This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2008-2009 (archived)
Module MATH2061: ALGEBRA AND NUMBER THEORY II
Department: Mathematical Sciences
MATH2061: ALGEBRA AND NUMBER THEORY II
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 2 | 20 | Available in 2008/2009 | None. | Durham |
Pre-requisites
- Core Mathematics A (MATH1012)
Corequisites
- Linear Algebra II (MATH2021).
Excluded Combinations
- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Foundation Mathematics (MATH1641)
Aims
- To introduce further concepts in abstract algebra, develop their theory, and apply them to solve problems in number theory and other areas.
Content
- Examples of groups.
- Group actions.
- Homomorphisms and quotient groups.
- Finitely generated abelian groups.
- Rings and fields.
Learning Outcomes
Subject-specific Knowledge
- By the end of the module students will: be able to solve a range of predictable and unpredictable problems on Algebra and Number Theory.
- have an awareness of the abstract concepts of theoretical mathematics in the field of Algebra and Number Theory.
- have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Example of groups, generators, homomorphisms.
- Conjugacy, centre.
- Group actions, Equivalence relations.
- Cauchy's Theorem, Burnside's Theorem.
- Quotient groups.
- First Isomorphism Theorem.
- Structure of finitely generated abelian groups.
- Rings.
- Polynomial ring is one variable over a field.
Subject-specific Skills
- In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning.
Key Skills
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
- Tutorials provide active engagement and feedback to the learning process.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total Hours | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 42 | 2 per week for 19 weeks and 1 in term 3 | 1 Hour | 42 | |
| Tutorials | 10 | Fortnightly for 20 weels | 1 Hour | 10 | Yes |
| Problems Classes | 10 | Fortnightly for 20 weeks | 1 Hour | 10 | |
| Preparation and Reading | 138 | ||||
| Total | 200 |
Summative Assessment
| Component | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | three hour written examination | 100% |
Formative Assessment
One written assignment to be handed in every third lecture in the first 2 terms. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment.
Students who do not attend monitored activities shown under Teaching Methods
and Learning Hours, or who fail to complete the summative or formative
assessment(s) specified above, may be subject to the Academic Progress
procedures defined in the University's General Regulation V, and may be
required to leave the University.