This spring I am teaching undergraduate graph theory (syllabus is here), and the second semester graduate algebra. Graph Theory, Math 428, meets Tuesdays and Thursdays in ARC 204 from 3:40-4:20. Abstract algebra, Math 552, will meet on Mondays and Thursdays from 12-1:20 in Hill 425.
Second semester graduate algebra is generally meant for beginning graduate students.
Continuing last semester’s topics, I will cover:
Field Theory (Field extensions: finite, separable, normal, algebraic and transcendental. Existence of algebraic closure. Galois theory. Finite fields. Hilbert theorem 90); Commutative algebra (Local rings and Nakayama lemma, Integral extensions, Krull dimension, Noether normalization lemma, Hilbert Nullstellensatz, localization. Prime ideal spectrum and Zariski topology, Algebraic sets and rings of regular functions. Discrete valuation rings and Dedekind domains), and Modules (Tensor product, flatness, local properties of modules, exterior and symmetric powers. Graded rings and modules, Hilbert functions and polynomials).
If there is time we will also do a little bit of algebraic geometry.
I’ll use Jacobson, (Basic Algebra), as well as, Artin (Algebra), and Dummit and Foote (Abstract Algebra). We will meet on Mondays and Thursdays from 12-1:20 in
in Hill 425.
Graph Theory, Math 428, meets Tuesdays and Thursdays in ARC 204 from 3:40-4:20.
We will sample a number of topics from the theory of finite linear graphs including colorability, connectedness, tournaments, eulerian and hamiltonian paths, orientability, with an emphasis on applications.
I’ll use A First Course in Graph Theory, by Gary Chartrand and Ping Zhang.