Spring 2017 Math 603 schedule
| Monday |
Wednesday |
Friday |
Jan. 9
| Jan. 11
In Lecture:
| Jan. 13
In Lecture:
- Outline of the second semester
- The fundamental theorem on finitely generated modules over a PID
Associated Reading:
Video of class (downloadable)
|
Jan. 16
| Jan. 18
We will have a class from 1:30 to 3:00 in room 3C2 of DRL labs
- In Lecture
- Some open problems about P.I.D.s. Cohen Lenstra heuristics.
- The fundamental theorem on finitely generated modules over a PID.
Associated Reading:
Video of class (downloadable)
Jan. 20
No class
| |
Jan. 23
In Lecture:
- The basis theorem for vector spaces, Zorn's Lemma
- End of the proof of the fundamental theorem about finitely generated modules over a PID
Associated Reading:
- D-F: 12.1, 12.3
- Lang: 5.1 - 5.3.
Video of class (downloadable)
| Jan. 25
In Lecture: (room 3C2 of DRL labs)
Associated Reading:
- D-F: 12.3, 11.5
- Lang: 5.2. 26.7 - 26.8, 29.1
Video of class (downloadable)
| Jan. 27
No class
|
Jan. 30
In Lecture:
Associated Reading:
- D-F: 12.1, 12.3
- Lang: 5.1 - 5.3.
Video of class (downloadable)
| Feb. 1
In Lecture: (room 3C2 of DRL labs)
- More on canonical forms for endomorphisms of locally free modules over a ring
- Quiver algebras and the rational canonical form
Associated Reading:
Video of class (downloadable)
| Feb. 3
No class
|
Feb. 6
In Lecture:
- Representations of quiver algebras
- Fine and coarse moduli schemes
- Calculating rational canonical forms
Associated Reading:
Video of class (downloadable)
| Feb. 8
In Lecture: (room 3C2 of DRL labs)
- Calculating rational canonical forms (continued)
- Elementary divisors
- Jordan normal form
Associated Reading:
- D-F: 12.3, 11.5
- Lang: 5.2. 26.7 - 26.8, 29.1
Video of class (downloadable)
| Feb. 10
No class
|
Feb. 13
In Lecture:
Associated Reading:
- D-F: 13.1, 13.2
- Lang: 5.1
Video of class (downloadable)
| Feb. 15
In Lecture:
- Distinguished extensions
- Straightedge and compass constructions
Associated Reading:
Video of class (downloadable)
| Feb. 17
No class
|
Feb. 20
In Lecture:
- End of straightedge and compass constructions
- Algebraic closures
Associated Reading:
- D-F: 13.3, 13.4
- Lang: 5.2.
Video of class (downloadable)
| Feb. 22
In Lecture:
- Extending embeddings
-
Separable extensions
Associated Reading:
- D-F: 13.3, 13.4, 13.5
- Lang: 5.3, 5.4
Video of class (downloadable) d
| Feb. 24
No class
|
Feb. 27
In Lecture:
- Extensions of embedding of fields
- Hensel's Lemma
- Function fields
- Algebraic closures
Associated Reading:
- D-F: 13.3, 13.4
- Lang: 5.2.
Video of class (downloadable)
| Mar. 1
In Lecture:
- Separability and normality of field extensions
Associated Reading:
- D-F: 13.5, 13.6, 14.1
- Lang: 5.1, 5.2, 5.3, 5.4, 5.6, 6.1
Video of class (downloadable)
| Mar. 3
No class
|
March 6
No class - spring break!
| March 8
No class - spring break!
| March 10
No class - spring break!
|
Mar. 13
In Lecture:
- Separable extensions and polynomials
Associated Reading:
- D-F: 13.5
- Lang: 5.4, 5.6.
Video of class (downloadable)
| Mar. 15
In Lecture:
- Separable extensions and polynomials, continued
- Inseparable extensions, inseparable degrees
Associated Reading:
- D-F: 13.5
- Lang: 5.4, 5.6.
Video of class (downloadable)
| Mar. 17
In Lecture:
- Primitive element theorem
Associated Reading:
- D-F: 14.4, 14.3
- Lang: 5.4. 5.5
Video of class (downloadable)
|
Mar. 20
In Lecture:
- End of proof of the primitive element theorem
- Finite fields
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| Mar. 22
In Lecture:
- Statement of the main theorems of Galois theory
- Examples
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| Mar. 24
No class
|
Mar. 27
In Lecture:
- Galois groups as permutation groups
- Multiple transitivity of Galois groups
- The discriminant and the question of whether Galois groups lie in alternative groups
- Elementary symmetric functions and the canonical S_n action on F(x_1,...,x_n).
- Noether's problem.
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| Mar. 29
In Lecture:
- Explicit computations of some Galois groups
- Statement of the main theorem of Kummer theory
- Artin Schreier extensions
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| Mar. 31
In Lecture:
- Constructing S_n extensions of Q
- Abelian extensions of Q (statement of Kronecker Weber Theorem)
- Proof of the fundamental theorem of Galois theory for finite extensions
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
|
April 3
No class
| April 5
In Lecture:
- Proof of the fundamental theorem of Galois theory for infinite extensions
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| April 7
No class
|
April 10
In Lecture:
- Cyclotomic extensions
- Irreducibility of cyclotomic polynomials over Q
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| April 12
In Lecture:
- Galois groups of composita of fields
- Representations of groups
- Linear independence of characters
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| April 14
In Lecture:
- Galois groups of compositums of fields
- Hilbert theorem 90 (Multiplicative and additive versions)
- Applications to Kummer theory and Artin Schreier theory
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
|
April 17
In Lecture:
- Solvability by radicals
- Simple and semi-simple modules for rings
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
| April 19
In Lecture:
- Semisimple modules and rings, continued
- Wedderburn's theorem
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
No Video of class - technical difficulties!
| April 21
In Lecture:
- Representations of groups
- Linear independence of characters
Associated Reading:
- D-F: Chapter 14
- Lang: Chapter 5
Video of class (downloadable)
|
April 24
In Lecture: Final exam, 1:30 - 3:30.
| April 26
No class
| April 28
No class
|