M380C Fall 2019
This schedule is tentative.


Week
 Dates
 Daily schedule
Homework
1
 Aug 25-31
Mon:

Wed: (First day of class).

Plan for the week: We will be going through the Dummit-Foote book. To get started we will review groups, subgroups and homomorphisms from an axiomatic view, as covered in sections 1.1, 2.1, 1.6. Then we will review examples such as Z, Z/mZ, the circle, isometry groups, free groups, automorphism groups, Dihedral groups, symmetric groups, matrix groups as in sections 1.2-1.5 and 6.3.

Please bring questions! 

Fri:
 Homework #1

1.1: 9*, 22
1.2: 1*, 3, 10
1.3: 1, 5, 6, 16* 
1.4: 2, 7*, 10
1.6: 2*, 4, 7*
2.1: 4*, 12
6.3: 1, 3*, 6.

40% of the grade consists of the 8 starred problems which are 5 points each.

60% of the grade is based on completion. You get full credit for doing at least half of the problems.


Due: Fri Sept 6.

Also: please read Chapter 1 and sections 2.1, 6.3 (at least).
2
 Sept 1-7
 Mon: Labor Day (school holiday)

Tues: Last day of official add/drop period.

Wed:

Plan for the week: We will go over group actions (especially groups acting on themselves either by translation or conjugation), fields and matrix groups, the isomorphisms theorems, simple groups, Jordan-Holder Theorem, solvable groups and the class equation. Along the way, we'll prove A_5 is simple.

Fri:		 Homework #2

1.7: 10*, 11, 12, 23*
2.2: 4
2.3: 21, 22*, 23
2.4: 7, 10*, 11
2.5: 6, 8*, 11
3.1: 9, 11, 18*,
3.2: 10, 11*
 3.5: 4*

Same grading scheme as before.

Due: Wed Sept 11.

Also: please read Chapters 2 and 3.
3
Sept 8-14
 Plan for the week: We will go over simple groups, Jordan-Holder Theorem, solvable groups, the class equation, simplicity of A_5 and semi-direct products. If there is time, we'll start on Sylow's Theorems. 

Mon: Register to vote! (There's an election on Nov 5. You have to be registered 30 days in advance to vote. More details here).

Wed:

Fri: (Last day a graduate student may add a class)
 Homework #3

3.3: 7, 9
3.4: 3, 9, 10*
3.5: 10
4.1: 2, 10*
4.2: 8, 9, 10*
4.3: 19*, 28,
4.4: 2, 3, 5*,
 5.1: 18*
5.4: 11*, 15
5.5: 16*

Same grading scheme as before.

Due: Wed Sept 18.

Also: please read Chapters 4 and 5.
4
 Sept 15-21

Plan for the week: We'll continue with Sylow's Theorems, classifying groups of small order, nilpotent, solvable and p-groups. On Friday, we'll have a problem session.

Mon:

Wed:

Fri: Problem session.
 Homework #4

4.5: 6, 9, 11, 16, 29*, 30, 34, 40
4.6: 2, 4
5.2: 14*
6.1: 9, 23, 26abc*, 33*
6.2: 6, 9*, 12, 14.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full credit for doing at least 14 problems in total.

Due: Wed Sept 25.

Also: please read Chapters 5 and 6. 
5
 Sept 22-28
Plan for the week: We'll continue with nilpotent, solvable and p-groups. We'll start chapter 7 on Rings. We'll have a problem session on Friday.

Mon: Here is a memory jogger and practice problems for the upcoming exam 1.

Wed:

Fri:		 Homework #5

5.4: 7*, 8, 9
5.5: 7
7.1: 6, 9, 13*, 21, 26*, 27
7.2: 5*, 6, 7
7.3: 5, 10, 12, 17*, 21, 24, 34.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 16 problems in total.

Due: Wed Oct 2.

Also: please read Chapter 7. 
6
 Sept 29- Oct 5
 Sun: Shanah Tovah U'metukah!


Plan for the week: We'll continue with rings: zero divisors, nilpotent elements, units, ideals (esp. prime and maximal), fields, integral domains, isomorphism theorems, operations on ideals (+, intersection, times), localization and the Chinese Remainder Theorem.

Mon:

Wed:

Fri: I will hand out Exam 1.
 Homework #6

7.4: 11*, 14*, 15, 16, 26, 30*, 31, 32
7.5: 3*, 5
7.6: 5*

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 8 problems in total.

Due: Fri Oct 11.

Also: please read Chapters 7 and 8.
7
 Oct 6-12
Plan for the week: We'll continue with Chapter 8 on Integral Domains. This includes: kinds of elements (irreducible, prime, gcd's, associates), kinds of ID's: UFD's, PID's, ED's, and Noetherian rings, their relationships and examples (quadratic integer rings and polynomial rings).

Homework #6 will be due on Friday this week instead of Wednesday since the Exam is due on Monday.

Mon: Exam 1 due. (Last day to register to vote.)

Wed:

Fri:		 Homework #7

8.1: 1a, 2a*, 3, 4*, 6, 8a, 9, 12
8.2: 3, 5*
8.3: 4, 6*, 7, 8*.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 10 problems in total.

Due: Wed Oct 16.

Also: please read Chapters 8 and 9.
8
 Oct 13-19
 Plan for the week: We'll continue with Chapter 9 on Polynomial Rings. If there's time we'll go over some applications to algebraic integers.

I won't have office hours on Friday (I'll be traveling and won't arrive at UT until class time).

Mon:

Wed:

Fri:		 Homework #8

9.1: 5, 6*, 7
9.2: 1, 2, 3, 4*, 5*, 6
9.3: 1, 2,
9.4: 1, 2*, 5*, 6.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 12 problems in total.

Due: Wed Oct 23.

Also: please read Chapters 9 and 10.
9
 Oct 20-26
 Plan for the week: We'll continue with Chapter 9 on Polynomial Rings. We'll skip the last section 9.6 because we've already proven the Hilbert Basis Theorem and we're not going to cover Groebner bases. Probably if there's time we'll start on Chapter 10 (Modules) on Wednesday. Depending on student interest, we could have a problem session on Friday.

I won't have office hours on Wednesday (there's a talk I'm planning to attend).

Mon: Early voting begins.

Wed:

Fri:		 Homework #9

9.4: 10*, 11, 12, 18, 19a, 19d,
9.5: 3*
10.1: 8*, 9, 10*, 11, 13, 19
10.2: 3, 6, 12*, 13.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 12 problems in total.

Due: Wed Oct 30.

Also: please read Chapters 9 and 10.
10
 Oct 27-
Nov 2

Plan for the week: We'll continue with 10.3 and 10.4 (free modules and tensor products). We'll skip 10.5 (exact sequences) although we might come back to it later in the semester. We'll cover chapter 11 (vector spaces) very quickly because most of it is review. The last section 11.5 is on tensor algebras. We will cover that section more carefully. Depending on student interest, we could have a problem session on Friday.

Sun: Happy Diwali!
Mon:

Wed:

Thurs: Happy Halloween and Day of the Dead! (Last day
an undergrad can drop a class with Dean's approval, or change to pass/fail)

Fri:		 Homework #10

10.3: 3, 4*, 5
10.4: 2, 3, 7*, 10*, 11, 12, 16, 17, 18, 24*, 25.
11.2: 38
11.5: 5*, 13

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 12 problems in total.

Due: Wed Nov 6.

Also: please read Chapters 10 and 11.
11
 Nov 3-9
 Plan for the week: We'll continue with tensor products (10.4 and 11.5). Then we'll go over vector spaces 11.1-11.4. Depending on student interest, we could have a problem session on Friday. On Friday I will hand out exam 2. Here is a memory jogger and practice problems for the upcoming exam 2.


Mon:

Tues: Voting Day!

Wed:

Fri: I will hand out exam 2
12
 Nov 10-16
 Plan for the week: We'll continue with determinants (11.4), tensor algebras (11.5) and modules over PIDs (12.1). I changed the due date on Homework #11 and added some new problems. It is now due Wednesday of next week.

Mon: Exam 2 due.

Wed:

Fri:		 Homework #11

11.1: 2*
11.2: 1*, 2, 3, 39
11.3: 2*, 4
11.4: 2*, 3
12.1: 2*, 4, 14, 15, 20, 21.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 12 problems in total.

Due: Wed Nov 20.

Also: please read Chapters 11 and 12.
13
 Nov 17-23
 Plan for the week: We'll continue with modules over PIDs (12.1) and the rest of chapter 12. We'll skip the algorithmic (Groebner bases) parts. Then we'll continue with chapter 15 (introduction to algebraic geometry). Chapter 15 is very interesting! There are lots of connections with previous material.

Mon: 12.1.

Wed: 12.2 and 12.3

Fri: 15.1
 Homework #12

12.2: 4, 9 (first 2 only), 11, 17*, 18*
12.3: 5, 17*, 22*, 24, 37
15.1: 16, 19*, 23, 26, 28.

50% of the grade consists of the 5 starred problems which are 10 points each.

50% of the grade is based on completion. You get full completion credit for doing at least 12 problems in total.

Due: Wed Dec 4.

Also: please read Chapters 12 and 15.
14
 Nov 24-30
 Mon:

Wed: Thanksgiving (no class)

Thurs: Happy Thanksgiving.

Fri: Thanksgiving (no class)
15
 Dec 1-7

Plan for next week: We'll continue with Chapter 15 with the aim of getting to Hilbert's Nullstellensatz. Depending on student interest, we may have a problem session on Friday. 

Here is a memory jogger for the final.

I will post practice problems for the final soon.

Mon:

Wed:

Fri:
16
 Dec 8-14
 Mon: Last class day. I will hand out the final exam.

Wed:

Fri:
17
 Dec 15-22
 Mon: 9am-12noon is the official time of our final. The final is due on this day.