MT5862 Discrete Geometry

Academic year

2025 to 2026 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Module runs in alternating odd years

Planned timetable

Lectures - Mon (weeks 1, 3, 5, 8, 10), Wed & Fri- 12 noon

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module Staff

TBA

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

Discrete geometry is concerned with combinatorial properties of geometric objects such as point sets, arrangements of affine and projective subspaces, convex polytopes, and geometric graphs. This module introduces the area, covering the basic objects and selected key results.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2504 AND PASS MT3501 AND ( PASS MT3502 OR PASS MT3505 OR PASS MT3852 OR PASS MT4003 OR PASS MT4514 OR PASS MT4516 OR PASS MT4512 )

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hour lectures (9 weeks), 1 hour tutorial (10 weeks)

Scheduled learning hours

33

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

120

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Know how to work with the basic objects of discrete geometry: point configurations, hyperplane arrangements, polytopes, and geometric graphs. This means being able to define them, state the important properties, and use them to construct proofs that solve unseen problems.
  • Be able to define projective duality and translate problems about point configurations to ones about hyperplane arrangements and vice versa.  In particular, students will know and use the building blocks of the proof of the Main Theorem of Polytopes and apply the theorem itself
  • Know how to apply combinatorial methods to geometric problems and use geometric representations of combinatorial objects to go in the other direction.  Examples include using Ramsey’s Theorem to find large cyclic subsets of point configurations and solving combinatorial partitioning problems using the Ham Sandwich Theorem
  • Be able to state and prove Euler’s formula for planar graphs (assuming appropriate topological results) and be able to apply it to derive structural properties of planar graphs and results such as the Crossing Number Lemma