MA Public Opinion and Political Behaviour
BSc Mathematics with Physics options

Year 2, Component 07

Option(s) from list
Abstract Algebra

The module introduces you to the key abstract algebraic objects of groups, rings and fields and develops their fundamental theory. The theory will be illustrated and made concrete through numerous examples in settings that you will already have encountered.

Optimisation (Linear Programming)

Are you able to solve a small linear programming problem using an appropriate version of the Simplex Algorithm? Learn to formulate an appropriate linear programming model and use the MATLAB computer package to solve linear programming problems. Understand the methods of linear programming, including both theoretical and computational aspects.

Numerical Methods

How can we solve a problem that does not have a nice pen-and-paper solution? How do we ensure our computers use the available data efficiently to deliver accurate and reliable results? Understand the practical techniques for carrying out numerical computations on a range of mathematical problems. Build your knowledge of mathematical computing. Learn how to implement and execute algorithms in Matlab.

Riemann Integration and Lebesgue Measure

We learned integration in Calculus module in the first year, and we can integrate most of the functions with hand or computers. For example, we know very well that the integral of 1 is x+constant. Why is this the case? Do we just made this up and ask you to memorize? What does integral really mean geometrically? We know it is the area below the curve. But why is this case? Can we see this for complicated functions? We know that integral and derivate are dual (or inverses) to each other, how can we see this? Is there any function whose integral does not exist? Real life application: suppose we want to find the average temperature of Colchester in 2020. We may look at the temperature every day and then take the average. We can improve this by looking the temperature at every hour during the year and find the average. Can we make it any better? How is this related with integral? This module aims to answer all these questions.

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