Undergraduate

modules

Modules

MAS1602 : Introductory Algebra: Complex Numbers, Vectors and Matrices

Semesters
Semester 1 Credit Value: 15
ECTS Credits: 8.0

Aims

The module aims to provide students of differing mathematical backgrounds with a common algebraic foundation for more advanced mathematical study. The first part of the module is devoted to complex numbers and polynomial equations in one variable. The second part treats elementary concepts of linear algebra, in particular systems of linear equations and matrix methods for their solution and applications to geometry.

Outline Of Syllabus

Complex numbers, arithmetic, Argand diagram, polar form, de Moivre's theorem, powers and roots of unity.

Vectors: sums, products (scalar, dot, cross), equations of lines and planes, orthogonality, norm.

Linear algebra: row operations, solution of linear equations, Gaussian elimination, matrix operations, determinants, inverting matrices, eigenvectors, quadratic forms.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture31:003:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture341:0034:00Formal lectures
Guided Independent StudyAssessment preparation and completion19:009:00Revision for class test
Guided Independent StudyAssessment preparation and completion119:0019:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:302:30Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Assignment laboratory
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study132:3032:30Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study53:0015:00Review of coursework assignments and course test
Guided Independent StudyIndependent study46:0024:00Preparation for coursework assignments
Total150:00
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. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1501A80N/A
Written Examination401M10Class test
Exam Pairings
Module Code Module Title Semester Comment
PHY1032Introductory Algebra: Complex Numbers, Vectors and Matrices1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of one written assignment (approximately 3%), one assignment laboratory (approximately 3%) and two computer based assessments (each approximately 2%). The coursework assignments and the (in class, therefore 40 minute) coursework test allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable