Grad Algebra II

Textbook: None. All lecture notes will be posted right here. You might notice that the lectures borrow heavily from Paolo Aluffi's Algebra: Chapter 0.
Item Date Information
Homework 1
Thurs Feb 4 Course Notes
Differences between Ab and Grp
Concrete vs. Abstract Rings
The category Rng
The category R-Mod
The definition of "Abelian Category"
Homework 2
Thurs Mar 3 Course Notes
Field => Euclidean => PID => UFD
Free Modules
Modules over a field have dimension
Modules over a domain have rank
Key Lemma for PIDs: submodule of free is free
F.T.F.G.M.P.I.D., Part I
Midterm Exam Review Notes
Tues Mar 15 Total = 32
Average = 24.5
Median = 26
St Dev = 6.1
Homework 3
Tues, Apr 12 Course Notes
The Category/ies R-Alg
Matrix Notation
RREF, Hermite Normal Form
Smith Normal Form
F.T.F.G.M.P.I.D., Part II
Homework 4
Wed, Apr 27 Course Notes
Fundamental Theorem of f.g. Abelian Groups
Rational & Jordan Canonical Forms
Minimal & Characteristic Polynomials
Epilogue: Restriction & Extension of Scalars
Final Exam Review Notes
Wed May 4 Total = 34
Average = 25.4
Median = 26
St Dev = 6.6
Qualifying Exam
List of Topics
Thurs May 26 Total = 43
Average = 35.6
Median = 35.8
St Dev = 4.7