Statistics. E: Optimal Robust Statistical Methods. F: How to Avoid Paralysis of Neural Networks. G: Estimating Computer Prices. H: Allocating Bandwidth on Computer Networks. I: Algorithm Complexity Revisited. J: How Can a Robot Avoid Obstacles: Case Study of Real-Time Optimization. K: Discounting in Robot Control: A Case Study of Dynamic Optimization. Index.