The measurement and quantification of information. These ideas are applied to the probabilistic analysis of the transmission of information over a channel along which random distortion of the message occurs.
Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.
This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.
Combinatorial problem-solving techniques including the use of generating functions, recurrence relations, Polya theory, combinatorial designs, Ramsey theory, matroids, and asymptotic analysis.
Introduction to linear error correcting codes with an emphasis on the algebraic tools required, including matrices, vector spaces, groups, polynomial rings, and finite fields.
This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.
MATH 3215, MATH 3235, MATH 3670, and MATH 3740 are mutually exclusive; students may not hold credit for more than one of these courses.
Minimization of functionals, Euler Lagrange equations, sufficient conditions for a minimum, geodesic, isoperimetric and time of transit problems, variational principles of mechanics, applications to control theory.
