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If you want to learn abstract algebra for the first time and you're anything like me, don't just read a book about it. It'll start to sound like a bunch of abst
by qntty 10y ago
If you want to learn abstract algebra for the first time and you're anything like me, don't just read a book about it. It'll start to sound like a bunch of abstract nonsense. Eventually you'll have the skills needed to "bring it alive" for yourself with a set of concrete examples that you'll learn to refer to again and again. I would recommend starting by watching some lectures about it (you can find some here [1] under the lecture schedule).
[1] https://www.math.upenn.edu/~ted/371F14/math371.html https://www.math.upenn.edu/~ted/371F14/math371.html
- j2kun 10y agoHaving a set of concrete examples in mathematics is like unit testing in software. The second you get stuck on a theorem, you fall back on your examples. The second you run out of examples that explain a behavior or new theorem, you write down new examples.
- pizza 10y agoAgreed. Google images is a surprisingly decent source of visual examples for intuition building/testing, although the signal-noise ratio is a crapshoot.
- westoncb 10y agoI don't see how a lecture would improve things over a book (assuming you still can't ask questions), though it does of course depend on the book. I'd just pick up Pinter's 'Abstract Algebra'—lots of good concrete examples, one of most readable math texts (in any subject) I've come across. Edit: also, there's a Dover edition you can get for < $15.
- eriknstr 10y agoExperienced lecturers might have insights into what kinds of difficulties students typically experience with the material, leading them to organize their lecture in a way that is different from a book. Then again, experienced lecturers might also write books as well where they consider the same things for their book.
- M_Grey 10y agoIt's the difference between something mixing up a 30,000 piece jigsaw puzzle and throwing it on the floor, versus that person laying out a framework, with key pieces where they need to be.
- posterboy 10y ago> mixing up a 30,000 piece jigsaw puzzle and throwing it on the floor that'd be wikipedia. A book might just be a lecture written down, albeit with less room to answer questions.
- dominotw 10y agoDover book is the best if you are just getting started (i.e not on a path to specialization in group theory/ algebraic geometry ect ) I found a pdf link to the book googling for its name http://www2.math.umd.edu/~jcohen/402/Pinter%20Algebra.pdf http://www2.math.umd.edu/~jcohen/402/Pinter%20Algebra.pdf
- Myrmornis 10y agoI highly recommend Benedict Gross's harvard lecture series: https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra https://www.extension.harvard.edu/open-learning-initiative/a... He has a very engaging style. I'm about 1/3 of the way through, but had to pause for other commitments. It's mostly possible to track down the homework questions that he sets and solutions for them.
- stablemap 10y agoGross links to this archive, which has more material: http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra http://wayback.archive-it.org/3671/20150528171650/https://ww...
- dfan 10y agoI went through all of these a few years ago, including the homework, and it was a great experience.
- swordswinger12 10y agoI second this - Gross is a phenomenal lecturer. These videos would probably be a great supplement to any self-study of algebra.
- ianai 10y agoI would diversify my sources. i.e. Sometimes it takes seeing the same thing reworked in another book or in lecture instead of a book to 'get it'. The general rule of thumb is you need at least 3 different solutions or approaches to a problem to really be able to say you know "what's going on."
- albertTJames 10y agoWow ! Thanks for the ressource !!
- gunnihinn 10y agoFor a counterpoint, read Shafarevich's "Basic notions of algebra". (Beware: author's meaning of "basic" may differ from own.) It's a book that explains all those abstract algebra concepts by introducing motivating examples for each one of them. It's the next best thing to finding the natural setting for them yourself.