Zawada's Rules: Rob '13 Publishes Mathematics Paper

Middlesex School

Rob Zawada MX’13 is the author of an upcoming article in the 2014 edition of the journal of the National Council of Teachers of Mathematics (NCTM).  A rising sophomore at the University of North Carolina at Chapel Hill, Rob is pursuing a BSBA in business administration with a concentration in entrepreneurship and a minor in psychology.  Read on about how Rob’s academic article emerged during his junior year at Middlesex.

During my junior year at Middlesex, I was taking a pre-calculus test. Towards the end of the test I reached a set of problems that required a specific formula to determine the correct number of maximum possible turning points from a polynomial function. The formula (n-1), where n is the highest degree in the function, was supposed to provide this answer, but it escaped my memory at the time, so I spent 15 minutes fiddling with various formulas on my graphing calculator in an attempt to derive the solution myself.  The problem was I couldn’t. My teacher agreed she couldn’t find a manual solution to the problem either, and she suggested that I figure out a better solution myself.

After a week of researching math papers, fiddling on my calculator, and scribbling in a notebook, I was getting nowhere. I consulted Mr. Pandolfini, a math and economics teacher at Middlesex, who suggested I start teaching myself elements of calculus in order to better grasp the problem at hand. He also mentioned that I may be taking on a task bigger than I thought, for he explained how Fermat’s last theorem took a man 7 years in isolation in an attic to mathematically prove. Over the next two months, Mr. Pandolfini would repeatedly disprove my ideas, but I was determined to figure this problem out. Mr. Pandolfini’s insight and fascination into math, numbers, theory, and logic was truly inspirational.

A few months later, it clicked – I put together Descartes’ rule of signs with certain elements of calculus in order to comprise what are now called “Zawada’s Rules” to deduce a formula that either matches the accuracy of the (n-1) rule for maximum possible turning points or beats it in every single case. From this (n-1) rule I was also able to deduce a formula that proves more precise than the (n-2) rule for calculating maximum possible inflection points.

Thanks to the encouragement and insight of the math department, I was able to turn seven pages of furiously written math work into a polished, 13-page piece for the National Council of Teachers of Mathematics, which produces a national math journal every year. The article will appear in the 2014 edition, coming out in September. 

Recently, Rob has been busy growing his company and building a sales team for BitSafe Investments LLC, a hedge-fund structured investment platform that offers investors secure exposure to price changes in Bitcoin, a new and emerging digital currency.

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