Environmental Measurement, Assessment and  Law (BENV0013)

The purpose of environmental policy is to improve the nature and quality of the use of the environment and its resources. In order to know whether or not this has taken place, the environmental outcomes before and after the policy have to be measured; compliance with legal norms and regulations is necessary for the environmental policy to be effectively designed and implemented; and the effect of the policy has to be assessed before it is put in place (ex ante) and evaluated after it has had time to take effect (ex post). The module will present some of the legal foundations of environmental policy and the main methods by which both environmental impacts, and the effects of environmental policy, are measured.

This module will introduce the concepts and theories of Stochastic calculus and the use of Monte Carlo techniques for the solution of high dimensional problems...

Stochastic Calculus and Uncertainty Analysis (BENG0091)

This module will introduce the concepts and theories of Stochastic calculus and the use of Monte Carlo techniques for the solution of high dimensional problems prevalent in modern Engineering (and Finance) applications. Students will be introduced to concepts and techniques in (quasi-) random number generation and the sampling of multidimensional spaces. This will provide a link between stochastic calculus and uncertainty and (global) sensitivity analysis.

The aim of this module is to provide the core mathematical, numerical and analytical skills that underpin the study of complex high-dimensional phenomena and/or phenomena with uncertain, unknown or random aspects. A link between stochastic calculus and the techniques discussed in the first two modules of this Minor will be provided in the form of uncertainty (sensitivity) analysis. An overview of state-of-the-art sensitivity analysis methods will be presented and their suitability to analyze “real-life” problems covering a range of topics (Engineering, Environmental Safety, Finance) will be discussed.

On successfully completing the module, students will be able to:

Recognize the connections between stochastic processes, stochastic calculus and how stochasticity is embedded in real-life applications;
	Understand the basic concepts of Stochastic Calculus
	Perform integration of simple stochastic processes
	Perform integration of continuous stochastic processes
	Understand the operating principles and limitations of Random Number Generators
	Identify appropriate methods for and perform Sensitivity Analysis on real-life models sourced from various disciplines
	Present and interpret quantitative results in effective and appropriate ways to varied audiences, including non-mathematical or engineering audiences.