Syllabus


Week    Sections in Texbooks    Brief Description
Week 1 [S] 7.2-7.3, 7.6
[L] II.1 - II.2 (II.3); IV.1
[J] Chapters 16-17
Overview of the spectrum: integral domains, UFDs, Noetherian domains, PIDs, Euclidean domains. Characteristic of a ring, prime subfield, polynomials in one and several variables and their universal mapping properites, general division algorithm, roots of polynomials, prime and maximal ideals, operations on ideals.
Week 2 [S] 8.1 (8.5)
[L] II.5, IV.1-3
Correspondence theorem, CRT, irreducible and prime elements, UFDs, PIDs, Noetherian rings, Gauss's lemma and corollaries, irreducibility tests?
Week 3 IV.3, IV.4, V.1 Irreducibility tests, cyclotomic polynomials, begin field theory
Week 4 V.1, V.2 Finite and algebraic extensions, splitting fields, composite fields, distinguished classes of extensions
Week 5
Week 6
Week 7
Week 8
Week 9
3/12 Final Exam 8-11am


Thomas R. Shemanske
Last updated January 21, 2018