Per Alexandersson

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

(pdf) Linear Algebra II - A collection of exercises and solution aimed for the course Linear Algebra II.
Here is a phone version.

(pdf) Mathematica - Some tips for researchers using Mathematica.

Note: these files are updated frequently and I am happy to get suggestions on improvements.


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#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*.