Math 343 Homework 1
Due Wednesday February 3, 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 fr

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 f

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Math 343 Homework 3
Due Wednesday February 17, 2010.
1
To be handed in for grading
1. Is the cuspidal cubic cfw_(x, y ) R2 | y 2 = x3 a submanifold of R2 ? Why or why not? Hint: Review the denition of a submanifold from Lecture 1. 2. Take a smooth real v

Math 343 Homework 4
Due Wednesday February 24, 2010.
1
To be handed in for grading
1. Suppose that Z is an l-dimensional submanifold of X and that z Z . Show that there exists a local coordinate system cfw_x1 , x2 , . . . xk dened in a neighborhod U of z

Math 343 Homework 5
Due 4pm Friday March 12, 2010.
I will be away at MSRI in Berkeley CA from March 719. We can set up times to discuss this homework via Skype while I am away. The homework will be collected for me at 4pm on the day it is due.
1
To be han