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Advanced mathematical analysis – LSE
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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 and continuity of functions mapping between Rn and Rm
- The topology of Rn
- Metric spaces
- Uniform convergence of sequences of functions
If you complete the course successfully, you should be able to:
- Have a good knowledge of the mathematical concepts in real analysis
- Be able to use formal notation correctly and in connection with precise statements in English
- Be able to demonstrate the ability to solve unseen mathematical problems in real analysis.
- Be able to prove statements and to formulate precise mathematical arguments.
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