# Teaching

Wolfram currently teaches the following courses at Imperial College Business School:

#### BA1803: Optimisation and Decision Models (MSc Business Analytics)

This module provides a rigorous introduction to the theory and applications of linear, discrete and nonlinear (convex) optimization. In terms of theory, we will cover what it means to “solve” an optimization problem, the structural properties of optimization problems that enable (or preclude) their efficient solution, as well as state-of-the-art algorithms used to solve them. From a practical viewpoint, we will discuss the formulation of decision-making problems as optimization problems, together with commonly employed reformulation “tricks”, as well as applications in machine learning, operations management and finance.

Topics covered in this module include:

• Linear Optimization: formulating decision-making problems as linear programs; algorithms for solving linear programs; sensitivity analysis; duality theory; examples.
• Discrete Optimization: formulating decision-making problems as mixed-integer linear programs; logical constraints; algorithms for solving mixed-integer linear programs; examples.
• Nonlinear Optimization: introduction to convex analysis; optimal it’s conditions for unconstrained and constrained nonlinear problems; algorithms for solving nonlinear problems; examples.

#### BA1806: Introduction to Machine Learning (MSc Business Analytics)

This module provides an introduction to the theory, the state-of-the-art algorithms, as well as some of the applications of machine learning. From a theoretical perspective, we will explore the assumptions needed to learn concepts beyond past observations. In terms of algorithms, we will cover some of the most popular supervised and unsupervised learning schemes. Our discussion will be complemented by real-life data sets from finance, IT, biology and sports analytics.

Topics covered in this module include:

• Generalization Theory: when is learning possible?; a simple generalization bound.
• Evaluating Predictive Performance: the bias-variance tradeoff; training, validation and test sets; performance measures for regression, classification and ranking problems; oversampling; cross-validation.
• Nearest Neighbours Methods: nearest neighbours methods for classification problems; nearest neighbours methods for regression problems; the curse of dimensionality.
• Naive Bayes: Bayes’ Theorem revisited; exact Bayes classifiers; class-conditional independence; naive Bayes classifiers;
• Classification and Regression Trees: divide-and-conquer and greedy search; purity measures (entropy, Gini index) and information gain; classification trees; regression trees; pre- and post-pruning; bagging, boosting and random forests.
• Cluster Analysis: similarity measures between samples and clusters; data normalization; hierarchical clustering; k-means clustering; convergence of k-means clustering.
• Support Vector Machines: linear separation through hyperplanes; hard-margin SVMs; the kernel trick and Mercer’s condition; soft-margin SVMs; SVMs for more than two classes. (If time permits).

#### BS0929: Business Analytics (MSc Management)

This module provides an introduction to prescriptive analytics, which is the study of advanced analytical and computational methods to support informed managerial decision-making based on data. The principal idea of prescriptive analytics is to formulate managerial decision problems as mathematical problems, which can subsequently be solved with analytical or numerical techniques. Typical applications include revenue management (e.g. revenue-maximal pricing of hotel rooms and airline tickets), logistics (cost-effective transport of products in a supply chain), production planning (e.g. increase of production output or reduction of late deliveries) and financial portfolio management (construction of asset portfolios with a good return/risk tradeoff).

Topics covered in this module include:

• Decision Trees: payoff tables and decision criteria; decision trees; sensitivity analysis.
• Linear Optimization: formulating decision-making problems as linear programs; algorithms for solving linear programs; sensitivity analysis; examples.
• Discrete Optimization: formulating decision-making problems as mixed-integer linear programs; logical constraints; algorithms for solving mixed-integer linear programs; examples.
• Nonlinear Optimization: introduction to convex analysis; the Markowitz portfolio problem. (If time permits.)

#### Executive Education

Wolfram occasionally teaches on Executive Education programmes in London, Abu Dhabi, Jeddah and Ryadh.

Teaching is a very important–and perhaps the most impactful–part of our academic life, and as a group we take great pride in it. We are therefore very happy when our efforts do not go unnoticed: Our post-doctoral researchers regularly receive the highest marks in student evaluations, and Wolfram has received Imperial College Business School Dean’s Teaching Awards in 2013/14 and 2014/15, nominations for Imperial College’s Student Academic Choice Awards in 2015/16, 2016/17, 2017/18 and 2018/19, as well as a Teaching Excellence Award for MSc and MRes Core Module Teaching in 2018.