THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2024/2025

Timetable information in the Course Catalogue may be subject to change.

University Homepage
DRPS Homepage
DRPS Search
DRPS Contact
DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Introduction to Linear Algebra (MATH08057)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryAn 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, pure-mathematical 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 student-focused activities equivalent to approximately three lecture-theatre-hours 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, Gram-Schmidt, orthogonal Diagonalization.
- Introduction to abstract vector spaces and subspaces.
- Selected applications (taught in sequence where appropriate)

Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 1a (MATH08074) OR Mathematics for the Natural Sciences 1a (MATH08072)
Other requirements Higher Mathematics or A-level at Grade A, or equivalent.

Due to limitations on class sizes, students will only be enrolled on this course if it is specifically referenced in their DPT.
Information for Visiting Students
Pre-requisitesVisiting 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:  649
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 hand-in 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:
  1. Solve systems of linear equations and demonstrate an understanding of the nature of the solutions.
  2. Perform accurate and efficient calculations with vectors, matrices, eigenvalues and eigenvectors in arbitrary dimensions.
  3. Demonstrate a geometrical understanding of vectors and vector operations in 2 and 3 dimensions.
  4. Demonstrate an understanding of orthogonality and projection in arbitrary dimensions.
  5. Argue in a formal style (definition/theorem/proof or use examples) about statements in linear algebra, as the first step towards a more abstract, pure-mathematical 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 print-on-demand, 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
KeywordsILA
Contacts
Course organiserDr Andreas Grothey
Tel: (0131 6)50 5747
Email: Andreas.Grothey@ed.ac.uk
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk
Navigation
Help & Information
Home
Introduction
Glossary
Search DPTs and Courses
Regulations
Regulations
Degree Programmes
Introduction
Browse DPTs
Courses
Introduction
Humanities and Social Science
Science and Engineering
Medicine and Veterinary Medicine
Other Information
Combined Course Timetable
Prospectuses
Important Information