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                         :




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.






Homework       30%


Midterm           30%


Final                 40%




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