# MTH2199 Special Topics in Mathematics

### Credits

### Notes

SP15: A Mathematical Introduction to Cryptography; 4 credits (Patel)

Public key encryption systems are the cornerstone of secure electronic communication. At their heart is the notion of an asymmetric key: roughly speaking, mathematical operations that are easy to carry out, but hard to ""undo"". In this course, we'll develop some of the beautiful mathematics -- from areas such as number theory and algebra -- that underlie these methods, and see how they lead to the Diffie-Hellman key exchange, the RSA cryptosystem, Elliptic Curve Cryptography, and other such systems. There are no mathematical prerequisites but some experience with abstract mathematical reasoning, such as in a course on Discrete Mathematics, may be useful.

This is an expanded version of the 2-credit cryptography course offered in Spring 2014.

SP15: MTH2199A: Structure in Randomness: A Mathematical Perspective; 2 credits in Session II (Patel)

An intriguing phenomenon in mathematics is the occurrence of patterns and order in situations that seem inherently disordered. Within any large network, there are clusters that show uniform behavior; among the prime numbers, we can find arbitrarily long sequences that are evenly spaced; even chaotic dynamical systems, such as those giving rise to fractal images, are fundamentally deterministic. In this course we will survey some mathematical results that illustrate the phenomenon of ?structure in randomness', and explore their causes and applications. There are no prerequisites for taking the course except curiosity about the subject matter. Student input is strongly encouraged; if you have questions or suggestions, please email the instructor.