Undergraduate Course: Honours Algebra (MATH10069)

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 3 Undergraduate)	Credits	20
Home subject area	Mathematics	Other subject area	None
Course website	None	Taught in Gaelic?	No
Course description	Core course for Honours Degrees involving Mathematics. This course showcases the theme of abstraction and the power of the quotient construction. The syllabus first covers abstract vector spaces, quotient spaces, inner product spaces and various normal forms. It then builds on the group theory aspects of Fundamentals of Pure Mathematics(MATH08064) by introducing quotient groups, and classifies groups of small order. These topics are finally tied together by the study of modules over a Euclidean domain. The final result, the Cyclic Decomposition Theorem, gives a proof of both Jordan Canonical Form and the classification of finite abelian groups. In the 'skills' section of this course we continue work with the computer algebra system Maple, learning aspects of it more useful for work in Pure Mathematics. We will learn how to use the rich data structures and programming features of Maple in workshops to investigate in detail some topics in Algebra and students will carry out a group project using Maple and submit Maple work and give a short group presentation on the work.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Fundamentals of Pure Mathematics (MATH08064)	Co-requisites
Prohibited Combinations		Other requirements	Students must not have taken : MATH10021 Algebra
Additional Costs	None

Information for Visiting Students
Pre-requisites	None
Displayed in Visiting Students Prospectus?	No

Course Delivery Information

Delivery period: 2013/14 Semester 1, Available to all students (SV1)			Learn enabled: Yes	Quota: None
Web Timetable	Web Timetable
Course Start Date	16/09/2013
Breakdown of Learning and Teaching activities (Further Info)	Total Hours: 200 ( Lecture Hours 35, Seminar/Tutorial Hours 10, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 138 )
Additional Notes	Students must pass exam and course overall.
Breakdown of Assessment Methods (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet	Paper Name	Hours:Minutes
Main Exam Diet S2 (April/May)	Honours Algebra	3:00

Delivery period: 2013/14 Semester 1, Part-year visiting students only (VV1)			Learn enabled: Yes	Quota: None
Web Timetable	Web Timetable
Course Start Date	16/09/2013
Breakdown of Learning and Teaching activities (Further Info)	Total Hours: 200 ( Lecture Hours 35, Seminar/Tutorial Hours 10, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 138 )
Additional Notes	Students must pass exam and course overall.
Breakdown of Assessment Methods (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet	Paper Name	Hours:Minutes
Main Exam Diet S1 (December)	Honours Algebra (Semester 1 Visiting Students only)	2:00

Summary of Intended Learning Outcomes
1. Ability to work with abstract vector spaces over general fields. 2. Understanding of quotient constructions in linear algebra, groups, rings and modules. 3. Familiarity with bilinear forms and inner product spaces. 4. Ability to calculate with various canonical forms. 5. Familiarity with the first isomorphism theorem in the context of linear algebra, groups, rings and modules. 6. Understanding of modules over a Euclidean domain, and its applications to linear algebra and group theory. 7. Confidence in using some Maple data structures and programming features. 8. The ability to use Maple to investigate suitable topics in pure mathematics. 9. An enhanced understanding of chosen examples obtained by working on them in Maple. 10. Experience of working on a group project. 11. Enhanced presentation skills.

Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above.

Special Arrangements
None

Additional Information
Academic description	Not entered
Syllabus	Linear Algebra 1. Basic concepts in abstract linear algebra, abstract vector spaces, linear maps, dimension, images and kernels. 2. Quotient vector spaces, rank-nullity and the first isomorphism theorem. 3. Bilinear forms and inner product spaces. 4. Diagonalization, Jordan canonical form and the Cayley-Hamilton theorem. Group Theory 5. Normal subgroups, quotient groups and the first isomorphism theorem. 6. Groups of small order, including the classification of finite abelian groups. Rings and Modules 7. Rings, ideals, factor rings and the first isomorphism theorem 8. Modules, submodules, factor modules and the first isomorphism theorem. 9. Modules over a Euclidean domain. 10. The Cyclic Decomposition Theorem via Smith Normal Form. 11. Application of the Cyclic Decomposition Theorem to linear algebra and group theory. Skills 12. Use of a selection of Maple data structures and programming features and using these in different mathematical contexts.
Transferable skills	Not entered
Reading list	www.readinglists.co.uk
Study Abroad	Not Applicable.
Study Pattern	See 'Breakdown of Learning and Teaching activities' above.
Keywords	HAlg

Contacts
Course organiser	Prof Iain Gordon Tel: (0131 6)50 4879 Email: i.gordon@ed.ac.uk	Course secretary	Mrs Kathryn Mcphail Tel: (0131 6)50 4885 Email: k.mcphail@ed.ac.uk