Foundations and Theory

  • Algorithms
  • Optimization
  • Stochastic processes
  • Distributed algorithms
  • Network science
  • Communication theory
  • Information theory
  • Logic and formal methods

Design and analysis of modern computing systems and algorithms rely on many advanced mathematical techniques. This specialization is geared toward providing interested students with a deep foundation in a broad range of mathematics, and especially prepares them for pursuing graduate studies in the more analytical aspects of computing. It overlaps with both communications and control.

Propagation of viral memes in distributed systems can be studied through the lens of spectral theory of graphs. Verification algorithms for modern systems draw from ideas in model theory and control theory. Similarly, solving Big Data problems can be approached from the perspective of signal processing. ECE ILLINOIS is indeed a nerve center where many of the connections between computing and applied mathematics are developed and routinely used for solving important practical problems. This specialization will give the students exposure to several areas of mathematics and algorithms with applications to computer engineering.

The University of Illinois offers a large number of courses that could fit in this category. We suggest a sequence that draws from the following set:

Semester 6 ECE 374, ECE 313, MATH 415/416
Semester 7 Graph theory, Algorithms 2, ECE 428, CS 476, ECE 486, ECE 361 Digital Communication
Semester 8 CS 431, ECE584

Other suggested technical electives:

Core Faculty in this area