Bruce Reznick

Professor
"The John and Harriet J. Absentminded Professor of Mathematics"
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, Illinois 61801-2975

Office: 327 Altgeld Hall
Office Tel: (217)333-4284
Dept. FAX: (217) 333-9576
e-mail:reznick@math.uiuc.edu

Spring 2009 Teaching

  • Math 496

    CV-type links


  • Biographical Sketch
  • List of Research Publications
  • List of Other Publications

    • Notices of the AMS Book review

  • "From Zero To Infinity, 50th Anniversary Edition" by Constance Reid


    • When it comes to advice, I'm full of it

  • "Teaching Philosophy" , added April 2009
  • "Chalking It Up: Advice to a new TA"
  • "Resources for research"
  • "One introduction to mathematical research", or "You've proved a theorem, now what?"
  • "Some thoughts on writing for the Putnam"



    • Areas of Specialization

    Combinatorial methods in algebra, analysis and number theory, usually involving polynomials or polytopes.

    .pdf files of some recent papers (most recent at top)

  • Preprint On Hilbert's construction of positive polynomials
  • Preprint Regularity properties of the Stern enumeration of the rationals
  • Preprint Clean lattice tetrahedra
  • Preprint A quantitative Polya's theorem with corner zeros (with Vicki Powers)
  • Preprint Almost alternating sums (with Kevin O'Bryant and Monika Serbinowska)
  • Preprint Polynomials positive on unbounded rectangles (with Vicki Powers)
  • Preprint On the absence of uniform denominators in Hilbert's 17th problem
  • Preprint A new approach to Hilbert's theorem on ternary quartics (with Vicki Powers, Claus Scheiderer and Frank Sottile)
  • Preprint On the Diophantine equation xy = ymx (with Michael Bennett)
  • Preprint Patterns of dependence among powers of polynomials
  • Preprint Lattice polytopes with distinct pair-sums (with M. D. Choi and T. Y. Lam)
  • Preprint A new bound for Polya's Theorem with applications to polynomials positive on polyhedra (with Vicki Powers)
  • Preprint Notes towards a constructive proof of Hilbert's Theorem on ternary quartics (with Vicki Powers)
  • Preprint Polynomials that are positive on an interval (with Vicki Powers)
  • Preprint Some Concrete Aspects of Hilbert's 17th Problem
  • Preprint On the non-monotonicity of (|Im(zn)|)
  • Preprint The maximum angular gap among rectangular grid points (with Zoltan Furedi)
  • Preprint Homogeneous polynomial solutions to constant coefficient PDE's over fields
  • Reprint Uniform denominators in Hilbert's Seventeenth Problem

    • Seminar Notes

  • Notes Equal sums of higher powers of quadratic forms

    • Ph.D. Students

    Prof. Julie Simon (Ph.D. 1989)
    Prof. William Harris (Ph.D. 1992)
    Ms. Colleen Kilker (1977-2002)
    Ricardo Rojas (Ph.D. 2008)
    Han Duong (Ph.D. 2008)
    Melissa Simmons Dennison
    Supawadee Prugsapitak