Mathematics

ECM2712 - Linear Algebra (2015)

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MODULE TITLELinear Algebra CREDIT VALUE15
MODULE CODEECM2712 MODULE CONVENERDr Gihan Marasingha (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
Number of Students Taking Module (anticipated) 203
DESCRIPTION - summary of the module content

Building on knowledge from ECM1706 or its equivalent, this module will acquaint you with some fundamental notions of modern algebra, and provide you with a solid base for linear algebra. You will learn to use algorithms to solve linear equations. This is a necessary foundation for subsequent further modules, including Coding Theory. Topics will include linear maps; rings and fields; vector spaces and inner product spaces. Furthermore, you will learn that abstract theories are often required for the solution of concrete problems.


Prerequisite module: ECM1701 or equivalent
 

AIMS - intentions of the module

This module builds on the algorithmic knowledge of vectors and matrices and the introduction to abstract algebraic reasoning from study in stage one, developing this into some of the fundamental notions of modern algebra. After covering the concepts of rings and fields, the module will mainly focus on vector spaces and linear maps, giving a rigorous basis for linear algebra. The material of this module will be required in several subsequent modules.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:
 

Module Specific Skills and Knowledge:
1 demonstrate familiarity with the notions of rings and fields, and the most important examples of each;
2 understand the relationship between linear maps and matrices, and how the properties of each influence the solvability of systems of linear equations;
3 comprehend algorithms for solving linear equations and finding eigenvalues and eigenvectors in rigorous and formal terms.
Discipline Specific Skills and Knowledge:
4 tackle problems in many branches of mathematics that are linearisable, using the core skills of solving linear systems;
5 reveal sufficient knowledge of the fundamental algebraic concepts needed for subsequent studies in pure mathematics.
Personal and Key Transferable / Employment Skills and Knowledge:
6 appreciate that concrete problems often require abstract theories for their solution;
7 show the ability to monitor your own progress, to manage time, and to formulate and solve complex problems.

 

SYLLABUS PLAN - summary of the structure and academic content of the module

- rings and fields: review of field properties of Q, R and C; definitions of rings and fields; the fields Fp; other examples of rings, including Z and K[X] (for K a field); existence of greatest common divisors in Z and K[X]; extended Euclidean Algorithm;
 

- vector spaces: axioms of vector spaces; examples; subspaces, linear dependence and independence; spanning sets, bases and dimension; finite and infinite dimensional spaces;
 

- linear maps: definition and examples; image and kernel of a linear map and the dimension formula; isomorphisms; every finite dimensional vector space is isomorphic to a space of column vectors; linear maps and matrices; base change; the Jordan Canonical Form;
 

- inner product spaces: bilinear forms and inner products; norms; unitary matrices; normal matrices and diagonalisability.
 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 44.00 Guided Independent Study 106.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities
33
Lectures including example classes
Scheduled learning and teaching activities 11 Tutorials
Guided independent study 106 Lecture and assessment preparation; wider reading

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Fortnightly exercise: four coursework sheets with assessed and non assessed exercises 60 per cent of the exercises are non-assessed All Exercises discussed in tutorials: solutions handed out. 
       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 20 Written Exams 80 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 Two hours All Exam mark
Coursework – based on questions submitted for formative assessment 20   All Written
         
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
All above Written exam (100%) All August Ref/Def period
       
       

 

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.



If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.
 

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk
 

Other Resources: Details will be supplied at lectures

 

 

 

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Axler S, Gehring,F W, Ribet, K A Linear Algebra done right 2nd Springer 1997 978-0387982588 [Library]
Set Bauldry W.C., Evans B. & Johnson J. Linear Algebra with MAPLE Wiley 1995 000-0-471-06368-1 [Library]
Set Cohn P.M. Elements of Linear Algebra 1st Chapman & Hall/CRC 1994 978-0412552809 [Library]
Set Griffel D.H. Linear algebra and its applications. Vol.1, A first course Ellis Horwood Limited 1989 000-0-745-80571-X [Library]
Set Griffel D.H. Linear algebra and its applications. Vol.2, More advanced Ellis Horwood Limited 1989 000-0-470-21354-X [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM1701
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 5 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Friday 09 January 2015 LAST REVISION DATE Friday 09 January 2015
KEY WORDS SEARCH Axioms of vector space; linear maps; scalar products; orthogonal vectors; linear independence; spinning sets; subspaces.