Algebraic Structures: Groups, Rings, and Fields

This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.

[mikegoldsmith]

Extremely clear and covers all the basics. The best gentle introduction to algebraic structures I've been able to find!

[arify]

Good luck in your Algebra exams, fellow students

[nadaabdulla]

I finished the course 2 years ago, I didn't understand it then, but now I'm interested and regret that I didn't do my best :(

[johntryl]

The example of Z mod n (when n=prime) being a field and not a ring is the coolest thing ever. Furthermore, your explanation of why complex numbers are a vector space made things finally click ... it has scalar multiplication and it has addition, but it just has even more properties. This was so helpful. Thank you for being super approachable and clear!

[lamalamalex]

I do agree with you that you built up according to complexity of the structures. With vector spaces appropriately at the end. So that’s why I find it very strange that that’s where we start students at. Linear algebra being such an early class students takes. It can even be taken before a multi variable calculus course.

[plaustrarius]

cannot thank you enough for this video!!

[leylaalkan]

Thanks for these amazing clarifications.

[rithikseth]

Thanks very helpful for my engineering studies ....

[AkamiChannel]

This was great. I just wish you had gone into what an algebra is. I'm on a mission to understand that, but google and youtube search results are completely worthless to me because they're full of content explaining ordinary algebra.

[Ivane.h]

Single-handedly getting me trough ADM mit Gittenberger...

[ct]

Very good explanation! Thank you so much!

[LucyMuthoni]

Thank you very much for this video. Be blessed!

[anantrelan]

@12:01 Field is a ring with two operations .
@18:12 F is a Field under (only) Multiplication .
Q. Why is there only 1 operation for the field F at @18:12 ?
Thanks

[monsieurfrog]

Wouldn't Monoids be the simplest algebraic structure? When defining a group (M, #), it must first be a monoid, in addition for each element having an inverse.

[fraktallyfractals]

About Z as a group, at the beginning of the video, does that mean that zero is its own opposite?

[asmamokr]

thk'x a lot but i have a question ... for groups the first example for the inverse (-a) don't belong to Z ( but in the rule it should belong ) ...i am confusing 😣😣

[TheHuggableEmpire]

So addition and multiplication in rings doesn't necessarily mean the usual sum and product?

[Caleb-qrlo]

lol I see xor symbol and get really confused.

[andreiparaschiv]

great video
one of my concerns is that people could get the idea that you can prove a property by trying out random examples, as you did with the multiplicative inverse over Q[radical 2] by choosing a=3 and b=4. it has to be generalised, and that means not assigning specific values. that could have been made a little clearer in the clip.

[DavidVonR]

Too cool! I love group and ring theory :)