Module finder

This course aims to introduce some advanced techniques that hold potential for applications in the future generations of wireless communication systems. Currently, research and development in wireless communications is focused on the sixth generation (6G), which is expected to significantly enhance 5G in both techniques and services. This course will cover several candidate techniques designed to enable 6G wireless systems.

The course begins by covering the principles of cooperative communications. Various relay/cooperation protocols are considered and analysed to demonstrate their advantages and challenges.

Next, it focuses on non-orthogonal multiple access (NOMA), a technique that allows densely deployed users (or devices) to simultaneously transmit their information.

Subsequently, the course addresses the principles of full-duplex communication, exploring the challenges of self-interference and corresponding self-interference cancellation techniques, as well as examining the potential of full-duplex for wireless system design.

Then, it introduces integrated sensing and communication (ISAC), providing several examples to explain the principles and illustrate the design trade-offs.

A review of the fundamentals of MIMO is then provided, followed by analysing the potential of MIMO for meeting the requirements of future wireless systems. A range of technical options for MIMO transceiver optimisation are discussed. Built on the above theoretical foundation, the course then covers the multi-user MIMO and massive MIMO, with the emphasis on their principles, characteristics, and implementation challenges.

Finally, the course covers millimeter wave (mmWave) communications. It begins with an overview of mmWave technology, then characterizes mmWave channels, highlighting key differences from conventional radio frequency (RF) communication channels. The course concludes with an introduction to several advanced techniques for the design and optimization of mmWave systems.

This course aims to introduce some advanced techniques that hold potential for applications in the future generations of wireless communication systems. Currently, research and development in wireless communications is focused on the sixth generation (6G), which is expected to significantly enhance 5G in both techniques and services. This course will cover several candidate techniques designed to enable 6G wireless systems.

The course begins by covering the principles of cooperative communications. Various relay/cooperation protocols are considered and analysed to demonstrate their advantages and challenges.

Next, it focuses on non-orthogonal multiple access (NOMA), a technique that allows densely deployed users (or devices) to simultaneously transmit their information.

Subsequently, the course addresses the principles of full-duplex communication, exploring the challenges of self-interference and corresponding self-interference cancellation techniques, as well as examining the potential of full-duplex for wireless system design.

Then, it introduces integrated sensing and communication (ISAC), providing several examples to explain the principles and illustrate the design trade-offs.

A review of the fundamentals of MIMO is then provided, followed by analysing the potential of MIMO for meeting the requirements of future wireless systems. A range of technical options for MIMO transceiver optimisation are discussed. Built on the above theoretical foundation, the course then covers the multi-user MIMO and massive MIMO, with the emphasis on their principles, characteristics, and implementation challenges.

Finally, the course covers millimeter wave (mmWave) communications. It begins with an overview of mmWave technology, then characterizes mmWave channels, highlighting key differences from conventional radio frequency (RF) communication channels. The course concludes with an introduction to several advanced techniques for the design and optimization of mmWave systems.

In the last 30 years derivatives have become increasingly important in finance and many different types of derivatives are actively traded on exchanges throughout the world. This module explores the pricing and use of forwards, futures and options with a particular focus on contracts where the underlying asset is a financial asset - for example, a stock index (i.e. stock index futures or stock index options). Students will learn how to price these derivatives using various techniques as well as understand how we can use them for (i) speculation, (ii) hedging strategies and (iii) arbitrage. The nature of the subject makes the module more suitable for students with a solid background in mathematics and familiarity with differential calculus and systems of equations.

In the last 30 years derivatives have become increasingly important in finance and many different types of derivatives are actively traded on exchanges throughout the world. This module explores the pricing and use of forwards, futures and options with a particular focus on contracts where the underlying asset is a financial asset - for example, a stock index (i.e. stock index futures or stock index options). Students will learn how to price these derivatives using various techniques as well as understand how we can use them for (i) speculation, (ii) hedging strategies and (iii) arbitrage. The nature of the subject makes the module more suitable for students with a solid background in mathematics and familiarity with differential calculus and systems of equations.

In the last 30 years derivatives have become increasingly important in finance and many different types of derivatives are actively traded on exchanges throughout the world. This module explores the pricing and use of forwards, futures and options with a particular focus on contracts where the underlying asset is a financial asset - for example, a stock index (i.e. stock index futures or stock index options). Students will learn how to price these derivatives using various techniques as well as understand how we can use them for (i) speculation, (ii) hedging strategies and (iii) arbitrage. The nature of the subject makes the module more suitable for students with a solid background in mathematics and familiarity with differential calculus and systems of equations.

In the last 30 years derivatives have become increasingly important in finance and many different types of derivatives are actively traded on exchanges throughout the world. This module explores the pricing and use of forwards, futures and options with a particular focus on contracts where the underlying asset is a financial asset - for example, a stock index (i.e. stock index futures or stock index options). Students will learn how to price these derivatives using various techniques as well as understand how we can use them for (i) speculation, (ii) hedging strategies and (iii) arbitrage. The nature of the subject makes the module more suitable for students with a solid background in mathematics and familiarity with differential calculus and systems of equations.

We will start from outlining fundamental questions we must answer in order to build up a picture of an astrophysical object, e.g., what is it made of? How luminous? How big? How old? How fast? How heavy? These seemingly simple questions are surprisingly difficult to answer but we will cover the different astrophysical tools used to answer them.

We will then move outwards to consider the demography, spatial distribution, and environment of galaxies, in the ‘field’ and in clusters. We will then consider galaxies very distant from us in space and time, discuss galaxy formation and evolution, and have an overview of Active Galaxies, super-massive black holes and their co-evolution with their host galaxies.

We will start from outlining fundamental questions we must answer in order to build up a picture of an astrophysical object, e.g., what is it made of? How luminous? How big? How old? How fast? How heavy? These seemingly simple questions are surprisingly difficult to answer but we will cover the different astrophysical tools used to answer them.

We will then move outwards to consider the demography, spatial distribution, and environment of galaxies, in the ‘field’ and in clusters. We will then consider galaxies very distant from us in space and time, discuss galaxy formation and evolution, and have an overview of Active Galaxies, super-massive black holes and their co-evolution with their host galaxies.

We will start from outlining fundamental questions we must answer in order to build up a picture of an astrophysical object, e.g., what is it made of? How luminous? How big? How old? How fast? How heavy? These seemingly simple questions are surprisingly difficult to answer but we will cover the different astrophysical tools used to answer them.

We will then move outwards to consider the demography, spatial distribution, and environment of galaxies, in the ‘field’ and in clusters. We will then consider galaxies very distant from us in space and time, discuss galaxy formation and evolution, and have an overview of Active Galaxies, super-massive black holes and their co-evolution with their host galaxies.

This module is designed for students in their third year and aims to introduce the basic concepts and techniques of Galois theory, building on earlier work at level 2. As such, it will provide an introduction to core concepts in rings, fields, polynomials and certain aspects of group theory.

Galois theory arose out of attempts to generalize to polynomials of higher degree the well-known formula for the roots of a quadratic polynomial. This turns out to be possible for cubic and quartic polynomials but impossible for polynomials of degree five or more. This impossibility result is one of the main applications of Galois theory. Further applications to be considered are ruler-and-compass constructions; for instance, we determine all natural numbers n for which the regular n-gon can be constructed.

Much of this beautiful and fascinating theory was discovered by the French mathematician and revolutionary Évariste Galois, shortly before he was killed in a duel in 1832, aged twenty. It has
considerably influenced the development of Algebra and is nowadays a basic tool also in Number Theory and (Algebraic) Geometry. For instance, it features prominently in the famous proof of Fermat's Last Theorem by Andrew Wiles in the 1990s.

The main theorem of Galois theory gives a correspondence between the intermediate fields of a finite extension L/K of fields on the one hand and the subgroups of the automorphism group G = Aut (L / K) on the other hand. In particular, this module will introduce the concepts of rings and fields including, for example, the notions of polynomial rings, ideals, quotient rings and homomorphisms, building on material from MATH2046 Algebra and Geometry. Some group theory is also assumed, such as normal subgroups, quotient groups, and familiarity with permutation groups. These topics are all covered in MATH2003 Group Theory, which is also a pre-requisite for this module.

On successful completion of the module the students should be able to:
• show familiarity with the concepts of ring and field, and their main algebraic properties;
• correctly use the terminology and underlying concepts of Galois theory in a problem-solving context;
• reproduce the proofs of its main theorems and apply the key ideas in similar arguments;
• calculate Galois groups in simple cases and to apply the group-theoretic information to deduce results about fields and polynomials.

One of the pre-requisites for MATH3078 and MATH6156