Component
Integrated Master in Mathematics: Mathematics options

# Year 2, Component 07

Option(s) from list
MA205-5-SP
Optimisation (Linear Programming)
(15 CREDITS)

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.

MA209-5-SP
Numerical Methods
(15 CREDITS)

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.

MA213-5-SP
Riemann Integration and Lebesgue Measure
(15 CREDITS)

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.

MA222-5-SP
Analytical Mechanics
(15 CREDITS)

This module concerns the general description and analysis of the motion of systems of particles acted on by forces. Assuming a basic familiarity with Newton's laws of motion and their application in simple situations, you will develop the advanced techniques necessary to study more complicated, multi-particle systems. You will also consider the beautiful extensions of Newton's equations due to Lagrange and Hamilton, which allow for simplified treatments of many interesting problems and provide the foundation for the modern understanding of dynamics.

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