Mathematical Foundations for Cyber Security (FIC 507)

The objective of this course is to introduce the mathematical tools necessary for developing new algorithms in cybersecurity. In the course, we study probability theory and linear algebra, and optimisation techniques.

Textbooks: 

• Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong. 

• Sheldon Ross, A First Course in Probability, 7th Edition, Pearson, 2006. 

• Kenneth M Hoffman, Ray Kunze, Linear Algebra, 2nd Edition, Pearson. 

Reference Books: 

• J. Medhi, Stochastic Processes, 3rd Edition, New Age International, 2009. 

• S. M. Ross, Stochastic Processes, 2nd Edition, Wiley, 1996. 

• Stephen H Friedberg, Arnold J Insel, Lawrence E. Spence, Linear Algebra. 4th Edition, Pearson, 2006.

Topics covered:

Lecture 1: Began with some standard set-theory notations. Introduced basic notions of probability theory (for example, random experiments, sample spaces and events, etc.) Studied and explained the basic axioms of probability theory.

Lecture note: 1-basic notions of probability theory.pdf

Lecture 2: Studied one of the most fundamental concepts in probability theory, which is called conditional probability. For a given event A of a random experiment with additional condition B, how should we obtain the probability P(A|B) of A given B from the prior probability P(A)?

Lecture note: 2-conditional probability.pdf