##### Speaker

Dr. Paul Fabel, Associate Professor, Department of Mathematics and Statistics, MSU

##### Title

Mathematics Seminar Series

##### Subtitle

Stories from the trenches, the use of calculus, randomness, and other statistical methods in discrete math courses at Mississippi State

##### Physical Location

Allen 411

##### Digital Location

https://msstate.webex.com/msstate/j.php?MTID=m9e5b618e666004aac2d307c0fd2e100f

**Abstract:** Modern crpytography rests heavily on basic tools in abstract algebra and number theory, and notably questions surrounding prime numbers. Basic questions about prime numbers can be notoriously difficult to answer. However, in this talk we mention a few such questions that arise naturally, and how we are able to harness tools from calculus and probability to obtain useful answers. Questions of interest include

- Estimating the asymptotic density of the square free numbers.
- Finding a one-sided estimate of the density of primes, adequate to certify divergence of the sum of the reciprocals of the primes.
- Finding a fast statistical method to find a multiplicative generator of the units in Z_p, in the absence of a fast deterministic method.
- Finding a fast statistical method to certify primality or compositeness, in the absence of a fast method for factoring large numbers.