HN Books @HNBooksMonth

Thanks for both references. It's been a while since I studied algebra in college and I'm hoping to get back into it and solidify my understanding. What do you think of Artin's Algebra? http://www.amazon.com/Algebra-2nd-Michael-Artin/dp/013241377...

⬐ bmer

Sorry, I can't comment on that book as I haven't read it!

⬐ Ec_K

Artin's Book would provide a great reference text for a refresh but it covers a lot of areas, and you sometimes lack the motivation to study the area without seeing it from a book devoted to it or from seeing it occur naturally. I have not used the book for a couple of years but looking back I would recommend combining it with a book on linear algebra and a book on elementary/ algebraic number theory.

If you are comparing it to Pinter or burns - Artin is a lot harder.

⬐ E_cK

If you are going from Burns/ Pinter to Artin you might have a hard time - I would recommend looking into books on Linear algebra, group theory ( more advanced than Pinter), Galios Theory, elementary/ Algebraic number theory or if you have the background Algebraic geometry/ topology.

Then when going through these refer back to Artin if there is something you do not understand or want to see the Algebra from a different perspective.

It is often hard to motivate Alegbra without having seen it occur naturally elsewhere. All this being Artin is a great book. Good luck.

I'm a big fan of SICP. I'd describe it as "hard-core": requiring hard work, but extremely rewarding for the people who take the time and effort to go through it.

I'd recommend the following three books to similarly cover the three main areas of higher mathematics (analysis, algebra, and topology):

1. Principles of Mathematical Analysis by Rudin (http://www.amazon.com/Principles-Mathematical-Analysis-Inter...)

2. Algebra by Artin (http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/d...)

3. Topology by Munkres (http://www.amazon.com/Topology-2nd-James-Munkres/dp/01318162...)

Working through all three (including the exercises!) will give you a solid understanding of the basis of modern mathematics. If you don't have experience with proofwriting, you might find them difficult at first - the activity is very different from performing calculations or solving equations. It's also best to have someone trained in mathematics talk to you about the proofs, until you develop a feel for the needed level of logical rigor.

Rudin, in particular, leaves a lot of work to the reader; going through that book is the most intellectually difficult work I've ever done. If you find it hard-going (which is completely natural), you might want to try Artin first, especially since you have some background in algebra.

(Incidentally, these are the three books used to teach analysis, algebra, and topology to MIT mathematics majors. You can look up the assignments and exams for the three courses - 18.100B, 18.701, and 18.901 - for a good list of exercises to work through.)

⬐ swordswinger12

Personally I have heard nothing but bad things about Artin. Most people I know recommend Dummit and Foote instead; its increase in difficulty is supposedly offset by superior presentation of the material.

⬐ radmuzom

Great list. Another addition to the list would be

4. Topics in Algebra by I.N.Herstein.

It has a slightly better (and tougher) set of problems than what you would find in the book by Artin.