MA103 Introduction to Abstract Mathematics

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Course Information for 2009/10

Timetable

Monday   12:00 - 13:00 in E171
Monday   17.00 - 18.00 in E171

This is a full unit course, with lectures in both Michaelmas and Lent Term.
There will also be revision lectures in the Summer Term

Extra Examples Sessions (optional).

Mondays 10.00 - 11.00 in NABLG08 in MT and first week of LT
Tuesdays 10.00 - 11.00 in D202 from week 2 of LT

Classes

Each student will have one class each week, starting in Week 3 of the Michaelmas Term. There will be several Class Groups. In Week 2 students can find out which group they belong to, and the time and place when their class will meet. The easiest way to find this information is via the personalised timetables in "LSEforYou".

Course materials - Moodle

A set of lecture notes for Section A of the course (Michaelmas term) is provided. This is also available on the Moodle page|. You will also find a link to a set of lecture notes used in 2008/9 for the second half of the course: these notes will be updated for the current year, and distributed to students at the beginning of Lent Term.

There are two books that are suitable as textbook for the Michaelmas Term:

• "Discrete Mathematics" by Norman L. Biggs (2nd edition, Oxford University Press, 2002)
  ISBN: 0198507178; Library code: QA76.9 M35 B59
• "An Introduction to Mathematical Reasoning - Numbers, Sets and Functions" by Peter J. Eccles (Cambridge University Press, 1997)
  ISBN: 0521597188; Library code: QA9.54 E11

The following books are recommended for background reading:

• "Numbers and Proofs" by R. Allenby; ISBN: 0340676531; Library code: QA9.54 A42
• "A Concise Introduction to Pure Mathematics" by M. Liebeck; ISBN: 1584881933; Library code: QA8.4 L72
• "Introduction to Real Analysis" by R. Bartle and D. Sherbert; ISBN: 0471321486; Library code: QA300 B28
• "Yet Another Introduction to Analysis" by V. Bryant; ISBN: 052138835X; Library code: QA300 B91
• "Elementary Linear Algebra" by H. Anton; ISBN: 0471170550; Library code: QA184 A63

Further information can be found on the Course Materials| page on Moodle.

Lectures

During the lectures, the theory will be developed and explained, proofs given, and many examples demonstrated.

In the Summer Term there will be additional lectures, mainly for revision purposes.

Extra Examples Sessions

In these weekly sessions, the lecturers will study further examples and problems illustrating the theory taught in lectures. These sessions are optional, and no new material will be taught; recordings of the sessions will be placed online.

Exercises

Exercises are set every week during the lectures on Monday. The exercises will also be available via the Moodle page|. Students are expected to hand in solutions to the exercises by the deadline set by their class teacher, to the homework boxes (on the Ground Floor of Columbia House). No late work can be accepted. The homework exercises are discussed in the classes in the following week. So the first set of exercises are given out on Monday of Week 1, and covered in the classes in Week 3. For this first week, the deadline for handing in exercises is 5pm on Wednesday of week 2. In this course, as in other courses in Mathematics, it is very important that all homework questions are attempted and handed in for grading. There is a big difference between watching other people carry out calculations and being able to do them yourself, and it is vital to get practice in the various techniques covered in the course. It is also important to hand in homework, so that feedback on it can be given.

Corrected work will be handed back and discussed as soon as possible. A complete set of solutions to the homework exercises will also be made available.

Presentation of work is a very important part of this course. It is not enough to obtain the correct answer; it is expected that the arguments used to arrive at that answer should be correct and understandable. Students are expected to explain their reasoning using proper English, and to use mathematical notation and terminology correctly.

Office Hours

The office hours are meant for any questions and problems with the course material that have not or cannot be covered in the normal lectures and classes. You are strongly recommended to make use of them.
It is expected that students utilise the office hours| of their class teacher.

Assessment

This course is assessed by a 3-hour written examination in the Summer Term. The examination will contain four questions in each of two sections; students will have to answer three questions from each section for full marks. Calculators will not be allowed in the examination for this course.

Past exam papers from the last three years, with solutions, can be downloaded from the Course Materials| page on this web-server.

Course description of MA103: Introduction to Abstract Mathematics

Overview

This course is an introduction to mathematical reasoning. Students are introduced to the fundamental concepts and constructions of mathematics. They are taught how to formulate mathematical statements in precise terms, and how such statements can be proved or disproved.

The course is designed to enable you to:

• develop your ability to think in a critical manner;
• formulate and develop mathematical arguments in a logical manner;
• improve your skill in acquiring new understanding and expertise;
• acquire an understanding of basic pure mathematics, and the role of logical argument in mathematics.

Aims

To introduce students to the techniques and subject matter of pure mathematics, and to enhance students' capability to reason precisely. To provide students with the skills required for more advanced courses in mathematics.

Learning outcomes

Knowledge of basic mathematical concepts in discrete mathematics, algebra, and real analysis. Ability to use formal notation correctly and in connection with precise statements in English. Ability to solve mathematical problems that are variants of homework examples. Ability to find and formulate simple proofs.

Connections to other courses

The course covers material that is an essential prerequisite for anyone taking further mathematics courses (except those that are designated as 'methods' courses). In particular, students taking the degree in Mathematics and Economics will require this material in the follow-up courses MA203 Real Analysis|, MA208 Optimisation Theory|, MA209 Differential Equations| and MA210 Discrete Mathematics|.

The course covers the following topics:

MA103 Course Guide in the LSE Calendar
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MA103 Course Materials on Moodle|