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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Intro to Rings
Chapter 1-5
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7.1--7.3
(6) Oct 3, 5 Rings (2)
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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)
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Rational Canonical Form
Ch. 8, 10, 12
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12.2
HW8 (due Nov 16)
(12) Nov 14, 16 The Jordan canonical form
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Linear algebra/Vector Spaces
12.3
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Ch 11
HW9 (due Nov 28)
(13) Nov 21 Linear algebra/Vector Spaces Ch 11
(14) Nov 28, 30 More on polynomials Ch 9 HW10 (due Dec 5)
(15) Dec 5, 7 Review
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Final: Tuesday, Dec 7 (in class)