Please note the following changes for Monday November 7:

• No changes to Multivariable & Vector Calculus: class still meets at 9 in Sem 2 D3105.
• Krishna will only be available for open hours in Sem 2 D3105 from 11 – 11:55.
• Classical Mechanics meets at 12:30 in CAL West, not in Sem 2 D3105.

You can access the Week 7 Classical Mechanics Reading Response below.

• Part 1 due Mon. Nov. 7 by 9am. NOTE: This repeats some questions from Week 6 Reading Response, Part 2. If you completed that Reading Response, you can skip those questions and begin with the questions on section 8.5.
• Part 2 due Thu. Nov. 10 by 9am

• CM: Taylor Ch. 8 (skip 8.8, note that 8.1-8.4 were assigned for week 6 reading); 9.1-9.5
• DE: Boyce/DiPrima 5.4-5.5; 10.1-10.3
• MVVC: Hughes-Hallett 18.1-18.2; 18.3-18.4
  
• Note: the Week 8 Seminar reading was handed out as a paper copy at the week 6 DE exam. Copies are still available if you didn’t pick one up.

Classical Mechanics Homework Assignment #11, due by 5 pm Monday November 7 to Krishna’s office Lab 2 3255. All problems from Taylor except as indicated.

1. Choose one of 7.20, 7.22, or 7.23 that you didn’t do for Homework #10
2. Choose one of 7.29, 7.30, or 7.35 that you didn’t do for Homework #10
3. 7.50
4. 7.52 (see note)
5. Consider a simple pendulum with mass m and (massless) string of length b, released from rest at an angle θ₀ with respect to vertical. Determine the tension in the string as a function of angle θ and other given and known constants. Check that your answer makes sense in the limit cases when θ = θ₀ (i.e. at the top of the swing) and when θ = 0 (the bottom of the swing). This is the problem we discussed in class; recall from that discussion that we could only get so for with the Lagrangian method, so don’t hesitate to use a Newtonian framework as needed. (see note)
6. There are only five problems on this homework set.

Notes:

• For 7.52, convince yourself that the geometry requires x = RΦ, so that the constraint is f(x, Φ) = x – RΦ = 0.
• For Problem 5, here’s a necessary intermediate step you can use to check your work: v² = 2gb(cos θ – cos θ₀)

The classic movie Frames of Reference has a good discussion of non-inertial reference frames and centrifugal forces. This has come up a bit for us in our current work, and we’ll delve into it deeply in Taylor Chapter 9. The entire film is really amazing and I encourage you to watch it when you have half an hour, but the particular part relevant for centrifugal forces is a gripping five minute segment from 17:00 – 22:00.

Classical Mechanics Homework Assignment #10, due by 9 am Friday Nov. 4 to Krishna’s office Lab 2 3255. All problems from Taylor except as indicated.

1. your team problem from workshop on Tue 11/1
2. another team’s problem from 11/1 workshop, your choice (see table below), however: between your team problem and the second team’s problem, you must have at least one ** problem. You are encouraged to consult members of the other team.
3. 7.21
4. 7.27
5. 7.34 (see note)
6. 7.41

Notes:

• For 7.21, does it help to remember that mω² r = mv²/r?
• For 7.34, (a) may be difficult. For part (b), you can use the result from (a) even if you can’t figure out how to derive it, so don’t let part (a) slow you down. In order to attemp part (a), make sure to look at Figure 5.2, and notice that the left end of the spring is held fixed so that the left end’s velocity is zero, while the right end of the spring is attached to the cart, so the right end’s velocity is dx/dt.

Tue. 11/1 workshop problems & teams:

• The Public Solutions Guidelines have been updated to include information about Peer Reviews (see the bottom of the linked page).
• Because this information was published late, the due date has been extended to the end of week 6.

You can access the Week 6 Classical Mechanics Reading Response here:

• Part 1 due Mon. Oct. 31 by 9am
• Part 2 due Thu. Nov. 3 by 9am

Natalie Hobson will be visiting our program on Monday October 31. She’ll be giving a guest lecture in our regular classroom Sem 2 D3105 from 3:15 – 4:15, and will be available for informal conversation before and after.

Title: You Decide! How the math behind our voting system might swing the election. 

Abstract: Do you think voter turn out, policy issues, and debate performance will determine the upcoming election? Well it turns out the mathematics behind the voting system itself has a significant influence on the winner. In fact, different fair voting systems can lead to different outcomes in an election even when the same ballots are used. Given this issue, how is power in the US Electoral College currently distributed across states? In this talk, we will investigate the voting paradox and discuss current power distributions in the upcoming election. We will also consider some intriguing questions that have been open for over 100 years related to power distributions in elections.

She adds “I’ll be giving a talk on my education work earlier in the week, so I’d be happy to share any of that with you during the visit, too”.

Bio: Natalie Hobson is a graduate student in the mathematics Ph.D. program and mathematics education masters program at the University of Georgia. Her research interests have focused on the interactions between algebraic geometry and combinatorics, and students’ covariational reasoning. She is involved in many outreach programs and loves working with students. Natalie is originally from Shelton, Washington and holds a bachelors degree in mathematics with minors in education and diversity from the University of Washington. When not doing math Natalie can usually be found riding her bike, swing dancing, or sewing.

• CM: Taylor 7.5-7.10 (skip 7.9); 8.1-8.4
• DE: Boyce/DiPrima 5.2-5.3
• MVVC: Hughes-Hallett 16.5; 17.3-17.4
• Seminar (paper copies were handed out on week 5 Thursday):
  • Mathematics, Gender, and Generation
  • Emmy Noether bio (short)
  • Emmy Noether bio (brief)