MAT 535 (Algebra II) - Spring 2020

Time and Place : MW 2:30-3:50; Physics P113 (starting March 30, on Zoom)

Instructor : Radu Laza

Office : Math Tower 4-120
Email :  radu.laza@stonybrook.edu

Office Hours: Wed 1-2:30pm

TA: Lisa Marquand

Overview

Second graduate class in Algebra. We will cover: Linear and multilinear algebra; Rudiments of linear algebra; Representation of finite groups; Galois theory.

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:

  • [DF] David S. Dummitt and Richard M. Foote, Abstract algebra
  • [L] S. Lang, Algebra

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    Schedule

    WeekTopicSections CoveredHW Assigments
    (1) Jan 27, 29 Vector Spaces, Matrices, Tensor algebras [DF] Ch. 11, [L] XIII \S1-5
    (2) Feb 3, 5 Characteristic Polynomial, Normal Forms [DF] Ch. 12
    (3) Feb 10, 12 Bilinear forms (symmetric/alternating/Hermitian) [Lang] Ch. XV HW1 (due Feb 19)
    (4) Feb 17, 19 Bilinear forms (2) [Spectral Theory] [Lang] Ch. XV (esp. \S7) HW2 (due Feb 26)
    (5) Feb 24, 26 Review - Feb 24
    Midterm: Wednesday, February 26 (in class)
    (6) Mar 2, 4 Field Theory (1) [DF] Ch. 13 HW3 (due Mar 13)
    (7) Mar 9, 11 Field Theory (2) [DF] Ch. 13
    March 16--29 Spring Break (no classes)
    (9) Mar 30, Apr 1 Galois Theory (1) [DF] Ch. 14 HW4 (due Mar 13)
    (10) Apr 6, 8 Galois Theory (2) [DF] Ch. 14
    (11) Apr 13, 15 Galois Theory (3)
    [DF] Ch. 14 HW5 (due Apr 29)
    (12) Apr 20, 22 TBD
    (13) Apr 27, 29 TBD HW6 (due May 8)
    (14) May 4, 6 Review
    Final Exam (May 6, details TBD)