Mathematics of Information

ECE 2066/APMA 2501: Mathematics of Information (Fall 2019)

Time and Location:
MoWe 2:00PM – 3:15PM, Thornton Hall E316

Instructor:
Farzad Farnoud, farzad@virginia.edu

GTA:
Elisa Pantoja, rep9cy@virginia.edu

This course is an introduction to the mathematical principles of the science of information. These principles apply broadly to information storage, processing, and transmission on any device. They allow us to understand how digital devices interact with an analog world; how different types of data (music, video, apps) can be stored reliably on unreliable devices; what makes it possible to communicate without error in the presence of noise; and how information is stored securely. Topics include: mathematical representation of information; spectral analysis and the sampling theorem; probability, uncertainty, and information; linear/abstract algebra and error correction; number theory and encryption; Boolean algebra and computation.

A tentative schedule of the course is posted below. You can also see the material from the last two offerings. In addition to the instructor, Dr. Scott Acton and Dr. Dan Weller have contributed to the course design and material.

Course information and policies (UVa only)


Spring 2019:

Instructor: Dr. Dan Weller.

  1. Welcome to mathematics/science of information
  2. Sets & signals
  3. Digitizing analog signals
  4. Frequency and Spectrum
  5. Digital systems and filtering
  6. Sampling signals
  7. Signal reconstruction
  8. Probability and information
  9. Probability distributions
  10. Information theory
  11. Compression & coding
  12. Quantization and compression
  13. Communication of information
  14. Review of vectors and matrices
  15. Linear algebra with matrices
  16. Error correction
  17. Hamming codes; midterm review
  18. Multiple access communication
  19. Amplitude modulation
  20. Frequency and phase modulation
  21. Number systems and arithmetic
  22. Encryption
  23. Encryption and number theory
  24. Public key cryptography
  25. Boolean algebra and digital logic
  26. Digital computation, wrap-up

Fall 2018:

Instructor: Dr. Farzad Farnoud. The following material is from a previous version of this course called the Science of Information.