Expository papers

These were written up for various reasons: to accompany a talk for a (mathematically) general audience, to hand out as part of some notes in a course, or for some other purpose that I have since forgotten. If you find typographical or other errors in these files, please let me know.

Algebra

     The Hurwitz theorem on sums of squares (by linear algebra or by representation theory )

     Pfister's theorem on sums of squares

     The Artin-Schreier theorem

     Relativistic addition and group theory

     The fundamental theorem of algebra via linear algebra

     Simultaneous commutativity of operators

     Representations of finite abelian groups

     The degree may not divide the size of the group

Number theory

     Heuristics for prime statistics

     Quadratic reciprocity in odd characteristic

     Quadratic reciprocity in characteristic 2

     Rings of integers without a power basis

     A Non-free Relative Integral Extension

     Ideal Classes and SL2

     Ideal Classes and Matrix Conjugation

     Totally ramified primes and Eisenstein polynomials

     Kummer's lemma

     Fermat's last theorem for regular primes

     The character group of Q

     The Existence of Frobenius Elements (aprés Frobenius)

     Carlitz extensions

     Euclidean proofs of Dirichlet's theorem

     Invariants of the splitting field of a cubic, I

     Invariants of the splitting field of a cubic, II

     Invariants of the splitting field of a cubic, III

     Invariants of the splitting field of a cubic, IV

     Invariants of the splitting field of a cubic, V

Analysis

     The contraction mapping theorem

     The fundamental theorem of algebra via multivariable calculus

     Probability distributions and maximum entropy

     Lp spaces for 0 < p < 1