Instructor

Rekha Santhanam

Semester

Autumn ‘19

Course Difficulty

The course is not very difficult, but the problem solving involves some rigorousness somewhere along the same line as MA 105. Initially, the course will be easy dealing with definitions of abstract mathematical structures and their properties, the difficulty increases as the course proceeds, but it should be manageable as all the necessary details and basics are covered in the course.

Time Commitment Required

I would say a little more than the core courses but what matters is sincerity as all the basics are covered in class. If you are regular then it should be manageable.

Grading Policy and Statistics

It was relative grading, the average/median of the class was lying in BB-BC range.

Attendance Policy

There was no attendance policy but there were short in-class quizzes every week or sometime twice a week and thus attendance was a sort of mandatory, this might vary with the instructor.

Pre-requisites

There were no prerequisites for this course and as such is not required.

Evaluation Scheme

In-class short quizzes - (25) , Midsem - (25) , Endsem - (40), Presentation - (10). It is highly subjected to change depending on the instructor.

Topics Covered in the Course

The course starts with the introduction to algebraic structures Groups and goes on to include Rings and Fields. It goes on deriving/proving many properties and relations on these algebraic structures. Many interesting theorems and proofs will be derived which relates to number theory , polynomials and other fields of mathematics etc, Here is a very brief list :

Groups, subgroups , factor groups , cyclic groups, generators and relations, Lagrange’s Theorem, homomorphisms, isomorphisms , normal subgroups, Quotients of groups , Direct product , Cayley’s Theorem, group actions, Sylow Theorems.

Rings , Integral Domains , Ideals and Factor rings, Polynomial rings, Factorization of polynomials , Divisibility in Integral Domains etc.

Teaching Style

It was an offline class during my time, and no slides were given. The prof was considerate and would explain everything clearly. The professor would solve the problems on board after giving the students some time to attempt it.

Tutorials/Assignments/Projects

There were no Assignments, Tutorials were discussed in class, there used to be a separate tutorial session every Wednesday, it was not graded, the professor used to solve the problems during the class hours. There was also a presentation at the end of the course in which we had to take a problem from the set of problems and explain the proof( if it’s theorem) or the solution.

Feedback on Exams

Quizzes were simple as they were short 10-15 mins. The Midsem and Endsem expected the solutions to be rigorous. Every exam consisted of subjective type of questions in which you had to prove something and all exams were closed book and closed notes.

Motivation for taking this course

I took this course because of my interest in Mathematics and particularly this was one field that I had not known much and wanted to explore.

Course Highlights

It’s a good introduction to the field of Abstract Algebra.

Course Importance

The course might be most helpful for the students interested in Computer Science (mostly cryptography) and physical systems where there are symmetries involved, especially in the laws of physics, modeling structures like solid structure or molecular structure in chemistry. Note that this course does not deal with application and just gives the introduction.

How strongly would I recommend this course?

If you like Mathematics and do not mind the abstract part of it then this course is a good introduction to abstract algebra.

When to take this course?

I took this course in third semester, i would recommend taking in 3 or 5th semester

References Used

1) David S. Dummit, Richard M. Foote - Abstract Algebra-Wiley (2003)
2) Joseph Gallian - Contemporary Abstract Algebra (2009, Brooks Cole)
3) Michael Artin - Algebra (1991, Prentice Hall)

Review By: Praneet Nayak