*1. State and prove the Pythagorean Theorem for right triangles in the plane. (Study your insights from our prior class discussion but write it up without copying.)*

File Upload, Proofs 1

*2. (a) Prove that there are infinitely many prime numbers. (b) Describe an algorithm that takes as input a positive integer n and outputs a prime number greater than n. Prove that your algorithm satisfies the required property. (You may assume that testing a number for primality is a primitive operation; that is, you don't need to explain how to check if a given number is prime.)*

File Upload, Proofs 1 & 2

*3. Briefly describe your mathematics background, what you would like to get out of the class, and any concerns you might have.*

My experience with math involves high school AP Calculus AB and BC as well as a semester of MATH114. I am also currently enrolled in MATH240. By taking this class I hope to get further insight into the math major; if I enjoy this class I will probably continue with the major. Going into this class I am worried about my level of preparation. I do not feel confident in my ability to come up with a proof on the spot.