| Lecturer: | Professor Martin Anthony |
| Room: | B311, Columbia House |
| E-mail: | m.anthony@lse.ac.uk |
| Office Hours: | Please see the office hours page |
Lectures and Classes
This is a half-unit course. Lectures will take place in the Michaelmas term and there will also be revision lectures in the Summer term.
Classes start in Week 2, and run until the first week of Lent term (inclusive).
See the Timetables website for more details: http://www.lse.ac.uk/admin/timetables/confirmed/module_sessional/ma/6.htm
Exercises
Exercises will be distributed in lectures, and will also be available via this website. It is very important that you attempt all the assigned exercises, and hand in work to your class teacher by the arranged time. Work handed in will be marked, graded, and returned within one week. Answers to all the exercises will be made available after the work has been discussed in class.
Books
No single book I know adequately covers the whole course. The following books provide useful reading for various parts of the course.
I shall provide hand-outs. These will not contain all the details of proofs, but will otherwise be fairly complete.
Asssessment
There will be a formal 2-hour examination in the Summer term. Past papers can be obtained below.
Overview
What is this course? This is a course in real analysis, designed for those who already know some real analysis (such as that encountered in MA103, Introduction to 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.
What will it achieve? After studying this course, you 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 economics and other areas. For example, as we shall see, compactness is a very important idea in optimisation. The course will also enable you to set the real analysis you previously encountered in a larger context, to see that there is a 'bigger picture'. More generally, a course of this nature, with the emphasis on abstract reasoning and proof, will help you to think in an analytical way, and be able to formulate mathematical arguments in a precise, logical manner.
Who should take it? Most students taking this course will have already taken Introduction to Abstract Mathematics (MA103) or some other course based on formal definitions and proofs and, ideally, covering the concept of limit: indeed, such a course is a formal pre-requisite. Students who have not covered the notion of a limit may be able to take this course after carrying out some preliminary reading (chapters 1 to 3 of Bryant's 'Yet Another Introduction to Analysis', for example), but familiarity with proof techniques really is essential. Some of you (for example, B.Sc Mathematics and Economics students) will be required to take this course: others will simply be interested in learning more about real analysis.
Aims The course is designed to:
We study the formal mathematical theory of:
Lectures, Classes and Exercises
Lecture notes will be given out, but these are not substitutes for the lectures, where full proofs, extra examples, and background information will be given. Exercises will be assigned in lectures on a weekly basis, and will also be available via this website. It is very important that you attempt all the assigned exercises, and hand in work to your class teacher by the arranged time. Working through examples is an important way of ensuring you understand key concepts and techniques. Work handed in will be marked, graded, and returned within one week. Answers to all the exercises will be made available after the work has been discussed in class.
Office Hours
The class teachers have office hours, and you should certainly consult your
class teacher during his or her office hour if you are having problems and think
you would benefit from one-to-one advice. If you are unable to see your class
teacher, then you should see me. If you cannot attend my office hours, then I
can see you at other times, by arrangement. Alternatively, if I am not around, call into the Maths
department office.)
Please note: students are advised not to rely too heavily on past exam papers when revising for their exams, as they can only offer a limited indication of what might be covered in a future exam. For further information, please see the guidance here: http://www.maths.lse.ac.uk/examinations_in_mathematics.html#past_papers
Exam paper of
2006
Exam paper of
2007
Exam paper of
2008
Solutions
to exam paper of
2008