**EE436**

**Mathematical
Foundations of Signal Processing and Control**

**Meeting times** : Friday; 14:30, 15:30, 16:30

**Instructor** : Bilge Karaçalı, PhD

**Office** : EEE Building Room
209

**Phone** : 6719

**E-mail** :
bilgekaracali@iyte.edu.tr

**Summary**

Introduction to set theory. Metric spaces. Neighborhood and continuity. Convergence of sequences. Normed vector spaces. Completeness, Banach spaces. Linear operators and functionals. Inner product spaces, Hilbert spaces.

**Grading **

Homework 30%

Midterm 30%

Final 40%

**Text**

N. Kolmogorov, S. V. Fomin, “Introductory real analysis,” Dover, New York, 1975

E. Kreyszig, “Introductory functional analysis with applications,” John Wiley & Sons, New York, 1989

**Weekly schedule**

Week 1: Introduction to set theory: Basics and definitions

Week 2: Decomposition of a set into classes

Week 3: Ordered sets and set systems

Week 4: Metric spaces

Week 5: Neighborhood and continuity

Week 6: Convergence, Cauchy sequences and completeness

Week 7: Midterm

Week 8: Completion of metric spaces

Week 9: Vector spaces, normed spaces

Week 10: Banach spaces

Week 11: Finite dimensional normed spaces

Week 12: Linear operators

Week 13: Inner product spaces, Hilbert spaces

Week 14: Orthogonal complements and direct sums