Undergraduate Course: Numerical Linear Algebra and Applications (MATH10059)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 10 (Year 3 Undergraduate)	Availability	Available to all students
SCQF Credits	10	ECTS Credits	5
Summary	Driven by the needs of applications, this course studies reliable and computationally efficient numerical techniques for practical linear algebra problems. As well as traditional theoretical assessment of the techniques studied, Matlab is used to perform practical experiments to complement studentsż insight into the subject. As a consequence, in addition to the assessment of theoretical understanding and hand calculation via a closed book examination, the course is also assessed via a Matlab class test.
Course description	Linear Algebra is one of the most widely used topics in the mathematical sciences. At level 8 or 9 students are taught standard techniques for basic linear algebra tasks including the solution of linear systems, finding eigenvalues/eigenvectors and orthogonalisation of bases. However, these techniques are usually computationally too intensive to be used for the large matrices encountered in practical applications. NLAA will introduce students to these practical issues and will present, analyse, and apply algorithms for these tasks which are reliable and computationally efficient. The course includes significant lab work using Matlab and this is assessed in a class test. The theoretical material is assessed in a closed book examination. Syllabus 1. Solution of linear systems of equations: condition, direct and iterative methods, consequences of inexact arithmetic, computational cost and exploitation of symmetry, positive definiteness and sparsity 2. Finding a single eigenvalue and eigenvector: condition, iterative methods 3. Applications: superficial general overview and detailed study of particular examples 4. Matlab: commands pertinent to experiments in numerical linear algebra

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations		Other requirements	None

Information for Visiting Students
Pre-requisites	Previous study of linear algebra: matrix (non-)singularity, linear systems of equations, Gaussian elimination, eigenproblem, and matrix transpose, symmetry, positive definiteness and orthogonality
High Demand Course?	Yes

Course Delivery Information

Academic year 2015/16, Available to all students (SV1)		Quota: 57
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 59 )
Assessment (Further Info)	Written Exam 70 %, Coursework 30 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 30%, Examination 70%
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S1 (December)	MATH10059 Numerical Linear Algebra and Applications		2:00

Academic year 2015/16, Part-year visiting students only (VV1)		Quota: 0
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 59 )
Assessment (Further Info)	Written Exam 70 %, Coursework 30 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 30%, Examination 70%
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S1 (December)	MATH10059 Numerical Linear Algebra and Applications		2:00

Learning Outcomes
On completion of this course, the student will be able to: Understanding of numerical linear algebra methods for solving linear systems of equations and finding one or more eigenvalues and/or eigenvalues of a matrix. Ability to analyse and discuss the computational efficiency of a method, including the influence of sparsity. Understanding the concept of conditioning and consequences of using floating-point arithmetic. Ability to code simple methods and experiments in Matlab. Appreciation of applications which generate subproblems requiring numerical linear algebra techniques.

Reading List
Numerical Linear Algebra and Applications by Biswa Nath Datta

Additional Information
Graduate Attributes and Skills	Appreciation that theoretical and textbook techniques may be wholly inadequate in the context of problems of practical interest. Further development of programming skills through the medium of Matlab.
Study Abroad	Not Applicable.
Additional Class Delivery Information	18 one-hour lectures 4 two-hour labs 5 one-hour workshops
Keywords	NLAA,Numerical methods,Linear algebra,Application,Matlab

Contacts
Course organiser	Dr Julian Hall Tel: (0131 6)50 5075 Email: J.A.J.Hall@ed.ac.uk	Course secretary	Mr Thomas Robinson Tel: (0131 6)50 4885 Email: Thomas.Robinson@ed.ac.uk