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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

Definitions, proofs and examples

Definitions, proofs and examples

During the academic year 2011-12, Dr Joel Feinstein gave five optional example classes to his second-year Mathematical Analysis students on Definitions, Proofs and Examples. Dr Feinstein recorded videos of these classes (presented here) to go along with his previous videos on 'How and why we do mathematical proofs'. These sessions are intende...   More

Editing files and Emacs

Editing files and Emacs

This emacs lecture is given as part of the course G51UST, Unix Software Tools. The course gives an introduction to the Unix operating system. It teaches students how to use the Command Line Interface that is part of Unix and also teaches them how to write shell, sed and awk. In doing so the course covers the use of editors such as Emacs and vi...   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

Heuristic local search tutorial

Heuristic local search tutorial

The Problem: Real-world problems are usually (if not always) considered hard to be solved because: * Problems cannot always be represented and solved with a straightforward mathematical approach. * A lot of parameters and constraints are involved. * The number of possible solutions to a problem can be huge. * Good solutions need to be found ...   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

Levels of measurement

Levels of measurement

Aimed at statistics beginners, this learning object describes, and gives examples of, the four levels of measurement of data: nominal, ordinal, interval and ratio.   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

Number for Nurses: Division

Number for Nurses: Division

The Number for Nurses Computer Assisted Learning Package begins with a basic principles section which is followed by application to nursing practice. The basic principles section deals with addition, subtraction, multiplication, division, S.I. units and scales and gauges. In each area a variety of methods are used to enable the student to unde...   More

Pre-sessional mathematics

Pre-sessional mathematics

As taught Autumn 2011 ‘Pre-Sessional Mathematics' Module Guide Module Code: L14201 Total Credits: 0 Offering School: Economics Suitable for study at: postgraduate Level The content presented here provides information for prospective students on module L14201 – ‘Pre-Sessional Mathematics’, offered by the School of Economics, University o...   More

Quantitative economics 1

Quantitative economics 1

As taught Autumn Semester 2010. There are no pre-requisites for this module. In particular, there is no assumption that Mathematics has previously been studied to A-level standard. In common with practically all subjects, theory in Economics is intrinsically mathematical, and those areas of Mathematics - principally differential calculus and ...   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

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