Onan7572

The purpose of this document is to comprehensively view the area of elliptic curves within algebra for exam preparations. This text explains in detail many problems which usually come in tests related to elliptic curves: explanation of the group law, addition formula of two complex points, Mordell-Weil theorem, application to number theory and cryptography. The paper gives an excellent understanding of the Weierstrass equations defining elliptic curves and problem-solving over finite fields. Thi...

This document provides a clear-cut solution to a minimization problem in stochastic control theory. It details with much clarity how to apply the Euler-Lagrange equation to minimize a functional and how to solve the differential equation arising from it by using the boundary conditions. The step-by-step explanation makes it easy for readers to understand the process from finding the general solution to using boundary conditions, leading to the correct answer. This solution has very clear and ...