Sam Vandervelde's Math Home Page

I am an Assistant Professor of Mathematics at St. Lawrence University, located in Canton, NY; I joined the department in the fall of 2007. I enjoy any beautiful mathematical ideas, although I tend to be inclined towards problems in number theory, graph theory, combinatorics, and Euclidean geometry. Current research projects include work on arithmetic graph sums and new partition identities, while my dissertation focused on Mahler measure. During the Fall 2009 semester I will be teaching MATH136 (Integral Calculus) and MATH280 (Bridge to Higher Math). I am in the process of writing a textbook for the latter course, which should be completed by the end of the semester. At St. Lawrence I have also taught Multivariable Calculus, College Geometry, Number Theory, Combinatorics, and a problem solving seminar.

Contact Info • Publications • Current CV • Snow Bowl
High School Math Contests • Math Circles • Bridge

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Contact Info

Dr. Sam Vandervelde Dept of Math, CS & Stats St. Lawrence University 23 Romoda Drive Canton, NY 13617

Office: Valentine 212 Phone: 315-229-5946 Fax: 315-229-7413 Email: svandervelde@stlawu.edu

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Publications

• Circle in a Box, American Mathematical Society, Providence, RI, 2009. Link to PDF
• Expected Value Road Trip, Mathematical Intelligencer, 30(2) (2008) 17–18. PDF
• The Mahler Measure of Parametrizable Polynomials, Journal of Number Theory, 128(8) (2008) 2231–2250. PDF
• A Formula for the Mahler Measure of axy+bx+cy+d, Journal of Number Theory, 100(1) (2003) 184–202. PDF
• Mathematics as a Liberal Art, Journal of Education, 183(3) (2002) 7–15.
• The First Five Years, Greater Testing Concepts, Cambridge, MA, 2004. Order
• The Mandelbrot Problem Book, Greater Testing Concepts, Cambridge, MA, 2002. Order

Currently submitted
• Balanced Partitions, Ramanujan Journal. PDF
• Level Three Arithmetic Graph Sums, Annals of Combinatorics. PDF
• On Rational Cubic Residues, Hardy-Ramanujan Journal. PDF

In preparation
• Bridge to Higher Math, textbook for the St.Lawrence University proofs course.
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Curriculum Vitae

My curriculum vitae was last updated during the summer of 2009. PDF
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The Snow Bowl During the fall of 2007 I initiated a friendly math rivalry among Colgate, Hamilton, Skidmore, and St. Lawrence. The Snow Bowl rotates among the math departments at these four schools, awarded annually to the school whose top five students have the highest total score on the Putnam Competition. The bowl is residing at Hamilton during the 2009-10 academic year. The purpose of the rivalry is to promote interest and participation in mathematical problem solving for students at these schools.

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High School Math Competitions

I am the author and coordinator of the Mandelbrot Competition, a math contest taken by over 4500 high school students from across the country last year. I oversee all aspects of the competition, including test composition, web site maintenance, and contest administration. My goal is to introduce students to exciting topics outside the normal curriculum and engage them in mathematical writing. I also write questions for and serve on the committee that produces the US Math Olympiad (USAMO).
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Math Circles

I am an enthusiastic supporter and promoter of math circles, an extracurricular activity which brings students interested in mathematics together with professional mathematicians who are able to engage them in exciting mathematical investigations. I founded the Stanford Math Circle in 2005 and the Lawrence Avenue Elementary Math Circle in 2007. I was also the first director of the board that created The Teacher's Circle, an analogous activity for middle school math teachers. I helped to organize a minicourse at MathFest 2008, designed to aid participants in launching their own successful math circles. Most recently I was one of the organizers for the Great Circles Workshop hosted by MSRI in April 2009. For more information, visit the National Association of Math Circles web site.
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Bridge to Higher Mathematics

During 2009 I am in the process of writing and revising a text for our "proofs" course, called Bridge to Higher Mathematics. Although this text is a work in progress, the front matter, first three chapters, and answers to the exercises are available for download. If you are interested in using this text on a trial basis with your course, please contact the author at the addresses listed above.

Front Matter • Chapter One • Chapter Two • Chapter Three • Answers