Last Blog Ever!! Until Next Fall :)

Ok, so I went to Brian Conrey's lecture last tuesday on Riemann's Hypothesis. It was very interesting and it was fun. A few things that I learned were that Gauss's Guess was that the number(primes < x)~ x/ln(x), and that was also called the prime number theorem, and RH was that Gauss's conjecture is accurate to 1/2 the number of digits of n. He also found that there was a set of numbers intimately connected with the primes. These are the first 9 zeros. Also, the key to understanding the primes is to understand the zeta function. Whis I can't type out, because I don't know the right keys, but I know it. I also found out that my 315 teacher Dr. Li discovered that RH is true iff lambda is greater than or equal to zero. It was a fun and interesting lecture.

Ok, something that I would like to go over today would be anything from this last section of learning that we've been going over. Maybe 8.3 #14 again, that was rushed when I learned it, but if that won't be on the test then that's fine :)

8.5, due April 10th

1. Um... well I thought I understood most of this section, but maybe I didn't. I'll choose the one that I guess I understood the least...Ok well in theorem 8.4 I didn't remember what a Quaternion was, so maybe that might be nice to know, I suppose I could go look it up and probably will, but yeah I thought that I understood most because they were basically telling us what was isomorphic to what. Hmm, we'll see in class today!
2. Ok, so I started reading this section and it was so cool! They all of a sudden have all these shortcuts and theorems about stuff! This would've been nice to have known during some of the homework!! But it was so cool, I started reading and BOOM, there was a shortcut, I need to read ahead more often!! Oh, and Hahahaha, Corollary 8.31, thanks... that was our number 23 in our homework last time!! sheesh! I also like that it gave us a nice long list of what groups can be isomorphic to, that's very nice!

8.4, due April 8th

1. I think that theorem 8.25 was kind of confusing, it's basically the same as theorem 8.21 I think, but it was just a little tricky to me to think of the proof for theorem 8.25, who knows, I'll just read it some more.
2. I thought this was a neat section, and I felt like I remembered a lot of stuff that was in this section from other sections, and it was cool to learn about it in a different way!

8.3, due April 6th

1. I felt like I really understood this section, but if I had to choose something confusing and difficult for me to understand, it would probably be corollary 8.18. I always feel like I understand the theorems and stuff, but then I start the homework problems and I get lost, but we'll see what happens this time.
2 I really thought this section was cool. It was fun to learn about the Sylow theorems and it seemed like I understood the stuff! Plus the section was short and that is always a plus :)

8.2, due April 3rd

1. Wow, You were right! This is like the longest section on earth! :) There were a few confusing theorems such as lemma 8.6 and thm 8.10, they seemed the most difficult for me, but I'm sure you'll explain them well enough in class!
2. Although this section was long, it was pretty interesting. It's funny that there is a fundamental theorem of finite abelian groups. There seems to be a fundamental theorem for almost anything! And there were so many, I mean sooo many theorems and lemmas in this section, it was crazy!! But good :)

8.1, due April 1st

1. I don't really understand what they mean when they say that Gi is NOT a subgroup of the direct product G1 x G2 x...x Gn.... So yeah, that's kind of confusing to me. Also, the proof of Thm 8.1 is kinda really long and a little confusing. I'm sorry, it's just a rough day!
2. I do think it is all quite interesting however! Especially the things I think I understand, like the bolded words on p 245, and the other theorems. Yea for learning abou Group Theory!