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Sam Vandervelde Presents Special Undergraduate Lecture on October 11

Oct. 9, 2012

Dr. Sam Vandervelde, a mathematician from St. Lawrence University in Canton, NY gave a special undergraduate colloquium this Thursday, October 11 in SR 207 to a packed audience (Fire Marshall beware: the room holds 40 people....and there were at least 75 at his lecture!). The title of his lecture, was "Where is the middle of a Fibonacci sequence?".

Sam Vandervelde
Professor Sam Vandervelde

Dr. Vandervelde earned his Ph.D. degree in mathematics from the University of Chicago in 2004. His main research specialty is number theory, a subject for which he has several publications. Prior to his current position at St. Lawrence University where he is an Associate Professor, Sam taught at Stanford, Wellesley College, Phillips Academy, and Northeastern University.

Sam's interests in teaching,for which he has won several national awards, go well beyond the classroom. Indeed, he is active in developing, and participating, in workshops (like Math Circles, Circle-in-a-Box, and Teacher's Circle) with teachers organized through the Mathematical Association of America, the Mathematical Sciences Research Institute, and the American Institute of Mathematics.

Sam also runs the Mandelbrot Competition, a high school mathematics competition, that served more than 6000 students last year. As an undergraduate student, Sam won a silver medal for the US team in the 1989 International Mathematical Olympiad and also placed in the top 15 (twice) in the Putnam examination.

Here is the abstract of Dr. Vandervelde's lecture:

Where Is The Middle of a Fibonnaci Sequence?
(Thursday, October 11; 3:30 pm, SR 207)

Abstract

The Fibonacci sequence is constructed by beginning with 1, 1 and then successively including more numbers (on both sides) so that the sum of any two terms equals the next, yielding ..., 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, ... We would all agree that 0 is in the "middle " of this sequence. But try to guess the middle term when we start with a different pair of numbers, such as 1, 6 leading to ..., -13, 9, -4, 5, 1, 6, 7, 13, 20, ... (Hint: it's not 1). Correctly identifying the middle terms leads to a breathtakingly beautiful array that organizes all Fibonacci sequences and provides a clever means of answering questions such as "In the Fibonacci sequence generated by 1492, 2013 are there any multiples of 2017?"