Mathematical analysis of peer to peer communication networks

Distributed protocols for peer to peer file sharing, streaming video, and video on demand have revolutionised the way the majority of information is conveyed over the Internet. The peers are millions of computers, acting as both clients and servers, downloading and uploading information. Information to be shared is broken into chunks, and the chunks are traded among peers in the network. There can be turnover in the set of chunks of information being collected and/or in the set of peers collecti

What's in a mathematical model?

Professor James Mirrlees says we should keep faith with economic modelling - it works!

Quilts as Mathematical Objects

The connection between textiles and mathematics is intimate but not often explored, possibly because textiles and fiber arts have traditionally been the domain of women while mathematics was viewed as a male endeavour. How times have changed!

Mathematical Methods of Engineering Analysis

Mathematical Methods of Engineering 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, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associate

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 proofs. 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

Mathematical language

In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this unit we examine ways in which language is adapted to express mathematical ideas.

Mathematical Visualization Toolkit

This site consists of a collection of plotting and solving applets featuring a uniform user interface. This site was selected as the 2005 MERLOT Classics Award winner for the Mathematics discipline due to its value and effectiveness as a set of teaching/learning tools. Visualizing mathematical concepts, especially in three-dimensional space, can be quite difficult for students. These tools and applications enable students to see the concepts in action and to come a deeper understanding of the un

Teach your students about the mathematical concept of estimation

Estimate is a great interactive site that allows students to estimate a number that an arrow is pointing to on a number line. This is great for students who are first learning about estimation. It is an easy to use site that is fairly robust and would

Mathematical Modeling Using Real Radioactivity Data

In this lab, you can explore how radioactive radiation changes as a function of distance. This curriculum sets the Radioactivity iLab in the context of mathematics curriculum, asking you to consider:
What type of mathematical function governs the intensity of radiation over distance?

Perform four basic rules mathematical calculations

Understanding how to do calculations is important when measuring and marking out lengths of material for specific jobs. Trying to reduce waste and cost is always necessary. To do any simple calculations there are four main rules that you need to follow.

Further Mathematical Methods

A level 3 course in Mathematics for (Theoretical) Physics students. Contains lecture notes, examples, ... as well as the files used to create these resources. Discusses:
1 Introduction and Prerequisites
2 Linear vector spaces
3 Operators, Eigenvectors and Eigenvalues
4 Green functions
5 Variational calculus
A Contour Integration

Mathematical analysis

This is a module framework. It can be viewed online or downloaded as a zip file. As taught in 2007-2008 and 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, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the a

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 proofs. 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

6.251J Introduction to Mathematical Programming (MIT)

This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include:
Theory and algorithms for linear programming
Network flow problems and algorithms
Introduction to integer programming and combinatorial problems

18.466 Mathematical Statistics (MIT)

This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis.

18.091 Mathematical Exposition (MIT)

This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

18.086 Mathematical Methods for Engineers II (MIT)

This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

18.369 Mathematical Methods in Nanophotonics (MIT)

Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the physics and mathematics of nanophotonics—electromagnetic waves in media structured on the scale of the wavelength.
Topics include computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode theories, to u

18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathemati

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.