Undergraduate Course: Introduction to Linear Algebra (MATH08057)
|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
|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, 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.
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)
Information for Visiting Students
|Pre-requisites||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?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|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.
|No Exam Information
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, pure-mathematical treatment of vector spaces.
| 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. |
|Graduate Attributes and Skills
|Course organiser||Prof Christopher Sangwin
Tel: (0131 6)50 5966
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050