- #1

bacte2013

- 398

- 47

My name is Phoenix, a sophomore with major in mathematics and an aspiring applied mathematician in the theoretical computing. I wrote this email to seek your recommendation on the textbooks for abstract algebra. I want to self-study the abstract algebra during this Summer to gain the knowledge of abstract algebra at undergraduate level, fall in love with the abstract algebra, prepare for upcoming undergraduate research in the theoretical computing, and (possibly) prepare for Abstract Algebra I course that I might take on Fall 2015 (the required text is textbook by Dummit/Foote).

Please let me inform you about my mathematical background: I took the computational single-variable calculus course and I am currently taking the computational vector calculus course. I self-studied the proof-writing book (Chartrand), therefore acquired the basics of proof methodology and set theory. I am currently self-studying the theoretical linear algebra (Friedberg/Insel/Spence) and mathematical analysis (Apostol, Pugh) textbooks. I learned the basic topics in linear algebra, such as determinants and matrix, through my Friedberg book and vector calculus books.

I bought I.N. Herstein's two books: "Abstract Algebra" and "Topics in Algebra" and borrowed C.C. Pinter's abstract algebra book because I heard that they are good books for beginner in abstract algebra. However, I often heard good things about M. Artin's "Algebra", and also books by Fraleigh, Gallian, MacLane, and Lang (undergraduate version); I particularly heard that Artin is the best algebra book for an undergraduate, providing both details and excellent insights; I also hard that Artin covers the linear algebra in the abstract level. Therefore, I am curious if I should purchase Artin and study it instead of Herstein and Pinter. I looked at some sample pages (Group chapter) of Artin and I seem to comprehend the presented materials but I am not sure if Artin will be a better book for beginners than Herstein and Pinter. I could use both Artin and Herstein/Pinter but I prefer to firmly stick with only one book to gain everything that author want to present in the book. Please provide me of your advice and experience regarding to abstract algebra books I mentioned and which book I can use for loving the abstract algebra! And please forgive me about this long post.

PK