Time and Place : TuTh 10-11:20; Earth&Space 181
Instructor : Radu Laza
Office : Math Tower 4-121
Email : radu.laza@stonybrook.edu
Office Hours: Thr 4-6
Grader Lilya Lyubich
Textbook : David S. Dummitt and Richard M. Foote, Abstract algebra, 3rd ed.
We will cover roughly the following topics: Groups: normal subgroups, quotient groups, Lagrange's theorem, class formula, finite p-groups and solvable groups, Sylow's theorems, finitely generated abelian groups. Rings and modules: subrings, fields, prime and maximal ideals, quotient rings, ID's, PID's, UFD's, polynomial rings, field of fractions, the Wedderburn theorem, Hilbert basis theorem, finitely generated modules over a PID. Vector spaces: basis, linear maps and matrices, dual spaces, determinants, eigenvalues and eigenvectors, inner products, spectral theorem for normal operators.
Week | Topic | Sections Covered | HW Assigments |
(1) Aug 29, 31 |
Intro to Groups Subgroups |
Ch 1 Ch 2 |
|
(2) Sept 7 | Quotient Groups | Ch 3 | HW1 (due Sept 14) |
(3) Sept 12, 14 | Group Actions Sylow Theorems |
Ch 4 | HW2 (due Sept 21) |
(4) Sept 19, 21 | Direct and Semidirect products Abelian Groups Further Topics |
Ch 5 (time permitting Ch 6) |
HW3 (due Sept 28) |
(5) Sept 26, 28 |
Midterm 1: Tuesday, Sept 26 (in class) ------------------------------------------ Intro to Rings |
Chapter 1-5 ------------------------------------------ 7.1--7.3 |
|
(6) Oct 3, 5 | Rings (2) ------------------------------------------ Euclidean Domains, PID, UFD |
7.4--7.6 Ch 8 |
HW4 (due Oct 12) |
(7) Oct 10, 12 | Euclidean Domains, PID, UFD (2) Polynomial Rings |
Ch 8 Ch 9 |
HW5 (due Oct 19) |
(8) Oct 17, 19 | Modules | Ch 10 | HW6 (due Oct 26) |
(9) Oct 24, 26 | Modules | Ch 10 | HW7 (due Nov 2) |
(10) Oct 31, Nov 2 | Modules over PID | Ch 12 | |
(11) Nov 7, 9 | Midterm 2: Tuesday, Nov 7 (in class) ------------------------------------------ Rational Canonical Form |
Ch. 8, 10, 12 ------------------------------------------ 12.2 |
HW8 (due Nov 16) |
(12) Nov 14, 16 | The Jordan canonical form ------------------------------------------ Linear algebra/Vector Spaces |
12.3 ------------------------------------------ Ch 11 |
HW9 (due Nov 30) |
(13) Nov 21 | Linear algebra/Vector Spaces | Ch 11 | |
(14) Nov 28, 30 | More on polynomials | Ch 9 | (15) Dec 5, 7 |
Review |
Dec 11 | Final Exam |