Welcome to the course page for MA3101 in Semester 1 of 2024-25.
Geometry is the branch of mathematics that deals with the concepts of shape and distance.
Lectures
Monday 12.00, AC202
Wednesday 12.00, Larmor Lecture Theatre
Lectures will run for 12 weeks from Monday September 9.
Course Content
We will study the following topics. The theme of Euclidean geometry will run through all of them. Euclidean geometry is the “familiar” geometry of coordinate space.
- Spherical Geometry
Distance, “straightness”, angles and triangles on the surface of a sphere. - Hyperbolic Geometry
How our 3-dimensional surroundings can’t show us everything that we’d like to see. - Projective Geometry
The geometry of perception. How our 3-dimensional surroundings are represented on a 2-dimensional screen.
The first five lectures or so will consist of an informal introduction to all of these topics, and their origins in very practical questions about how we understand our surroundings. We will develop the accompanying mathematical machinery as we need it.
Lecture Notes
This collection of notes is the main “text” for the course, but also see the references below.
- Lecture 1: The window-taping experiment
- Lecture 2: Perspective
- Lecture 3: What does “straight” mean? (updated September 17, really this was 2.5 lectures)
- Lecture 4: Geometry: measuring the earth (Monday September 23)
- Lecture 5: Euclid’s postulates and spherical geometry (Wednesday September 25)
- Lecture 6: The spherical cosine rule (Monday September 30)
- Lecture 7: Arc length (Wednesday October 2 and Monday October 7)
- Lecture 8: The area of a spherical triangle (Wednesday October 9, updated after the lecture)
- Lecture 9: Curvature
- Lecture 10: Gaussian Curvature
- Lecture 11: Introduction to hyperbolic geometry (Monday October 21)
Assessment
Assessment will consist of the following elements:
- Two homework assignments, with due dates on Wednesday October 16 (Week 6) and Wednesday November 13 (Week 10).
Submission will be via the MA416 Canvas page. - A project that involves creating something that exhibits or explains some concept or object of geometry (more details on this later).
- A formal exam in the winter exam session in December.
The two homework assignments and the project will each account for 15 marks. You are not obliged to do all three of these, and can get full marks for any two of them. The exam accounts for 70 marks.
Homework Sheets
- Homework 1, due date October 16
- Homework 2 (to be updated with more questions!), this version 17 October