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)
Prerequisites 
Students MUST have passed:
Fundamentals of Pure Mathematics (MATH08064)

Corequisites  
Prohibited Combinations  
Other requirements  Students must not have taken :
MATH10021 Algebra 
Additional Costs  None 
Information for Visiting Students
Prerequisites  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, Partyear 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, ranknullity and the first isomorphism theorem.
3. Bilinear forms and inner product spaces.
4. Diagonalization, Jordan canonical form and the CayleyHamilton
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 

