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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2010/2011
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Jewels of Algebra (MATH10050)

Course Outline
School School of Mathematics College College of Science and Engineering
Course type Standard Availability Available to all students
Credit level (Normal year taken) SCQF Level 10 (Year 4 Undergraduate) Credits 20
Home subject area Mathematics Other subject area Specialist Mathematics & Statistics (Honours)
Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic? No
Course description Course for final year students in Honours programmes in Mathematics.

This course will cover some of the jewels in the crown of undergraduate mathematics, drawing together group, ring and number theory to solve problems that resisted the efforts of the world's best mathematicians for many centuries. The powerful central ideas of this course are now crucial to many modern problems in algebra, geometry, number theory and differential equations.

Groups and their actions : isomorphism theorems; Sylow theorems, Cauchy's theorem; nilpotent groups and solvable groups.

Rings : examples and groups acting on rings; Hilbert's basis theorem; integrality; finiteness of group invariants.

Fields and polynomials; Galois groups; the fundamental theorem of Galois theory; ruler & compass constructions; insolubility of the quintic.
Entry Requirements
Pre-requisites Students MUST have passed: Algebra (MATH10021) AND Numbers & Rings (MATH10023) AND Pure & Applied Analysis (MATH10008) AND Complex Variable & Differential Equations (MATH10033)
Co-requisites
Prohibited Combinations Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisites None
Displayed in Visiting Students Prospectus? Yes
Course Delivery Information
Delivery period: 2010/11 Full Year, Available to all students (SV1) WebCT enabled:  Yes Quota:  None
Location Activity Description Weeks Monday Tuesday Wednesday Thursday Friday
King's BuildingsLecture1-22 11:10 - 12:00
King's BuildingsLecture1-22 11:10 - 12:00
First Class Week 1, Monday, 11:10 - 12:00, Zone: King's Buildings. JCMB, room 6206
Additional information The above times are for 1st Semester only.

For 2nd Semester lecture times are:

Mon (JCMB Th C) 14:00-14:50
&
Thu (JCMB Th B) 14:00-14:50
Exam Information
Exam Diet Paper Name Hours:Minutes Stationery Requirements Comments
Main Exam Diet S2 (April/May)3:0016 sides
Summary of Intended Learning Outcomes
1. Familiarity with abstract ideas.
2. Working knowledge of fundamental notions and techniques in group and ring theory.
3. Ability to apply this knowledge to concrete examples.
4. Working knowledge of field theory and polynomials and their roots.
5. Ability to calculate Galois groups and understand their properties.
Assessment Information
Coursework: 15%; Degree Examination: 85%.
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 JoA
Contacts
Course organiser Dr Tom Mackay
Tel: (0131 6)50 5058
Email: T.Mackay@ed.ac.uk
Course secretary Mrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk
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copyright 2011 The University of Edinburgh - 31 January 2011 7:59 am