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I am a college sophomore with double majors in mathematics and microbiology. I apologize for this interruption but I wrote this email to seek your advice and recommendation on linear algebra textbook. I will be taking the "theoretical, proof-based" introductory linear algebra on upcoming Spring Semester that will not only teach the theoretical linear algebra but also the introduction to proof methodology (this course is required before advancing to analysis and advanced mathematics in my university). The professor will use the online textbook (free) known as "Linear Algebra Done Wrong!" by Sergei Treil (which is free on online). However, I want to purchase the two hardcopy textbooks on theoretical, introductory linear algebra because I always enjoy studying from different textbooks. I am constantly hearing about the books written by Hoffman & Kunze, Friedberg, Axler, Lang, etc. Among those books or others you recommend, which two linear algebra textbooks should I purchase? I usually pick one for the great depth and explanation and another one for more challenging introduction & advanced knowledge. I never took the computational linear algebra before...is it difficult to learn the computational aspect if I only study the theoretical aspect of the linear algebra? Also which book is better to learn the proof methodology, one by Velleman's How to Prove It or Polya's How to Solve It?

I apologize for asking questions in row and I look forward to your great advice!

Sincerely,

MSK