| MTH 419H | Spring 2017 |
Course Page: http://www.math.msu.edu/~magyar/Math419H .
Dates below are tentative. Changes will be announced in class and on our course page.
Homework will be assigned weekly on the Course Page. Section numbers refer to Michael Artin, Algebra (2nd ed).
| # | Date | Section Topic | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1 | 1/9 | 9.1 Classical groups | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2 | 1/11 | 9.2 Spheres 9.3 Unitary group SU2 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 3 | 1/15 | 9.4 Rotation group SO3 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1/16 |
M.L. King Day, no classes
| 4 | 1/18 |
Problem session
| 5 | 1/20 |
9.7 Coordinates on a Lie group
| 6 | 1/23 |
10.1 Intro to group representations
| 7 | 1/25 |
10.2 Irreducible representations
| 8 | 1/27 |
10.4 Characters
10.5 One-dimensional characters
| 9 | 1/30 |
10.6 Regular representation
| 10 | 2/1 |
10.7 Schur's Lemma
| 11 | 2/3 |
10.8 Orthogonality relations
| Last day to drop course with refund 12 | 2/6 |
Representation theory
| 13 | 2/8 |
Representation theory
| 14 | 2/10 |
Representation theory
| 15 | 2/13 | 10.9 Representations of SU2
| 11.1 Definition of a ring 11.3 Homomorphisms and ideals 11.4 Quotient rings 16 | 2/15 |
11.4 Quotient rings and fields, maximal ideals, Euclidean algorithm
| 17 | 2/17 |
15.1 Intro to fields
15.2 Algebraic elements
| 15.3 Degree of an extension 15.4 Irreducible polynomials 18 | 2/20 |
Fields
| 19 | 2/22 |
Fields
| 20 | 2/24 | Review
| 21 | 2/27 |
Midterm Exam
| 22 | 3/1 |
Discuss midterm
| Last day to drop course with no grade reported 23 | 3/3 |
Fields
| 3/4−12 |
Spring Break, no classes
| 24 | 3/13 |
15.6 Adjoining roots
| 26 | 3/17 |
15.8 Primitive elements
| 25 | 3/15 |
15.5 Ruler and compass constructions
| 27 | 3/20 |
16.3 Splitting fields
| 28 | 3/22 | 16.4 Isomorphisms of field extensions
| 29 | 3/24 | 16.6 Galois extensions
| 30 | 3/27 | 16.5 Fixed fields
| 31 | 3/29 | 16.7 Main theorem of Galois theory
| 32 | 3/31 |
16.8 Cubic equations
| 33 | 4/3 |
16.1 Symmetric functions | 16.2 Discriminant 16.10 Roots of unity 16.11 Kummer extensions 16.12 Quintic equations 34 | 4/5 |
| 35 | 4/7 |
| 36 | 4/10 |
| 37 | 4/12 |
| 38 | 4/14 |
| 39 | 4/17 | Additional topics: 12 Gauss primes?
| 40 | 4/19 | 13 Quadratic number fields?
| 41 | 4/21 | 11.9, 15.9 Algebraic geometry?
| 42 | 4/24 | Review
| 43 | 4/26 | Review
| 44 | 4/28 | Review
| 5/4 | Final exam Thu, May 4, 2017, 12:45−2:45pm, Wells Hall A-108
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