Course Title:  Abstract Algebra
Course Number: MATH 520
Course Credits: 3 credits

Instructor: Dr. Janet Vassilev
Office: SMLC 324
Office Hours:  WF 11 am - 12 noon and M 3 - 4 pm or by appointment.
Telephone: (505) 277-2214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil

Class Time: MWF 1-1:50 pm
Class Location: SMLC 352
Semester: Fall 2019

Course Description:  This is a graduate level course in group and ring theory.  We will delve into group and ring theory in this first semester.

Course Goals:  This course is one of the fundamental courses for pure math graduate students where students solidify their proof writing skills and learn the relevant group and ring theory to prepare themselves for the Algebra Qualifying Exam.

Student 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 3rd Edition by Dummit and Foote

Course Requirements

1) Homework (200 points):  Homework will be assigned weekly on Wednesdays and will be collected the following Thursday by 8 am under my office door.  Homework will not be graded unless it is written in order and labeled appropriately.   The definitions and theorems in the text and given in class are your tools for the homework proofs. If the theorem has a name, use it. Otherwise, I would prefer that you fully describe the theorem in words, than state by Theorem 3.  Each week around 4 or 5 of the assigned problems will be graded. The weekly assignments will each be worth 20 points. I will drop your lowest two homework scores and the remaining homework will be averaged to get a score out of 200.

2) Exams (400 points):  I will give two midterms (100 points each) 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 using the percentage that you receive on the final exam.  The Midterms are tentatively scheduled for Monday September 30 and Monday, November 11.  The Final is on Friday, December 13, from 12:30-2:30 pm.

GradesGeneral guidelines for letter grades (subject to change due to the class "curve"; 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 Modern Algebra II):

 Date Section Topic Homework 8/19 1.1-1.5 Groups and Examples 8/21 1.6-2.1 Subgroups, Homomorphisms and Actions 1.1 29, 31 1.3 8, 12, 14 1.4 7, 10 1.6 17, 18, 23 Due 8/29 8 am 8/23 2.2 Subgroup Examples 8/26 2.3 Cyclic groups 8/28 2.4, 3.1 Subgroups generated by a subset, Cosets and Quotient Groups 2.1 6, 8, 12 2.2 9, 14 2.3 16, 24, 26 2.4 14, 18 Due 9/5 8 am 8/30 3.2 Lagrange's Theorem 9/4 3.3 Isomorphism Theorems, Composition Series 3.1 22, 24, 36, 38 3.2 4, 10, 18, 19 3.3 3, 8 Due 9/12 9/6 3.4, 3.5 Holder's Theorem 9/9 3.5 The Alternating Group 9/11 4.1 Groups Actions and Representations of Permutations 3.4 5, 7, 11 3.5 3, 4, 12, 15 4.1 1, 7 Due 9/19 9/13 4.2 Cayley's Theorem 9/16 4.3 Class Equation 9/18 4.4 Automorphisms 4.2 9, 11, 14 4.3 5, 13, 17, 23, 27, 33 Homework Due 9/26 9/20 4.5 Sylow's Theorems 9/23 4.5 Sylow's Theorems 9/25 4.5 Sylow's Theorem Examples 9/27 Review 9/30 Midterm 1 10/2 4.6 Simplicity of An 10/4 5.1-5.2, 5.4 Direct products of groups and the , Recognizing Direct Products 10/7 5.2 Fundamental Theorem of Finitely Generated Abeliean Groups 10/9 5.2 Fundamental Theorem of Finitely Generated Abeliean Groups 10/14 5.2 Fundamental Theorem of Finitely Generated Abeliean Groups 10/16 5.5 Semidirect Products 10/18 5.5 Semidirect Products continued 10/21 6.1 Nilpotent Groups 10/23 6.1 More on nilpotent and solvable groups 10/25 6.2, 6.3 Groups finale 10/28 7.1-7.2 Rings, Polynomial Rings, Matrix Rings and Group Rings 10/30 7.1, 7.3 Ring Homomorphisms and Quotient Rings, Ideals 11/1 7.4, 7.5 Properties of Ideals and Rings of Fractions 11/4 7.6 Chinese Remainder Theorem 11/6 8.1 Euclidean Domains 11/8 Review 11/11 Midterm 2 11/13 8.2, 8.3 Principal Ideal Domains, Unique Factorization Domains 11/15 8.3 Unique Factorization Domains 11/18 9.1-9.3 Polynomial Rings over Fields, Gauss' Lemma 11/20 9.4, 9.5 Irreducibility Criteria, Polynomial Rings over Fields II 11/22 10.1 Modules 11/25 10.2 Module Homomorphisms 11/27 10.3 Free Modules 12/2 Review 12/4 Review 12/6 Review 12/13 Final Exam 12:30 - 2:30 pm

Accomodation Statement: Accesibility Resource Center (Mesa Vista Hall 2021, 277-3506) provides academic support to students who have disabilities.  If you think you need alternative accessible formats for undertaking and completing your coursework, you should contact this service right away to assure your needs are met in a timely manner.

Title IX Statement: A note about sexual violence and sexual misconduct:  As a UNM faculty member, I am required to inform the Title IX Coordinator at the Office of Equal Opportunity (oeo.unm.edu) of any report I receive of gener discrimination which includes sexual harrassment, sexual misconduct, and/or sexual violence.  You can read the full campus policy regarding sexual misconduct.  If you have experienced sexual violence or sexual misconduct, please ask a faculty or starr memeber for help or contact the LoboRESPECT Advocacy Center.

Academic Integrity Statement: Collaborating with your peers can be an effective way to learn mathematics.  If you so choose to work with your peers, make sure that you each write up homework solutions in your own words.  Working with your peers and copying solutions is quite a separate matter.  If you attempt to copy someone's solution on the homework, you are only hurting yourself when it comes to taking the exams.  Struggling through a problem allows for much more understanding than just rewording someone else's argument.  You are more likely to solve the problems on in class exams, which are not a collaborative effort, if you have made an honest effort on the homework.  If a student attempts to cheat during an in class exam and I can prove this dishonesty, I reserve the right to take disciplinary actions against such a student which may result in a failing grade for that exam