Homework 1

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.

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