Overview

Description

CALENDAR DESCRIPTION:

The topics included in this course will vary from term to term depending on faculty availability and student interest.

COURSE DETAILS:

The modelling and analysis of data is becoming an important area of modern applied mathematics. In this course we will introduce a variety of mathematical approaches to data which form part of the growing domain known as data science. This course is in two halves, centred first on machine learning and then on complex networks. We will begin with an introduction to the R language and to visualisation and exploratory data analysis. We will describe the mathematical challenges and ideas in learning from data. We will introduce unsupervised and supervised learning, starting with the theory of common used methods (for example, decision trees, random forests, support vector machines). We will apply this foundational toolkit to real datasets on topics ranging from the Titantic to heart disease and voting patterns. Moving to networks, we will discuss model graphs used to describe social and biological phenomena (including Erdos-Renyi graphs, small world and scale-free networks). We will illustrate how networks can be a useful framework to model and analyze data. We will define ways to characterize data-derived networks at the node level (for example page rank centrality) and more globally (e.g. modularity and other properties). Finally, we will discuss connections between graph-based descriptions of data and learning.

This course focuses on the mathematics behind a suite of tools for data. It does not focus on obtaining data (web scraping), data cleaning and imputation, nor on the implementation of algorithms; we make use of R packages in which algorithms are available.

Grading

Materials

RECOMMENDED READING: