Math 113: to Abstract Algebra

Instructor:

Andrey Smirnov, smirnov@math.berkeley.edu

Lectures:

Section 1: GPB 107, Tuesdays and Thursdays from 12:30-14:00 Section 2: Hearst Mining 310, Tuesdays and Thursdays 14:00-15:30,

Office hours:

Tuesdays and Thursdays from 11.00-12.00 am Evans Hall 859

If you have any questions about the course and matherial please come see me.
Please email me and ask for appointment if the office hours time is not convenient for you.

Text Book:

John Fraleigh, A fist course in Abstract Algebra, 7th edtition

Additional books:

David Dummit, Abstract Algebra

Grading: 30% Homework, 30% Midterms, 40% Final. 


GSI:

Justin Chen will be helping with questions and proble solving

Tuesday: 11 am - 3 pm; Wednesday: 2 pm - 7 pm; Friday: 11 am - 12 pm; All office hours are held in 959 Evans.

Homework

There will be one homework every one or two weeks. They will be posted on this page together with the due date. Late homework will not be accepted under any circumstance. However, your two lowest homework grades will not be included in the final grade calculation. Discussing of the problems with other students is encouraged.

Exams

There will be two midterm exams on September 26 and ??. The midterms will be in class. The final exam is on ??, ?? am - ?? pm at ??. In the case of a fire alarm during either of the midterms or the final exam, leave your exams in the room, face down, before evacuating. Under no circumstances should you take the exam with you.

Special Accommodations

If you have a documented disability and require special accommodations of any kind, please e-mail me as soon as possible, and no later than September 15.

 

 

Tentative Schedule

Numbers in the reading section correspond to John Fraleigh, 7th edtition.

# Date Topic Readings Hw Notes
1 8/24 Introduction, sets, functions, relations Section 0 HW1 Out  
2 8/28 Binary operations Section 1
3 8/31 Isomorphisms Section 2 HW2 Out, HW 1 Due  
4 9/5 Cyclic Groups Section 5,6    
5 9/7 Permutations Section 8,9 HW3 Out, HW 2 Due  
6 9/11 Permutations and orbits Section 8,9  
7 9/14 Cosets and orbits Section 9, 10 HW4 Out, HW 3 Due  
8 9/19 Direct product. Finitely generated abelian groups. Section 11    
9 9/21 Direct product. Finitely generated abelian groups. Section 11 HW5 Out, HW 4 Due  
9 9/26 Midterm 1 Sections 1-11  
10 9/28 Homomorphisms. Normal subgroups. Quotients. Section 13, 14 HW6 Out, HW 5 Due  
11 10/3 Rings and fields. Basic examples. Section 18  
11 10/5 Rings and fields. Basic examples. Section 18 HW7 Out, HW 6 Due  
12 10/10 Integral domains. Section 19  
12 10/12 Integral domains. Section 19 HW8 Out, Hw 7 Due  
13 10/17 Fermat's and Euler's theorems Section 20
14 10/19 Quotient field of an integral domain. Section 21 HW9 Out, Hw 8 Due
15 10/24 Rings of polynomials. Section 22  
16 10/26 Factorization of polynomials over a field Section 23 HW10 Out, Hw 9 Due  
17 10/31 Homomorphisms and factorrings Section 26  
18 11/2 Prime and maximal ideals Section 27 HW11 Out, Hw 10 Due  
19 11/7 Midterm2 Sections 18-23, 26,27  
20 11/9 Extension Fields Section 29 No homework, Hw 11 Due  
21 11/14 Vector Spaces, Algebraic extensions Sections 30, 31  
22 11/16 extensions fields Section 29 HW12 Out  
23 11/21 algebraic extensions Section 31  
24 11/23 No class No class  
25 11/28 finite fileds Section 31 Hw12 Due  
26 11/30 finite fileds Sections 51