Core Topics in University Mathematics University of Nottingham

 Courses
This series of videos is aimed primarily at firstyear undergraduate mathematics students.
It covers some of the topics which students often find hard, but which are fundamental to success in university mathematics.
One example of such a topic is curve sketching, which can reveal the qualitative behaviour of a function where perhaps the mathematical expression for the function is rather impenetrable. Proficiency with curve sketching comes with practice, and it is often hard to know where to begin. The videos in this series provide some useful tips.
Another example of a core topic in university mathematics is the idea of proof. Rigorous proof allows us to establish the truth of mathematical statements. Videos in this series highlight two ways of proving mathematical statements: by induction and by contradiction. Further videos highlight the generalisation of a familiar preuniversity mathematical concept (a vector) to a more abstract setting (vector spaces).

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01. Proof by Induction
This video describes how Proof by Induction works and applies it to an example.

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10. Proof by Induction
This video describes the induction step in Proof by Induction.

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09. Exponential Function
This video tells us some things we never knew about the exponential function!

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05. Bases for Vector Spaces
This video describes the concept of a basis for a vector space.

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04. Intro to Vector Spaces
This video shows the ABC of Vector Spaces, with examples.

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08. Think of a Function
This video discusses how to choose a function with specified properties.