Undergraduate Course: Group Theory: An Introduction to Abstract Mathematics (CPD only) (MATH08053)
Course Outline
School |
School of Mathematics |
College |
College of Science and Engineering |
Course type |
Standard |
Availability |
Not available to visiting students |
Credit level (Normal year taken) |
SCQF Level 8 (Year 1 Undergraduate) |
Credits |
10 |
Home subject area |
Mathematics |
Other subject area |
None |
Course website |
None
|
Taught in Gaelic? |
No |
Course description |
Core first year course for Honours Degrees in Mathematics and/or Statistics. Syllabus summary: True and false mathematical statements. Functions between sets. Infinite sets, countable and uncountable. Numbers: primes, proof of the existence of infinitely many primes. Rational numbers, irrationality of the square root of 2. Modular arithmetic: elementary exercises in reasoning. Ideas of addition and multiplication mod n. Euclidean algorithm, congruence equations. Permutations: definition, construction of multiplication table for S3. Groups: the idea of a group, identity, inverses, subgroups. The above examples, invertible matrices, symmetries of geometrical figures. Theory of groups: definition of group. Uniqueness of inverses, etc., as examples of proof, associativity of multiplications assumed throughout. Cosets and Lagrange's theorem, Fermat's little theorem. The idea of isomorphism. |
Entry Requirements
Pre-requisites |
|
Co-requisites |
|
Prohibited Combinations |
|
Other requirements |
None
|
Additional Costs |
SEED Funding Required |
Course Delivery Information
|
Delivery period: 2010/11 Semester 2, Not available to visiting students (SS1)
|
WebCT enabled: Yes |
Quota: None |
Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
No Classes have been defined for this Course |
First Class |
Week 1, Wednesday, 12:10 - 13:00, Zone: Central. David Hume Tower, Lecture Theatre C |
Exam Information |
Exam Diet |
Paper Name |
Hours:Minutes |
Stationery Requirements |
Comments |
Main Exam Diet S2 (April/May) | | 2:00 | | | Resit Exam Diet (August) | | 2:00 | | |
Summary of Intended Learning Outcomes
1. Appreciation of and the ability to handle abstract arguments in set theory and group theory.
2. Ability to apply such arguments in number theory and geometry. |
Assessment Information
Coursework (which may include a Project): 40%
Examination: 60%. |
Special Arrangements
None |
Additional Information
Academic description |
Not entered |
Syllabus |
Not entered |
Transferable skills |
Not entered |
Reading list |
Not entered |
Study Abroad |
Not entered |
Study Pattern |
Not entered |
Keywords |
GThCPD |
Contacts
Course organiser |
Dr Antony Maciocia
Tel: (0131 6)50 5994
Email: A.Maciocia@ed.ac.uk |
Course secretary |
Miss Fiona Curle
Tel: (0131 6)50 5043
Email: F.Curle@ed.ac.uk |
|
copyright 2011 The University of Edinburgh -
13 January 2011 6:20 am
|