Linear Algebra I - A collection of exercises and solution aimed for the first semester.

Linear Algebra II
- A collection of exercises and solution
aimed for the course Linear Algebra II.

Here is a phone version.

Mathematica - Some tips for researchers using Mathematica.

Current address: per.w.alexandersson@gmail.com or per.alexandersson@math.uzh.ch.

#About me
Since February 2014, I am working as a a post-doc, at Universität Zurich, Schweiz.
My field of research is representation theory and combinatorics, more specifically,
polynomials given by structure constants (Kostka-coefficients, characters of the symmetric group)
and Jack generalizations of these.
In spring 2013 I defended my thesis titled _Combinatorial Methods in Complex Analysis_,
where Boris Shapiro was my primary advisor. My research interests are mainly combinatorics,
complex analysis and algebraic geometry.
My research my favorite research tools are _Mathematica_, _OEIS_, _FinstStat_, _MathOverflow_, _WolframAlpha_ and _Google_.
I am also a bit interested in special polynomials,
for example real-rooted polynomials, and polynomials obtained from
combinatorial statistics.
Finally, I must admit that I have a soft spot for discrete dynamical systems,
machine learning, neural networks and cellular automata.
##List of publications
* Gelfand-Tsetlin patterns, integrally closedness and compressed polytopes, (2014), (submitted), (arxiv)
* A combinatorial proof of a Kostka analogue of the K-saturation theorem, (2013), (to appear in Discrete Mathematics), (arxiv)
* (With B. Shapiro) Around Mutlivariate Schmidt-Spitzer Theorem, (2013), (accepted, Lin. Alg. and its Appl.), (arXiv)
* Stretched skew Schur polynomials are recurrent, *Journal of Combinatorial Theory, Series A 122C (2014) 1-8*, (electronic version)
* Schur polynomials, banded Toeplitz matrices and Widom's formula, *Electr. Jour. Comb. 19, No.4 (2012)*
* (With B. Shapiro) Discriminants, symmetrized graph monomials, and sums of squares, *Experimental Math. 21 No. 4 (2012) 353-361*
* On eigenvalues of the Schrödinger operator with an even complex-valued polynomial potential, *CMFT 12 No.2 (2012) 465-481*
* (With A. Gabrielov) On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential, *CMFT 12 No.1 (2012) 119-144*
##Other projects
In my spare time, I tinker a bit with a flame fractal renderer written in Java.
You can browse the source on Sourceforge.
On this website, you will also find several of my smaller projects.
They revolve around
* Mathematica
* LaTeX
* Programming
* Generative art
* Various texts related to mathematics
##About this website
I use MathJax for rendering mathematics, and a Markdown converter for the contents.
The server side code is written in PHP.
All in all, I use the following syntaxes: *HTML, Javascript, PHP, CSS3, Markdown* and *LaTeX*.