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Description

The course aims to:

• Provide a basic introduction to calculus and basic statistical methods
• Provide an introduction to mathematical and computational methods for modelling applications
• Introduce general conceptual frameworks for the problems and issues of developing forward and inverse models
• Provide practical analytical and numerical examples for both forward and inverse modelling, particularly linear v non-linear, approaches to solving and generic aspects of implementation
• Provide example applications of the techniques covered, including use of Jupyter Python notebooks
• Cover generic issues arising in application of analytical and numerical approaches including the discretisation, detail vs computation time, stochastic processes etc.
• To provide exposure to numerical tools that are used in a wide range of modelling applications, including an introduction to Bayes Theorem and Monte Carlo methods among others.

The module will provide an introduction to a range of fundamental concepts and principles for handling and manipulating data. The first half of the module (taught with CEGE) provides a basic introduction to stats and linear algebra, and important basic concepts; the second half covers slightly more advanced applications of methods and tools for data analysis. The module will cover:

• Elementary differential and integral calculus and its applications (equations of motion, areas and volumes etc),
• Linear algebra and matrix methods, including computational issues (decomposition for eg) and generalised linear models
• Differential equations and applications
• Overview of statistical methods including an intro to Bayes Theorem
• Numerical methods, model fitting, numerical optimization Monte Carlo and Metropolis-Hastings

The main sessions include:

• Introduction to calculus methods
• Introduction to linear algebra, matrices
• Statistics and further statistics
• Least Squares and further least squares
• Differential equations
• Introduction to Bayes Theorem
• Model selection
• Linear & non-linear model inversion
• Monte Carlo methods and related numerical tools,

Mode of study

In person

Useful pre-requisite knowledge

This course requires some basic mathematical background, approximately high-school level e.g. algebra, geometry, trigonometry, basic stats. The module moves beyond that to introducing calculus and more advanced methods. If you come a background of physics, maths or computer science or engineering, you should know some / much of this material but it ought to provide a useful refresher. For other students, this module will bring you up to a level where you have the core analytical and numerical skills to carry out data analysis and modelling tasks to help throughout your MSc as well as providing valuable transferrable skills. If you are unsure about your background, contact Prof. Disney and he can discuss this with you in relation to your background.

Transferrable career skills developed in the module

• Critical thinking: ability to assess data and ideas
• Statistical / quantitative analysis: introduction to simple physical principles, computational methods, tools and practical skills in implementing in code (via Jupyter Python notebooks)
• Modelling skills: data analysis and display, model fitting, parameter estimation, model uncertainty and sensitivity analysis

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