This course is an introduction to theoretical statistics for students with a background in probability. A mathematical formalism for inference on experimental data will be developed.
This course is a mathematical introduction to probability theory, covering random variables, moments, multivariate distributions, law of large numbers, central limit theorem, and large deviations.
MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses.
Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.
MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses.
This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.
Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms.
An introduction to proofs in advanced mathematics, intended as a transition to upper division courses including MATH 4107, 4150 and 4317. Fundamentals of mathematical abstraction including sets, logic, equivalence relations, and functions. Thorough development of the basic proof techniques: direct, contrapositive, existence, contradiction, and induction. Introduction to proofs in analysis and algebra.
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.
