MMath MASTER OF MATHEMATICS

Code MTHA4008Y - (30 Credits)

In this module you will study: (a) Complex numbers. (b) Vectors. (c) Differentiation; power series. (d) Integration: applications, curve sketching, area, arc-length. (e) First and second-order, constant-coefficient ordinary differential equations. Reduction of order. Numerical solutions using MAPLE. Partial derivatives, chain rule. (f) Line integrals. Multiple integrals, including change of coordinates by Jacobians. Green's Theorem in the plane.

Code MTHA4001A - (20 Credits)

The module provides you with a thorough introduction to some systems of numbers commonly found in Mathematics: natural numbers, integers, rational numbers, modular arithmetic. It also introduces you to common set theoretic notation and terminology and a precise language in which to talk about functions. There is emphasis on precise definitions of concepts and careful proofs of results. Styles of mathematical proofs you will discuss include: proof by induction, direct proofs, proof by contradiction, contrapositive statements, equivalent statements and the role of examples and counterexamples. In addition, this unit will also provide you with an introduction to producing mathematical documents using Latex, and an introduction to solving mathematical problems computationally using both Symbolic Algebra packages and Excel.

Code MTHA4001B - (10 Credits)

Probability is the study of the chance of events occurring. It has important applications to understand the likelihood of multiple events happening together and therefore to rational decision-making.

Code MTHA4003A - (20 Credits)

Algebra plays a key role in pure mathematics and its applications. We will provide you with a thorough introduction and develop this theory from first principles. We develop the theory of matrices, mainly (though not exclusively) over the real numbers. The material covers matrix operations, linear equations, determinants, eigenvalues and eigenvectors, diagonalization and geometric aspects. Another topic underlying all mathematics is Real Analysis. We will explore the mathematical notion of a limit and see the precise definition of the limit of a sequence of real numbers and learn how to prove that a sequence converges to a limit. After studying limits of infinite sequences, we move on to series, which capture the notion of an infinite sum.

Code MTHA4003B - (20 Credits)

In the Real Analysis thread, this module extends the material studied in the first semester module “Linear algebra, sequences and series” (MTHA4003A) We learn about limits of functions and continuity before moving on to study precise definitions of differentiation and integration. This then leads to the Fundamental Theorem of Calculus. We are introduced to Group Theory via the study of symmetry and Group Axioms. The basic concepts are subgroups, Lagrange’s theorem, factor groups, group actions and the Isomorphism Theorem.

Code MTHA4007B - (20 Credits)

Computation and modelling are essential skills for the modern mathematician. While many applied problems are amenable to analytic methods, many require some numerical computation to complete the solution. The synthesis of these two approaches can provide deep insight into highly complex mathematical ideas.

Code MTHA5003A - (20 Credits)

One thread of this module covers the standard basic theory of the complex plane. The areas covered include continuity, power series and how they represent functions for both real and complex variables, differentiation, holomorphic functions, Cauchy-Riemann equations. The second thread follows on from the Linear Algebra studied in Year One. We introduce the concept of a vector space over a field. Throughout the module we will see examples of different vector spaces which will illustrate the results presented. We will learn about vector subspaces. We will see the definition of a basis of a vector space, why this construction is useful and how we can then talk about the dimension of the space. We will then look at linear transformations between pairs of vector spaces, which will lead to the definitions of the kernel and the image of a linear transformation and hence to the rank-nullity theorem. We will see how by fixing bases, a linear transformation can be encoded in matrix form and how changing the bases changes that matrix, which will lead on to the study of eigenvectors and the diagonalization of matrices.

Code MTHA5003B - (20 Credits)

Study of complex integration will include consideration of the topology of the complex plane along with proof of the Cauchy and Laurent theorems along with applications including residue calculus. The other area of mathematics studied in this module is Ring Theory. After an introduction to rings using integers as a model, we develop the theory with many examples related to familiar concepts such as substitution and factorisation. Important examples of commutative rings include fields, domains, polynomial rings and their quotients.

Code MTHA5002A - (20 Credits)

In this module, building on knowledge from Calculus, you will develop skills in a variety of mathematical techniques for solving differential equations, and how they can be applied to model a range of applications. As a particular focus, you will consider how we can describe mathematically how a fluid behaves. Techniques for solving differential equations will consider both Ordinary Differential Equations, including series solutions and the method of Frobenius, and Partial Differential Equations, where the method of separation of variables will be introduced. Fourier series (representations of functions as infinite series in Sin and Cos) are also considered. You will also discover the fundamentals of Vector Calculus, how differentiation can be applied to vector fields such as fluid velocity. You will encounter a variety of important Partial Differential Equations from applied mathematics, including deriving the heat equation and the wave equation. The knowledge of vector calculus will also be applied to formulating the differential equations that govern fluid flows, and solving problems such as the flow out of a reservoir.

Code MTHA5002B - (20 Credits)

A range of methods applicable to solving physical problems are studied, including the Method of Characteristics for solving Partial Differential Equations and Fourier Transforms. This is followed by an introduction to Dynamical Systems – understanding the behaviour of nonlinear differential equations. In the other part of this module, solving equations of fluid flow are considered using both numeric and analytic methods.

Code CMP-5034A - (20 Credits)

This module introduces the essential concepts of mathematical statistics deriving the necessary distribution theory as required. In consequence in addition to ideas of sampling and central limit theorem, it will cover estimation methods and hypothesis-testing.

Code MTHF5031Y - (20 Credits)

Combinatorics is one of the most applicable and accessible part of mathematics, yet it is also full of challenging problems. We shall cover many basic combinatorial concepts including counting arguments (enumerative combinatorics) and Ramsey theory. Linear Algebra underpins much of modern mathematics and is the key to many applications. We will introduce bilinear forms and symmetric operators on vector spaces leading to the diagonalization of linear maps and the spectral theorem. This theorem is key to many applications in statistics and physics. Other topics covered will include polynomials of linear maps, the Cayley-Hamilton theorem and the Jordan normal form of a matrix.

Code MTHF5032Y - (20 Credits)

Mathematical modelling is concerned with how to convert real problems, such as those arising in industry or other sciences, into mathematical equations, and then solving them and using the results to better understand, or make predictions about, the original problem. This topic will look at techniques of mathematical modelling, examining how mathematics can be applied to a variety of real problems and give insight in various areas. The topics will include approximation and non-dimensionalising, and discussion of how a mathematical model is created. We will then apply this theory to a variety of models such as traffic flow as well as examples of problems arising in industry. We will consider population modelling, chaos, and aerodynamics.

Code CMP-5020B - (20 Credits)

You will be introduced to a number of programming concepts at the start of your programming career, using a modern programming language common to many digital industries, with specific focus on applications within STEM fields. We structure learning through lectures, delivering core materials, and tutor supported exercises to reinforce learning, and to prepare you for programming in your following studies.

Code CMP-5042B - (20 Credits)

This module considers both the theory and practice of statistical modelling of time series. Students will be expected to analyse real data using R.

Code CMP-5043B - (10 Credits)

This is a module designed to give you the opportunity to apply linear regression techniques using R. While no advanced knowledge of probability and statistics is required, we expect you to have some background in probability and statistics before taking this module. The aim is to provide an introduction to R and then provide the specifics in linear regression.

Code ECO-4006Y - (10 Credits)

The aim of this module is to introduce students to the economic way of reasoning, and to apply these to a variety of real world macroeconomic issues. Students will begin their journey by learning how to measure macroeconomic aggregates, such as GDP, GDP growth, unemployment and inflation. 

Code EDUB5012A - (20 Credits)

This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education.

Code NBS-4108B - (20 Credits)

This module provides a foundation in the theory and practice of accounting and an introduction to the role, context and language of financial reporting and management accounting. The module assumes no previous study of accounting. It is be taken to provide a foundation to underpin subsequent specialist studies in accounting.

Code PHY-4003A - (20 Credits)

In this module, you will learn about the methods used to model the physics of the Earth and Universe. You will explore the energy, mechanics, and physical processes underpinning Earth's systems. This includes the study of its formation, subsequent evolution and current state through the understanding of its structure and behaviour - from our planet's interior to the dynamic surface and into the atmosphere. In the second part of this module, you will study aspects of astrophysics including the history of astrophysics, radiation, matter, gravitation, astrophysical measurements, spectroscopy, stars and some aspects of cosmology. You will learn to predict differences between idealised physics and real life situations. You will also improve your skills in problem solving, written communication, information retrieval, poster design, information technology, numeracy and calculations, time management and organisation.

Code ENV-5043A - (20 Credits)

The weather affects everyone and influences decisions that are made continuously around the world. From designing and siting a wind farm to assessing flood risk and public safety, weather plays a vital role. Have you ever wondered what actually causes the weather we experience, for example why large storms are so frequent across north western Europe, especially in Winter? In this module you will learn the fundamentals of the science of meteorology. We will concentrate on the physical processes that underpin the radiation balance, thermodynamics, wind-flow, atmospheric stability, weather systems and the water cycle. We will link these to renewable energy and the weather we experience throughout the Semester. Assessment will be based entirely on a set of practical reports that you will submit, helping you to spread your work evenly through the semester. You will learn how Weather is a rich fusion of descriptive and numerical elements and you will be able to draw effectively on your own skill strengths while practising and developing others, guided by Weatherquest’s Meteorologists.

Code CMP-6004A - (20 Credits)

This module covers two topics in statistical theory: Linear and Generalised Linear models and also includes Stochastic processes. The first two topics consider both the theory and practice of statistical model fitting and students will be expected to analyse real data using R. Stochastic processes including the random walk, Markov chains, Poisson processes, and birth and death processes.

Code MTHD6015A - (20 Credits)

Mathematical logic analyses symbolically the way in which we reason formally, particularly about mathematical structures. The ideas have applications to other parts of Mathematics, as well as being important in theoretical computer science and philosophy. We give a thorough treatment of predicate and propositional logic and an introduction to model theory.

Code MTHD6018B - (20 Credits)

Dynamical meteorology is a core subject on which weather forecasting and the study of climate and climate change are based. This module applies fluid dynamics to the study of the circulation of the Earth's atmosphere. The fluid dynamical equations and some basic thermodynamics for the atmosphere are introduced. These are then applied to topics such as geostrophic flow, thermal wind and the jet streams, boundary layers, gravity waves, the Hadley circulation, vorticity and potential vorticity, Rossby waves, and equatorial waves. Emphasis will be placed on fluid dynamical concepts as well as on finding analytical solutions to the equations of motion.

Code MTHD6020A - (20 Credits)

Fluid dynamics has wide ranging applications across nature, engineering, and biology. From understanding the behaviour of ocean waves and weather, designing efficient aircraft and ships, to capturing blood flow, the ability the understand and predict how fluids (liquids and gasses) behave is of fundamental importance. This Module considers mathematical models of fluids, particularly including viscosity (or stickiness) of a fluid. Illustrated by practical examples throughout, we develop the governing differential Navier-Stokes equations, and then consider their solution either finding exact solutions, or using analytical techniques to obtain solutions in certain limits (for example low viscosity or high viscosity).

Code MTHD6021A - (20 Credits)

Mathematical Biology is a rapidly developing and hugely exciting field with many areas the focus of dedicated research. In this module you will discover how to use the mathematics you have learned to date to understand a wide range of interesting biological problems. In many cases, important biological insights can be gained from quite simple mathematical models. Examples include the diffusion-limited growth of solid tumours, and the reasons why animal coats patterns are so widely varied - for example, why does the tiger have stripes and the leopard have spots? Mathematics has made fundamental contributions in these and many other areas which we will explore during the module. Further examples may include the propagation of wave-fronts in migrating animal populations, blood flow in arteries and veins and the onset of arterial disease, cochlear mechanics in the ear, and tear film dynamics on the human eye. No prior knowledge of biology is required to be able to take this module.

Code MTHD6025A - (20 Credits)

Cryptography is the science of coding and decoding messages so as to keep these messages secure, and has been used throughout history. In the past, encryption was mainly used by a small number of individuals in positions of authority. Nowadays the universal presence of the internet and e-commerce means that we all have transactions that we want to keep secret. The speed of modern home computers means that an encrypted message that would have been perfectly secure (that is, would have taken an inordinately long time to break) a few decades ago can now be broken in seconds. But as decryption methods have advanced, the methods of encryption have also become more sophisticated. 

Code MTHD6032B - (20 Credits)

Modern cryptosystems depend on mathematics, in particular Number Theory and Algebra. The most famous example of a public key cryptosystem, RSA, relies on the fact that it is 'hard' to factor a large number into a product of primes. In this course, we will look at the mathematics underpinning both classical and modern methods of cryptography and consider how these methods can be applied. 

Code MTHD6033B - (20 Credits)

This course will compare material on symmetric key cryptography and public key cryptography. Examples of both will be given, along with discussion of their strengths and weaknesses, with the emphasis being on the mathematics. We will look at how prime numbers can be used in cryptography, with material on primality testing and factorisation. We will also define and study elliptic curves in order to investigate the relatively new field of elliptic curve cryptography.

Code MTHD6034A - (20 Credits)

TBC

Code MTHE6004B - (20 Credits)

A prerequisite of this module is that you have studied the Algebra module. Galois theory is one of the most spectacular mathematical theories. It gives a beautiful connection between the theory of polynomial equations and group theory. In fact, many fundamental notions of group theory originated in the work of Galois. For example, why are some groups called "solvable"? Because they correspond to the equations which can be solved (by some formula based on the coefficients and involving algebraic operations and extracting roots of various degrees). Galois theory explains why we can solve quadratic, cubic and quartic equations, but no similar formulae exist for equations of degree greater than 4. In modern exposition, Galois theory deals with "field extensions", and the central topic is the "Galois correspondence" between extensions and groups.

Code PHY-6002Y - (20 Credits)

On this module you will study a selection of advanced topics in classical physics that provide powerful tools in many applications as well as provide a deep theoretical background for further advanced studies in both classical and quantum physics. The topics include analytical mechanics, electromagnetic field theory and special relativity. Within this module you will also complete a computational assignment, developing necessary skills applicable for computations in many areas of physics

Code EDUB6014A - (20 Credits)

The aim of the module is to introduce you to the study of the teaching and learning of mathematics with particular focus to secondary and post compulsory level. In this module, you will explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum. Also, you will learn about knowledge related to mathematical teaching. If you are interested in mathematics teaching as a career or interested in mathematics education as a research discipline, then this module will equip you with the necessary knowledge and skills.

Code ENV-6004A - (20 Credits)

Our aim is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. Problems will be described conceptually, then defined mathematically, then solved numerically via computer programming. 

Code MTHA6002B - (20 Credits)

We will trace the development of mathematics from prehistory to the high cultures of ancient Egypt, Mesopotamia, and the Indus Valley civilisation, through Islamic mathematics, and on to mathematical modernity, through a selection of topics. We trace the rise of calculus and algebra, from the time of Ancient Greek and Indian mathematicians, up to the era of Newton and Leibniz. Other topics are also discussed. We will explore mathematical practice and conceptual developments in different historical and geographical settings.

Code MTHA6005Y - (20 Credits)

This module is reserved for students who have completed an appropriate number of mathematics modules at levels 4 and 5. It is a project on a mathematical topic supervised by a member of staff within the school, or in a closely related school. The focus of the project is on independent study; you will have the opportunity to undertake research in an area which is interesting to you. You will write an in-depth report on your topic, using the mathematical typesetting system LaTeX. You will also give a short oral presentation on your topic.

Code BIO-6018Y - (20 Credits)

You will gain an understanding of how science is disseminated to the public and explore the theories surrounding learning and communication. You will investigate science as a culture and how this culture interfaces with the public. Examining case studies in a variety of different scientific areas, alongside looking at how information is released in scientific literature and subsequently picked up by the public press, will give you an understanding of science communication. You will gain an appreciation of how science information can be used to change public perception and how it can sometimes be misinterpreted. You will also learn practical skills by designing, running and evaluating a public outreach event at a school or in a public area.

Code CMP-5020B - (20 Credits)

You will be introduced to a number of programming concepts at the start of your programming career, using a modern programming language common to many digital industries, with specific focus on applications within STEM fields. We structure learning through lectures, delivering core materials, and tutor supported exercises to reinforce learning, and to prepare you for programming in your following studies.

Code CMP-5034A - (20 Credits)

This module introduces the essential concepts of mathematical statistics deriving the necessary distribution theory as required. In consequence in addition to ideas of sampling and central limit theorem, it will cover estimation methods and hypothesis-testing.

Code EDUB5012A - (20 Credits)

This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education.

Code ENV-5004B - (20 Credits)

In this module you will learn about the processes that shape the Earth's shallow subsurface, and how to detect and map subsurface structures and resources. Physical properties of solid materials and subsurface fluids will be explored, including how fluid movement affects these properties. Methods to image the subsurface will be introduced using real datasets, collected by the class where possible. We will apply the theory to real-life problems including risk mitigation, engineering and resource exploration. This module will include fieldwork on campus where possible, specialist computer software, and some light mathematical analysis (trigonometry, rearranging linear equations, logarithms).

Code ENV-5009B - (20 Credits)

This module will build upon material covered in Meteorology I, by covering topics such as synoptic meteorology, weather hazards, micro-meteorology, further thermodynamics and weather forecasting. The module includes a major summative coursework assignment based on data collected on a UEA meteorology fieldcourse in a previous year.

Code ENV-5043A - (20 Credits)

The weather affects everyone and influences decisions that are made continuously around the world. From designing and siting a wind farm to assessing flood risk and public safety, weather plays a vital role. Have you ever wondered what actually causes the weather we experience, for example why large storms are so frequent across north western Europe, especially in Winter? In this module you will learn the fundamentals of the science of meteorology. We will concentrate on the physical processes that underpin the radiation balance, thermodynamics, wind-flow, atmospheric stability, weather systems and the water cycle. We will link these to renewable energy and the weather we experience throughout the Semester. Assessment will be based entirely on a set of practical reports that you will submit, helping you to spread your work evenly through the semester. You will learn how Weather is a rich fusion of descriptive and numerical elements and you will be able to draw effectively on your own skill strengths while practising and developing others, guided by Weatherquest’s Meteorologists.

Code MTHF5030Y - (20 Credits)

This module introduces you to quantum mechanics and special relativity. In quantum mechanics focus will be on: 1. Studying systems involving very short length scales – eg structure of atoms. 2. Understanding why the ideas of classical mechanics fail to describe physical effects when sub-atomic particles are involved. 3. Deriving and solving the Schrodinger equation. 4. Understanding the probabilistic interpretation of the Schrodinger equation. 5. Understanding how this equation implies that certain physical quantities such as energy do not vary continuously, but can only take on discrete values. The energy levels are said to be quantized.

Code MTHF5033Y - (20 Credits)

This module provides an introduction to two self-contained topics. Topology: This is an introduction to point-set topology, which studies spaces up to continuous deformations and thereby generalises analysis, using only basic set theory. You will begin by defining a topological space, and will then investigate notions like open and closed sets, limit points and closure, bases of a topology, continuous maps, homeomorphisms, and subspace and product topologies. Logic: This will cover some of the theoretical foundations of mathematics, such as propositional logic, Boolean algebras, or computability.

Code NBS-5101A - (20 Credits)

What are the rules that dictate how company accounts should be prepared and why do those rules exist? This is the essence of this module. Whilst company directors may wish to present the financial condition of a business in the best possible light, rules have been developed to protect investors and users of the accounts from being misled. You’ll develop knowledge and skills in understanding and applying accounting standards when preparing financial statements. You will also prepare and analyse statements of both individual businesses and groups of companies. Large UK companies report using International Financial Reporting Standards, and these are the standards that you’ll use. You’ll begin by preparing basic financial statements and progress, preparing accounts of increasing complexity by looking at topics including goodwill, leases, cashflow statements, foreign currency transactions, financial instruments and group accounts. You will also deepen your analytical skills through ratio analysis. You’ll learn through a mixture of lectures, seminars and self-study, and be assessed by one three-hour examination. On successful completion of this module, you’ll have acquired significant technical skills in both the preparation and analysis of financial statements. This will give you a strong basis from which to build if you are planning on a career in business or accounting.

Code NBS-5104B - (20 Credits)

The module aims to develop students’ understanding of the theory and practice of management accounting. It develops underpinning competencies in management accounting and builds on topics introduced in the first year. It extends comprehension of the role and system of management accounting for performance measurement, planning, decision making and control across a range of organisations. Additionally, it introduces recent developments in management accounting practice, particularly those which underpin its growing strategic role.

Code MTHA7029Y - (40 Credits)

You will complete a fourth year dissertation on a mathematical topic that is a compulsory part of some Master of Mathematics degrees.

Code MTHE7003B - (20 Credits)

Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory. Advanced topic: Constructibility.

Code MTHE7007B - (20 Credits)

The ocean is an important component of the Earth's climate system. This module covers mathematically modelling of the large-scale ocean circulation and oceanic wave motion. This module builds upon the techniques in fluid dynamics and differential equations that you developed in previous years of study. It then uses these techniques to explain some interesting phenomena in the ocean that are relevant to the real world. We begin by examining the effects of rotation on fluid flows. This naturally leads to the important concept of geostrophy, which enables ocean currents to be inferred from measurements of the sea surface height or from vertical profiles of seawater density. Geostrophy also plays a key role in the development of a model for the global scale circulation of abyssal ocean. The role of the wind in driving the ocean will be examined. This enables us to model the large-scale circulation of the ocean including the development of oceanic gyres and strong western boundary currents, such as the Gulf Stream. The module concludes by examining the role of waves, both at the sea surface and internal to the ocean. The differences between wave motion at mid-latitudes and the Equator are examined, as is the roll of the Equator as a wave-guide. The equatorial waves that you will study are intimately linked with the El Niño phenomenon that affects the climate throughout the globe. The advanced topic is a study of barotropic and baroclinic instability.

Code MTHE7026B - (20 Credits)

The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. Introduction to options, futures and the no-arbitrage principle. Mathematical models for various types of options are discussed. We consider also Brownian motion, stochastic processes, stochastic calculus and Ito's lemma. The Black-Scholes partial differential equation is derived and its connection with diffusion brought out. It is applied and solved in various circumstances. Further advanced topics may include American options or stochastic interest rate models.

Code MTHE7030A - (20 Credits)

This module will give an introduction to ideas of differential geometry. Key examples will be curves and surfaces embedded in 3-dimensional Euclidean space. We will start with curves and will study the curvature and torsion, building up to the fundamental theorem of curve theory. From here we move on to tangent spaces and the first and second fundamental forms, Gaussian curvature, and further topics, including the advanced topics for 4th year students.

Code MTHE7031B - (20 Credits)

You will gain an introduction to the theory of waves. You will study aspects of linear and nonlinear waves using analytical techniques, and Hyperbolic Waves and Water Waves will also be covered. It requires some knowledge of hydrodynamics and multi-variable calculus. The module is suitable for those with an interest in Applied Mathematics.

Code MTHE7032A - (20 Credits)

This module covers the laws of physics described by quantum mechanics that govern the behaviour of microscopic particles. The module will focus on non-relativitic quantum mechanics that is described by the Schrodinger equation. Time-dependent and time-independent solutions will be presented in different contexts including an application to the hydrogen atom. Approximation schemes will also be discussed, with particular emphasis on variational principles, WKB approximation. Extensions of this content to describe quantum fluids such as ultra-cold Bose gases and superfluids in terms of the Gross-Pitaevskii equation will also be presented.

Code MTHE7033A - (20 Credits)

This module is about further topics in algebra. It builds on the knowledge obtained on groups, rings and vector spaces in the first two years. Groups can be studied directly, or via objects called algebras (which have the structures of both rings and vector spaces). On the other hand, algebras can also be studied in their own right. Some of these concepts will be explored in this module.

Code MTHE7034A - (20 Credits)

Partial Differential Equations (PDEs) are ubiquitous in applied mathematics. They arise in many models of physical systems where there is coupling between the variation in space and time, or more than one spatial dimension. Examples include fluid flows, electromagnetism, population dynamics, and the spread of infectious diseases. It is therefore important to understand the theory of PDEs, as well as different analytic and numerical methods for solving them. This module will provide you with an understanding of the different types of PDE, including linear, non-linear, elliptic, parabolic and hyperbolic; and how these features affect the required boundary conditions and solution techniques. We will study different methods of analytical solution (such as greens functions, boundary-integral methods, similarity solutions, and characteristics); as well as appropriate numerical methods (with topics such as implicit versus explicit schemes, convergence and stability). Examples and applications will be taken from a variety of fields.

Code MTHE7035B - (20 Credits)

Number Theory is the study of arithmetical properties of the integers: properties of, and patterns in, prime numbers, integer solutions of equations with integer coefficients, etc. Gauss called Number Theory the queen of mathematics and, following on from work of Fermat and Euler, is responsible for the emergence of Number Theory as a central subject in modern mathematics. Since then, Number Theory has developed in many directions, including Algebraic, Analytic and Probabilistic Number Theory, Diophantine Geometry and has found surprising applications in modern life (notably in Cryptography). In this module, building on first year material on prime factorization and basic congruences, and second year material on groups, rings and fields, you will study various aspects of Number Theory, including certain diophantine equations, polynomial congruences and the famous theorem of Quadratic Reciprocity. The Advanced Topics will be on applications of Number Theory in Cryptography.