A Rigorous Introduction to the Reals
A rigorous construction of the field of real numbers: the unique (up to isomorphism) completely ordered field with the least upper bound property; along with various formulations of completeness and with a postlude on the measure of sets.
A paper on some curious properties of rectangular circumhyperbolae of triangles, developed primarily without the use of barycentric or trilinear coordinates.
Euler Circle Spring Paper: Čebotarev Density Theorem
In this paper, we do exactly what the title implies: prove the Čebotarev Density Theorem. This is an extremely valuable theorem because it is a vast generalization of Dirichlet's Theorem on primes in an arithmetic progression. Our theorem goes even further to the case of other number fields; we will show that the prime ideals in an imaginary quadratic field K are virtually equidistributed among the conjugacy classes of Artin symbols in the Galois group of a Galois extension L over K. Note that L need not be abelian over K!
Version 1.0 (10/11/12)
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Note: This is a modified version of the original template by Dana Ernst.
Sarah Wright (based on the a original by Dana Ernst)