MATH426-21S1 (C) Semester One 2021

Geometry

15 points

Details:
Start Date: Monday, 22 February 2021
End Date: Sunday, 27 June 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 7 March 2021
  • Without academic penalty (including no fee refund): Friday, 14 May 2021

Description

The course deals with advanced topics in geometry

Geometry is the area of mathematics that studies the notions of shape, space and relative position. Attempts to prove Euclid’s parallel postulate led to the discovery of many different types of geometry.

In this course, we will focus on projective geometry as many other geometries such as affine, hyperbolic or Euclidean can be modelled using projective spaces. Projective geometry also forms the base for more advanced algebraic geometry.

We will investigate the role of the classical theorems of Desargues, and Pappus, study the cross ratio, investigate groups acting on projective spaces and study conic sections and quadrics. Finally, we will take an axiomatic approach to deal with non-Desarguesian projective planes.

Additional topics may include the link of projective spaces over a finite field with latin squares, coding theory and design theory.

Learning Outcomes

  • Competently use projective concepts such as homogeneous coordinates and cross-ratios over different fields.
  • Prove basic but fundamental theorems about collineations, polarities and conics in projective planes and spaces.
  • Relate the study of group theory to projective geometry.
  • Explore projective planes from an axiomatic point of view.
  • Develop a good understanding of what a mathematical proof entails.
  • Develop written and oral communication skills, emphasising the ability to explain what the mathematics means.

Pre-requisites

Subject to approval of the Head of School.

Timetable 2021

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Wednesday 12:00 - 13:00 Jack Erskine 505
22 Feb - 4 Apr
26 Apr - 6 Jun
Lecture B
Activity Day Time Location Weeks
01 Tuesday 10:00 - 11:00 Jack Erskine 505
22 Feb - 4 Apr
26 Apr - 6 Jun
Lecture C
Activity Day Time Location Weeks
01 Friday 11:00 - 12:00 Jack Erskine 505 (26/2-26/3, 30/4, 14/5-4/6)
Jack Erskine 239 (7/5)
22 Feb - 28 Mar
26 Apr - 6 Jun

Course Coordinator / Lecturer

Geertrui Van de Voorde

Assessment

Assignments 20%
Test 25%
Presentation 25%
Exam 30%

Indicative Fees

Domestic fee $1,000.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH426 Occurrences

  • MATH426-21S1 (C) Semester One 2021