MA6051 - Mathematics of Infinity (2023/24)
| Module specification | Module approved to run in 2023/24 | ||||||||||||
| Module title | Mathematics of Infinity | ||||||||||||
| Module level | Honours (06) | ||||||||||||
| Credit rating for module | 15 | ||||||||||||
| School | School of Computing and Digital Media | ||||||||||||
| Total study hours | 150 | ||||||||||||
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| Running in 2023/24(Please note that module timeslots are subject to change) |
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Module summary
The module is designed to be accessible to both mathematics and non-mathematics students alike. The prerequisite for this module is basic arithmetic and desire to think about abstract ideas.
This module is centred around Cantor’s theory of infinite sets. The historical background of the idea of infinity will be given from the ancient Greek philosophers up to Immanuel Kant. The main ideas behind the Cantor’s theory of transfinite numbers will be developed and then we will look at some of the consequences of Cantor’s work present in Mathematics, Computer Science and Philosophy.
Syllabus
The idea of infinity through history: Greeks to Kant. Cantor and the origin of his Set Theory. LO1
Transfinite numbers: Ordinals (definition and arithmetic). Transfinite numbers: Cardinals (definition and arithmetic). LO2
Cantor's Theorem and Continuum Hypothesis. Self-reference and Gödel’s Incompleteness Theorem(s). Limitations of Thought. LO3
Balance of independent study and scheduled teaching activity
The module will be taught in 3-hour blocks divided into 1-hour lecture and 2-hour tutorial. Tutorials will be used for open discussion of the main topics covered in lectures. Students will be asked to read relevant material beforehand and offer their understanding during the tutorials. In addition to standard VLE presence there will be links available for further readings and discussion groups.
Learning outcomes
LO1: Understand the origins of Cantor's set theory.
LO2: Understand definitions and arithmetic of transfinite numbers.
LO3: Understand the implications of the limitations of any formal system.
Assessment strategy
There will be a comprehension test in form of a take-away work which will give students opportunity to demonstrate their understanding of selection of topics (LO1, LO2). The final assessment will be an essay where students will select one question and write an in-depth critical analysis (LO1 to LO3).
There will be weekly general feedback on students’ progression through material in the form of seminars/tutorials. The first assessment will be opportunity for individual detailed feedback.
Bibliography
Core Text:
A.W. Moore (2001) The Infinite 2ND Edition Routledge
Recommended Reading:
Dauben, J. W.( 1979), Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press, ISBN 0-691-02447-2. Rucker, R.( 1995), Infinity and the Mind, Princeton University Press, ISBN 0-69-100172-3
Priest, G. (2006), Beyond the Limits of Thought, Oxford University Press, ISBN 0-19-924421-9.
Fatconi, T.G.( 2006), The Mathematics of Infinity, John Wiley & Sons, Inc., ISBN 10 0-471-79432-5.