Introduction:

Current:

• Number Theory
  • Codes, Lattices, Lie Algebras, Elliptic Curves, and Modular Forms (dvi, pdf)
  • English translation of Gerald Hoehn's "Self-dual Vertex Operator Superalgebras and the Baby Monster"(dvi, pdf)

Putnam Exam:

• My solutions to the 1988 Putnam Exam (dvi, pdf).
• The 1998 Putnam Exam (dvi, pdf). No solutions yet.

Other interesting problems:

• Crux Mathematicorum

  • A simple solution to a Crux Mathematicorum challenge problem involving products of transpositions (dvi, pdf).
• A strange recursive sequence (dvi, pdf).
• An optimal fence (dvi, pdf).

Problem and exercise solutions:

• Algebraic Number Theory
  • Exposition of Cassels' article on global fields
  • Exposition of Humphrey's book on arithmetic groups
  • Exposition of a paper of Skorobogatov
  • Rational Triangles and a Family of Quadratic Twists
• Group Theory
  • A Graph-Theoretic Interpretation of Primitivity
  • Some Results on Highly Transitive Permutation Groups
  • Simplicity of A_n
  • Simplicity of PSL
• Modular Forms
  • Surjectivity of the Map SL_n -> SL_n (mod N)
• Humphreys, Introduction to Lie Algebras and Representation Theory
  • Section 1
  • Section 2
  • Section 3
  • Section 4
  • Section 5
• Kahn, combinatorics exercises
• Diamond, modular forms exercises
• Iwaniec, analytic number theory exercises
• Hida, L-functions
• Ireland & Rosen, Number Theory
• Iwaniec, Automorphic Forms
• Marcus, Number Fields
• Wheeden, Measure Theory

Doctoral qualifier problems:

• Berkeley
• Harvard
• Rutgers