Start Math 114 Fall 2016

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.

Linear Algebra for teachers - A collection of exercises and solution plus some short notes on theory.
Here is a phone version.

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

Me

#About me I recently started as a postdoc at KTH, Stockholm, working with Svante Linusson. Before that, (2015-2017) I worked as a postdoc at University of Pennsylvania, with Jim Haglund, funded by a grant from the Knut and Alice Wallenberg foundation. In 2014, I worked as a postdoc at Universität Zurich, Schweiz with Valentin Féray. 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, as well as chromatic symmetric functions, LLT polynomials and so on. 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 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 tilings, discrete dynamical systems, machine learning, neural networks and cellular automata. ##List of publications * *(W. Mehtaab Sawhney) Properties of non-symmetric Macdonald polynomials at $q=0$ and $q=1$*, (arxiv) * *(W. Greta Panova) LLT polynomials, chromatic quasisymmetric functions and graphs with cycles*, (submitted) (arxiv) * *(W. Mehtaab Sawhney) A major-index preserving map on fillings*, Electronic Journal of Combinatorics **24**, No.4 (2017) * *Polytopes and large counterexamples*, Experimental Mathematics, (2017) 1–6 * *Non-symmetric Macdonald polynomials and Demazure-Lusztig operators*, (submitted), (arxiv) * (With. V. Féray) *Shifted symmetric functions and multirectangular coordinates of Young diagrams*, Journal of Algebra **483** (2017), 262–305 * *Polynomials defined by tableaux and linear recurrences*, Electronic Journal of Combinatorics **23**, No.1 (2016) * *Gelfand–Tsetlin polytopes and the integer decomposition property*, European Journal of Combinatorics, **54**, (2016) * *A combinatorial proof the skew K-saturation theorem*, Discrete Mathematics (2015), 93–102 * (With B. Shapiro) *Around Mutlivariate Schmidt-Spitzer Theorem*, Linear Algebra and its Applications **446** (2014), 356–368 * *Stretched skew Schur polynomials are recurrent*, Journal of Combinatorial Theory, Series A **122** (2014) 1–8. * *Schur polynomials, banded Toeplitz matrices and Widom's formula*, Electronic Journal of Combinatorics **19**, No.4 (2012) * (With B. Shapiro) *Discriminants, symmetrized graph monomials, and sums of squares*, Experimental Mathematics **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* and other things related to mathematics. ##About this website I use MathJax for rendering mathematics and a Markdown converter for the contents.