Course Syllabus

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Location

Tuesday Thursday 8:00A-9:30A. The room is 60 Evans Hall. There are also some pre-recorded lectures available on youtube: see below for links. Office hours 2:00-3:30 Tuesday Thursday 927 Evans Hall or https://berkeley.zoom.us/j/8267015874  (send me an email message to surname at berkeley dot edu if you want to see me on zoom). 

Schedule page for math 250A

The GSI for this course is Tahsin Saffat, who will be holding office hours MW 10-11:30 in Evans 853.

There is a course discussion site here

Textbook

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

Syllabus

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.

The lectures will emphasize examples and calculations over theorems or proofs.  Course philosophy: theorems will only be  proved in lectures when they are needed for an example. 

Prerequisites

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

Grading

Grading will be based on 2 midterms, the final, and homework.  There will be no makeup exams.  The lowest exam score and the two lowest 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.

Reading and homework

Homework is due on Sunday the week after it is assigned. Homework will not be accepted after the final exam. Homework and the midterms and final should be submitted on gradescope (entry code )

There are also some youtube lectures on groups (optional extra: representations of finite groups ), categories, rings and modules (optional extra: homological algebra), and fields which are similar to the lectures in class. 

  The following table is provisional and may be changed. 

List of topics and homework
Lecture Date Topic Reading Homework
1  Aug 26  Groups I.1-2 I 1, 2, 9, 10,
2, 3 Aug 31, Sept 2 Subgroups I.3-5 I 12, 13,  19, 20,  24,  26,
4, 5 Sep  7, 9 Sylow theorems, abelian groups  I.6-10 I 30, 31, 32, 34, 35, 38, 41, 42,
6, 7 Sep 14, 16 Categories, Free groups I.11-12 I 50, 51, 52, 53
8 Sep 21 Rings II.1-3 II 1, 8, 11, 12 
9 Sep 23 Midterm 1 I (groups)
10, 11 Sep 28, 30 Localization, UFD II.4-5, III.1-2 II 5, 9,13, 14  III 1, 3,
12, 13 Oct 5, 7 Modules, tensor products III.3-6 III 5, 9, 10
14, 15 Oct 12, 14 Duality, limits, homology III.7-10 III 14, 15, 17, 21,
16, 17 Oct 19, 21 Polynomials, Noetherian rings IV.1-6 IV 1, 3, 5, 7, 10,
18, 19 Oct 26, 28 Symmetric functions, Resultants, power series IV.7-9 IV 13, 18, 25, 26, 27
20 Nov 2 Algebraic extensions V.1-4 V 1, 4, 6, 7, 9, 11, 19
21 Nov 4 Midterm II II, III, IV (rings)
22 Nov 9 Galois extensions V.5-6 VI.1-2 V 22, 23, 24  VI 1
Nov 11 Veterans day (no lecture)
23, 24 Nov 16, 18 Cyclic extensions VI.3-6 VI 7, 8, 13ab, 18, 19, 21
25 Nov  23 Norm and trace VI.7-12 VI 23, 30, 31, 32, 33
Nov 25 Thanksgiving (no lecture)
26, 27 Nov 30, Dec 2 Solvable and infinite extensions VI.13-15

VI 43, 44, 46
Wed Dec 15 3:00-6:00  Final V,  VI (fields)

Using TEX: I encourage students to write up their problem-set solutions in TEX, more specifically LATEX. This is a powerful mathematical typesetting program which is the standard way to write papers in math, physics, and computer science. Thus learning to use TEX is a valuable skill if you work in such fields.

The easiest way to use TeX is overleaf which works in any browser. 

You also can freely download versions of TEX onto your computer.
If you use Mac OS, you can find it at MacTex.
If you use Windows, you can find it at proTeXt

Several guides to using TEX are listed on the department's computer support web pages. One beginner's guide can be found at texman A more comprehensive guide can be found at this link

The best way to start learning TEX is not by trying to compose the long header, but rather by having a file that already has a header, and then gradually modifying that file as you learn how TEX works.
For such a TEX file with a header, click LATEX-sample . Make a copy to play with, once you have downloaded TEX onto your computer. At first, don't modify anything above "\begin{document}".

 

 

 

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