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Advanced mathematical analysis MT3041

Half Course

This half course is a course in real analysis, designed for those who already know some real analysis (such as that encountered in course MT2116 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.

Prerequisite

If taken as part of a BSc degree, courses which must be passed before this half course may be attempted:

  • MT2116 Abstract mathematics.

Topics covered

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
  • Differentiation
  • The topology of Rn
  • Metric spaces
  • Uniform convergence of sequences of functions

Learning outcomes

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.

Assessment

Unseen written examination (2 hrs). 

Essential reading

  • Bartle, R.G. and D.R. Sherbert Introduction to Real Analysis. (John Wiley and Sons: New York)
  • Binmore, K.G. Mathematical Analysis: A Straightforward Approach. (Cambridge University Press: Cambridge)
  • Bryant, Victor Yet Another Introduction to Analysis. (Cambridge University Press: Cambridge)

Course information sheets

Download the course information sheets from the LSE website.