Math 103B Winter 2006
Instructors
Professor:
Name 
Office 
Email 
Phone 
Office Hours 
Lecture Time 
Lecture Place 
Prof. Daniel Rogalski 
AP&M 5131 
drogalsk@math.ucsd.edu 
5344421 
W 45 
MWF 22:50pm 
WLH 2113 

Teaching Assistant:
Name 
Office 
Email 
Office Hours 
Section Times 
Section Place 
John Farina 
AP&M 5018 
jfarina@math.ucsd.edu 
W 34 
W 77:50pm 
WLH 2110 

General Course Information
Textbook: Contemporary Abstract Algebra, 6th Edition, by Joseph Gallian.
The main topic of this course is the theory of rings and fields.
We plan to cover most of chapters 1223 and chapter 31 of Gallian.
There will be 2 inclass midterms on Wed. 2/1/06 and Wed. 3/1/06, and a final exam on Mon 3/20/06 from 36pm.
No makeup exams will be given.
Homework assignments will be due weekly on Fridays in class.
The final grade will be determined as follows: Homework 25%, Midterms 25%, Final Exam 50%.
More detailed descriptions, including a tentative syllabus, may be found in the first day course
handout here: Course syllabus
Check below for more uptodate information about the schedule of homework and lectures.
Schedule of Lectures:
1/9/06 Chap 12: Definition of ring, examples.
1/11/06 Chap 12,13: Basic properties of rings. Subrings. (Integral) domains.
1/13/06 Chap 13: Fields. Characteristic.
1/16/06 NO CLASS
1/18/06 Chap 14: Ideals, factor rings.
1/20/06 Chap 14: Examples of factor rings. Prime and maximal ideals.
1/23/06 Chap 15: Homomorphisms. 1st homomorphism theorem.
1/25/06 Chap 15: The characteristic homomorphism Z to R for a ring R. Ideals = kernels.
1/27/06 Chap 15: Field of quotients of a commutative domain.
1/30/06 Chap 16: Introduction to polynomial rings. + Exam Review.
2/1/06 Exam I
2/3/06 Chap 16: Division algorithm for polynomials.
2/6/06 Chap 16: F[x] is a PID. Evaluation. R[x]/(x^2 + 1) is isomorphic to C.
2/8/06 Chap 16,17: Remainder and Factor theorems. A polynomial of degree n has at most n roots.
Irreducible polynomials.
2/10/06 Chap 17: Irreducibility tests.
2/13/06 Chap 17: Proof of mod p test. Principal ideals (f) are maximal if and only if f
is irreducible. Construction of finite fields.
2/15/06 Chap 18: Irreducibility and prime elements in rings, UFDs.
2/17/06 Chap 18: Rings of the form Z[sqrt(d)].
2/20/06 NO CLASS
2/22/06 Chap 18: A PID is a UFD. Euclidean domains.
2/24/06 Chap 18: Z[i] is a Euclidean domain. Z[x] is not a PID.
2/27/06 Exam Review
3/1/06 Exam II
3/3/06 Chap 19: Vector Spaces
3/6/06 Chap 2021: Field extensions. Splitting Fields over Q.
3/8/06 Chap 2021: Big Theorem on Field extensions F(alpha).
3/10/06 Chap 31: Error correcting codes part I
3/13/06 Chap 31: Error correcting codes part II
3/15/06 Insolvability of the Quintic
3/17/06 Review day
3/20/06 FINAL EXAM
Homework Assignments and Exam review sheets:
Homework #1, due 1/13/06
Homework #2, due 1/20/06
Homework #3, due 1/27/06
Exam 1 review sheet
Exam 1 solutions (includes exam)
Homework #4, due 2/10/06
Homework #5, due 2/17/06
Homework #6, due 2/24/06
Exam 2 review sheet
Exam 2 solutions (includes exam)
Homework #7, due 3/10/06
Homework #8, due 3/17/06
Final Exam review sheet