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Beyond infinity

Beyond infinity

This popular maths talk 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 lea...   More

Functional analysis

Functional analysis

As taught in 2006-2007 and 2007-2008. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the pri...   More

Functional analysis 2010

Functional analysis 2010

This is a module framework. It can be viewed online or downloaded as a zip file. As taught Autumn semester 2010. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensi...   More

How and why we do mathematical proofs

How and why we do mathematical proofs

This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009/10 The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing pro...   More

Introduction to compact operators

Introduction to compact operators

The aim of this session is to cover the basic theory of compact linear operators on Banach spaces. This includes definitions and statements of the background and main results, with illustrative examples and some proofs. Target audience: This material is accessible to anyone who has a basic knowledge of metric space topology, and who kn...   More

Mathematical analysis

Mathematical analysis

This is a module framework. It can be viewed online or downloaded as a zip file. It is as taught in 2009-2010. This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiatio...   More

Quantum field theory

Quantum field theory

This is a module framework. It can be viewed online or downloaded as a zip file. Last taught in Spring Semester 2006 A compilation of fourteen lectures in PDF format on the subject of quantum field theory. This module is suitable for 3rd or 4th year undergraduate and postgraduate level learners. Suitable for year 3/4 undergraduate and post...   More

Regularity conditions for Banach function algebras

Regularity conditions for Banach function algebras

In June 2009 the Operator Algebras and Applications International Summer School was held in Lisbon. Dr Joel Feinstein taught one of the four courses available on Regularity conditions for Banach function algebras. He delivered four 90 minute lectures on and this learning object contains the slides, handouts, annotated slides and audio podcasts...   More

Statistics - an intuitive introduction : central tendency

Statistics - an intuitive introduction : central tendency

Statistical data have a tendency to cluster around some central point. How do we determine this point? Is there just one way of doing it or more than one?   More

Statistics - an intuitive introduction : graphical display

Statistics - an intuitive introduction : graphical display

Different ways of displaying data: boxplots, histograms and distributions.   More

Statistics - an intuitive introduction : introduction

Statistics - an intuitive introduction : introduction

Things you need to know before looking at the statistics courses here.   More

Statistics - an intuitive introduction : normal distribution

Statistics - an intuitive introduction : normal distribution

One of the most common statistical distributions is the normal distribution. What does it tell us and how do we use it?   More

Statistics - an intuitive introduction : standard deviation

Statistics - an intuitive introduction : standard deviation

A standard way of measuring statistical variability: standard deviation and the associated concepts of variance and degrees of freedom.   More

Statistics - an intuitive introduction : summation sign

Statistics - an intuitive introduction : summation sign

Understanding the summation sign: what does it do … why does it exist?   More

Statistics - an intuitive introduction : variability

Statistics - an intuitive introduction : variability

Statistical data vary: range and inter-quartile range measure this. Are they good measures?   More

Uniform convergence and pointwise convergence

Uniform convergence and pointwise convergence

The aim of this material is to introduce the student to two notions of convergence for sequences of real-valued functions. The notion of pointwise convergence is relatively straightforward, but the notion of uniform convergence is more subtle. Uniform convergence is explained in terms of closed function balls and the new notion of sets absorb...   More

Why do we do proofs?

Why do we do proofs?

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 st...   More

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