Methods without saturation in computational mathematics

Methods and Problems of Computational Mathematics

Computational mathematics being part of mathematics has currently at its disposal powerful techniques for solving problems of science and engineering. The range of computational methods is so wide that it is practically impossible to cover them to a full extent in one report. A series of interesting investigations by Bellman, Greyfus et al. devoted to dynamic programming and some related proble...

Computational mathematics - models, methods, and analysis with MATLAB and MPI

Computational Discovery in Pure Mathematics

We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and theory formation programs on the body of knowledge in pure mathematics. We discuss to what extent the output from certain programs can be consid...

Notes on Computational Mathematics

This document is a summary of the notes from UW-Madison’s Math 714, fall 2012 (taught by Prof. Shi Jin) and Math 715, spring 2013 (taught by Prof. Saverio Spagnoli). This summary was written by and for me, so a lot may be unclear to others. If you are reading this and are not me, email me with questions: [email protected]. I probably can’t answer them, but then again you probably aren’t g...

Mathematical Modeling / Computational Mathematics

My research is focused on mathematical modeling in the interdisciplinary areas of materials science and crystal growth and on development of advanced computational methods for tracking material/fluid surfaces and interfaces. Primarily, I am interested in modeling formation of a micro(nano)structure arrays as a result of the morphological (shape) instabilities of a solid film surfaces, material ...