Print this page Number, Chaos, Infinity
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Number, Chaos, Infinity
<p>What are numbers? What are irrational, algebraic, and transcendental numbers? How do we represent numbers? Are numbers random? These ideas are related to chaos theory, about the possibility (or not
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What are numbers? What are irrational, algebraic, and transcendental numbers? How do we represent numbers? Are numbers random? These ideas are related to chaos theory, about the possibility (or not) of predicting the future. Some collections of numbers can be counted, like "1,2,3,etc". Some other collections of numbers cannot be counted. So, some objects are strictly more infinite than others! The emphasis in this course is on mathematical thinking, rather than calculations. There are interesting historical aspects and philosophical implications. Some background in high school mathematics is desirable but not mandatory, students may care to look at the tutor’s website for more: https://documents.uow.edu.au/~nillsen/
DELIVERY MODE
- Face-to-Face
COURSE OUTLINE
- Discussion of different types of numbers
- Visualising numbers as points on a line
- Interpreting numbers as a sequence of random coin tosses
- Connections with chaos theory and the possibility of prediction
- Discussion of infinity and infinities
- Historical and philosophical aspects
LEARNING OUTCOMES
By the end of this course, students should be able to:
- Have a greater conceptual understanding of numbers
- Appreciate some of the ideas in chaos theory and the notion of infinity
- Be aware of associated historical and philosophical issues
- Gain a greater awareness of rigorous thought, exemplified by mathematics
