Steve Yeh doesn’t get intimidated easily. The Huntington High School senior developed and presented a highly technical and detailed project and walked away with first place honors and a gold medal at the Al Kalfus Long Island Math Fair at Hofstra University last weekend.
Huntington’s Class of 2017 valedictorian, Mr. Yeh was selected to compete in the contest through the high school science research program led by teacher Lori Kenney. The veteran educator has mentored the teenager.
The title of Mr. Yeh’s project is enough to make a person dizzy: Methodology of Calculation of Areas under Polynomial, Rational, Logarithmic, Trigonometric and Exponential Functions without Explicit Usage of Antiderivatives.
Huntington senior Steve Yeh
won a gold medal at the LI Math Fair.
The fair was sponsored by Hofstra, the Suffolk and Nassau mathematics teachers’ association and the Nassau County Association of Mathematics Supervisors.
“It was great to hear the details of other projects, including one about the nature of prime numbers and another dealing with statistically predicting elections using data from specific state primaries,” Mr. Yeh said.
A National Merit finalist, the Huntington senior is headed to Cornell University to pursue an academic major in mathematics, physics and/or economics. Known as a very hard worker who never gives up, Mr. Yeh keeps an open mind in all situations and circumstances. Humble, calm and collected, he’s unflappable even when faced with intense pressure.
The teenager has interned with high school math teacher Monica Racz in an AP Calculus BC class. President of Math Honor Society, captain of Huntington’s Quiz and Science Bowl teams, president of Chinese foreign exchange club, treasurer of Spanish Honor Society and founder and president of stocks analysis club, Mr. Yeh even found time to volunteer as a homework helper at the Huntington Public Library’s Huntington Station branch.
“Rational, logarithmic, trigonometric and exponential functions, especially when found in combinations of each other, may be extremely difficult or impossible to find the area under the curve by usage of antiderivatives and integral calculus,” said Mr. Yeh in an abstract of the project. “The methodology is comprised of the incorporation of the summation of the Left and Right Riemann sums, its partial multiplicative inverse and unique finite or infinite series that mirrors that of the polynomial partition of the Binomial Theorem of each function derived from the respective Maclaurin series. Though the derivation of the methodology did involve the knowledge and use of the Fundamental Theorem of Calculus and antiderivatives, the process of the methodology does not. The subsequent components for the methodologies were programmed using the Java language and the truncated error was calculated for each.”
The Huntington senior compared program execution times and memory usage between the programmed alternate methodologies and that of usage of antiderivatives and the Fundamental Theorem of Calculus.
“Statistical significance in difference of execution times or memory usage was found to be in which the alternate methodologies were both statistically slower (in nanoseconds) and used up more memory,” said Mr. Yeh in the project abstract. “However, a theoretical efficacy of the alternate methodology was proposed, describing the process of how a computer using various data unit sizes, could calculate with a relatively gradual increase in memory used, which could potentially allow for simultaneous processes to happen, compared to the full punctuated attainment of memory needed when antiderivatives and the Fundamental Theorem of Calculus are used.”
