HOMEWORK

HOMEWORK: (click here for comments / solutions to the HW)

Please spend at least 2 hours a night reading the material/looking at the proofs/making sure you understand the details. Below is a tentative reading list and homework assignments. It is subject to changes depending on the amount of material covered each week. I strongly encourage you to skim the reading before class, so you are familiar with the definitions, concepts, and the statements of the material we'll cover that day.

Week 13: November 27 to December 1

Read Chapter 17, read notes on Uncertainty Principle
Suggested HW problems: Find $C_1, C_2$ with $0 < C_2 < C_1$ such that for all $x \in [0, 1/2]$ we have $C_2 x \le \sin(\pi x) \le C_1$.

Week 12: November 20, 2017:

Chapter 17
Video: GOE Joint Density I, Integration Challenge: https://youtu.be/kUtFBg9IeGI
Work on project

Week 11: November 13 to 17

Read: Chapters 16, 17 (Chapter 15 should have been read by now)

Week 10: November 6 - 10, 2017:

Chapters 16, 17 (Chapter 15 should have been read by now)
Suggested HW: Prove formula for Tr(A^k). Prove by induction Catalan Formula. Use Newton's Binomial Theorem to finish proof.
Work on project

Week 9: October 30 - November 3, 2017:

Read: Chapter 12 (Sections 12.4 - 12.7), Chapter 15
Suggested HW: Choose N independent points uniformly in [0,1] and investigate the gaps between neighbors. Redo for N independent points but from other distributions: is it still exponential?
Work on project

Week 8: October 23 to 27, 2015:

Read: Chapter 12 (Sections 12.4 - 12.7), Chapter 15
Work on project

Week 7: Oct 16 - 20, 2017:
- Read Chapter 9, Chapter 12 (Sections 12.4 - 12.7).
- Video: Mon: Hershey Game, Fibonacci numbers are Benford: https://youtu.be/fP-zhIkXMmE
- HW: Due Wednesday, Oct 18: Exercise 12.3.8, 12.3.16, 12.3.19, and 5.5.6 (just think about the sine part of the question, no need to write anything).
Week 6: Oct 11, 2017: no class Mon, no class Fri
- Read Chapter 9, Read Chapter 12 through and including 12.3. Will prove Weyl's theorem (k=1) on Wednesday from Chapter 12.
- HW: Due Wednesday, Oct 18: Exercise 12.3.8, 12.3.16, 12.3.19, and 5.5.6 (just think about the sine part of the question, no need to write anything).
Week 5: Oct 2-6, 2017
- Read Chapter 9 of the book and Chapter 12 up through and including Section 12.3.1.
- Send me a one page description of what you are doing with your project.
- For Monday: find the Fourier Transform of the Gaussian: $\int_-{\infty}^\infty (1/\sqrt{2\pi \sigma^2}) \exp(-x^2/2\sigma^2) \exp(-2\pi i x y) dx$.
Week 4: Sept 25-29, 2017
- Read Chapter 11 of the book and Chapter 9 of the book
- HW: No one needs to turn in as were in class on time and it's interview season, or emailed me before class started: (1) Consider the function $f(x) = 1/2 - |x|$ for $-1/2 \le x \le 1/2$. Investigate how well the Fejer and Dirichlet series converge pointwise for $x \in \{0, \pm 1/4, \pm 1/2\}$. Also look at the $L^2$-distance of the approximations to the function: $\in_0^1 |T_Nf(x) - f(x)|^2 dx$ and $\in_0^1 |S_Nf(x) - f(x)|^2 dx$. Choose several values of $N$, or even better get your results in terms of $N$.

Week 3: Sept 18-22, 2017
- Read Chapter 11 of the book.
- Homework Due Friday, September 22: (1) Problem 11.2.5. (2) Problem A.2.7. (3) Problem 11.2.10. (4) Problem 11.3.6.
Week 2: Sept 11-15, 2017
- Read Chapter 11 of the book.
- Homework Due Friday, September 15: (1) Consider the solution to assigning Chapter 70 aid by Linear Regression. For each explain why or why not. (a) Will a solution exist for all data sets? (b) Will the percentages always be between 0 and 1? (c) Are the percentages stable under small changes? (d) Will the three percentages sum to 1? (2) Was \$70,000 a good price for the Cleveland Indians winning 15 or more games in a row?

Week 1: Sept 8, 2017
- Read the graduation speech http://www.graduationwisdom.com/speeches/0018-uslan.htm
- Homework: To be emailed to me by noon on Sunday, September 10: Email me a short note on what you want to get out of this course, and what lesson you learned from the graduation speech (http://www.graduationwisdom.com/speeches/0018-uslan.htm). Full credit, 20/20, so long as you answer both questions on time.
- Homework: Due Friday, September 15: (1) Consider the solution to assigning Chapter 70 aid by Linear Regression. For each explain why or why not. (a) Will a solution exist for all data sets? (b) Will the percentages always be between 0 and 1? (c) Are the percentages stable under small changes? (d) Will the three percentages sum to 1? (2) Was \$70,000 a good price for the Cleveland Indians winning 15 or more games in a row?
- Read Chapter 11 of the book.