What is the course about?
Mathematics can sometimes seem abstract and remote, but some parts of mathematics offer fascinating insights into the language of nature, potentially revealing underlying truths about the reality we inhabit. In this course we look at some of the most important developments in mathematics such as Plato's concept of numbers as forms, Leonhard Euler's identity e^ip+1=0 which uses five of the most important numbers in mathematics, Georg Cantor's "paradise" of infinities, and Kurt Gödel's incompleteness theorem which seems to imply that mathematics exists independently of human thought.
This is a live online course. You will need:
- Internet connection. The classes work best with Chrome.
- A computer with microphone and camera is best (e.g. a PC/laptop/iMac/MacBook), or a tablet/iPad/smart phone/iPhone if you don't have a computer.
We will contact you with joining instructions before your course starts.
What will we cover?
- Plato’s mathematics – the Platonic solids – what they are and what they signify
- Euler’s identity – what does it mean and why is it “beautiful”?
- Cantor’s paradise – the existence of not one but many infinities
- Gödel’s Incompleteness Theory – the implication that mathematics is not a human construct
- Putting the pieces together – what conclusions can we draw from mathematics?
What will I achieve?
By the end of this course you should be able to...
- Explain the contributions made to mathematics by Plato, Euler, Cantor and Gödel
- Identify the importance of these contributions to the development of mathematics
- Describe the wider implications of these contributions beyond mathematics in both the sciences and arts.
What level is the course and do I need any particular skills?
The course is suitable for beginners. No prior knowledge of mathematics is assumed or required, but the course is designed to be of interest to those who have studied mathematics as well.
How will I be taught, and will there be any work outside the class?
You will be taught online in a number of different ways including presentations with visual examples, discussions and group work. Work outside class will be optional.
Are there any other costs? Is there anything I need to bring?
There are no additional costs. If you wish to take notes you will find it useful to have a pen and paper, but the Powerpoints will be made available online.
When I've finished, what course can I do next?
Anyone interested in mathematics may also be interested in the application of mathematics within physics – the following two physics courses deal with the development of particle physics and touch upon various intriguing applications of mathematics to physical reality.
HS251: The Search for the Ultimate Particle – the development of the concept of an “ultimate particle” from ancient Greek times through to the modern concepts leptons and quarks
HS253: Physics Unravelled? Navigating the Maze of String Theory – this course follows on closely from the material covered in the Ultimate Particle course.