Sections 3.4-3.5, Due October 4

Difficult: I've worked with the Chinese remainder theorem before, but I found their explanation in this book difficult to follow. It seems like to solve the system of congruences x \equiv 3 (mod 7), x \equiv 5 (mod 15) you wouldn't have to reduce mod mn at the end, and so your solution would not be "unique" so much as "lowest". I suppose it is just that it is unique mod mn, but there doesn't seem to be a particular benefit to that. I think that the application of the theorem would be more understandable if they had been more explicit with their examples. They seemed to just say "oh, so this is 80" without showing how they calculated that (except the general method they show afterwards, I'd rather see the calculation more concrete. And with smaller numbers than 12345 and 11111).

Reflective: Didn't have too much to reflect on this time, the sections were quite short. I think the trick they used for modular exponentiation was pretty clever, and I had not seen that before. Just follows the rules of exponents that people should have learned way back in algebra. I suppose it is nice to see a different application of these.