Julian Schnidder

As a mathametician by training I continue to be interested in this field.

Subjects

Optimization

In numerical optimisation we solve this problem $$\underset{x\in X}{\min }f(x)$$ where $f$ is the objective function and the set $X$ can be modelled by other functions, such that they give the suitable conditions. The elements can be very general and thus mathematical optiimisation can be applied in many circumstances (or the problem can be transformed into a form, that is amenable to it).

My special interest is in derivative-free optimisation, where the objective function $f$ does not need to have derivatives.

Topology and Geometry

To compensate for the applicability, my pet subject in mathematics is topology and geometry. Some actors call algebraic topology "abstract nonsense".

An interested reader may form an own oponion with a textbook like the one by Allen Hatcher.

Societies

Here are the societies that I am a member of

SMS

The Swiss Mathematical Society provides a weekly digest of events of interest at Swiss universities.

EMS

The European Mathematical Society has a wider vantage point. They feature severeal journals and books at their publishing house and a free magazine.

Software

Albeit most of the work in mathematics takes place in the mind, software is a useful tool in authering and computations. And with the increase in performance of modern computers mathematical computations may help to generate hypotheses. This as well coined the term of experimental mathematics as a valid approach in doing mathematics.

For performing such computations I use the following solutions:

Octave

With this software, that is wiedely compatible with another software solultion, I performed numerical mathematics, numerical optimisation in particular.

Julia

is the rising star in open source numeical computation environments. It is fast an easy to use and more and more packages are available.

SymPy

For easy symbolic manipulations, SymPy is handy. It is implemented purely in Python including its single dependency mpmath.

SAGE

If there is the need for more involved symbolic computations, SAGE is my choice (despite it being a tad slow).

Due to the complexities in mathematical notation, commonly used word processors are difficult to use in this domain. Thus LaTeX has become the lingua franca. My choice of an editor for LaTeX is TeXstudio. And for this page, MathML (partially generated from LaTeX using TeMML) is used.

Fortran

Despite all the software solutions that are available for doing numerical computation, Fortran has stood the test of time thanks to excellent libraries like BLAS and LAPACK and is commonly used in engineering. Thus decades of know how is accumulated in the Fortran ecosystem. And with the recent efforts in modernising this language, it has become easier in use. Why not try it for yourself?

Python

Being a very popular programming language, Python offers a good selection of libraries for scientific computing. Frequently used are NumPy for matrix computations, SciPy for its collection of higher level algorithms, Matplotlib for data visualisation, pandas for handling data, the aforementioned SymPy, and other libraries to add functionality.