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A selection of recordings suitable for students with some mathematical background, such as A-level maths students.

# Pre-university Mathematics University of Nottingham

• コース

A selection of recordings suitable for students with some mathematical background, such as A-level maths students.

• video
iPod version - Beyond Infinity? Dr Joel Feinstein

## iPod version - Beyond Infinity? Dr Joel Feinstein

This popular maths talk by Dr Joel Feinstein gives an introduction to various different kinds of infinity, both countable and uncountable. These concepts are illustrated in a somewhat informal way using the notion of Hilbert's infinite hotel. In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should learn that many apparently different types of infinity are really the same size. However, there are genuinely "more" real numbers than there are positive integers, as is shown in the more challenging final section, using Cantor's diagonalization argument.
This last part of the talk is relatively technical, and is probably best suited to first-year mathematics undergraduates, or advanced maths A level students. Others may find the technical details hard to follow, and should focus on the overview.
Dr Joel Feinstein's blog is available at http://explainingmaths.wordpress.com/

• 24分
• video
iPod version - Why do we do proofs? - Dr Joel Feinstein

## iPod version - Why do we do proofs? - Dr Joel Feinstein

This is the first of three sessions by Dr Joel Feinstein on how and why we do proofs.

Dr Feinstein's blog is available at http://explainingmaths.wordpress.com/

The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. In particular, the student will learn the following: proofs can help you to really see WHY a result is true; problems that are easy to state can be hard to solve (Fermat's Last Theorem); sometimes statements which appear to be intuitively obvious may turn out to be false (Simpson's paradox); the answer to a question will often depend crucially on the definitions you are working with.

Target audience: suitable for anyone with a knowledge of elementary algebra and prime numbers, as may be
obtained by studying A level mathematics.

• 30分
• video
Beyond Infinity? Dr Joel Feinstein

## Beyond Infinity? Dr Joel Feinstein

This popular maths talk by Dr Joel Feinstein gives an introduction to various different kinds of infinity, both countable and uncountable. These concepts are illustrated in a somewhat informal way using the notion of Hilbert's infinite hotel. In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should learn that many apparently different types of infinity are really the same size. However, there are genuinely "more" real numbers than there are positive integers, as is shown in the more challenging final section, using Cantor's diagonalization argument. This last part of the talk is relatively technical, and is probably best suited to first-year mathematics undergraduates, or advanced maths A level students. Others may find the technical details hard to follow, and should focus on the overview. Dr Joel Feinstein's blog is available at http://explainingmaths.wordpress.com/

• 24分
• video
Why do we do proofs? - Dr Joel Feinstein

## Why do we do proofs? - Dr Joel Feinstein

This is the first of three sessions by Dr Joel Feinstein on how and why we do proofs.

Dr Feinstein's blog is available at http://explainingmaths.wordpress.com/

The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. In particular, the student will learn the following: proofs can help you to really see WHY a result is true; problems that are easy to state can be hard to solve (Fermat's Last Theorem); sometimes statements which appear to be intuitively obvious may turn out to be false (Simpson's paradox); the answer to a question will often depend crucially on the definitions you are working with.

Target audience: suitable for anyone with a knowledge of elementary algebra and prime numbers, as may be
obtained by studying A level mathematics.

• 30分