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MATH6624 - Topics in Mathematical Analysis

The aim of the course is to teach students the tools of modern analysis as it related to further study in mathematics, especially numerical analysis, differential equations, functional analysis, topology, stochastic processes. This course is intended to develop the ability of the students to work with abstract ideas.

Complex Variables

The course develops the properties of the complex number system, treated as a generalisation of the real number system. We explore the parallel analysis that results, with a particular emphasis on differentiability, analyticity, contour integrals, Cauchy’s  theorem, Laurent series representation, and residue calculus.

What is the content of the programme?

With the support and guidance of highly-qualified tutors, students work intensively in groups of no more than six students on the following topics:



1.    Calculations and Calculators;

2.    Fractions, Decimals and Percentages;

3.    Algebra - Variables and Expressions;

4.    Algebra - Equations;

5.    Algebra - Indices;

6.    Logarithms and exponentials;

7.    Trigonometry;

8.    Functions and Graphs;

9.    The Straight Line;

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