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MTH2011  Linear Algebra (2022)
MODULE TITLE  Linear Algebra  CREDIT VALUE  15 

MODULE CODE  MTH2011  MODULE CONVENER  Prof Jan Sieber (Coordinator) 
DURATION: TERM  1  2  3 

DURATION: WEEKS  0  11  0 
Number of Students Taking Module (anticipated)  230 

This module aims to develop the theories and techniques of modern algebra, particularly in relation to vector spaces and inner product spaces.
On successful completion of this module, you should be able to:
Module Specific Skills and Knowledge:
1 understand the relationship between linear maps and matrices, and how the properties of each influence the solvability of systems of linear equations;
2 comprehend algorithms for solving linear equations and finding eigenvalues and eigenvectors in rigorous and formal terms.
Discipline Specific Skills and Knowledge:
3 tackle problems in many branches of mathematics that are linearisable, using the core skills of solving linear systems;
4 understand fundamental concepts in linear algebra for subsequent studies in pure mathematics.
Personal and Key Transferable / Employment Skills and Knowledge:
5 appreciate that concrete problems often require abstract theories for their solution;
6 show the ability to monitor your own progress, to manage time, and to formulate and solve complex problems.
 vector spaces and subspaces
 linear independence, spanning sets;
 linear maps, matrices of linear maps, change of basis;
 kernel and image of linear maps;
 dimension of vector spaces;
 rank and nullity theorem;
 generalization of concepts and key results over arbitrary fields;
 characteristic and minimal polynomials; CayleyHamilton theorem; Jordan Canonical Form;
 normed and inner product spaces: bilinear forms and inner products; norms; CauchySchwartz inequality; GramSchmidt;
 unitary matrices; selfadjoint operators, including the spectral theorem; diagonalisability; dual spaces and examples; adjoint maps.
Scheduled Learning & Teaching Activities  38.00  Guided Independent Study  112.00  Placement / Study Abroad  0.00 

Category 
Hours of study time 
Description 
Scheduled learning and teaching activities 
33 
Lectures including example classes 
Scheduled learning and teaching activities 
5 
Tutorials 
Guided independent study 
112 
Lecture and assessment preparation; wider reading 
Form of Assessment 
Size of Assessment (e.g. duration/length) 
ILOs Assessed 
Feedback Method 
None 

Coursework  20  Written Exams  80  Practical Exams  0 

Form of Assessment 
% of Credit 
Size of Assessment (e.g. duration/length) 
ILOs Assessed 
Feedback Method 
Written Exam – closed book 
80% 
2 hours (summer) 
All 
Written/verbal on request, SRS 
Coursework Exercises 1  4%  10 hours  All  Annotated script and written/verbal feedback 
Coursework Exercises 2  4%  10 hours  All  Annotated script and written/verbal feedback 
Coursework Exercises 3  4%  10 hours  All  Annotated script and written/verbal feedback 
Coursework Exercises 4  4%  10 hours  All  Annotated script and written/verbal feedback 
Coursework Exercises 5  4%  10 hours  All  Annotated script and written/verbal feedback 
Original Form of Assessment 
Form of Reassessment 
ILOs Reassessed 
Time Scale for Reassessment 
Written exam* 
Written Exam (2 hours) (80%) 
All 
August Ref/Def period 
Coursework Exercises 1*  Coursework Exercises 1 (4%)  All  August Ref/Def period 
Coursework Exercises 2*  Coursework Exercises 2 (4%)  All  August Ref/Def period 
Coursework Exercises 3*  Coursework Exercises 3 (4%)  All  August Ref/Def period 
Coursework Exercises 4*  Coursework Exercises 4 (4%)  All  August Ref/Def period 
CourseworkExercises 5*  Coursework Exercises 5 (4%)  All  August Ref/Def period 
*Please refer to reassessment notes for details on deferral vs. Referral reassessment
information that you are expected to consult. Further guidance will be provided by the Module Convener
Web based and Electronic Resources:
ELE: http://vle.exeter.ac.uk
Reading list for this module:
Type  Author  Title  Edition  Publisher  Year  ISBN  Search 

Set  Axler, S.  Linear Algebra Done Right  2nd  Springer  1997  9780387982588  [Library] 
Set  Cohn P.M.  Elements of Linear Algebra  1st  Chapman & Hall/CRC  1994  9780412552809  [Library] 
Set  Griffel, D.H.  Linear Algebra and Its Applications. Vol.1, A First Course  Ellis Horwood Limited  1989  000074580571X  [Library]  
Set  Griffel D.H.  Linear Algebra and Its Applications. Vol.2, More Advanced  Ellis Horwood Limited  1989  000047021354X  [Library]  
Set  Cameron, P.J.  Fields Introduction to Algebra  Second  Oxford Science Publications  2008  9780198527930  [Library] 
CREDIT VALUE  15  ECTS VALUE  7.5 

PREREQUISITE MODULES  MTH1001 

COREQUISITE MODULES 
NQF LEVEL (FHEQ)  5  AVAILABLE AS DISTANCE LEARNING  No 

ORIGIN DATE  Wednesday 26 February 2020  LAST REVISION DATE  Monday 30 May 2022 
KEY WORDS SEARCH  Vector spaces; linear maps; scalar products; orthogonal vectors; linear independence; spanning sets; subspaces; Jordan form; adjoint; dual; rings; groups; fields; isomorphism; irreducibility; characteristic polynomial. 
