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More in this section Undergraduate

Course units

Course units you can expect to study during your undergraduate degree programme are listed below by year of study. Please be aware that these are example course units to give you an insight into what you'll study at Royal Holloway and are liable to change.


Year 1

Term one courses


Code
Description
  MT1100

From Euclid to Mandelbrot -   This course aims to show you how mathematics has been used to describe space over the last 2,500 years and uses this to motivate your study of various aspects of the subject.


Calculus -  Your confidence and skill in dealing with mathematical expressions will be built on this course unit, while your understanding of calculus will be expanded. You may even be introduced to topics you didn't cover at A-Level.

 

Number Systems  You'll be introduced to fundamental algebraic structures used in subsequent course units as well as the notion of formal proofs. You'll learn how to illustrate these concepts with examples on this course unit.

 


Numbers and Functions - This course will kindle an interest in analysis by providing a taste of what this subject is about as well as introducing you to the key ideas of analysis illustrated by plenty of examples.


 

Term two courses

Code
Description


Introduction to Applied Mathematics - You'll be introduced to some key ideas and methods of classical mechanics, chaos theory and special relativity on this course unit.

Principles of Statistics  During this course unit, you'll be introduced to the notion of probability and the basic theory and methods of statistics.

 

Functions of Several Variables  - During this course, you'll be introduced to the calculus of functions of more than one variable and will be shown how it may be used in such areas as geometry and optimisation.   

 

Matrix Algebra -  You'll gain a working knowledge of basic linear algebra, with an emphasis on an approach via matrices and vectors by taking this course.

 

 

Year 2

   

Term one courses

Code
Description

Vector Analysis and Fluids -   On this course, you'll study scalar and vector fields, partial differential equations (such as Laplace's equation), as well as the dynamics of inviscid liquids.

Statistical Methods -   You'll study principles of statistical modelling and technology, simple and multiple linear regression, qualitative explanatory variables and the analysis of variance, to name just a few areas. 

Linear Algebra and Project This course develops the matrix theory covered in Matrix Algebra, gives you the chance to learn how to put together different aspects of mathematics via a project and to improve your spoken and written communication.

Primes and Factorisation You'll be introduced  to the elementary theory of rings on this course. You'll learn how this theory can be applied to study the problem of factorising integers into primes and how this situation can be generalised in a natural way.

Real Analysis  - During this course, you'll cover sequences and series, differentiation, the powder series and the Riemann integral. 

   

Term two courses

 

Code
Description

Probability  - On this course, you'll be introduced to the formalism of the mathematical theory of probability and learn the foundations of applying probability to virtually all areas of science, such as economics and quantum theory.

Graphs and Optimisation -  You'll be acquainted with graph theory and linear programming and given the opportunity to develop the skill to formulate and solve linear programmes and their duals on this course.

Ordinary DEs and Fourier Analysis -  This course aims to introduce the concepts of eigenvalues and eigenfunctions in the familiar situation of the trigonometric differential equation and to show how these yield Fourier series expansions for a general function. 

Further Linear Algebra and Modules -  The purpose of this course is to cover some further topics in linear algebra, such as Euclidean domains, and to familiarise you with the theory of modules.

Complex Variable -  You'll be provided with an outline of the basic complex variable theory with some proofs.

 

Year 3


Term one courses

Code
Description


Mathematics Project - You'll be able to make a detailed investigation into one topic of mathematics, which will help you develop your skills in finding information from a variety of sources and in writing and talking about mathematics.


Quantum Theory 1 - This course will give you a complete introduction to the major methods and concepts of quantum theory at a level suitable for third year students.


Interference - The aim of this course is to provide the theory underlying the main principles and methods of statistics, in particular, to provide an introduction to the theory of parametric estimation and hypotheses.

Time Series Analysis -   Time series are observations collected through time and there are correlations among successive observations. This course aims to familiarise you with some of the descriptive methods and theoretical techniques that are used to analyse time series. 


Mathematics of Financial Markets - You'll discover how mathematics and statistics are used (or misused) by those who work in securities markets, which is an area in which many of our graduates find employment. You'll cover portfolio analysis, pricing models, market movements and futures and options on this course.


Cipher Systems - The purpose of this course is to introduce both symmetric key cipher systems and public key cryptography covering methods of obtaining the two objectives of privacy and authentication.


Computational Number Theory - You'll become acquainted with many major methods currently used for testing/proving primality and for the factorisation of composite integers.


Channels - On this course, you'll investigate the problems of data compression and information transmission in both noiseless and noisy environments.


Combinatorics - The purpose of this course is to introduce you to some standard techniques and concepts of combinatorics, including methods of counting, generating functions, probabilistic methods and Ramsey theory.



Electromagnetism - You'll gain an understanding of the development from elementary ideas of electromagnetism up to Maxwell's equations and the existence of electromagnetic waves.


Term two courses

Code
Description


Mathematics Project - You'll be able to make a detailed investigation into one topic of mathematics, which will help you develop your skills in finding information from a variety of sources and in writing and talking about mathematics.


Further Linear Algebra and Modules -  The purpose of this course is to cover some further topics in linear algebra, such as Euclidean domains, and to familiarise you with the modules. 


Mathematics in the Classroom - This course will help you develop a range of communication and teaching skills appropriate to a particular Key Stage and teach you how to act as a role model to pupils. You'll also gain confidence in communicating mathematics as well as learn how to develop projects and teaching methods suitable for school children.


Number Theory - You'll become acquainted with some of the elementary tools used to analyse the additive and multiplicative structures of the set of integers.


Non-Linear Dynamical Systems - The aim of this course is to introduce you to the fundamentals of the analysis of nonlinear dynamical systems and, in particular, to investigate whether the behaviour of a nonlinear system can be predicted from the corresponding linear system.


Applied Probability -   You'll become familiarised with a range of examples of probabilistic methods used to model systems that exhibit random behaviour.


Error Correcting Codes - This course will provide an introduction to the theory of error correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.


Complexity Theory - You'll be introduced to the technical skills needed to help you understand the different classes of computational complexity, to recognise when different problems have different computational hardness and to be able to deduce cryptographic properties of related algorithms and protocols.


Quantum Theory II - On this course, you'll cover variational principles in quantum mechanics, perturbation theory, the electron's spin, radiative transitions and scattering theory.


Advanced Financial Mathematics -  You'll investigate the validity of various linear and non-linear time series occurring in finance. The course also extends the use of stochastic calculus to interest rate movements and credit rating.

   MT4660


Public Key Cryptography - This course introduces you to some of the mathematical ideas essential for an understanding of public key cryptography, such as discrete logarithms, lattices and elliptic curves.


Applications of Field Theory - You'll be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

 

Year 4



Term one courses

Code
Description


MSci Project (one unit) -   You'll once again be given the opportunity to conduct a detailed study into a topic of mathematics helping you develop your sourcing and communication skills even further.


Computational Number Theory - On this course, you'll be introduced to many major methods currently employed for testing/proving primality and for the factorisation of composite integers.


Channels - MSci students will have the opportunity to study this course about the problems of data compression and information transmission if they didn't study it in the third year.


Combinatorics - Same as above. You can learn about methods of counting, generating functions, probabilistic methods and Ramsey theory.


Advanced Cipher Systems - You'll be able to study the mathematical and security properties of both symmetric key cipher systems and public key cryptography, while covering methods for obtaining confidentiality and authentication.

  

Term two courses


Code
Description


MSci Project (one unit) -  Another opportunity to study a topic of mathematics of your choice and create a developed project.


Complexity Theory - You have another chance to study this course about the different classes of computational complexity if you didn't in the third year.


Quantum Theory II - If you missed out on this course about quantum mechanics in Year 3, you can study it in Year 4.


Advanced Financial Mathematics - Once again, you have the chance to learn about the validity of both linear and non-linear time series occurring in finance.


Public Key Cryptography - This course, which introduces you to some of the mathematical ideas essential for an understanding of public key cryptography, is open to those who didn't study it in Year 3.


Applications of Field Theory -  A second chance to take this course, which introduces you to some of the basic theory of field extensions.


Theory of Error-Correcting Codes - This course, which you can also take in Year 3, covers the basic theory of coding, the main coding theory problem, linear codes and cyclic codes.


 
 
 
 

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