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This module is designed to familiarise students with the principal theories, concepts, and research methods relevant to the area of nostalgia. The lectures and readings are designed to acquaint students with both classic and current research trends in the area of nostalgia. This module will help students to discover ways in which to apply the subject matter to their day-to-day experiences, and to better understand themself and others. Lectures will include discussion and class presentations. Discussion and class activities are important to class dynamics and the learning environment, and active participation will increase students understanding of the subject matter.

Students will learn about Nuclear Scattering, various properties of Nuclei, the Liquid Drop Model and the Shell Model, radioactive decay, fission and fusion. By the end of the course, the students should be able to classify elementary particles into hadrons and leptons, and understand how hadrons are constructed from quarks. They will also learn about flavour quantum numbers such as isospin, strangeness, etc. and understand which interactions conserve which quantum numbers. They will study the carriers of the fundamental interactions and have a qualitative understanding of QCD as well as the mechanisms of weak and electromagnetic interactions.

This course provides an introduction to nuclear and particle physics. There are approximately 16 lectures for each section supplemented by directed reading. Lectures delivered using mainly blackboard and with a slight admixture of computer presentation for selected topics.

There will be three problem sheets with respective three sessions devoted to going over these problem sheets. Model solutions will be provided after the problem sheets are due to be handed in. The problem sheets also contain non-assessed supplementary questions usually of a descriptive nature designed for deeper understanding of the material.

Students will learn about Nuclear Scattering, various properties of Nuclei, the Liquid Drop Model and the Shell Model, radioactive decay, fission and fusion. By the end of the course, the students should be able to classify elementary particles into hadrons and leptons, and understand how hadrons are constructed from quarks. They will also learn about flavour quantum numbers such as isospin, strangeness, etc. and understand which interactions conserve which quantum numbers. They will study the carriers of the fundamental interactions and have a qualitative understanding of QCD as well as the mechanisms of weak and electromagnetic interactions.

This course provides an introduction to nuclear and particle physics. There are approximately 16 lectures for each section supplemented by directed reading. Lectures delivered using mainly blackboard and with a slight admixture of computer presentation for selected topics.

There will be three problem sheets with respective three sessions devoted to going over these problem sheets. Model solutions will be provided after the problem sheets are due to be handed in. The problem sheets also contain non-assessed supplementary questions usually of a descriptive nature designed for deeper understanding of the material.

The aim of this module is to introduce students to some of the basic ideas of number theory, and to use this as a context in which to discuss the development of mathematics through examples, conjectures, theorems, proofs and applications. The module will introduce and illustrate different methods of proof in the context of elementary number theory, and will apply some basic techniques of number theory to cryptography.

One of the pre-requisites for MATH3078

The aim of this module is to introduce students to some of the basic ideas of number theory, and to use this as a context in which to discuss the development of mathematics through examples, conjectures, theorems, proofs and applications. The module will introduce and illustrate different methods of proof in the context of elementary number theory, and will apply some basic techniques of number theory to cryptography.

One of the pre-requisites for MATH3078

The solution of differential equations is essential in most mathematical sciences. This module introduces the numerical techniques needed when the problems are not analytically tractable, and the mathematical techniques to analyse the resulting numerical methods.

The solution of differential equations is essential in most mathematical sciences. This module introduces the numerical techniques needed when the problems are not analytically tractable, and the mathematical techniques to analyse the resulting numerical methods.

Introduce the students to the practical application of a relatively wide spectrum of numerical techniques and familiarise the students with numerical coding.

Often in mathematics, it is possible to prove the existence of a solution to a given problem, but it is not possible to "find it". For example, there are general theorems to prove the existence and uniqueness of an initial value problem for an ordinary differential equation. However, it is in general impossible to find an analytical expression for the solution. In cases like these numerical methods can provide an answer, albeit limited: for example, there are numerical procedures (called algorithms) that, given an initial value problem, will compute its solution.

This module is designed to cover four key areas: linear equations, quadratures (ie the evaluation of definite integrals) and the solution of Ordinary and Partial Differential Equations.

The nature of the module is eminently practical: we will cover relatively little of the mathematical background of the numerical techniques that we will study. On the other hand students will be required to do a reasonable amount of programming in a language such as Matlab or Python; part of the assessment will test their ability to code in Matlab or Python and to put into practice the theoretical methods studied at lectures. Computer laboratory sessions are associated to this module and will
complement the lectures.

One of the pre-requisites for MATH6149

Introduce the students to the practical application of a relatively wide spectrum of numerical techniques and familiarise the students with numerical coding.

Often in mathematics, it is possible to prove the existence of a solution to a given problem, but it is not possible to "find it". For example, there are general theorems to prove the existence and uniqueness of an initial value problem for an ordinary differential equation. However, it is in general impossible to find an analytical expression for the solution. In cases like these numerical methods can provide an answer, albeit limited: for example, there are numerical procedures (called algorithms) that, given an initial value problem, will compute its solution.

This module is designed to cover four key areas: linear equations, quadratures (ie the evaluation of definite integrals) and the solution of Ordinary and Partial Differential Equations.

The nature of the module is eminently practical: we will cover relatively little of the mathematical background of the numerical techniques that we will study. On the other hand students will be required to do a reasonable amount of programming in a language such as Matlab or Python; part of the assessment will test their ability to code in Matlab or Python and to put into practice the theoretical methods studied at lectures. Computer laboratory sessions are associated to this module and will
complement the lectures.

One of the pre-requisites for MATH6149

Often in mathematics, it is possible to prove the existence of a solution to a given problem, but it is not possible to "find it". For example, there are general theorems to prove the existence and uniqueness of an initial value problem for an ordinary differential equation. However, it is in general impossible to find an analytical expression for the solution. In cases like these numerical methods can provide an answer, albeit limited: for example, there are numerical procedures (called algorithms) that, given an initial value problem, will compute its solution.

This module is designed to cover four key areas: linear equations, quadratures (ie the evaluation of definite integrals) and the solution of Ordinary and Partial Differential Equations.

The nature of the module is eminently practical: we will cover relatively little of the mathematical background of the numerical techniques that we will study. On the other hand students will be
required to do a reasonable amount of programming in eg python; part of the assessment will test their ability to code in a suitable language and to put into practice the theoretical methods studied at lectures. Seven computer laboratory sessions are associated to this module and will complement the lectures.