Real analysis is the area of mathematics dealing with real numbers and the analytic properties of real-valued functions and sequences. In this course we shall develop concepts such as convergence, continuity, completeness, compactness and convexity in the settings of real numbers, Euclidean spaces, and more general metric spaces.Real analysis is part of the foundation for further study in mathematics as well as graduate studies in economics. A considerable part of economic theory is difficult to follow without a strong background in real analysis. For example, the concepts of compactness and convexity play an important role in optimisation theory and thus in microeconomics. This course will be taught in two components:1. Foundation (10-14 August 2015) - this introductory part of the course will be delivered online before students arrive at LSE, and will consist of short video lectures and lecture notes and exercises. It is intended to get students up to the level of understanding required to understand the rest of the course.2. Core (17-28 August 2015) - to be delivered on campus over 9 lectures and 8 classes. Most lectures will involve the use of Class Response System "clickers" to help students think about the concepts and clarify the material covered before attempting exercises.Topics covered:Part I: Foundations- Preliminaries: revision of logic, methods of proof, set theory, and properties of real numbers- Sequences in %E2%84%9D- Infinite series in %E2%84%9DPart II: Core- Metric spaces- Continuity in %E2%84%9D and in metric spaces- Differentiation in %E2%84%9D and in Euclidean spaces- Fixed point theorems- Convex functions and sets- Separation theorems- Applications

Course leader
Dr Eleni Katirtzoglou

Target group
This course in real analysis is designed to meet the needs of economics students who are planning to study at postgraduate level. It is also suitable for mathematics and statistics students.

Course aim
This course aims to help students gain knowledge of concepts of modern analysis, such as continuity, metric spaces, convexity and integration; develop a higher level of mathematical maturity combined with the ability to think analytically; and be able to follow more advanced treatments of Real Analysis and study its applications in disciplines such as economics.

Credits info
5 ECTS The decision to award credits is at the discretion of the student's home institution. Students should always check with their home institution to confirm the number of credits that can be awarded.

Fee info
GBP 1435: Student rate - available to current university (including PhD) students.Academic staff and staff of UK charities are eligible for a reduced rate of 1,930. GBP 2425: Standard rate

Scholarships
Previous students of LSE may be eligible for a 15% discount on their tuition fees.

London School of Economics
Address: Houghton Street
Postal code: WC2A 2AE
City: London
Country: United Kingdom
Website: http://www.lse.ac.uk/study/summerSchools/Methods/home.aspx
E-mail: summer.methods@lse.ac.uk
Phone: +44 (0)20 7955 6422