# Winter 2020

#### Office Hours

All office hours will be held online via Zoom. A link has been posted in the announcements section of iLearn.

• Wednesday, 2–4 pm
• Thursday, 5:30–6:30 pm

My Wednesday office hours are primarily for students in Math 005, while the Thursday office hours are primarily for students in Math 151C. Those students will be given priority at those times, though everyone is welcome to attend.

#### Math 005.003 (Dr. David Weisbart, primary instructor)

Discussion sections meet on Monday and Wednesday at 11–11:50 am via Zoom. The link has been posted in the announcements section of iLearn.

A colleague of mine suggested that the website webwhiteboard.com might be useful for collaboration. I have not used this website myself, but it appears that you can create a shared workspace which can be edited by anyone with an appropriate link. This might make it easier to share ideas during discussion.

Notes

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#### Math 151C.002 (Dr. Bin Sun, primary instructor)

Discussion sections meet on Wednesday at 12–12:50 pm via Zoom. The link has been posted in the announcements section of iLearn.

Notes

Other Files

• Solution to Problem 8.20: many of you struggled with Rudin’s approximation of Stirling’s formula. In particular, it was clear that there was not a lot of intuition happening, which is a shame, as the exercise is motivated by a couple of very nice, intuitive ideas. I’ve written up a (long, possibly overly detailed) set of notes on that problem, which you may or may not find helpful.
• A Norm Satisfying the Parallelogram Law Induces an Inner Product: in discussion, there were questions about an inner product coming from a norm which satisfies the parallelogram law. I have written up some notes on this problem. The first part of the notes develops the polarization identity, while the second part discusses how to verify that the polarization identity gives you an inner product. The key step is showing that $(u_1 + u_2, v) = (u_1, v) + (u_2, v),$ which follows from the parallelogram law. It then remains to show that $$(\lambda u,v) = \lambda(u,v)$$ for all $$\lambda\in\mathbb{C}$$. For integers, use an induction argument. Rationals follow from a scaling argument, and reals by the density of the rationals. Finally, show that it works for complex $$\lambda$$.

#### Math 194

Our goal this quarter is to read and understand as much of Hutchinson’s 1981 paper Fractals and Self Similarity as we can.

Notes