Math Modelling

Class Info

          Math Modelling is a class that is all about finding patterns. That one concept is key in this class. We are encouraged to find patterns in anything that we do and, through these patterns, develop mathematical models about various problems. Then, taking these patterns and models, as well as assumptions and variables we set along the way, we attempt to write analytical or logical proofs. It is a really interesting class. The work is generally challenging, but it is very rewarding when you finally figure out a difficult problem. This class is definitely much harder than anything a Junior at a normal high school would do, but you also learn a lot more than you would in a normal math class, so it is well worth the work. The teacher, Mr. Barys, stresses correct mathematical terms and exploration of math topics to form conjectures and prove them. We do not have a textbook in class. We learn math in "units" which are designed to both prepare us for college and teach us to think mathematically rather than just do math problems. We also use computers (well, Apple Macs) a lot in class. Primarily, we use Mathematica, a powerful (though sometimes buggy) program. In order to use the program, we are continuously learning new functions and ways to employ the high-level programming language that Mathematica uses. We also use Geometer's Sketchpad from time-to-time, mostly to make conjectures. We also use other programs, though rarely. One such program was Garageband. We used it in our study of the formal system of the First Species Counterpoint, and how we could make a harmoic musical tune, given an axiom (an already existing tune) and using a set of given rules.

Sample Work

Basketball Player Lab: A lab about modeling data using statistics about basketball players
Babylonian Year Lab: A lab about the babylonian year and the sexagesimal number system
Leaning Tower of Pisa Lab: A lab about the leaning tower of pisa's lean, data modeling, and extrapolation/interpolation
World Population: This was just a homework assignment, but I found it interesting. This problem was asked at the beginning of the most recent unit and we were given only a few seconds to answer it. It was interesting to revisit it at the completion of the unit and see that I was able to solve it quite easily.
Shuttling Around POW: This problem of the week was based on a board game that had a set of rules. The goal was to explore the game and find a generalization that can be used to find the number of moves required to finish the game with a given starting position. It was really interesting to do, so I decided to post it here.

External Links

Ask Dr Math: Got any math questions? Check this site out. Just don't use it on the math problems that are assigned. You're only allowed to use your brain on those!
Google Calculator Guide: Check this helpful guide out for info on how to use google's powerful built-in calculator.