Midterm 1 (Practice)
Name: ________________________
Date: ________________________
| Problem | Points | Score |
|---|---|---|
| 1 | 10 | |
| Total | 10 |
You are responsible for following the instructions below:
Write neatly, box answers, and show work. I want to give you partial credit if possible!
Do not refer to calculators, computational engines, or other outside resources. You may use results proved in previous homework, the Lecture Notes, or class unless otherwise stated. If you are asked to prove a statement in the exam, you are free to use it in subsequent problems (e.g., if problem 2c asks you to demonstrate a lemma that you could then use to solve part 3b, you may do so freely even if you are unable to complete the proof of 2c).
Do not discuss the exam with anyone before it is due.
Do not share copies of the exam for any reason.
Good luck!
I agree to these conditions and furthermore I understand that failing to follow these instructions (e.g., by using or accessing disallowed resources, sharing exam materials, etc.) is a violation of academic integrity as defined within the Carleton College student handbook: https://apps.carleton.edu/handbook/.
On my honor, I have neither received or given unauthorized assistance on this examination!
Signature: ________________________
Problem 1. (10 points) Prove that if the transport operators on the four edges of a 2-face are given by reflection matrices \(R_\theta\)…