from The Open University
Alternatively you can skip the navigation by pressing 'Enter'.
A History of Ideas - Aristotle on flourishingTuesday, 31st March 2015 12:04 - BBC Radio 4In this episode of A History of Ideas, philosopher Jules Evans wants to prove there's been a revival of Aristotle's... Watch now: OU on the BBC: A History of Ideas - Aristotle on flourishing
Kim Cattrall on Antony & CleopatraWednesday, 1st April 2015 07:00 - Sky Arts 1 HD
A History of Ideas - Max Weber and the Protestant EthicWednesday, 1st April 2015 12:04 - BBC Radio 4
Thinking Allowed: Citizenship ceremonies and family tiesWednesday, 1st April 2015 16:00 - BBC Radio 4
A History of Ideas - How do I live a good life?Available until Wednesday, 30th March 2016 14:15Melvyn Bragg and his four guests delve deeper into the philosophy of how we live a good life. Read more: OU on the BBC: A History of Ideas - How do I live a good life?
Is there a problem with OpenLearn? OpenLearn status updatesWe hope OpenLearn works normally, around the clock, through the year. If we know something's... Read more: Is there a problem with OpenLearn? OpenLearn status updates
Take the photographic memory testCan you capture scenes just by looking at them? Find out with our photographic memory test. Launch now: Take the photographic memory test
The business of footballWelcome to this free new OpenLearn course produced by The Open University working in partnership... Try: The business of football now
Succeed with maths – Part 1[BETA] If you feel that maths is a mystery that you want to unravel then this short 8-week course... Try: Succeed with maths – Part 1 now
In our everyday lives we use we use language to develop ideas and to communicate them...
In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this unit we examine ways in which language is adapted to express mathematical ideas.
By the end of this unit you should be able to:
- Section 1: Sets
- use set notation;
- determine whether two given sets are equal and whether one given set is a subset of another;
- find the union, intersection and difference of two given sets.
- Section 2: Functions
- determine the image of a given function;
- determine whether a given function is one-one and/or onto;
- find the inverse of a given one-one function;
- find the composite of two given functions.
- Section 3: The language of proof
- understand what is asserted by various types of mathematical statements, in particular implications and equivalences;
- produce simple proofs of various types, including direct proof, proof by induction, proof by contradiction and proof by contraposition;
- read and understand the logic of more complex proofs;
- disprove a simple false implication by providing a counter-example.
- Section 4: Two identities
- understand and use the Binomial Theorem;
- understand and use the Geometric Series Identity;
- understand and use the Polynomial Factorisation Theorem.
When we try to use ordinary language to explore mathematics, the words involved may not have a precise meaning, or may have more than one meaning. Many words have meanings that evolve as people adapt their understanding of them to accord with new experiences and new ideas. At any given time, one person's interpretation of language may differ from another person's interpretation, and this can lead to misunderstandings and confusion.
In mathematics we try to avoid these difficulties by expressing our thoughts in terms of well-defined mathematical objects. These objects can be anything from numbers and geometrical shapes to more complicated objects, usually constructed from numbers, points and functions. We discuss these objects using precise language which should be interpreted in the same way by everyone. In this unit we introduce the basic mathematical language needed to express a range of mathematical concepts.
Please note that this unit is presented through a series of downloadable PDF files.
This unit is an adapted extract from the Open University course