Mathematical Biology

It sounds like everybody enjoyed our day of mathematical biology brought to you by Professor Mogilner and Swati Patel. Applications of mathematics to science are vast, deep, and ever-expanding. Many people are surprised to hear that mathematics can be so successfully applied to biology, probably since these topics haven’t made it very far into the high school curriculum.

Prof. Mogilner’s talk on allometric scaling was based on research published in the 1990s (West_Brown_Enquist_1997) that has been cited thousands of times. Since wikipedia is always a mere click away, you should try to read this. Here is an article that explains the paper a little more clearly than the original: Demystifying the West, Brown & Enquist model of the allometry of metabolism. And, here is an article talking a bit more about the biology of allometry using the example of fiddler crabs with one ginormous claw and one itty-bitty claw. I guess they look like they’re playing the fiddle? Cellist crab might be more apt.

fiddler crab

 

 

Once you learn about fractals, it’s hard not to see them everywhere in nature.

capillary branchingbranching out

 

Swati’s talk about modeling populations provided ideas that get your foot in the door to understanding chaos theory. And who wouldn’t want to know more about chaos??

chaosstatic bifurcation

The only limit to the applications of math is the imagination of the mathematician. We’ll have more professors and graduate students share some examples of applied math with you later this quarter.

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Math Skill Comes from Practice!

I recently read an interesting article supporting what many of us who work in math and mathematics education believe from experience: practice makes you better at math.

http://www.sciencedaily.com/releases/2013/12/131216102844.htm

However, this somehow manages to be simultaneously completely obvious and nearly impossible to convince people of. Better at algebra than geometry? Practice some more geometry. Trouble with word problems? Practice them as well as your reading in general. The analogy with athletics is completely apt.

As students, we tend to do more of what makes us feel good, which is of course what we are already good at. I have seen many students pride themselves so much on their ability at one thing that they neglect other studies and activities. This will of course lead to the student becoming better and better at that one activity and worse and worse at everything else. Many believe that students showing this one-dimensionality were somehow born different, but I’d venture to say that the vast, vast majority of such students have just engaged in overly narrow practice. Of course, there are a handful of people out there with such enormous capacity at such a young age that it doesn’t seem possible for there to have been sufficient hours in their life for their abilities to be due to practice alone, but I bet the differences between their inherent ability and that of others is much smaller than most people suppose.

What is the point of this rant? You can be good at math! Hurray! The difference between math people and non-math people is that math people do more math, not that they were born with some sort of abstract antenna in their brain that makes them sensitive to mathematical ideas or whatever.

Speaking of getting better at these things, see you at AMC practice on Saturday at 1pm! If you will be joining us for lunch, bringing a few bucks to cover cost of pizza would be much appreciated (but not required).

Email me if you’d like electronic copies of a few old AMC exams for practice.

Math Circle Schedule for Winter 2014

This Saturday, George Mossessian will discuss the geometry and topology (he’ll tell you what that means) of 2D surfaces like beach balls, doughnuts, and Klein bottles. As always, only mathematical enthusiasm (not knowledge) is required, and this one should be quite hands-on and fun.

turning-a-sphere-inside-out-o Mug_and_Torus_morph

Next time, on Jan 25, we’ll have two speakers, Professor Alex Mogilner and Swati Patel, talking about different topics from the exciting area of mathematical biology.
On February 1st, Patrick Weed will give an introduction to logic using the island of Knights and Knaves created by author, logician, and magician Raymond Smullyan. The other topic is TBA.
AlphRalphlabyrinth_puzzle
On February 8th, Math Circle will be cancelled since so many of you will be at Mathcounts right across campus. Email sacmathcontests@gmail.com for more info on this.
On February 15th, Professor Becca Thomases will introduce you to how mathematicians study interesting fluids, and Professor Janko Gravner will talk about the growth of random snowflakes (related to but quite different from the fractals that Owen Lewis discussed last quarter).
Non+Newtonian+Fluid+PoolLet’s take a slower look at that…
fluid-walking
The rest of our schedule is still being worked out, but we have many more professors and phd students lined up who will introduce you to exciting ideas in quantum mechanics, group theory, protein folding, knot theory, complex systems, and much more.

Math Circle Redux and AMC 10

We had a great turnout on Saturday for both the Math Circle portion and the AMC time. In future AMC sessions, now that we have some measure of where you all are, we’ll focus on a particular topic and/or strategy. Remember that doing well on these problems means getting anything at all! We hope you enjoy learning outside of school in a zero-stress environment.

Email me to register for the AMC 10 or 12 which will be at 7pm in MSB 2112 (the usual place) on February 4th and 19th. If you’re not sure which, just tell me your grade and which date works better for you. You can take it on both dates if you like.

Jamie introduced some of you to the wonderful game of Set, and those who had already played learned about some of the mathematics hidden in the structure of the game. Anything so elegant must involve math!

setgod Oops! Wrong Set. The talk was about this one:

SetCardsFamily fun! Not desert storms and chaos.

For a more mind-bending (but honestly less fun) experience, try ProSet, a version of Set created by thinking about the projective plane. Ever wonder what happens when you sew a Möbius strip to a disk?

crosscap2A version of the projective plane, duh!

Eric gave an introduction to harmonic numbers and hinted at applications to prime numbers, leaning towers, randomized algorithms, and rovers. Expanded notes for Eric’s talk.

erdos-crazy NASA_Mars_Rover bronte

Next week, George will give a very accessible talk about surfaces and knots. He has experience teaching with Cosmos, so come and enjoy!

If you plan on staying for lunch between our two events, donating to help for the cost of food is much appreciated but not required. Any money made on this site goes to support Math Circle.

Math Circle in Winter Quarter (Jan-March)

Hello Everybody!

I hope you enjoyed the winter break. We will be meeting again starting on Saturday Jan 11 at 10am-noon in our same location of MSB 2112. We will also do some practice focusing more on math competition skills after math circle for those who interested in competitions like the AMC 10/12, ARML, mathcounts, etc. We will meet every Saturday unless otherwise stated.

Speaking of mathcounts, UCD will be hosting for this region! Let us know if you are interested in participating.

And now for a few cool things I’ve read about recently:

Levitating Objects with Sound

soundlevitation

Balancing/Walking Cube

cubli

Levitating Superconductor on a Möbius Strip

mobiuslevitate