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I am a college sophomore in US with a major in mathematics, and an aspiring algebraic number theorist and cryptographer. I wrote this email to seek your advice about taking the Analysis I (Real Analysis I), Abstract Algebra I, and Linear Algebra with Proofs. At my university, it is recommended to take Linear Algebra with Proofs (basically LA course + Intro. Proof course) before taking both Analysis I and Abstract Algebra. However, I have been self-studying the introductory number theory (Niven), mathematical analysis (Apostol), and abstract algebra (Pinter, Herstein), and the number theory + abstract algebra textbooks gretly helped me to strengthening my proof methodology. Should I take all three courses together for Fall 2015 or should I take both abstract algebra and linear algebra first and then take analysis on Spring 2016? I am planning to read Friedberg and one more book for LA during this Summer along with my research and other books since I am very interested in learning about the LA and also to study ahead of the formal course.

My Analysis I course uses Strichartz & Rudin, abstract algebra course uses Dummit & Foote, and LA course uses Friedberg.

Sincerely,

PK