Gallery — Math

This is a cheatsheet made for the final exam of Berkeley Physics 137B. It mainly covers chapters from Variational Method to the end (except for Adiabetic Approximation).

Section 6 solution

El sistema axiomático de los números reales. Los números reales forman un conjunto denotado por ℝ, provisto de dos operaciones: la adición (+), la multiplicación (⋅) y una relación de orden (<) “menor que” que verifica los siguientes tres grupos de propiedades básicas (axiomas).

Demonstração do teorema de Morley

Template for the class practice 6

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!

Homework 2 for Discrete Math at CU Boulder in Summer 2019

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