$Udemy – Abstract Algebra: Group Theory with the Math Sorcerer 2020-1$

Udemy – Abstract Algebra: Group Theory with the Math Sorcerer 2020-1

Published on: 2023-02-15 02:54:15

Categories: 28

Descriptions

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

What you’ll 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
How to Prove Various key results surrounding Cyclic Groups
Knowledge of Subgroups
Examples of Various Subgroups
How to Prove a Set is a Subgroup
How to Prove Various Key Results Surrounding Subgroups
The Center of a Group