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This module teaches you the fundamental clinical skills needed to engage with adult clients, to help you assess their readiness to change, and to plan appropriate behavioural interventions. You will make use of these skills in workshop based teaching for other modules on the Programme and will learn how to adapt your approach when working with clients from diverse backgrounds.

You will build on your skills to prepare clients for ending therapy and reduce the risk of relapse. Teaching will cover face to face and consideration of online delivery of therapy.

This module teaches you the fundamental clinical skills needed to engage with adult clients, to help you assess their readiness to change, and to plan appropriate behavioural interventions. You will make use of these skills in workshop based teaching for other modules on the Programme and will learn how to adapt your approach when working with clients from diverse backgrounds.

You will build on your skills to prepare clients for ending therapy and reduce the risk of relapse. Teaching will cover face to face and consideration of online delivery of therapy.

This module teaches you the fundamental clinical skills needed to engage with adult clients, to help you assess their readiness to change, and to plan appropriate behavioural interventions. You will make use of these skills in workshop based teaching for other modules on the Programme and will learn how to adapt your approach when working with clients from diverse backgrounds.

You will build on your skills to prepare clients for ending therapy and reduce the risk of relapse. Teaching will cover face to face and consideration of online delivery of therapy.

This module teaches you the fundamental clinical skills needed to engage with adult clients, to help you assess their readiness to change, and to plan appropriate behavioural interventions. You will make use of these skills in workshop based teaching for other modules on the Programme and will learn how to adapt your approach when working with clients from diverse backgrounds.

You will build on your skills to prepare clients for ending therapy and reduce the risk of relapse. Teaching will cover face to face and consideration of online delivery of therapy.

Physical Chemistry is concerned with the application of physics to the study of chemical systems. Through physical chemistry one can understand and predict the behaviour of chemical systems, thereby allowing these systems to be optimised. This module will provide an introduction into the fundamentals of physical chemistry, focusing on basic chemical thermodynamics, the principle of equilibrium and its application to acid-base and electrochemical systems.

Vibration is the oscillation of a mechanical structure, and engineers meet it everywhere. Sometimes it is the whole point, as in the strings of a guitar or the human vocal cords, but far more often it is unwanted, as in an electric motor or an entire car. In either case, modelling lets the designer understand and predict that motion, so vibration can be deliberately achieved or reliably avoided. The most effective and economical control comes from careful engineering early in the design cycle, yet engineers are often called upon to tame vibration late, when major structural changes are too costly or would compromise other performance targets.

This module introduces the fundamentals of mechanical vibration to students from a range of backgrounds and with little or no prior experience of the subject. You will learn to model, analyse and control vibrational behaviour, and you will gain hands-on experience of vibration measurement. Along the way, you will see how vibration considerations shape the design of mechanical structures and you will build a practical toolkit of techniques for diagnosing and troubleshooting vibration problems when they arise.

By the end of the module, you will be able to model and analyse the vibration of engineering structures, interpret measurements, and select appropriate strategies to control unwanted vibration. These are core skills for any engineer working in dynamics, noise and vibration, or mechanical design, and they provide the foundation for the more advanced vibration, acoustics and structural dynamics topics you will meet later in the programme.

Vibrations are the oscillation of a mechanical structure. Vibration may be desirable as in the strings of a guitar or in the human vocal cords. More often vibrations are undesirable as for the vibrations of an electrical motor or of an entire car. In both case modelling can inform the designer so that vibration can be precisely obtained or avoided. Although the optimal and cost effective way to minimise the vibration of a structure is by careful engineering early in the design cycle, frequently the engineer must turn to palliative measures to control vibration at a stage in the design when even minor modifications to the structure are prohibitively costly or detrimental to other performance targets.

The general aims of this module are to introduce students with little or no previous experience of mechanical vibrations, and with quite different backgrounds, to the basic concepts of vibrational
behaviour, to provide a general introduction to vibration modelling, analysis and control and to give students some experience of vibration measurement. This module also promotes the principles which can influence the design process of mechanical structures and it presents a number of commonly adopted techniques for trouble-shooting vibration problems.

Vibration is the oscillation of a mechanical structure, and engineers meet it everywhere. Sometimes it is the whole point, as in the strings of a guitar or the human vocal cords, but far more often it is unwanted, as in an electric motor or an entire car. In either case, modelling lets the designer understand and predict that motion, so vibration can be deliberately achieved or reliably avoided. The most effective and economical control comes from careful engineering early in the design cycle, yet engineers are often called upon to tame vibration late, when major structural changes are too costly or would compromise other performance targets.

This module introduces the fundamentals of mechanical vibration to students from a range of backgrounds and with little or no prior experience of the subject. You will learn to model, analyse and control vibrational behaviour, and you will gain hands-on experience of vibration measurement. Along the way, you will see how vibration considerations shape the design of mechanical structures and you will build a practical toolkit of techniques for diagnosing and troubleshooting vibration problems when they arise.

By the end of the module, you will be able to model and analyse the vibration of engineering structures, interpret measurements, and select appropriate strategies to control unwanted vibration. These are core skills for any engineer working in dynamics, noise and vibration, or mechanical design, and they provide the foundation for the more advanced vibration, acoustics and structural dynamics topics you will meet later in the programme.

Number Theory is the study of integers and their generalisations such as the rationals, algebraic integers or finite fields. The problem more or less defining Number Theory is to find integer solutions to equations, such as the famous Fermat equation x^n + y^n = z^n.

In this module we build on the group, ring and number theoretic foundations laid in MATH1001, MATH2003 and MATH3086.

We will first prove a structure theorem for the group of units modulo n. We then move on to the famous Gaussian Quadratic Reciprocity Law which yields an algorithm to decide solvability of quadratic equations over finite fields. Using geometric as well as algebraic methods, we will then characterise which integers can be written as the sum of two and four squares, respectively. The former leads us naturally to the study of binary quadratic forms, a central topic of this module.

In the final part of this module, we will explore rings of integers in algebraic number fields; they generalise the role the integers play within the rational numbers; the simplest new example is the ring of Gaussian integers, Z[i]. We will investigate to what extent certain central properties of the integers, such as unique prime power factorisation, generalises to these rings. The deviation from unique prime factorisation is measured by the so-called ideal class group, probably the most important invariant of algebraic number fields. It can be seen that it is finite and that its order for quadratic number fields is intimately related to the number of equivalence classes of quadratic forms introduced earlier in the module.

One of the primary domains where number theory finds applications is cryptography. We will study some of the famous cryptosystems where number theory has applications. In particular, Rabin cryptosystem, Goldwasser-Micali cryptosystem, lattice based cryptosystems, elliptic curve cryptography are among those.

Number Theory is the study of integers and their generalisations such as the rationals, algebraic integers or finite fields. The problem more or less defining Number Theory is to find integer solutions to equations, such as the famous Fermat equation x^n + y^n = z^n.

In this module we build on the group, ring and number theoretic foundations laid in MATH1001, MATH2003 and MATH3086.

We will first prove a structure theorem for the group of units modulo n. We then move on to the famous Gaussian Quadratic Reciprocity Law which yields an algorithm to decide solvability of quadratic equations over finite fields. Using geometric as well as algebraic methods, we will then characterise which integers can be written as the sum of two and four squares, respectively. The former leads us naturally to the study of binary quadratic forms, a central topic of this module.

In the final part of this module, we will explore rings of integers in algebraic number fields; they generalise the role the integers play within the rational numbers; the simplest new example is the ring of Gaussian integers, Z[i]. We will investigate to what extent certain central properties of the integers, such as unique prime power factorisation, generalises to these rings. The deviation from unique prime factorisation is measured by the so-called ideal class group, probably the most important invariant of algebraic number fields. It can be seen that it is finite and that its order for quadratic number fields is intimately related to the number of equivalence classes of quadratic forms introduced earlier in the module.

One of the primary domains where number theory finds applications is cryptography. We will study some of the famous cryptosystems where number theory has applications. In particular, Rabin cryptosystem, Goldwasser-Micali cryptosystem, lattice based cryptosystems, elliptic curve cryptography are among those.