Math 430 - Schedule















Schedule of topics: Math 430

Date Chapter  Description 
Jan 12       2.1-2.2       Introduction, Group defintion and examples
Jan 14 2.3-2.4 Basic facts, subgroups
Jan 16 2.4 Subgroups and cosets

Jan 19 Martin Luther King day! (no class)
Jan 21 Counting, normal subgroups
HW 1 due
Jan 23 Homomorphisms, isomorphisms, and automorphisms

Jan 26 Kernels and the Isomorphism Theorem
Jan 28 The Isomorphism Theorem and Sylow sgs
HW 2 due
Jan 30 The Correspondence Theorem

Feb 2 The Diamond Theorem; automorphisms
Feb 4 Group actions and Cayley's Theorem
HW 3 due
Feb 6 Group actions, normal subgroups, and orbits

Feb 9 Group actions and counting
Feb 11 Sn: cycle decomposition and conjugacy
HW 4 due
Feb 13 Sn: transpositions and sign

Feb 16 An; The Sylow E Theorem
Feb 18 In class midterm #1
Feb 20 The Sylow C and D Theorems
HW 5 due

Feb 23 Sylow subgroups -> normal subgroups; Direct products
Feb 25 Introducing rings
Feb 27 Ideals and quotients

Mar 2 Isomorphism Theorems and maximal ideals
Mar 4 Maximal ideals, Zorn's Lemma, and fraction fields
Mar 6 Euclidean domains

Mar 9 Spring Break! (no class)
Mar 11 Spring Break! (no class)
Mar 13 Spring Break! (no class)

Mar 16 More Euclidean domains
Mar 18 Polynomial rings
Mar 20 UFDs and polynomial rings

Mar 23 More UFDs and polynomial rings
Mar 25 Face rings; the Eisenstein criterion
Mar 27 Fields extensions: degree and dimension

Mar 30 Degree of algebraic field extensions
Apr 1 In class midterm #2
Apr 3 Algebraic over algebraic extensions

Apr 6 More algebraic over algebraic extensions
Apr 8 Algebraic extensions and roots
Apr 10 Splitting extensions and splitting fields

Apr 13 Splitting fields are unique up to isomorphism
Apr 15 Ruler and compass constructions
Apr 17 Matrix groups (with Raj Mehta)

Apr 20 Galois groups and the Galois correspondence
Apr 22 When is the Galois correspondence a bijection?
Apr 24 Galois answers; Conclusion

May 6 Final exam   (10:30 am - 12:30 pm)

Print-friendly version. (Opens in a new window.)