11/12/07

Difficult part: in general the reading seemed pretty straightforward; the only real tricky part was the sheer number of constants with which the paper bombards the reader.

Reflective part: most of the results from the model seemed to make sense, in this case. What's interesting about the model is its ability to predict how effective the changes will be, such as the results mentioned on page 27, before section 5.4. The prospect for a vaccine seems interesting, though I can't help but wonder why I haven't heard of it yet.

11/6/07 blog post

Difficult part: I don't entirely understand the correspondence between eigenvalues of the matrix of a system of differential equations and the stability of the equilibrium points of the system. Granted, this was from 3-12, rather than 12-22, but for the most part, I found 12-22 to be fairly straightforward. The math seemed ugly, but since it is largely done through numerical simulation, it's fairly understandable. The only part where I would potentially balk is equations 25-29, though the only difficult part seems to be keeping track of the constants.

Reflective part: Perelson's model seems to be a good example of a model that's only as complex as it needs to be, though in this case, it needs to be fairly complicated. It would be interesting to see how the model bears out empirically and if advancements in knowledge about HIV would change any of the model's assumptions.

October 23

Difficult part: It took me a fair amount of time to understand why N2 in figure 6.3 is an equilibrium point, though I think I realize why now (it should be because qEN is being subtracted from the other plot, and thus the result will be 0 at N2, indicating an equilibrium point). Other than that, I generally understood the reading, though "unit effort" struck me as an odd concept.

Reflective part: It's interesting that despite the depensation model seeming to account for damaged fish populations, Myers et al. found this generally not to be the case (assuming the validity of the study). Also, as I implied earlier, I'd be interested to see how exactly E translates into the real world.

October 16

Difficult part: for the most part, the reading seemed fairly straightforward, especially since I've already had differential equations. That said, I'm not sure where the constants in equations (1), (2), and (3) in Cayrel et al. come from.

Reflective part:
This seems somewhat different from what we've done thus far, in that the underlying math is not terribly complicated, but the scientific principles from which the math is derived are fairly involved and, in the case of Cayrel et al., comprise the bulk of the paper (contrast to the phyllotaxis paper, which focused almost exclusively on the math, while hand-waving the science). Cayrel et al. seems fairly obtuse, but much of the difficulty comes from astrophysics, rather than the math.

October 4th, 2007

Difficult part: the most difficult part was easily the derivation of the generalized Zipf's law. In particular, I'm not entirely sure what the normalization condition mentioned in 3 is (though I have some idea).

Reflective part: the two papers seem to demonstrate, quite effectively, the perils of neglecting to thoroughly examine one's model to make sure it really supports what one wants to say. Zipf assumed that the correlation seen between word rank and frequency was due to some "law of economy", when in fact it derived inherently from the nature of his model.

September 27

Difficult part:

I'm a little confused by the factoring done in the Vblood equation at the bottom of page 33, but other than that, I think I generally understood the math.

Reflective part:

On the one hand, the way much of life seems to obey simple scaling laws for metabolism and similar factors is impressive; on the other hand, the controversy around much of this, as well as some of the initial, incorrect suppositions of a 2/3 scaling factor shows that math cannot make predictions in a vacuum, even if the predictions are convenient.

September 25

Difficult part: overall, the section seems pretty easy to understand, but I was a little unsure of what the metabolism plot would look like on a linear scale; it should be some kind of geometric curve, right?

Reflective part: the regularity with which metabolism scales and the prevalence is quite interesting. This seems to be another example where mathematics can provide an explanation for how something occurs, even when biology is unable to explain why.

September 18

Difficult Part:

I found the most difficult part to be pages 658-660 of Atela et. al. I'm unsure how the quadrilateral Qm,n is defined and what points m,n refer to (arbitrary ones or specific ones). In addition, I was fairly confused by their definition of φ, in relation to S.

Reflective Part:

I find it interesting that, given the relatively simple Hofmeister rule, the paper's authors were able to extrapolate the math involved into something quite complex and byzantine (this, in turn, describes a fairly simple to describe phenomenon).

Second Post

Most difficult part: On the whole, I found the trickiest part to be understanding May's explanation of the existence of two cycles once a>3. I'm not completely sure why the slope of F^2(x) is the square of the slope of F(x), and I think Figures 2 and 3 might have been switched (it looks like Figure 3 has one point of intersection with the 45 degree line, whereas Figure 2 has two), unless I've misread this section.

Also, I found the derivation on Strogatz pg. 350 of the deviation near a fixed point to be a bit confusing; does the O(n) (not the actual symbol, but close enough) term refer to standard big O notation, or does it mean something else? If the former, where does that term come from?

Reflective part: This section seems quite similar to the information on bifurcation covered in my Differential Equations class last semester. However, this seems a bit different since it deals with plotting a variable against itself, with a time variable being implicit (I think; if not, I really got thrown by the reading and/or my differential equations abilities are rustier than they should be), and this was enough to throw me off a bit.

First Post

-Chris Dragga
-I'm a senior
-I'm majoring in computer science (possibly math as well if I can integrate math somehow into my honors project) and minoring in English
-I've taken multivariable calculus, discrete math, linear algebra, theory of computation, introduction to statistical modeling, differential equations, and algebraic structures.
-Probably probability and statistics.
-Most likely calculus.
-I'm taking the course because, as a computer scientist, I will likely find it useful, and it fulfills the requirement for a 400 math course for the math major. In addition, I'm also hoping it will give me some background to integrate mathematical modeling into my honors project.
-Other than what I've written above, there's nothing specific I'd like to get out of the class.
-As mentioned earlier, I'm an English minor and computer science major. I listen to a good amount of black and death metal, and enjoy playing games, both computer and otherwise. I play the flute and am an avid walker.
-The worst math teacher I ever had essentially acted as a study-hall monitor for the class. Students would demonstrate correct answers to the previous day's homework at the beginning of class, and the latter part of class would be dedicated to doing homework. Every once in a great while, the teacher would actually explain something, but she only did so for the more difficult topics and generally was fairly dull. (Note that this was a high school teacher, not a college professor, and she was a year from retirement)
-The best math teacher I have had took time to explain the material and did so in an engaging, fairly entertaining way. (I realize this is a rather generic answer)

Overall, I found the most difficult part of the reading to be the part involving the derivation of the recursive formula for the Fibonacci series. The standard formula derivation was fairly straightforward, though I should probably briefly refresh my differential equations knowledge. The most interesting part of the reading dealt with the various properties of the Golden Ratio (section 1.2)