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); so

Level 1 Mathematics

Why do we do proofs? - (iPod) 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 the

Beyond Infinity? (iPod) Dr Joel Feinstein

This is the first of two sessions on how to do proofs. See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ The aim of these sessions on how we do proofs is to help students with some of the relatively routine aspects of doing proofs. In particular, we focus on how to start proofs, and how and when to use definitions and known results. With practice, students should become fluent in these routine aspects of writing proofs, and this will allow them to focus instead on the more cr

How do we do proofs? (iPod) Part I - Dr Joel Feinstein

In this workshop, Dr Feinstein helps students to understand convergence of sequences in finite-dimensional Euclidean space using his terminology of sets absorbing sequences (absorption). For more on the advantages of this terminology, see Dr Feinstein's blog post at http//wp.me/posHB-c See also Dr Feinstein's blog, Explaining Mathematics, http//explainingmaths.wordpress.com/

Sequence convergence and absorption - (iPod) Dr Joel Feinstein

Sequence convergence and absorption - Dr Joel Feinstein

How do we do proofs? Part I - Dr Joel Feinstein

Why do we do proofs? - Dr Joel Feinstein

Beyond Infinity? Dr Joel Feinstein

A selection of recordings suitable for first-year mathematics undergraduate students at university.