Math Course Advice -- Harvard freshman planning to double major in physics and mathematics

[Quantum55151]

@mathwonk Sorry for the delay in my response. I was preparing for finals.

It is not entirely clear to me what preparation is expected, or usual, for success in 55.

Auroux writes in the course syllabus that no formal knowledge of linear algebra, group theory or analysis is required, but a familiarity with proof-writing and abstract reasoning as well as a commitment to a fast-paced course is. What this actually means in practice is a separate question.

As to learning differential forms, there was a thread here on PF devoted to that topic some years back, and they went through a very nice book by David Bachman, available from him free online:
https://faculty.washington.edu/seattle/physics544/2011-lectures/bachman.pdf

I'll check out, thanks!

As for Rudin's Principles of analysis book, it is famous for being very precise but very unmotivated, so I never recommend it for learning. But analysis professors love to recommend it, so you should take a look, maybe it will work for you. I prefer books by Spivak, Apostol, Berberian, Fleming, Lang, Simmons, and although quite difficult I admire Dieudonne'.

Do you know anything by Elements of Classical Analysis by Marsden and Hoffman? This is the book used in 25b.

On the topic of the student body in math 55: yes one will naturally feel intimidated at times, maybe most of the time. I definitely felt that way when there.

Even though you were the oldest student?

 

[Quantum55151]

But isn't that okay with you, since you intend to be a physicist and not a mathematician?

True. At the same time, I still want to major in math and do physics research that is more on the mathy side. So I do want to get a solid grasp on the material.

 

[mathwonk]

I don't know the book by Marsden/Hoffman. Reviewers on amazon say its helps that they teach n dimensions starting from 2,3 dimensions., which sounds user-friendly.


oldest ≠ best. when I was a freshman in math 11, there was another freshman who lived across the hall from me who was a year or 2 younger, and taking math 55. he occasionally helped me in math 11. I guess I wasn't so much intimidated by these very gifted students as impressed. The intimidation factor was greater later as a postdoc interacting with the professors.