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MA2004 Sets and Algebraic Structures

Turning up to lectures and tutorials is compulsory. Missing several lectures or two tutorials is likely to result in a C6, as is failing to turn in a continuous assessment exercise.

Course coordinator:
Professor David Benson.

Please note that Prof. Benson's university email account doesn't work.
Use the one on his home page.

Weight:
15 credit points (1/8 year).

Teaching:
36 one hour lectures and 11 weekly tutorials during the first half-session.

Assessment:
20% continuous assessment, 80% examination.

Prerequisites:
MA1502 (or MA1504 and permission from head of teaching).

Lectures:
Tuesday 9.00 - 10.00 NK10
Wednesday 11.00 - 12.00 Taylor A21
Thursday 9.00 - 10.00 NK14

Tutorials:
Thursday 10.00 - 11.00 KCT2
Thursday 14.00 - 15.00 NK3
Friday 10.00 - 11.00 MT010

Exam:
Syllabus:

This course provides an introduction to algebraic structures and elementary number theory.
The course includes a discussion of:

Sets (notation, functions, injections, surjections, bijections)
Countability of the rational numbers and uncountability of the real numbers
The integers and factorisation
Prime numbers, Euclidean algorithm, uniqueness of factorisation
The integers modulo n
Equivalence relations
Permutations
Group axioms
The symmetric group
Lagrange's Theorem
Fermat's Little Theorem
Definition of commutative ring and of a field with examples
Vector spaces and linear transformations.

Books:
The course notes for this course (see below) are reasonably complete, but if you particularly want books that cover a substantial part of the course in a readable way, here are some:

J. A. Green, Sets and Groups: First Course in Algebra.

S. Lipschutz and M. Lipson, Discrete Mathematics (Schaum's Outline Series).

N. Biggs, Discrete Mathematics.

Course notes:

The file ma2004.pdf will be continually updated as the course progresses.
Last updated: 18 Nov 2009.

Tutorial sheets: (pdf files)

Tutorial 1 Answers
Tutorial 2 Answers
Tutorial 3 Answers
Tutorial 4 Answers
Tutorial 5 Answers
Tutorial 6 Answers
Tutorial 7 Answers
Tutorial 8

NOTICE:

You are expected to do roughly 5-6 hours of work outside of classes/tutorials per week. This means AT LEAST that you should have attempted all the questions on the tutorial sheet before turning up to the tutorial, and that you should read the notes and learn the definitions. You should also be turning up to EVERY CLASS, not just when you happen to feel like it, don't have a hangover, and don't have anything better to do. If you do not do these things, you have only yourself to blame when you fail the course.

Revision week

Second week of Jan 2010.

Continuous Assessments

CA1 was due at 3pm on Thursday 5 November 2009 at G01 Meston; answers

The cover sheet can be found here.

Old Exam Papers: The syllabus for this course is not identical to the syllabus of the old MA2002 "Discrete Mathematics", but it is similar enough that the old exam papers should help you. Here they are, back to 1999.

MA2002 exam 1999
MA2002 exam 2000
MA2002 exam 2001
MA2002 exam 2002
MA2002 exam 2003
MA2002 exam 2004
MA2002 exam 2005
MA2002 exam 2006
MA2004 exam 2007
MA2004 exam 2008
MA2004 exam 2009

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© Dave Benson 2009.