Groups, Rings, and Fields (Fall 2017)

Groups, Rings, and Fields (Fall 2017)

Location

Tuesday Thursday 12:30-2:00, 247 Cory. Office hours 11:00-12:30  Tuesday Thursday 927 Evans Hall. The GSI is Justin Chen. His office hours are in  959 Evans Hall and will be held 2:00-3:00 Tuesdays, and 2:00-4:00 Wednesdays. 

Textbook

"Algebra" (3rd edition) by Serge Lang.  Click on the link to get a paper copy for $25 or a free electronic copy. We will cover chapters 1 to 6.  

Catalog Description

Group theory, including the Jordan-Holder theorem and the Sylow theorems. Basic theory of rings and their ideals. Unique factorization domains and principal ideal domains. Modules. Chain conditions. Fields, including fundamental theorem of Galois theory, theory of finite fields, and transcendence degree.

Prerequisites

Undergraduates who wish to take Math 250A are advised to take Math 113 and Math 114 first.

Grading

Grading will be based on 2 midterms, the final, and homework.  The lowest of the 3 exam scores will be dropped.  There will be no makeup midterms or finals. The lowest three homework scores will be dropped.

Midterm  and final questions will mostly be closely based on problems in the textbook, especially homework problems, or examples done in lectures. You may bring one sheet of notes to the midterms and final.

Reading and homework

Homework is due on Tuesday the week after it is assigned. 

Daniel Raban has some notes for the lectures here

 The following table is provisional and may be changed. 

Lecture Date Topic Reading Homework
1 Aug 24 Groups I.1-2 1, 2, 9, 10, 
2, 3 Aug 29, 31 Subgroups I.3-5 12, 13,  19, 20,  24,  26,
4, 5 Sep 5, 7 Sylow, abelian I.6-10  30, 31, 32, 34, 35, 38, 41, 42
6, 7 Sep 12, 14 Categories, Free groups I.11-12 50, 51, 52, 53
8 Sep 19, Rings II.1-3 1, 8, 11, 12
9 Sep 21 Midterm 1 I (groups)
10, 11 Sep 26, 28 Localization, UFD, modules II.4-5, III.1-2 II 5, 9,13, 14  III 1, 3, 
12, 13 Oct 3, 5 Free modules III.3-6 5, 9, 10
14, 15 Oct 10, 12 Homological algebra III.7-10 14, 15, 17, 21,
16, 17 Oct 17, 19 Polynomials IV.1-6 1, 3, 5, 7, 10, 
18, 19 Oct 24, 26 Resultants, power series IV.7-9 13, 18, 25, 26, 27
20 Oct 31 Algebraic extensions V.1-4 1, 4, 6, 7, 9, 11, 19
21 Nov 2 Midterm II II, III, IV (rings)
22, 23 Nov 7, 9 Galois extensions V.5-6 VI.1-2 V 23, 24  VI 1
24, 25 Nov 14, 16 Cyclic extensions VI.3-6 7, 8, 13ab, 18, 19, 21
26 Nov  21 Solvable extensions VI.7-12 23, 29, 30, 31, 32
27, 28 Nov 28, 30 Infinite extensions VI.13-15

43, 44

Dec 14 3:00-6:00 Final I to VI

 

 

Links related to the course:

Course Summary:

Date Details Due
Public Domain This course content is offered under a Public Domain license. Content in this course can be considered under this license unless otherwise noted.