*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.*

*erikamills*on June 23rd 2014