MAT 534 (Algebra I) - Fall 2017

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

Overview

Prerequisite : For graduate students in the mathematics Ph.D. program, there is no prerequisite. All other students should consult with the instructor regarding prerequisites.

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.

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Grading


Schedule

WeekTopicSections CoveredHW 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)
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Chapter 1-5
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(6) Oct 3, 5 HW4 (due Oct 12)
(7) Oct 10, 12 HW5 (due Oct 19)
(8) Oct 17, 19 HW6 (due Oct 26)
(9) Oct 24, 26 HW7 (due Nov 2)
(10) Oct 31, Nov 2 HW8 (due Nov 9)
(11) Nov 7, 9 Midterm 2: Tuesday, Nov 7 (in class)
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(12) Nov 14, 16 HW9 (due Nov 21)
(13) Nov 21
(14) Nov 28, 30 HW10 (due Dec 5)
(15) Dec 5, 7 ------------------------------------------
Final: Tuesday, Dec 7 (in class)
HW11* (due Dec 7)