- Algebraic Number Theory
- Diophantine Analysis
- p-adic Analysis
- Geometry of Numbers
- The Theory of Continued Fractions
Student Research Advised
- Honor's Thesis Advisor for Jennifer Sargent (1993): Real and p-adic
- Faculty advisor for SMALL REU-NSF undergraduate summer research programs in number
theory, 1993, 1996, 2000, 2005, 2010.
- Research Advisor for Chris Kollett and Colin Blakely (summer 1994);
Daniel Lucky (fall 1995, U.T. Austin); Jonathan Todd (summer 1995);
Brian Wecht (winter 1996).
- Honor's Thesis Advisor for Jonathan Todd (1996): Diophantine
- Honor's Thesis Advisor for Kariane Calta (1998): Asymptotics on generalized Zeckendorff decompositions
- Honor's Thesis Advisor for Heath Dill (1998): On a theorem of Wall
- Honor's Thesis Advisor for Mimi Huang (1998): The geometry of numbers and parallelograms in the plane
- Honor's Thesis Advisor for Rungporn Roengpitya (2001): An improvement to Legendre's theorem from diophantine approximation
- Honor's Thesis Advisor for Charles Samuels (2002): On Solutions to the Generalized
Pell Equation with Applications to Diophantine Approximation
- Honor's Thesis Advisor for Kari Lock (2004): Identifying best rational approximations through sharp Diophantine inequalities
- Honor's Thesis Advisor for Ashok Pillai (2005): On diophantine approximation along algebraic curves
- Honor's Thesis Advisor for Nicholas Yates (2006): Diophantine Approximation through Nonsimple Continued Fractions
and Planar Curves
- Mathematics External Review, Davidson College, 2009.
- Member, Editorial Board, Math Horizons Magazine.
- Mathematics External Review, Fordham University, 2007.
- Member, External Review Committee, Mathematics Program, Weston School District, Weston, MA, 2007.
- Member, Mathematical Association of America CUPM Subcommittee on Undergraduate Research, 2006-present.
- Member of the Board of Trustees, The Educational Advancement Foundation.
- Member, Editorial Board, AK Peters, Ltd.
- Associate Editor of The American Mathematical Monthly.
- Member of the AMS Committee on Committees.
- MAA Program Committee Member, AMS-MAA Joint Meetings, January, 2002.
- Chair of the Program Committee, MAA National Summer Meeting (Mathfest), August, 2001.
- MAA NExT Consultant, 2000-2001.
- Massachusetts Corporation for Educational Telecommunications, Advisory Panel Member.
- Science Curriculum External Reviewer, Massachusetts College of Liberal Arts, June 2000.
- Keynote Invited Address, AMS-MAA-SIAM Meeting,
Washington, DC, January 2000.
- Contributing writer, National Public Radio's ECO-Essays Series, fall 1999.
- Awarded a grant from the Educational Advancement Foundation, 1999.
- AMS Invited Special Session Speaker, March 1999.
- Program Chair for the Northeastern MAA Fall 1997 Conference.
- Delivered Invited Address, MAA MathFest, August, 1997.
- Awarded a two year grant from the Educational Advancement Foundation, 1997-1998.
- Delivered AMS-MAA Invited Address, August, 1996.
- M.A.A. Visiting Lecturer 1994-1997.
- Reviewer for:
Columbia University Press
Oxford University Press
John Wiley and Sons
St. Martin's Press
Wm. C. Brown Publishers
Addison Wesley Longman Publishing
- Referee for:
National Science Foundation Grant Proposals
Journal fur die reine und angewandte Mathematik
The Journal of the London Mathematical Society
The Transactions of the American Mathematical Society
The Journal of Number Theory
The Houston Journal of Mathematics
The Rocky Mountain Journal of Mathematics
The American Mathematical Monthly
The Fibonacci Quarterly
- President of the Gamma Chapter of the PBK Honor Society.
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