A Question about Pinter's A Book of Abstract Algebra

[jmjlt88]

Hello all,

I am currently doing a self-study in Abstract Algebra. I was a math major in college (not so long ago), so I have some exposure to upper level math. For one reason or another, I wanted to go back and re-learn Abstract. I was using Fraleigh until I discovered Pinter's text which is much more fun! Right now, I am through the first 10 chapters.

My question is, if I complete this book in its entirity [not EVERY exercises, but certainly a good sampling from each chapter], where would I be in terms of a book like Dummit & Foote?

Thanks.

Also, any recommendations for book similar (same level) in analysis, linear algebra, or topology to Pinter's would be great!

 

[Sankaku]

Here are some of my favourite, well-written, highly-motivated math books. There are other excellent books, but these would be more "Pinter-style," if you like. These books are not as good for reference because of the conversational style, but they are good for learning.

For algebra, if you are comfortable with everything in Pinter, I would recommend Aluffi:
https://www.amazon.com/dp/0821847813/?tag=pfamazon01-20

It is the most "motivated" upper-level Algebra book I have found and incorporates categories from the beginning. Dummit & Foote is decent, but some parts are better than others. At upper levels each author has a unique style which can be good or bad depending on your learning style, your current level, and the subject they are covering.

For (very basic) analysis, I like Abbott's "Understanding Analysis." If you have a math degree, it might be too basic, though. It has a very nice approach to the underlying questions of analysis.
https://www.amazon.com/dp/1441928669/?tag=pfamazon01-20

For complex analysis, nothing beats Needham. It is not an "easy" book, but it is superb.
https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20

Linear algebra doesn't have as clear a winner. Micromass has a good review of the main books on his blog. I like Axler, but it has a strong "flavour" and not everyone likes it. Take a look in the library and see what you think.
https://www.amazon.com/dp/0387982582/?tag=pfamazon01-20

For topology, a lot of people recommend Munkres. It is solidly written and very thorough, but I found it doesn't give much of an overview as it wades through the material. Although not as conversational as Pinter, the small Dover book by Mendelson is a good (brief) intro. Again, if you have done topology in the past, it might not be the right book for you.
https://www.amazon.com/dp/0486663523/?tag=pfamazon01-20

I would love to hear if there is a truly inspired general topology text out there. I have glanced through a lot of the standard books and many seem decent, but none seemed outstanding.