I will discuss some of the relationships between ODE IVPs, usually solved by marching, and ODE BVPs, usually solved by global discretizations.
Prime numbers have fascinated mathematicians since there were mathematicians to be fascinated, and the Prime Number Theorem is one of the crowning achievements of the nineteenth century. The theorem answers, in a precise form, a seemingly basic question: how many prime numbers are there?
We will explore the many guises under which groups of 2x2 matrices appear, such as isometries of the hyperbolic plane, mapping class groups and the modular group. Along the way we will learn some interesting and perhaps surprising facts.
Modern software allows us to draw symbols (such as Chinese characters, or mathematical symbols) that the computer will then recognise and turn into type. How can these systems be improved, so that they run faster and more accurately?
