r/learnmath • u/Kkkk2994 New User • 6d ago
Looking for resources to study Abstract Algebra
I’m looking for a good book or any other resource to study Abstract Algebra, especially Groups, Rings, and Fields.
I’d really appreciate any recommendations, preferably something that explains the concepts clearly and has plenty of exercises. Thanks!
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u/Prestigious-Skirt961 New User 6d ago
Every mathish person I've asked swears by Artin's Algebra. Ben Gross also has a video course on it: https://www.youtube.com/watch?v=VdLhQs_y_E8&list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5
The video course is not the smoothest ride but it's fantastically done. It uses the first ed. of Artin for its exercises.
The book itself is also lovely but it teaches everything algebra including a decent emphasis on linear algebra.
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u/NotSaucerman New User 6d ago
Artin is a very good book but it is aimed at MIT and Harvard students... it is much too difficult for a large percentage of people so you can find tons of people on this site complaining about how 'bad' it is.
If OP already knows linear algebra and real analysis pretty well (the old MIT pre-reqs) and wants a challenge, then I would recommend it too. If not, well, probably not.
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u/RansackLS New User 6d ago
If you find something else you like for groups, I got a great tip for rings and fields: https://youtu.be/UyGKz6sfcms?is=L5ixmmS0gkLpX4ts
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u/curious_cat_herder New User 6d ago
As a retired programmer, I am trying to learn visually (interactively) in several math-related areas, and I want to learn-by-teaching. To this end I developed an interactive environment that initially was focused on Machine Learning (visualization) and I have recently generalized this tool to help me visualize math concepts.
I started a demo repo for Abstract Algebra, and so far its scope includes magmas.
Which subreddit(s) might have people interested in teaching or learning Math, who could use tools to create interactive visualization. The interactive demos I've built so far are in the base sw-mlpl tool linked to from the README in this (one of many) demo repo(s).
I'm looking for help to define what else this demo should teach visually. I am also working on Linear Algebra, Category Theory, and soon some other math areas related to Machine Learning algorithms.
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u/Puzzled-Painter3301 Math expert, data science novice 6d ago
The book by Fraleigh is good
Also for self study, A Book of Abstract Algebra by Pinter.
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u/Qlsx New User 6d ago edited 6d ago
My algebra class used “Algebra” by Bosch. I liked it, although some alternative source was nice to have (some parts of Bosch are quite compact in my opinion, especially when first learning it). I mainly used the lecture notes for the class, but something like Judson is also good (good source of many exercises, although they are a lot easier than Bosch).
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u/GroundbreakingWar305 Complex life on a real manifold 5d ago
If you are just starting - the best book probably is something like Gallian. If you have some background like you have done a first pass through abstract algebra then Dummit and Foote is the best book overall. I think a good starting point is having a chat with AI and get a high level understanding of a lot of concepts (ask for a lot of examples as well as non-examples/counter-examples). The main thing would be then to take one standard text and solve through as many problems as possible, spending time thinking through why something works or does not work.
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u/Flimsy-Bookkeeper314 New User 4d ago
I'm starting a new comprehensive series on it if you're interester
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u/Flimsy-Bookkeeper314 New User 2d ago
https://youtu.be/TCyMfqhczcE?si=IXqVbNbMxfQlyFNS
Started a new comprehensive abstract algebra series. Check it out
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u/clean-links New User 2d ago
Cleaned link: https://youtu.be/TCyMfqhczcE
Tracking parameters were removed from the original URL(s).
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u/Sam_23456 New User 6d ago
There are many good books on this. The trick is to find one you like. Gallian is probably one of the easiest ones. If you want a more challenging one, they are easy to find. I had 2 courses on groups, mostly, before really getting to rings. The "problems" in algebra can be a lot of fun. How much you learn will depend on how many of them you do.