Introduction to Algebra II (MATH 30b, Spring 2007)

[ Policies & Procedures | Schedule of Lectures ]

Day & Time: Monday and Wednesday 3:40 — 4:55pm

Location: Goldsmith 0116

Office Hours: Tuesday 2:30pm-4:30pm and by appointment

Teaching assistant: Alex Charis

Textbook: John B. Fraleigh First Course in Abstract Algebra seventh edition, Adison-Wesley , 2003. ISBN 0201763907.

Prerequisites: Introduction to Algebra I or the equivalent.

Examinations: There will be two in class tests. The first will be on Wednesday, February 13 and the second on Wednesday, April 2. The final exam is a take-home exam

Assessment: The course grades will be computed as follows:: 30% Homework; 20% First test; 20% Second test; 30% Take-Home Final exam

Tests and Exams: There are no makeups for missed tests. You must take the final examination at the time scheduled by the university; no final exams will be given earlier.

Homework: There will be two kinds of homework:

Exercises give you a chance to practice and refine your basic calculus skills. They will not be collected.
Graded homework: There will be seven graded homework due at regularly spaced dates to be annouced in class. The lowest grade will be dropped. Each of the other six is worth 5% of the final garde.

Written work: We write to communicate. Please bear this in mind as you complete assignments and take exams. You must explain your work in order to obtain full credit; an assertion is not an answer. student or professor.

Help: Help is available if you have trouble with homework or lecture material. My office hours are a good place to start. Discussions with your classmates can also be very helpful and are strongly encouraged. You may also ask the TA.

Schedule of Lectures

Class	Topic	Read	Suggested Exercises	Due
Jan 16	Introduction. Rings and Fields	§18	18:3,7,8,11,15,19,27,33,38,43,46,52,55
Jan 23	Rings and Fields. Domains	§18,19	19:3,4,14,15,16,17,23,30
Jan 28	Domains. Little theorem of Fermat	§19,20	20:11,12,23,27,28
Jan 30	Euler's theorem. The field of quotients of a domain	§20,21	21:4,15
Feb 4	Rings of Polynomials	§22	22:7,12,18,23	Problems set 1 Solutions
Feb 6	Rings of Polynomials. Division of polynomials; roots	§22,23	23:9,14,25,34,35
Feb 11	Irreducible polynomials. Eisensetein's criterion	§23	23:16,17,18,19,20,21,31,36
Feb 13	Midterm I (Solutions)			Problems set 2 Solutions
Feb 25	Unique factorization of Polynomials. Kernel of an homormorphism and Ideals	§23,26	26:18,30
Mar 3	Factor Ring. Prime and Maximal Ideals.	§26,27	27:10,11,13
Mar 5	Prime and Maximal Ideals. Princial Ideals. Principal ideal domains	§27	27:15,18,19,28,34,35,	Problems set 3
Mar 12	Principal ideal domains. Z, and K[X] (K a field) are principal ideal domains. Application to the minimal polynomial of a matrix.	§27
Mar 19	Extensions Field	§29	29;1,6,9,19,20,21,25,29,30,31,32	Problems set 3
Mar 24	Vector Spaces. Algebraic Extensions	§30,31	30:1,4,5,6,7. 31:1,2,3,12,14,27
Mar 26	Geometric Constructions.	§32	32:1,2,4	Problems set 4
Mar 31	Review	Training exercises for midterm II	32:1,2,4
Apr 2	Midterm 2
Apr 7	Finite fields	33	33:1,2,3,8,9,10,11,12
Apr 9	Finite Fields. Introduction to Galois Theory	33,48
Apr 14	Automorphisms of fields	48	48:1,2,3,4,9,22,23,25,29
Apr 16	Automorphisms of fields. The isomorphism extension theorem	48,49	49:1,2,3,7	Exercises 5
Apr 28	Separable extensions.	51		Exercises 6
Apr 30	Galois extensions. The main results of Galois theory.