Reddit reviews Algebra

Any introductory abstract algebra book will have the basics of of rings, ideals, and quotient rings, as well as a few other things.

My class on intro to group theory used Gallian's Contemporary Abstract Algebra, which I'm a pretty big fan of as an introduction. It's gentle and doesn't rush into things, but has a large amount of exercises, some of which will really stretch your understanding.

If you want something a little harder, but a little deeper, Artin's Algebra is very popular, and for very good reason. It'll help you develop your group theory knowledge as well.

I know that in the long run competition math won't be relevant to graduate school, but I don't think it would hurt to acquire a broader background.

That said, are there any particular texts you would recommend? For Algebra, I've heard that Dummit and Foote and Artin are standard texts. For analysis, I've heard that Baby Rudin and also apparently the Stein-Shakarchi Princeton Lectures in Analysis series are standard texts.

I've been kinda sorta watching it but I think he was holding up Artin's book.. not sure..

edit: Okay, the beginning of the second video confirms my guess..

Hi there,

It'd be a good idea to know what your level of mathematics is like. I assume you know basic set theory? (I assume this is needed to analyze music from the second viennese school - but how detailed is the set theory you learn? Are there proofs?). What other maths do you have knowledge of? I believe the standard algebra book is Artin's but this may be too hard/dense for you. I can think of some easier books off the top of my head, but they start off with ring/fields instead of groups (such as the Hungerford)...

Just curious, do you have any suggestions on what a random person can read to learn about transformational theory on the net besides wikipedia?

Edit: Random googling found this. Seems like a good start for both mathematicians to learn about 20th century music theory and musicians to learn about set theory/algebra.

Michael Artin's Algebra's first few chapters is probably one of the best explanations of linear algebra that you'll get.

http://www.amazon.com/Algebra-Michael-Artin/dp/0130047635

I've heard some good things about Michael Artin's book (http://www.amazon.com/Algebra-Michael-Artin/dp/0130047635).

I would suggest combining the linear algebra and abstract algebra text into Artin's text. I have found it to be a very good text on algebra with a heavy emphasis on the theory of linear algebra. I glanced through Hungerford's text and didn't take to it. Too verbose with too many examples.

I second the Rudin and Munkres. I found that reading through Hocking and Young's text helped me get the intuition i needed to plow through Munkres.

I'm currently working through Munkres' book on Topology, and I am using the video lectures found here. I know these are in an annoying form factor, but, trust me, these are the only videos that go into any depth you will find on the internet. They use Munkres, too, which is a plus.

On the same site are video lectures for Algebraic Topology. For this, I definitely recommend buying Artin's "Algebra" (1st edition can be found cheaply, and I don't think there's really any significant difference from 2nd), and watch these video lectures by Harvard. Then, you can finally move on to the Algebraic Topology video lectures which uses the free textbook "Algebraic Topology" by Allen Hatcher.

Hope this helps.