Section 2.1,due on September 3

The most difficult parts of this material for me were understanding the definition of the congruence class of a modulo n. Congruence and modulus are fairly newer concepts to me (as far as using them in proofs and other mathematical problems) and so keeping track of what they actually mean seems to be a little tricky for me. Because of this, I also found the first part of Corollary 2.5 to be a little bit harder to follow because I had to do a couple of examples and convince myself that it actually is true as stated.

The most interesting part of this material to me was Theorem 2.3. Once I came to understand the congruence classes, I thought that this theorem and its proof were pretty neat. The patterns found in all of number theory related topics is really rather clever. The modulus is something that came in handy when I took a computer programming class. It was really useful in writing code when you wanted items to appear on the screen in a patterned way (like 4 items for every line). I have also heard, but am not sure, that modulus is used a lot in RNS cryptography and I find that to be really fascinating.