ME306: Real Analysis

Real Analysis is an area of mathematics that was developed to formalise the study of numbers and functions and to investigate important concepts such as limits and continuity.

These concepts underpin calculus and its applications. Real Analysis has become an indispensable tool in a number of application areas. In particular, many of its key concepts, such as convergence, compactness and convexity, have become central to economic theory.

This course covers the main aspects of real analysis: convergence of sequences and series and key concepts, including completeness, compactness and continuity, from the particular settings of real numbers and Euclidean spaces to the much more general context of metric spaces.

The course is particularly suitable for students who want to bolster their mathematical background as preparation for postgraduate study in economics and related areas and for professionals who want to follow recent developments in economic theory.

Prerequisites: Courses on multivariate calculus and linear algebra, both at intermediate level. In addition, students need to be familiar with methods of proofs and basic set theory. The course will begin with a brief review of this material. 

Level: 300 level. Read more information on levels in our FAQs

Fees: Please see Fees and payments

Lectures: 36 hours

Classes: 18 hours

Assessment: A midsession exam during the second week of the course and a comprehensive final exam on the Friday of the third week.

Typical credit: 3-4 credits (US) 7.5 ECTS points (EU)

Please note: Assessment is optional but may be required for credit by your home institution. Your home institution will be able to advise how you can meet their credit requirements. For more information on exams and credit, read Teaching and assessment

This course will suit you if you want to develop your mathematical skills. You will learn how to do rigorous proofs and you will understand the key concepts of Real Analysis. These concepts play a central role in Economic Theory and in other domains. 

After completing this course, students will:

• Have gained a thorough grounding in modern Real Analysis, including key concepts such as convergence, continuity, completeness and compactness
• Be able to comprehend and critically reflect on mathematical statements and their proofs and to write their own formal proofs of mathematical results
• Have developed a higher capacity for abstract and rigorous mathematical reasoning
• Be well-equipped to study advanced applications of Real Analysis in disciplines such as Economics

The design of this course is guided by LSE faculty, as well as industry experts, who will share their experience and in-depth knowledge with you throughout the course.