Debaditya Raychaudhury's Homepage

Basic information

Course: MATH 520 - Abstract Algebra I
Course Credits: 3 Credits
Class Time: MW 8:30 am - 9:45 am
Class Location: SMLC 352
Syllabus: Here

Instructor information

Instructor: Deba Raychaudhury
Email: draychaudhury@unm.edu
Office: SMLC 322
Office Hours: MW 11:00 am - 12:00 noon, F 1:00 pm - 2:00 pm, or by appointments

Course details

Course Description: This is a graduate level course in group and ring theory. Some of the important topics are groups, permutation groups, Sylow theorems, introduction to ring theory, polynomial rings, principal ideal domains, unique factorization domains.

Course Goals: This is a fundamental course for pure math graduate students to solidify their proof writing skills and to discuss the relevant group and ring theory needed for the Algebra Qualifying Exam.

Learning Outcomes:

Write clear and concise proofs pertaining to algebraic structures (groups, subgroups, rings, subrings, ideals).
Learn techniques to show a group is not simple.
Identify groups as solvable or nilpotent.
Learn techniques to classify groups of a given finite order.
Identify domains such as PIDs, UFDs and Euclidean domains.

Text: Abstract Algebra Third Edition by Dummit and Foote.

Method of Evaluation: Students will be evaluated based on Homework and Exams.

Homework (200 points): There will be 11 homework altogether, each worth 20 points (see the schedule below for homework due dates). The lowest homework score will be dropped.
Exams (400 points): There will be 2 midterms (100 points each) and 1 final (200 points) exam. See the schedule below for the tentative dates of the midterm exams.

Grades: (General guidelines for letter grades are subject to change; but they won't get any more strict) Letter grades A, B, C, D correspond to grades ≥ 88%, 77%, 66%, 55%, respectively. The letter grade F will be assigned if the grade is below 55%.

Note: For more details on the grading policy and other course related policies, please refer to the Syllabus.

Tentative schedule

Note: This color indicates the day a homework is due, and this color indicates the day of an exam.

Date	Chapter(s)	Topic(s)
Monday, August 17	1.1 - 1.5	Groups and (non)examples
Wednesday, August 19	1.6 - 1.7	Homomorphisms and group actions
Monday, August 24	2.1 - 2.2	Subgroups
Wednesday, August 26	2.3 - 2.4	Cyclic and finitely generated subgroups
Monday, August 31	3.1 - 3.2	Quotient groups, cosets, Lagrange's theorem
Wednesday, September 2	3.3	Isomorphism theorems
Monday, September 7		Labor day, no class
Wednesday, September 9	3.4	Isomorphism theorems
Monday, September 14	4.1 - 4.2	Composition series and Holder's theorem
Wednesday, September 16	4.3 - 4.4	Cayley's theorem
Monday, September 21	4.4 - 4.5	Class equation, automorphisms
Wednesday, September 23	4.5	Automorphisms
Monday, September 28	3.5, 4.6	Sylow theorems
Wednesday, September 30		Sylow theorems
Monday, October 5		Sylow theorems, alternating groups
Wednesday, October 7	5.1, 5.4	Exam 1
Monday, October 12	5.2	Direct products, Fundamental theorem of finitely generated abelian group
Wednesday, October 15	5.2	Fundamental theorem of finitely generated abelian group
Monday, October 19	5.3	Determining quotients of Free abelian groups
Wednesday, October 21	5.4	Semidirect products
Monday, October 26	6.1	Nilpotent and solvable groups
Wednesday, October 28	7.1 - 7.2	Rings and (non)examples
Monday, November 2	7.3 - 7.4	Ring homomorphisms, quotient rings and ideals
Wednesday, November 4	7.5 - 7.6	Rings of fractions, Chinese remainder theorem
Monday, November 9	8.1 - 8.2	Euclidean domains and PIDs
Wednesday, November 11	8.3	UFDs
Monday, November 16		Review
Wednesday, November 18		Exam 2
Monday, November 23	9.1 - 9.3	Polynomial rings
Wednesday, November 25	9.4 - 9.5	Irreducibility criteria
Monday, November 30	10.1 - 10.2	Introduction to modules
Wednesday, December 2		Review

Homework

Submission Guideline: Please submit all homework assignments on canvas.

Homework 1 (Due: August 26)

1.1: 25, 26, 29 (you are free to assume the assertions of 28), 31, 32
1.3: 10, 11, 14, 15
1.4: 10

Extra Credit. 1.3: 12
(Solution)

Homework 2 (Due: September 2)

1.6: 17, 18, 23
2.1: 3, 4 (remember that D_8 in DF is D_4 for us), 6, 8, 12

Extra Credit. 2.1: 9 (feel free to take F=Q, R or C), 10, 15
(Solution)

Homework 3 (Due: September 9)

2.2: 2, 3, 9, 10
2.3: 16, 24
2.4: 14, 18

Extra Credit. 2.3: 26
(Solution)

Homework 4 (Due: September 16)

3.1: 1, 22, 24, 36, 38

Extra Credit. 3.1: 40, 41
(Solution)

Homework 5 (Due: September 23)

3.2: 4, 10, 18, 19
3.3: 3
3.4: 1

Extra Credit. 3.3: 2

Homework 6 (Due: September 30)

4.1: 1
4.2: 8, 10, 14
4.3: 4, 5, 6

Extra Credit. 4.3: 23, 27

Homework 7 (Due: October 21)
TBD

Homework 8 (Due: October 28)
TBD

Homework 9 (Due: November 4)
TBD

Homework 10 (Due: November 11)
TBD

Homework 11 (Due: November 25)
TBD

Review materials

*This webpage is prepared following the course pages of Sarah Percival and Janet Vassilev.