Skip to main content

Module

MAS8703 : Geometries and designs (Inactive)

  • Inactive for Year: 2024/25
  • Module Leader(s): Dr Oli King
  • 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 introduce students to basic geometric ideas and constructions, and to train them to deal with geometric and combinatorial questions, problems and proofs.

Module Summary
We are all familiar with shapes, patterns and pictures from our earliest consciousness. So, too, geometry has been part of mathematics since the beginning of mathematical explorations. The serious study of geometry involves the systematic development of its basic concepts and the constant meeting of particular configurations that have pictorial elegance and beauty. This can occur in settings other than the ordinary Euclidean plane; for example, in the projective plane which has a line at infinity, or in planes where the co-ordinates belong to a finite field. Figures in the latter involve a finite number of points, lines and conics etc., which have combinational properties. These generalise to the ideas of designs, which figure in applications like the design of experiments. There is a wealth of possible material. The module will seek to convey an appreciation of some of this.

Outline Of Syllabus

Designs, Incidence matrices, symmetric designs, Hadamard matrices and Hadamard designs. The projective plane, co-ordinate systems, Desargues' Theorem, Pappus' Theorem. Conics, canonical form, Pascal's Theorem.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture41:004:00Problem classes
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Drop-ins in lecture room or office
Guided Independent StudyIndependent study122:0022:00Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and course test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
Jointly Taught With
Code Title
MAS3703Geometries and designs
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.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A90N/A
Written Examination401M5Class test
Exam Pairings
Module Code Module Title Semester Comment
1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments are expected to consist of two written assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and the (in class) 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