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MATH1091: Linear Algebra I (Maths Hons)

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Type	Tied
Level	1
Credits	20
Availability	Available in 2025/2026
Module Cap	None.
Location	Durham
Department	Mathematical Sciences

Prerequisites

Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

Corequisites

Calculus I (Maths Hons) (MATH1081)

Excluded Combinations of Modules

Calculus I (MATH1061), Linear Algebra I (MATH1071), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

Aims

This module is designed to follow on from, and reinforce, A level mathematics.
It will present students with a wide range of mathematics ideas in preparation for more demanding material later.
Aim: to give a utilitarian treatment of some important mathematical techniques in linear algebra.
Aim: to develop geometric awareness and familiarity with vector methods.

Content

A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.
A rigorous approach is expected.
Linear Algebra in n dimensions with concrete illustrations in 2 and 3 dimensions.
Vectors, matrices and determinants.
Vector spaces and linear mappings.
Diagonalisation, inner-product spaces and special polynomials.
Introduction to group theory.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will: be able to solve a range of predictable or less predictable problems in Linear Algebra.
have an awareness of the basic concepts of theoretical mathematics in Linear Algebra.
have a broad knowledge and basic understanding of these subjects demonstrated through one of the following topic areas:
Vectors in Rn, matrices and determinants.
Vector spaces over R and linear mappings.
Diagonalisation and Jordan normal form.
Inner product spaces.
Introduction to groups.
Special polynomials.

Subject-specific Skills:

Students will have basic mathematical skills in the following areas: Modelling, Spatial awareness, Abstract reasoning, Numeracy.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Tutorials provide active engagement and feedback to the learning process.
Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.
Initial diagnostic testing and associated supplementary problems classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level.
The examination provides a final assessment of the achievement of the student.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total	Monitored
Lectures	58	3 per week in terms 1, 2 or 3 per week in term 2 (alternating fortnightly with Problems Classes), 2 revision lectures in term 3.	1 Hour	58
Tutorials	9	Weeks 4, 6, 8, 10 (Term 1) and 14, 16, 18, 20 (Term 2), plus 1 revision tutorial in Easter term.	1 Hour	9	Yes
Problems Classes	4	Fortnightly in weeks 13-19	1 Hour	4
Support classes	18	Weekly in weeks 2-10 and 12-20	1 Hour	18
Preparation and Reading				111
Total				200

Summative Assessment

Component: Examination		Component Weighting: 90%
Element	Length / Duration	Element Weighting	Resit Opportunity
Written examination	3 hours	100

Component: Continuous Assessment		Component Weighting: 10%
Element	Length / Duration	Element Weighting	Resit Opportunity
Fortnightly assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment.		100

Formative Assessment

40 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment.

More information

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