Time and Place : TuTh 1:15-2:35; Physics P130
Instructor : Radu Laza
Office : Math Tower 4-121
Email : radu.laza@stonybrook.edu
Office Hours: Tue 2:45-3:45; Thr 11:30-12:30; by appointment
Grader Alexandra Viktorova
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. (See also official course description)
Week | Topic | Sections Covered | HW Assigments |
(1) Aug 24, 26 |
Intro to Groups Subgroups |
Ch 1 Ch 2 |
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(2) Aug 31, Sept 2 | Quotient Groups, Lagrange Theorem | Ch 3 | HW1 (due Sept 7) |
(3) Sept 7, 9 | Group Actions Sylow Theorems |
Ch 4 | HW2 (due Sept 14) |
(4) Sept 14, 16 | Direct and Semidirect products Abelian Groups Further Topics |
Ch 5 |
HW3 (due Sept 23) |
(5) Sept 21, 23 |
Review Groups ------------------------------------------ Midterm 1: Thursday, Sept 23 (in class) |
Chapter 1-5 |
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(6) Sept 28, 30 | More on groups Rings and Ideals |
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(7) Oct 5, 7 | Rings et al. | Ch 7 | HW4 (due Oct 19) |
(8) Oct 14 | Intro to divisibility in rings | Ch 8 | HW5 (due Oct 28) |
(9) Oct 19, 21 | Euclidean Domains, PID, UFD | Ch 8 | |
(10) Oct 26, 28 | Polynomial rings | Ch 9 | |
(11) Nov 2, 4 | Review Part II ------------------------------------------ Midterm 2: Thursday, Nov 4 (in class) |
Chapter 7-9 | |
(12) Nov 9, 11 | Modules | Ch 10 | HW6 (due Dec 2) |
(13) Nov 16, 18 | Vector Spaces | Ch 11 | HW8 |
(14) Nov 23 | Modules over PID | Ch 12 | HW7 (due Dec 14) | (15) Nov 30, Dec 2 | Modules over PID Review |
Dec 14 | Final Exam |