MATH 521 - Abstract Algebra

Spring 2018

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  TR 10:15-11:00 am, TR 1-1:45 pm and by appointment.
Telephone:  (505) 277-2214
email: jvassil@math.unm.edu

webpage: http://www.math.unm.edu/~jvassil

Text :  Abstract Algebra, 3rd Edition, by David Dummit and Richard Foote. 

Course Meetings:  The course lectures will be held in SMLC 352 on Tuesdays and Thursdays from 11:00 am-12:15 pm. 

Topics:  Module Theory, field theory, Galois theory.

Homework (200 points): Homework will be assigned on Thursday and collected the following Thursday any time during the day (It must be received by 8 am Friday morning).  Homework will not be graded unless it is written in order and labeled appropriately.  The definitions and theorems given in class and in the text will be your tools for the homework proofs.  If the theorem has a name, use it.  Otherwise, I would prefer you to fully describe the theorem with words, than state by Theorem 3.  Each week 4 or 5 of the problems will be graded.  The weekly assignments will be given a score out of 20 points.  I will drop the lowest two homework assignments and average the remaining to get a score out of 200.

Exams (400 points):  I will give two midterms (100 points) and a final (200 points). There are no make up exams. If a test is missed, notify me as soon as possible on the day of the exam. For the midterms only, if you have a legitimate and documented excuse, your grade will be recalculated without that test.  The Midterms are tentatively scheduled for Thursday, February 22 and Tuesday, April17.  The Final is tentatively scheduled for Tuesday, May 8, from 12:30 -2:30 pm. 

Grades:  General guidelines for letter grades (subject to change; but they won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F.  In assigning Final Grades for the course, I will compare your grade on all course work (including the Final)  and your grade on the Final Exam.  You will receive the better of the two grades.

Tentative Schedule (for Dr. Vassilev's Abstract Algebra):

DateSectionTopicHomework
1/1610.4Tensor Products
1/1810.5Exact Sequences/Projective Modules10.4 3, 6, 7, 12, 16, 17, 21
10.5 1, 2
1/2310.5Injective Modules
1/2510.5Flat Modules10.5 3, 4, 6, 7, 11, 15
1/3011.3Dual Vector Spaces
2/111.5Tensor Algebras10.5 5, 21, 22, 25
11.3 3, 4
11.5 1, 13
2/611.5Tensor Algebras
2/812.1/12.2Fundamental Theorem of f.g. Modules over PIDs/Rational Canonical Form11.5 7, 8, 12
12.1 5, 9, 16, 21, 22
2/1312.2Rational Canonical Form continued
2/1512.3Jordan Canonical Form12.2 4, 9, 10, 11, 14, 16, 18
2/2012.3Jordan Canonical Form
2/2213.1Field Extensions/Exam Review12.3 5, 7, 9, 18, 21, 37
2/27Midterm 1
3/113.1Field Extensions13.1 1, 3, 4, 6, 7
3/613.2Algebraic Extensions 
3/813.4Splitting Fields 13.2 3, 4, 7, 9, 11, 14, 16, 17, 22
3/2013.4-13.5Algebraic Closures and Separable Extensions
3/2213.6,14.1Cyclotomic Extensions and Field Automorphisms13.4 2, 3, 6
13.5 2, 3, 5, 7, 11
3/2714.2Fundamental Theorem of Galois Theory
3/2914.2Fundamental Theorem of Galois Theory continued13.6 4, 6, 9
14.1 1, 6, 8
14.2 3, 4, 5
4/314.3Finite Fields
4/514.4Composite and Simple Extensions14.2 6, 7, 14, 17, 18
4/1014.5,14.6Abelian Extensions/Galois Groups of Polynomials
4/1214.6Galois Groups of Polynomials/Exam Review
4/17Midterm 2
4/1914.7Solvable and Radical Extensions
4/2414.8Computation of Galois groups over the rationals
4/2614.9Transcendental Extensions
5/1Review for Final
5/3Review for Final
5/8Final Exam 12:30-2:30 pm (tentative)