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Abstract Algebra: Group Theory with the Math Sorcerer (Udemy.com)

A beautiful course on the Theory of Groups:)

Created by: The Math Sorcerer

Last updated May 2026

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What you will learn

  • The Definition of a Binary Operation
  • How to Determine if an operation is a binary operation
  • How to determine if a binary operation is commutative or associative
  • The Definition of a Group
  • Examples of Important Groups such as The Integers, Rationals, Reals, Complex Numbers under various operations
  • The General Linear Group
  • The Special Linear Group
  • The Klein Four-Group
  • The Additive Group of Integers Modulo n
  • Groups Defined on Powersets
  • Groups Defined with componentwise multiplication
  • How to Prove the Identity Element in a Group is Unique
  • How to Prove that Inverses in a Group are Unique
  • How to Prove various other Fundamental Properties of Groups
  • How to Find the Order of an Element in a Group
  • Knowledge of Cyclic Groups
  • How to Find Generators for Cyclic Groups
  • How to prove groups are cyclic and not cyclic

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Course Description

This is a college level course in Abstract Algebra with a focus on GROUP THEORY:)

Note: Abstract Algebra is typically considered the one of HARDEST courses a mathematics major will take.

This course is a step above a general mathematics course. Students should have familiarity with writing proofs and mathematical notation.

Basically just,

1) Watch the videos, and try to follow along with a pencil and paper, take notes!

2) Feel free to jump around from section to section. It's ok to feel lost when doing this, remember this stuff is supposed to be super hard for most people so don't get discouraged!

3) After many sections there is short assignment(with solutions).

4) Repeat!

If you finish even 50% of this course you will know A LOT of Abstract Algebra and more importantly your level of mathematical maturity will go up tremendously!

Abstract Algebra and the Theory of Groups is an absolutely beautiful subject. I hope you enjoy watching these videos and working through these problems as much as I have:)

Note this course has lots of very short videos with assignments. If you are trying to learn math then this format can be good because you don't have to spend tons of time on the course every day. Even if you can only spend time doing 1 video a day, that is honestly better than not doing any mathematics. You can learn a lot and because there are so many videos you could do 1 video a day. Good luck and I hope you learn a lot of math.

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Instructor Details

The Math Sorcerer

I was born on a small unnamed Island in the Pacific Ocean inhabited mostly by natives who practiced mathematics on a daily basis.

My mother was a witch who specialized in Calculus and my father was a warlock who was well versed in the dark arts of Algebra.

As I grew older so did my thirst for knowledge, and so I set out on  a long voyage to improve my mathematical skills. I traveled the world for years and learned a great deal of mathematics, but it wasn't until I met that raging Hobbit that my true powers started to show.

I am here today to share my magical powers with you.

Come join on me on this journey as we explore the world of mathematics together.


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Reviews

4.8

587 ratings on Udemy

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By Lex Townsend on 8/27/2026

Unlike some other lecturers, this guy doesn't have a microphone that assaults my eardrums. He also goes at a good pace. Thankyou for providing such an amazing resource for those who want to self study this material.

By Yair Stark on 12/12/2025

The course is excellent. The instructor presents the material in an engaging, very clear, and precise manner. However, it is unfortunate that there are assignments only at the beginning of the course, and that in some parts there is a lack of examples. These shortcomings are significant, especially when dealing with abstract topics such as the material covered in the course.

By Nitzan on 3/10/2025

well, I have some background in math and know how to prove theorems so it is not realy that hard for me yet. it is very interesting to study new math concepts and do the exercises. I think the math sorcerer is a great lecturer.

By Chris Staley on 10/12/2024

Great lectures and explanations. A clear and easy to understand intro to the subject. The one complaint I have is that there aren't a lot of problems to do, which I think is something you need to really internalize math concepts.

By Arles Rodríguez on 4/19/2024

The videos are really good! It helps to understand all the basic concepts of abstract algebra. After lesson 70 it may be necessary to follow additional bibliography as recommended in the Q&A section.

By Evan Pique on 12/18/2022

I really appreciate this courses, as the numerous exmaples help a lot to understand an abstract subject such that the group theory. I think the maths sorcerer has made a great job with this course.

By Nathan Rous on 10/13/2022

I've taken a course on abstract algebra before and I needed a refresher. You can't beat the price, and the content covered was a great rehash of everything i learned in my abstract algebra class. I recommend this to anyone who either needs a quick review, or is going to be taking an abstract algebra class and wants to start off with exceptional prerequisite knowledge

By Nithish Kumar CV on 6/20/2021

Honestly, there was a time when I was struggling in my classes to understand what is a set! Here I am, able to follow through the lectures and solve correctly all the assignment problems until now, thanks to the expert wizardry of the math sorcerer! Surely these lectures have changed my perception of proof writing making them seem doable for a person like me with a very average mathematical skills

By Patrik Dennis on 10/17/2020

I am a mathematics major and not one professor at my university explains abstract concepts in such clarity and enthusiasm as you do! Every professor och teacher should take notes from you! I have now purchased your calc courses and looking forward to integrations insanity when I am ready :)

By Julio Tr on 6/20/2019

It is really good, I recommend 100%. The Prof. answers every question and he is very kind and attentive. You do need to have some high level background though, but it is perfect for preparation before taking the course at university.

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Overall Score : 96 / 100