The one and only success which it is [ours] to command is to bring to [our] work a mighty heart.
      Oliver Wendell Holmes, Jr., In Our Youth Our Hearts Were Touched With Fire1884


Articles in Press









  • (with D. A. Goldston) On the differences between consecutive prime numbers, I, INTEGERS: Electronic Journal of Combinatorial Number Theory 12B (2013), #A3, 1–8; reprinted as pp. 37–44 in Combinatorial Number Theory: Proceedings of the ‘‘Integers Conference 2011,’’ Carrollton, Georgia, October 26-29, 2011, De Gruyter Proceedings in Mathematics, 2013.





Articles Submitted for Publication

  • The discrepancy of Farey points in short intervals, submitted for publication.

  • (with K. Ferrier, M. Jackson, D. Patel and H. Tran) The expected number of complex zeros of a random polynomial, submitted for publication.

  • (with E. Addison, S. Smith and R. Vrandenburgh) Average intensity of the distribution of complex zeros of a class of random polynomials, submitted for publication.


Articles in Preparation

  • Random orthogonal polynomials in the complex plane, in preparation.

  • (with D. A. Goldston) On the differences between consecutive prime numbers, II, in preparation.

  • The level crossings of a random harmonic polynomial, in preparation.

  • (with C. Gugg) Computations on integers of the form p + gk, preprint.


Master’s Thesis


Doctoral Dissertation

  • Distribution of Farey series and free path lengths for a certain billiard in the unit square, Doctoral Dissertation (Adviser: Professor A. Zaharescu), University of Illinois at Urbana-Champaign, Urbana, IL, May 2007. (95 pp.; ISBN: 978-0549-09626-9; ProQuest LLC).


“It is one of the chief merits of proofs that they instil a certain scepticism as to the result proved.”
       Bertrand Russell, The Principles of Mathematics, 1903, p. 360