Time and Place : TuTh 1011:20; Earth&Space 181
Instructor : Radu Laza
Office : Math Tower 4121
Email : radu.laza@stonybrook.edu
Office Hours: Thr 46
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 pgroups 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 15  7.17.3 

(6) Oct 3, 5  Rings (2)  Euclidean Domains, PID, UFD 
7.47.6 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 