hw2-difftop - Math 343 Homework 2 Due Wednesday February...

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Unformatted text preview: Math 343 Homework 2 Due Wednesday February 10, 2010. When writing up your solutions, pay attention to what you write. Im interested in seeing proofs written rigorously. What does this mean? Good proofs are: Correct ideally, every statement should follow from axioms or from what has been proved before. Concise a proof should not contain anything that is not necessary. Readable Human beings both write and read proofs. Dont be afraid to explain in words what you are doing. For example, before embarking on a long computation, it is a good idea to explain what you are doing and why you are doing it. 1 To be handed in for grading 1. Show that every k-dimensional vector subspace V of R n is a manifold diffeomorphic to R k . Show that all linear maps on V are smooth. If : R k V is a linear isomorphism, then the corresponding coordinate functions are linear functionals on V called linear coordinates. (Review definitions from Lectures 1, 2 and HW 1.) 2. Let V...
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This note was uploaded on 03/06/2010 for the course DEPARTMENT math434 taught by Professor Elizabethdenne during the Spring '10 term at Smith.

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hw2-difftop - Math 343 Homework 2 Due Wednesday February...

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