MT3041 Advanced mathematical analysis (half course)
MT2116 Abstract mathematics.
This is a course in real analysis, designed for those who already know some real analysis (such as that encountered in course 116 Abstract Mathematics). The emphasis is on functions, sequences and series in n-dimensional real space. The general concept of a metric space will also be studied.
After studying this course, students should be equipped with a knowledge of concepts (such as continuity and compactness) which are central not only to further mathematical courses, but to applications of mathematics in theoretical economics and other areas. More generally, a course of this nature, with the emphasis on abstract reasoning and proof, will help students to think in an analytical way, and be able to formulate mathematical arguments in a precise, logical manner.
Specific topics covered are:
- series of real numbers;
- series and sequences in n-dimensional real space Rn;
- limits, continuity and derivatives of functions mapping between Rn and Rm;
- closed and open sets, compactness and other 'topological' ideas in Rn;
- metric spaces
- uniform convergence of sequences of functions.