Real Analysis is the area of mathematics dealing with real numbers and the analytic properties of real-valued functions and sequences. It studies concepts such as continuity, differentiation and integration and it can be roughly described as rigorous calculus with real numbers. In this course we shall also develop concepts from calculus in more abstract settings such as 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 introduce students to concepts of modern analysis such as continuity, metric spaces, compactness, convexity and integration and will show the connections to economic theory.This course will be taught in three components:1. Foundation (11-15 August 2014) - 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 (18-22 August 2014) - 5 days of lectures and classes (on campus) 3. Branches (25-29 August 2014) - 4 lectures each on either Integration or Convexity, depending on which branch each student chooses. For full course information, please see the course website.
Period
11-08-2014 - 29-08-2014 (3 weeks)
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
5.0 ECTS creditsThe 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.
Course fee
GBP 1365[Convert to USD]Academic rate - available to students and staff of academic institutionsGBP 2310[Convert to USD]Standard rate
Course leader
Dr Eleni Katirtzoglou
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
Real Analysis
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Diverse
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2014-03-24, 00:00
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2025-09-29, 17:01
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Cristian Ion
