I bought Pinter's _Abstract Algebra_ (Dover Books). Glancing through it, it seemed so alien. Then I binge-watched this series; it didn't take long at all. Now a quick look through Pinter looks like familiar territory. I'm 100% positive it's going to make Pinter WAY more simple and enjoyable to read for self-study. THANK YOU SO MUCH!!!
This is so lovely to hear, thank you so much!! It really inspires us to make more of these videos when we hear that we're actually helping. Good luck and let us know how you get on!! 💜🦉
@@Socratica, well the series goes well beyond just being helpful. By providing a confidence-building overview, it positions one to be able to see the _beauty_ of the subject. And being able to see the beauty inspires motivation to continue exploration. So again, my sincerest thank you!
Yess I covered Pinter halfway and then started watching these videos.... I'd say Pinter set the ground for me appreciating why certain things are included in the videos Conversely, the videos help me make sense of a lot of things that I'd read in the first half of Pinter, for example, that normal groups part with the visual image shown in the video greatly helped me understand what all of that is about.... I have finished the video series, I am sure the second half of Pinter would be a much easier read now.... These videos really helped in putting the big picture in front of my eyes and allowed me to see how different topics are related.... Loved the videos!
That explanation of modules was better than every single time I've tried to just read about them. The examples really helped highlight where each piece was being used (the ring and the abelian group), as well as the differences betweeh vector spaces and modules. Thank you!
Wish there were more videos in this playlist. If I could accelerate through math at this rate in every subject, all of mathematics would be a one-year course.
This video series are good! If i were a Abstract Algebra teacher, I would play this video in my classroom and go get some coffee while watching this with my students ;)
We didn't do modules in my undergrad, but when I changed university to do my masters it seemed everyone on the course had done it in their undergrad; the lecturer assumed this and did a brief explanation but not one I was happy with. This video explained modules so much better than they did! Thank you!
I’m really sad that I’m at the end of this playlist; every single video was a real (mod)jewel! Time to console myself and go back to the Python videos!
Hi I am one of the follower of your channel, where are u socratica? We need next videos on Algebra as well as other subjects of maths. Please upload another videos.
Fascinating presentation, and very clear. I liked the examples, they were neither too advanced or too boring. I think modules are one of the lesser discussed structures in the undergraduate math classes. There are a few others about which I'd be interested to see coverage: monoids, groupoids, magmas (that's a recent one?). Also, what is meant by "an algebra"?
Thank you SOOOOOO much for this video!! Finding a video on modules was so frustrating, since the term "module" is more commonly used to mean "a section of a course". So, it took me FOREVER to find a video on what I wanted. (I finally stumbled on this video after using the search phrase "vector space generalization".)
This is really great. My introductory ring theory course didn't get as far as modules, and module theory always feels like a brick wall of abstraction when I try to read about it. Many thanks.
I wanted to take a step on abstract algebra, and I think I finally found a perfect series for me, which was such a hidden gem! Now Imma watch this whole series from now on :)
I've made it. All videos. Thank you so much. This overview helped me a lot to get a general understanding and diminish my anxious having in hands a big book of Abstracted Algebra.
Wonderful lecture series on abstract algebra.... Listened all the videos. Keep on doing such kind of work to other mathematics branches like topology, Real analysis etc
Awesome video series. We are eager to gain deep insights on mathematics.So , Socratica did this job really perfect but we still have more ways to reach the destination.
Where is Galois? The series and your presentations are just excellent,Thank you. You build a beautiful palace but did not finish the ceiling and the roof of that palace.What happened to Galois?? This series should end up showing that there is no general formula for polynomials of degree five and more. Am I correct? Does this series continue? Thank you
I wouldn't be surprised if they do some Galois videos at some point, though it might be difficult since understanding Galois theory requires a mastery of group actions and the basics of field theory - and they haven't covered these topics yet. I suppose, if done in a certain way, you can avoid group actions, but the basics of field theory are necessary. Also, sure, from a historical context, Galois theory, and in particular the Abel-Ruffini Theorem, is the crowning achievement of abstract algebra. But that's _only_ from a historical perspective. Abstract algebra is an _extremely_ useful tool a large variety of mathematics today (e.g., algebraic topology, algebraic geometry, algebraic number theory, mathematical logic, and category theory). The modern use of abstract algebra is to assign algebraic structures to other mathematical objects and use those algebraic structures to learn about the objects. In this sense, ending the series on vector spaces and modules is much more in line with how abstract algebra is used today.
Nice intro to Abstract Algebra. I wish you made a series that dived deeper on specific subjects, maybe group theory. At least cover other algebraic structures that were missing, like lattices.
Oh no! I’m at the end of this series! :( Socratica, will there be more? This has been an incredibly useful and well-made series, but there’s still so much more!
Nice style of teaching, i am also interested to teach mathematics like this way, can you guide please about the set up you use for making these awesome videos
Excellent !!! [Liliana, Michael and Kimberly have done a great service to Mathematics. Edward Freenkel's dream of uniting the various mathematical 'islands', seems easy for you. In your next video, I hope you can do justice to Edward's dream. ] If I could view this series 40 years ago, I probably could have the insight Witten have, enabling him to reveal the secrets of nature. But having viewed, I have a number of questions. 1) How does abstract Algebra provide insight into 'infinity' and 'zero'. What insight do we get about 'infinite sets', Cantor's cardinal/ordinal numbers, from abstract algebra. 2) What does abstract algebra tell us about 'self-reference'?
OK by the end of your explanation my brain hurts. So I need to watch the series from the beginning. I can tell you're saying something very important and profound but I need to come up to your speed. Many thanks for your simple, clear and concise presentation!
We're so glad you've found us! Starting from the beginning of the playlist is a great idea. Feel free to post questions! We get to them when we can, and also fellow viewers often contribute great answers. Thanks for watching! :)
I like to define modules in the language of actions. That is, if R is a ring and M and abelian group, M is an R-module when paired with a ring action. In the special case when R is a field, then M is an R-vector space. Modules are nothing but generalizations of vector spaces. They arise naturally when you examing ideals in a ring (that is one of the reasons why ideals are the meat and potatoes in ring theory). A nice example: every abelian group is a Z-module, it arises naturally from the endomorphism group of the abelian group structure and you get the Z-action from the canonical map from Z to any ring, it is just scaling by an integer multiple. Why are modules omitted altogether in introductory algebra courses? I don’t know to be honest.
We're so glad you are enjoying our videos!! That really inspires us to make more! We're recommending the following text for Abstract Algebra right now (link below). If we come up with some more, we'll add them to the description box of the video. Good luck with your studies, and keep us posted about your progress!! Dummit & Foote, Abstract Algebra 3rd Editionamzn.to/2oOBd5S
A very good one, with a different feel from Dummit and Foote, is Fred Goodman's Algebra: Abstract and Concrete, which Goodman has made free of charge at homepage.divms.uiowa.edu/~goodman/algebrabook.dir/algebrabook.html. (He requests that, if you download a copy and use it, you make a donation to the charity of your choice.) Another great book with many of the same concepts is Ian Stewart's Galois Theory, Fourth Edition: www.crcpress.com/Galois-Theory-Fourth-Edition/Stewart/p/book/9781482245820.
quick question, at the definition of module. is the 1·m=m equality a requirement or its own, or doesnt it follow from the associativity (r1·r2)·m = r1·(r2·m)? we have (1·1)·m = 1·(1·m) => 1·m = 1·(1·m). I suppose that from that, we can assume that 1·m=m. (or does it require an additional cancelability thing that isnt necessarily part of the definition?)
1·m=m is necessary to state. For example, let your ring be Z (the ring of integers), and let M be the set of rational numbers. Define the addition on M to be the same as rational number addition. Define your scalar multiplication on M to be n·m= 0 for all n in Z and for all m in M. This satisfies all of the conditions of a module _except_ for 1·m=m.
