Daniel Kane

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Daniel M. Kane, a student in mathematics who was born in Madison, Wisconsin in 1986, is currently a graduate student studying mathematics at Harvard University with National Defense Science Education (NDSEG) and National Science Foundation (NSF) Fellowships.

Contents

[edit] Childhood

Daniel Kane exhibited prodigious abilities in mathematics at a young age. By the end of 2nd grade, he had already mastered all of pre-high school mathematics. In 5th grade, he qualified for The Study of Mathematically Precocious Youth.[1] As a 7th grader, Daniel participated in the American Mathematics Competitions, becoming only the 2nd student, after Reid W. Barton, to qualify for the Mathematical Olympiad Summer Program (MOSP) at such a young age.[2] Daniel went on to become a three-time USAMO Award Winner (2001-2003), with a perfect score on the 2002 USAMO, and a two-time gold medalist in the International Mathematical Olympiad (IMO) as a member of the 2002 and 2003 USA IMO Teams.[3] While still in high school, Daniel also participated in the 2002 Virginia Tech Regional Math Contest, becoming the first student to achieve a perfect score in this intercollegiate mathematics competition.[4][5] Under the mentorship of Professor Ken Ono, Daniel wrote his first two important research articles as a 16-year-old. One, improving upon a famous Annals of Mathematics paper of the famous 20th-century mathematician, Paul Erdös, was published in the journal Integers. The other, resolving and extending an open conjecture of the famous number theorists, George Andrews and Richard P. Lewis (1942-2007), was published in The Proceedings of the American Mathematical Society. For this highly prodigious research in mathematics, Daniel was named a 2003 Fellow Laureate of the Davidson Institute for Talent Development.[6]

[edit] College Years

Daniel attended the Massachusetts Institute of Technology (MIT) as an undergraduate student, graduating Phi Beta Kappa with majors in physics and mathematics with computer science. He resided in Random Hall, along with numerous other math and computer science international competition medalists, including Reid W. Barton, Matt Ince, Tim Abbott, Anders Kaseorg, Eric Price, and Thomas Mildorf. During this time, Daniel wrote more than a dozen original research articles in several areas of mathematics and theoretical computer science, working both on his own and under the mentorships of Professors Cesar Silva of Williams College, Joseph A. Gallian of the University of Minnesota Duluth, and Erik Demaine of MIT. Daniel's articles with Silva and Demaine give him an Erdös Number of 3. "For establishing a research record that would be the envy of many professional mathematicians", Daniel was awarded the 2007 Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student jointly by the American Mathematical Society (AMS), the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM).[7] One of these articles, co-authored with Tim Abbott and Paul Valiant, received the 2005 Machtey Award for Best Student Paper at the IEEE Symposium on Foundations of Computer Science.

While at MIT, Daniel also participated in intercollegiate mathematics competitions. He was named Fellow (i.e., among the 5 top) four times in the William Lowell Putnam Mathematical Competition, one of only seven individuals to achieve Fellow four times in the 67 Putnam competitions held through 2007.[8] Along with Daniel Gulotta and Andrew Spann, Daniel Kane was also a member of MIT's "Dream Team" in the Mathematical contest in modeling (MCM); during their four years participating in this international intercollegiate competition, they won the Ben Fusaro Award for most creative solution in 2004 and the top rank of "Outstanding" in years 2005, 2006, and 2007, including the INFORMS Award in 2006 and the SIAM Award in 2007.[9]

[edit] Selected Publications

  • Daniel M. Kane, On Solving Games Constructed Using Both Shortened and Continued Conjunctive Sums, submitted.
  • Chris Dodd, Phakawa Jeasakul, Anne Jirapattanakul, Daniel M. Kane, Becky Robinson, Noah Stein, and Cesar E. Silva, Ergodic Properties of a Class of Discrete Abelian Group Extensions of Rank-One Transformations, submitted.
  • Daniel M. Kane, On Lower Bounds on the Size of Sums-of-Squares Formulas, Journal of Number Theory, 128 (2008) pp. 639-644.
  • Daniel M. Kane, Improved Bounds on the Number of Ways of Expressing t as a Binomial Coefficient, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 7 (2007), #A53 pp. 1-7.
  • Daniel M. Kane, Weak Mixing of a Transformation Similar to Pascal, Colloquium Mathematicum, 108 (2007), no. 1, pp. 135-140.
  • Daniel M. Kane, Asymptotics of McKay Numbers for Sn, Journal of Number Theory, 124 (2007) pp. 200-228.
  • Daniel M. Kane, Generalized Base Representations, Journal of Number Theory, 120 (2006) pp. 92-100.
  • Daniel M. Kane and Jonathan M. Kane, Dropping Lowest Grades, Mathematics Magazine, (2006) 79 (June) pp. 181-189.
  • Daniel M. Kane, An Elementary Derivation of the Asymptotics of Partition Functions, The Ramanujan Journal, Vol. 11 (2006) no. 1 pp. 49-66.
  • Tim G. Abbott, Daniel M. Kane, Paul Valiant, On the Complexity of Two-Player Win-Lose Games, Foundations Of Computer Science, 2005.
  • Tim Abbott, Erik D. Demaine, Martin L. Demaine, Daniel M. Kane, Setfan Langerman, Jelani Nelson,Vincent Yeung, Dynamic Ham-Sandwich Cuts of Polygons in the Plane, Proceedings of the 17th Canadian Conference on Computational Geometry, (2005) pp. 61-64.
  • Daniel M. Kane, On the Number of Ways of Writing t as a Product of Factorials, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 5 (2005), #A02, pp. 1-10.
  • Daniel M. Kane, Resolution of a Conjecture Involving Cranks of Partitions of Andrews and Lewis, Proceedings of the American Mathematical Society, Vol. 132 (2004) No. 8, pp. 2247-2256.
  • Daniel M. Kane, New Bounds on the Number of Representations of t as a Binomial Coefficient, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 4 (2004), #A07, pp. 1-10.

[edit] References

  1. ^ The Study of Mathematically Precocious Youth([1])
  2. ^ Mathematical Olympiad Summer Program([2])
  3. ^ International Mathematical Olympiad Historical Record of US Teams ([3])
  4. ^ Virginia Tech Regional Mathematics Contest Results and Prizes([4])
  5. ^ Peter A. Linnell, The Virginia Tech Regional Math Contest, Math Horizons, Volume 13, September 2005, page 31.
  6. ^ 2003 Davidson Fellows ([5])
  7. ^ Citation by the American Mathematical Society for the 2007 Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student Awarded to Daniel M. Kane ([6])
  8. ^ Joseph A. Gallian, The Putnam Competition from 1938-2006([7])
  9. ^ MIT's "Dream Team" Wins SIAM Award for MCM ([8])

[edit] External links

  • Daniel Kane's homepage at Harvard ([9])