Undergraduate Course: Introduction to Linear Algebra (MATH08057)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 8 (Year 1 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  An introduction to linear algebra, mainly in R^n but concluding with an introduction to abstract vector spaces.
The principal topics are vectors, systems of linear equations, matrices, eigenvalues and eigenvectors and orthogonality. The important notions of linear independence, span and bases are introduced.
This course is both a preparation for the practical use of vectors, matrices and systems of equations and also lays the groundwork for a more abstract, puremathematical treatment of vector spaces.
Students will learn how to use a computer to calculate the results of some simple matrix operations and to visualise vectors. 
Course description 
This syllabus is for guidance purposes only:
The course will have a range of studentfocused activities equivalent to approximately three lecturetheatrehours and a 90 minute Example Class per week. The course contents are given in the course textbook, Nicholson, predominantly Chapters 1 to Chapter 5, and the start of Chapter 8, with a selection (not all) of the applications covered and selected topics omitted.
 Vectors in R^n, and in general. Vectors and geometry
 Systems of linear equations, echelon form, Gaussian elimination, intro to span and linear independence.
 Matrices, multiplication, transpose, inverses, linear maps. Intro to subspaces and bases. Rank.
 Eigenvalues and eigenvectors. Determinants
 Orthogonality, GramSchmidt, orthogonal Diagonalization.
 Introduction to abstract vector spaces and subspaces.
 Selected applications (taught in sequence where appropriate)

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, Available to all students (SV1)

Quota: 743 
Course Start 
Semester 1 
Course Start Date 
16/09/2024 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 33,
Seminar/Tutorial Hours 17,
Supervised Practical/Workshop/Studio Hours 5,
Online Activities 15,
Summative Assessment Hours 3,
Revision Session Hours 4,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
119 )

Assessment (Further Info) 
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 100% Examination 0%
The assessment for this course will involve regular coursework throughout the assessment (probably weekly) with a combination of online assessments, written handin assessments, and synoptic coursework to be completed at the end of the semester. 
Feedback 
Not entered 
No Exam Information 
Learning Outcomes
On completion of this course, the student will be able to:
 Solve systems of linear equations and demonstrate an understanding of the nature of the solutions.
 Perform accurate and efficient calculations with vectors, matrices, eigenvalues and eigenvectors in arbitrary dimensions.
 Demonstrate a geometrical understanding of vectors and vector operations in 2 and 3 dimensions.
 Demonstrate an understanding of orthogonality and projection in arbitrary dimensions.
 Argue in a formal style (definition/theorem/proof or use examples) about statements in linear algebra, as the first step towards a more abstract, puremathematical treatment of vector spaces.

Reading List
Students will require a copy of the course textbook. This is currently "Linear Algebra with Applications" by W. K. Nicholson. This is available freely as a PDF, and printondemand, physical copies are available. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  ILA 
Contacts
Course organiser  Dr Andreas Grothey
Tel: (0131 6)50 5747
Email: Andreas.Grothey@ed.ac.uk 
Course secretary  Ms Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk 

