## 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.

- Welcome to mathematics/science of information
- Sets & signals
- Digitizing analog signals
- Frequency and Spectrum
- Digital systems and filtering
- Sampling signals
- Signal reconstruction
- Probability and information
- Probability distributions
- Information theory
- Compression & coding
- Quantization and compression
- Communication of information
- Review of vectors and matrices
- Linear algebra with matrices
- Error correction
- Hamming codes; midterm review
- Multiple access communication
- Amplitude modulation
- Frequency and phase modulation
- Number systems and arithmetic
- Encryption
- Encryption and number theory
- Public key cryptography
- Boolean algebra and digital logic
- 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.

- Module 1: Digital vs Analog, Sampling and Quantization, Number Representation and Encoding
- Module 2: Frequency Domain and Perfect Reconstruction
- Module 3: Probability and Information Theory
- Module 4: Noise, Error Correction, and Limits of Communication
- Module 5: Multiple-Access Communication and Networking
- Module 6: The Global Positioning System
- Module 7: Keeping Your Stuff Secret
- Module 8: A Computer in Your Pocket – the ICs of the iPhone
- Assignments: Assignment 1, Test Data; Assignment 2; Assignment 3; Assignment 4; Assignment 5; Assignment 6; Assignment 7; Assignment 8; Assignment 9; Assignment 10; Assignment 11