Graduate Mathematics
Graduate Mathematics
2021 Summer Term
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PROBABILITY AND STATISTICAL INFERENCE
MATH 649
Foundations associated with quantifying and modeling chance and randomness with a focus on the role probability plays in statistical inference. Topics include set theory, combinatorics, random variables, selected discrete and continuous probability distributions, probability distributions for commonly used statistics, and the logic and applied use of probability in formulating and conducting hypothesis tests.
COMBINATORICS
MATH 721
This course will cover topics in combinatorics and graph theory such as combinations, permutations, Pigeonhole Principle, Binomial and Multinomial Theorems, Inclusion-Exclusion Principle, Stirling numbers, partially-ordered sets, generating functions, connectedness, Cayley Theorem, graph coloring, Eulerian walks, Hamiltonian circuits, planar graphs, and Ramsey Theory. Connections will be made to undergraduate mathematics content.
ABSTRACT ALGEBRA
MATH 752
This course will cover fundamental algebraic structures such as rings, fields, and maps between these structures. Relations of these concepts to Algebra topics in undergraduate mathematics will be emphasized. Galois Theory will be introduced if time allows.