MAS1042 : Mathematical Methods B

  • Module Leader(s): Dr Stefan Kolb
  • Owning School: Mathematics & Statistics
Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To lay the foundations for more advanced mathematical study. Students will be able to manipulate complex numbers and find roots, and use matrix methods to solve equations.

Module Summary

Virtually every branch of mathematics and statistics can be developed only from a firm foundation. A clear understanding and appreciation of many fundamental topics is required, primarily, those of algebra and calculus. Of course, understanding alone is not sufficient: considerable manipulative skill (covering all the topics above) is an essential ingredient if progress is to be made. These skills form the toolkit which is required for further study. This module provides the algebraic basis for all this, by building on the ideas explored in A-level (or equivalent) studies. Not only are the ideas rehearsed -often in a different, but more complete way – but work on more advanced topics in algebra, linear algebra and complex numbers is included.

Much of this material can be better understood via graphs, diagrams and sketches, or by reproducing routine (but tedious) algebra in an automatic fashion. To this end, the module illustrates some of the ideas using the computer algebra package Maple. A facility for Maple will be assumed in other modules and in later stages.

Outline Of Syllabus

Complex numbers, Argand diagram, polar form, de Moivre's theorem, roots of unity. Linear algebra, row operations, solution of linear equations, matrix operations, determinants, eigenvectors.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture261:0026:00Formal lectures
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture41:004:00Problem classes
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen Exam
Guided Independent StudyAssessment preparation and completion11:301:30Unseen exam
Scheduled Learning And Teaching ActivitiesDrop-in/surgery240:000:00Office Hours in a staff office
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Guided Independent StudyIndependent study42:008:00CBAs
Guided Independent StudyIndependent study45:0020:00Written assignments
Guided Independent StudyIndependent study41:004:00Assignment review
Guided Independent StudyIndependent study117:3017:30Studying, practising and gaining understanding of course material
Total100:00
Jointly Taught With
Code Title
MAS2042Mathematical Methods B
Teaching Rationale And Relationship

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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination901A80unseen
Exam Pairings
Module Code Module Title Semester Comment
1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10N/A
Computer assessment1M10CBAs
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Approximately four written assignments of approximately equal weight (worth approximately 10% in total) and approximately four computer based assessments of approximately equal weight (worth approximately 10% in total) 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.

Reading Lists

Timetable

Disclaimer: The University will use all reasonable endeavours to deliver modules in accordance with the descriptions set out in this catalogue. Every effort has been made to ensure the accuracy of the information, however, the University reserves the right to introduce changes to the information given including the addition, withdrawal or restructuring of modules if it considers such action to be necessary.