The contraction mapping theorem
The fundamental theorem of algebra via multivariable calculus
Probability distributions and maximum entropy
Lp spaces for 0 < p < 1
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