Introduction to Mathematica

Julius

EIMI

Please register! :)

Abstract

This course will provide a working introduction to Mathematica, a symbolic computing software which has become ubiquitous in modern Physics and Mathematics research. The format will be of ninety minute sessions which will mainly focus on problem solving using Mathematica.

Plan

Basics

During the roughly the first two weeks, we will mainly focus on understanding how to use Mathematica. No prior programming experience is required, however such experience can be useful. The goal is to make ourselves comfortable with the main syntax and program-flow of the language. For the rest of the course, we will look at how to use Mathematica to solve various problems from mathematics and physics.

Numerical Analysis

We will learn how to use Mathematica as a tool for numerical analysis. The goal of these rougly four weeks is to and learn how to implement numerical methods for algebraic equation solving, differentiation, integration, and solving differential equations. We will learn how to maximise precision and efficiency in our code.

Non-commutative Algebra

We will spend the next roughly two weeks learning how to implement and work with non-commutative algebraic problems using Mathematica. The goal at the end of these weeks would be to implement the Yang-Baxter equation to derive the albegraic Bethe Ansatz for the Heisenberg spin-chain. Then we will implement the Baxter TQ-relation and compare the efficiency of the two approaches for diagomalising Hamiltonian operators, compared to direct diagonalisation.

Matrix Models

From the roughly eighth week onward, we will study Matrix Models, in a similar spirit to the course of Evgeny Sobko on Matrix Models, 2D Gravity and non-critical Strings. We will spend roughly six weeks studying Matrix Models, and solve problems having a large overlap with his course. Problems will be inspired also from the Mathematica Summer School on Theoretical Physics [1]. Finally we will also tackle problem from recent advances in the subject e.g. the Matrix Bootstrap [2].

References

[1] 8th edition (2016) of the Mathematica Summer School on Theoretical Physics - Random Matrix Theory and applications (http://msstp.org/?q=node/302)

[2] "Bootstraps to strings: solving random matrix models with positivite", H. Lin, 2020 (https://inspirehep.net/literature/1781501)