Group Definition (expanded) - Abstract Algebra

The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.

Our sincere thanks go out to our VIP Patron, Matt Peters. Matt supported us on Patreon, and thanks to his generous donation, we were able to make this video. Thank you for helping make this video happen, Matt!
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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

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[elgs]

A solid proof how important a good teacher is!

[stancartmankenny]

In college, I was amazed how one of the first major theorems you learn is the fundamental theorem of calculus, and how the last one you learn is the fundamental theorem of arithmetic.

[NervousNoodles]

Me: It's time to go to bed.
YouTube: _True but have you seen first "Group Definition (expanded) - Abstract Algebra"?_

[hellfirelordofevil]

This is the most well made course on the YouTube by a significant margin

[toomuchcandor]

I can't believe how this made hours of my confusion just vanish away in mere minutes. Truly thank you for helping me begin to see the beauty of this concept

[GPS]

I am a spanish teacher.
Sometimes
I also help students in High school with Math.
Thus, I am looking forward to improve my skill in this very important field.

[nathanlaney]

Extremely well crafted video; you're a great speaker!

[mrugankthatte]

The presenter was so calm and composed. Watching this video felt like meditation to me.

[almspb]

I am here just to express my gratitude as already valuable and well structured comments have been made regarding how you have made easier to understand "Group Definition" for us, who're having difficulties to understand this.
Thank you very much and my sincere, well wishes to your channel!

[goalkeeper]

I passed an exam on Modern Algebra thanks to your playlist Abstract Algebra, which helps a lot to imagine these boring theorems and formulas. Thank you and please continue doing so magnificent lectures!

[integrantedavidanoturna]

My algebra teacher made it seem completely random and arbitrary when talking about this subject. These videos made everything SO MUCH CLEARER

[AadarshLokhande]

I don't know how much time taken by mathematicians to define a group, but I only knew that it took me only 8 min to understand.

Purely Simplified ❤

[fahrenheit]

God, why isnt this the first course YouTube recommends on group theory, it's leagues clearer than the others. You've earned a sub

[frankx]

So nice to have something explained so clearly. I once went though a book on Group Theory where it failed to tell you what it was.

[hmeyer]

I'm so glad to have found this video. I'm teaching a survey/liberal arts class in mathematics, and students are required to do math history presentations. One student is presenting on Galois but needs help in understand what Group Theory is (at the most basic level). This is a FANTASTIC introduction - short and accessible and accurate. I will be sharing this video with him. Thank you!

[supersaiyan-goku-san]

This blew my mind!
Precise and to the point. Plus also be able to give the general overview! Excellent.

[mriel]

It's amazing how a new perspective can totally change the way you view and deal with a subject. For months I'm trying to make sense of how different groups and their operations really work, and this video has made a huuuge difference. I'm very grateful for your job.

[dohpamne]

Fantastic video. The structure and delivery of the material is great. It's incredible how intuitive this topic can be if it's taught properly.

[amitygames]

I don't know how I ended up here after watching a Miley Cirus video, but it feels like landing on a fresh, clean, wholesome, normal planet .... Awesome ! Keep it up.

[zoso]

This is a scintillating instance of great pedagogy! One just requires pretty basic conceptual background to grasp this video in its entirety. I'll support you... Please keep doing this. I'm grateful YouTube put this in my list.I was missing out on such great content.