Dr. Cristian Tomasetti, Colloquium, Extra Credit

I didn't fully understand everything that Dr. Tomasetti talked about.  I was unfamiliar with some of the math that he talked about, so probably the most difficult part of the talk was just when he was going over some of the formulas he derived.

I really enjoyed Dr. Tomasetti's presentation.  I've been interested in cancer research for a long time, and I would definitely like to go into mathematical biology to have a chance to do the kind of work that Dr. Tomasetti does.  It was very fascinating to learn of the correlation between the age of cancer patients upon diagnosis and the number of pre-cancer phase mutations in those same patients.  I would definitely be interested in learning more about what researchers are doing to find ways to differentiate between which mutations lead to proliferation of passengers and which lead to proliferation of drivers.

Section 16.2, due November 28

The hardest part of the reading was the part about using elliptic curves to represent plaintext. 

Elliptic curves are definitely strange and not one of the most intuitive mathematical concepts that I've encountered.  But I definitely do want to know more about how they can be used in a cryptosystem.  Looking at elliptic curves mod p seems like it is definitely be a lot simpler than just looking at elliptic curves on the real numbers. 

Dr. Dave Richeson, Focus on Math, Extra Credit

The most difficult part of Dr. Richeson's talk to understand was some of the explanations of how certain constructions were done.  A few of them were just a little hard to follow.

I enjoyed Dr. Richeson's talk.  I'm taking a class on the history of math this semester, so a lot of his talk dovetailed nicely with what I've learned about geometry and geometric constructions.  They do seem like very elementary problems (even though they're impossible), and they might not have important applications to the real world, but it is still very interesting to see what mathematics is (and is not) capable of.

Section 16.1, due November 26

The most difficult part of the section was the part about the addition law for elliptic curves.  It wasn't super difficult to understand, but an example would be very helpful.

I think the most important part of the section, at least as it pertains to cryptography, is the fact that elliptic curve systems can do with 313 bit keys what certain conventional systems can only do with 4096 bit keys.  The is vast improvement in efficiency, made possible by a creative cryptosystem built on powerful mathematics.

Section 2.12, due November 20

This wasn't a very difficult section, but a more in depth explanation of how the enigma worked would be helpful, though I think I basically understand it.

But I have always been pretty interesting in the Enigma system.  I read The Code Book a long time ago and had the chance to read about the history of the Enigma and its effect on World War II.  Although cryptography has many non-civilian applications, it seems that it will always be an important part of warfare, for good or ill.

Section 19.3 and Blog Post, due November 19

The most difficult part of the reading was the explanation of the Quantum Fourier transform.

I had never thought about how superposition of states could be used as an effective tool in solving the problems of RSA (namely, factoring a large integer).  However, it is an idea that correctly applied has the potential to work.  Indeed, it has been shown that it can be solved provided a quantum computer.  So the big obstacle here will just be actually building one, which could be a huge obstacle.  Or maybe the government already has one and we just don't know it...

Section 19.1 and 19.2, due November 16

I had a little trouble understanding the explanation in the beginning about the polarity of particles and how that applies to sending messages through quantum cryptography.

The most interesting part of this section was definitely the mention of the possibility of factoring integers in polynomial time using an appropriate quantum computer.  If this exists now, that could mean that RSA is totally open to anyone who has it.  However, I have no idea what the actually likelihood is of the existence of a quantum computer is, or what a quantum computer is even, but I definitely want to know more.