## Site Map

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## Mathematics will change

There is no doubt that computers/Mathematical softwares will change mathematics. Creating \seehttps ://en.wikipedia.org/wiki/Mathematical_table]{mathematical tables} was an important task for mathematicians. Now it's easy to find in formula manipulation systems such as Mathematica , Maple , Maxima (free), REDUCE (free?) etc.

Previously, in mathematics, the mathematical research on PDEs were proof that solutions exist in function space , so the mathematical results were far from application. However, nowadays, the existence of solution in the variational method means the stability of numerical calculation by FEM , and the mathematical results has become possible to get numerical calculation and visualization with computers.

Everybody may think that math is unnecessary if there is a computer, but since computers produce results even if they are not correct, people need to judge whether the calculated results are correct, and math is the only way to judge by human. The best way is to program with mathematics to get results such as formulas and numerical result. We may get results just by studying mathematics without mastering programming languages or computer operations, because at least mathematics can be understood by humans.

## Paper & Pencil and Library

We now have a tablet and can carry a lot of e-books/papers with us to write. Five years ago, as an experiment, I saved e-books/papers(pdf) only on an iPad without using personal computer, wrote them with GoodNotes , Noteshelf , PDF Expert , etc., and created slides (beamer) at a travel destination using TeXpad . The problem is that it's so convenient that we spend more time using tablets besides math.

## Finite Element Analysis

The finite element method (FEM) is one of the most common numerical methods for boundary and initial value problems of PDEs and can be solved in any region of arbitrary shape. It has a very high affinity for mathematics (variational method)

### FreeFEM

I have used FreeFEM , that is finite element analysis tool developed by J.L. Lions Laboratory of Pierre et Marie Curie University (UPMC), which can mathematically solve the boundary value problem of partial differential equations by finite element method (FEM). FreeFEM need not computer language such as Fortran , C/C++. so on,and has its own language based on the variational method and FEM.
FreeFEM is not a black box, but has instructions to extract simultaneous equations generated by meshes, finite element spaces, and boundary value problems. It can be used by beginners of the finite element method as a teaching material to understand the mechanism of the finite element method, and by researchers to realize functions not found in commercial software. In 2018, Sorbonne University was created by the merger of UPMC and Paris-Sorbonne University. Isn't Japan the only storm of university reorganization?