production
Skip to Content

Log In

  1. University Home
  2. Catalogue of Courses
  3. Undergraduate
  4. 2025-2026
  5. Mathematics
  6. MA2008: Linear Algebra I

MA2008: LINEAR ALGEBRA I (2025-2026)

Last modified: 13 Nov 2025 11:46


Course Overview

Linear algebra is the study of vector spaces and linear maps between them and it is a central subject within mathematics.

It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.

The two courses Linear Algebra I and II aim at providing a solid foundation of the subject.

Course Details

Study Type Undergraduate Level 2
Term First Term Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Jean-Baptiste Gramain

Qualification Prerequisites

  • Programme Level 2

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

Are there a limited number of places available?

No

Course Description

This is the first part of the two parts course on linear algebra. The whole course contains the following topics:

  • Fields
  • Vector spaces
  • Linear maps
  • Matrices
  • Linear equations
  • Eigenvalues and eigenvectors

Syllabus

  • Basic set theory: Naive understanding of a set and of relations, in particular equivalence relations. Maps (injective/surjective/bijective). The principal of induction.
  • Definitions, examples and elementary properties of groups, rings and fields. In particular integers mod n and fields of prime order.
  • Solving a linear system over a field. Elementary row operations, row echelon form, Gaussian algorithm for solving a linear system over a field.
  • Vector spaces and K-algebras. Definition of a vector space over a field. Examples.
  • Subspaces of a vector space, intersection and sum of subspaces.
  • Span, spanning sets. Linear independence. Basis, dimension. Elementary results about bases and dimension.
  • Linear transformations. Definition, kernel, image, the matrix of a linear transformation with respect to bases. The rank of a matrix and the rank-nullity theorem.
  • Invertible matrices and the Gauss-Jacobi method for finding the inverse of a matrix.
  • A brief introduction to determinants of matrices with entries in arbitrary fields.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2025 for 1st Term courses and 19 December 2025 for 2nd Term courses.

Summative Assessments

10 x Weekly Notes Summary

Assessment Type Summative Weighting 10
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualUnderstandUnderstand the relationship between matrix algebra and linear transformations, including change-of-bases matrices.
FactualApplyUse the language of naive set theory, including the notions of sets, relations and functions.
FactualRememberDefine basic notions of linear algebra, such as subspace, span, basis, dimension and linear transformation.
FactualRememberDefine algebraic structures such as groups, rings, fields and vector spaces.

Design Project: Individual

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Exercise Creation (4xA4)
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualUnderstandUnderstand the relationship between matrix algebra and linear transformations, including change-of-bases matrices.
ProceduralApplyApply the dimension formula to calculate the rank and nullity of a matrix.

10 x Weekly Quiz

Assessment Type Summative Weighting 15
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseProve basic results about algebraic structures using the axioms.
ConceptualApplyCarry out simple proofs using mathematical induction.
ConceptualUnderstandUnderstand the relationship between matrix algebra and linear transformations, including change-of-bases matrices.
FactualApplyUse the language of naive set theory, including the notions of sets, relations and functions.
FactualRememberDefine basic notions of linear algebra, such as subspace, span, basis, dimension and linear transformation.
FactualRememberDefine algebraic structures such as groups, rings, fields and vector spaces.
ProceduralApplyApply Gauss-Jordan elimination to systematically solve systems of linear equations.

Design Project: Group

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Exercise Creation (4xA4)
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseProve basic results about algebraic structures using the axioms.
ConceptualApplyCarry out simple proofs using mathematical induction.
FactualApplyUse the language of naive set theory, including the notions of sets, relations and functions.
FactualRememberDefine algebraic structures such as groups, rings, fields and vector spaces.
ProceduralApplyApply Gauss-Jordan elimination to systematically solve systems of linear equations.

Design Project: Group

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Exercise Creation (2xA4)
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseProve basic results about algebraic structures using the axioms.
FactualRememberDefine basic notions of linear algebra, such as subspace, span, basis, dimension and linear transformation.
FactualRememberDefine algebraic structures such as groups, rings, fields and vector spaces.

Formative Assessment

There are no assessments for this course.

Resit Assessments

Resubmission of failed element(s)

Assessment Type Summative Weighting 100
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Pass marks carried forward. Individual tasks will replace group work.
Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberDefine algebraic structures such as groups, rings, fields and vector spaces.
ConceptualUnderstandUnderstand the relationship between matrix algebra and linear transformations, including change-of-bases matrices.
ProceduralApplyApply the dimension formula to calculate the rank and nullity of a matrix.
ConceptualAnalyseProve basic results about algebraic structures using the axioms.
FactualApplyUse the language of naive set theory, including the notions of sets, relations and functions.
ProceduralApplyApply Gauss-Jordan elimination to systematically solve systems of linear equations.
FactualRememberDefine basic notions of linear algebra, such as subspace, span, basis, dimension and linear transformation.
ConceptualApplyCarry out simple proofs using mathematical induction.
 

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.