Module Catalogue

MAS2701 : Linear Algebra

  • Offered for Year: 2025/26
  • Available for Study Abroad and Exchange students, subject to proof of pre-requisite knowledge.
  • Module Leader(s): Dr Stefan Kolb
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System

Aims

To provide students with an introduction to modern abstract linear algebra. Building on their existing knowledge of matrix methods, students will experience the benefits of the abstract and rigorous mathematical theory of vector spaces for the deeper understanding of a mathematical subject.

Module Summary

Linear algebra is a fundamental subject that pervades many areas of modern mathematics. On the one hand it is often convenient to replace a complicated problem by a linear approximation which is easier to solve. On the other hand, linear algebra has beautiful applications in coding theory, projective geometry, and many other areas of mathematics and statistics. Initially linear algebra aims to solve systems of linear equations. In the first-year courses this led naturally to matrix algebra. In this module abstraction and generalisation are pushed one level further with the formal introduction of vector spaces and linear maps as a replacement for real n-dimensional space and matrices, respectively. This allows us to consider analogous problems in different settings simultaneously and eventually makes explanations easier and faster. We will need to introduce notions of dimension and basis in this general setting. A guiding question is how to transform matrices (or linear maps) to a simple form in which essential properties can be immediately read off.

Outline Of Syllabus

Vector spaces, span and bases, linear maps and their properties, inner product spaces and change of basis.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Drop in Sessions
Guided Independent StudyIndependent study531:0053:00Preparation time for lectures, background reading, review of coursework
Total100:00
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A85N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Problem solving exercises
Prob solv exercises1M5Problem solving exercises
Prob solv exercises1M5Problem solving exercises
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Approximately three assignments of roughly equal weight allow the students to develop their problem solving techniques, to practise the methods learnt in the module and to receive feedback; this is thus formative as well as summative assessment. The coursework assignments may be written assignments, computer based assessments or a combination of the two.

Reading Lists

Timetable