Engaged in Applications
Date:
In this seminar a brief overview of the computer-related applications of number theory was given. One important example I didn’t discuss in this seminar is the work of Lenore Blum leading to cryptographically secure pseudorandom number generator.
The images have been used in slides without permission from the copyright holders.
Download the presentation slides
Postscript: The following are some resources for mathematics majors interested in specializing in applied algebra. A general reference would be Slinko’s book “Algebra for Applications.”
- Cryptography (minor in Computer Science)
- An Introduction to Mathematical Cryptography - Hoffstein, Pipher, and Silverman
- Elliptic Curves: Number Theory and Cryptography - Washington
- Mathematics of Public Key Cryptography - Galbraith
- Coding Theory (minor in Electrical Engineering)
- Coding Theory and Number Theory - Hiramatsu and Köhler
- Lattices and Codes - Ebeling
- Algebraic Geometric Codes - Tsfasman, Vlǎduţ, and Nogin (Basic Notions and Advanced Chapters)
- Quasi-Monte Carlo methods (minor in Statistics)
- Exponential Sums and their Applications - Korobov
- Applications of Number Theory to Numerical Analysis - Keng and Yuan
- Introduction to Quasi-Monte Carlo Integration and Applications - Leobacher and Pillichshammer