ECEN 601: Linear Network Analysis

Course Information

• Syllabus (updated 01/14/14)
  

• Textbooks

  • Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan D. Bloch (errata)

  • Mathematical Methods and Algorithms for Signal Processing by Todd K. Moon and Wynn C. Stirling (errata)

• Course Notes

  • Contents (including date of last update)

  • All Chapters

  • Chapter 1: Set Theory and Logic

  • Chapter 2: Metric Spaces and Topology

  • Chapter 3: Linear Algebra

  • Chapter 4: Representation and Approximation

  • Chapter 5: Linear Transformations and Operators

  • Chapter 6: Matrix Properties and Factorizations

  • Chapter 7: Canonical Forms

  • Chapter 8: Singular Value Decomposition

  • Appendix

  • Index

• Advanced References

  • Topology by James Munkres

  • Linear Algebra by Kenneth Hoffman and Ray Kunze

  • Optimization by Vector Space Methods by David Luenberger

Handouts

• Class Project
  

Class Project: Connecting Theory with Real World Problems

• Example Project: A Tutorial on Recursive Methods in Linear Least Squares Problems

• Filtering as a Hilbert Space Problem

• CSMA in Ad Hoc Networks

• Non-Linear Filtering

• Yield Optimization for Circuit Design

• Bandlimited Signals and Non-Uniform Sampling

• Source Localization

• Compressed Sensing

• Multiuser Detection

• Alternating Projection Application (very nice pictures)

Wikipedia References

• First-Order Logic, Mathematical Proof, Theory, Equivalence Relation, Function
  

• Metric Space, Topology, Continuous Function, Complete Metric Space, Compact Space
  

• Contraction Mapping, Field, Vector Space, (Hamel) Basis, Topological Vector Space
  

• Normed Vector Space, Banach Space, Schauder Basis, Lp and lp Spaces, Inner Product Space
  

• Gram-Schmidt Process, Orthonormal Basis, Hilbert Space, Orthogonal Projection, Dual Space
  

• Fixed Point Theorems
  

Other Web Resources

• HowTo Wiki for Applied Math

• Biography of Stefan Banach

• Biography of David Hilbert