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Dissertation in mathematics

This module enables you to carry out a sustained, guided, independent study of a topic in mathematics. Currently there are four topics to choose from: history of modern geometry; advances in approximation theory; variational methods applied to eigenvalue problems; algebraic graph theory. You will be guided by study notes, books, research articles and original sources (or English translations where necessary), which are provided. You’ll need to master the appropriate mathematics and ultimately present your work in the form of a final dissertation.

Qualifications

M840 is a compulsory module in our:

MSc in Mathematics (F04)

Module

Module code

M840

Credits

Study level

OU	Postgraduate
SCQF	11
FHEQ	7

Study method

Distance learning
Find out more in Why the OU?

Module cost

See Module registration

Entry requirements

Find out more about entry requirements.

Module details Entry requirements Module registration Study materials

What you will study

Currently you can choose from four topics for your dissertation.We expect – but can’t at this stage guarantee – to offer two or three additional topics to students starting this October. We’ll provide further information to all postgraduate mathematics students as soon as possible.

History of modern geometry

This topic covers the history of geometry in the nineteenth century. It follows the history of projective geometry and the discovery of non-Euclidean geometry from the 1820s and 1830s. It concentrates on algebraic developments in projective geometry and the work on abstract axiomatic geometry. Differential geometric aspects of non-Euclidean geometry are discussed, as is their influence on Einstein. The module ends with a discussion of geometry and physics, formal geometry and geometry and truth. The module is about geometry, specifically the history of geometry, but it is not a geometry module. What will be discussed is the production and reception of ideas, and how this was affected by the social context. The ideas are those of mathematics and the practices those of mathematicians. All the necessary mathematics will be presented but the ideas are to be understood as a historian would treat them and a good standard of English is required

Advances in approximation theory

This topic extends the material in Approximation theory (M832) to the study of splines and piecewise polynomials, and their possible application to the approximate solution of differential equations. You will need to master the appropriate mathematics which includes topics such as orthogonal polynomials, Green's functions and the linearisation of non-linear differential equations. You will also need to carry out computational studies using the algebraic computing software, Maple, as introduced in Advanced mathematical methods (M833).

Variational methods applied to eigenvalue problems

This topic extends the theory developed in Calculus of variations and advanced calculus (M820) to deal with some types of linear partial differential equations. After establishing functionals for various types of partial differential equations, the Rayleigh-Ritz method will be extended to obtain upper bounds on the smallest frequency of the oscillations of various shaped membranes. The most important part of your dissertation will involve deriving asymptotic estimates of the number, N(λ), of eigenvalues smaller that a given (large number), λ, for a various types of boundary value problems with arbitrary shaped boundaries. A number of theorems that establish increasingly better estimates of N(λ) will be investigated.

Algebraic graph theory

Algebraic graph theory is a branch of mathematics that studies graphs and other models of discrete structures by a combined power of spectral methods of linear algebra (with basics treated in M208); group theory (covered in part in Further pure mathematics (M303)); and algebra over finite fields (as encountered in Further pure mathematics and Coding theory (M836)). You will need to get acquainted with appropriate mathematical tools by reading selected chapters from the book Algebraic Graph Theory by C. Godsil and G. Royle (Graduate Texts in Mathematics, Springer, 2001). About halfway through the module you will have the opportunity to choose a particular topic of your interest within algebraic graph theory which you will then develop into a dissertation.

You will learn

Successful study of this module should enhance your skills in understanding complex mathematical texts, working on open-ended problems and communicating mathematical ideas clearly.

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material and mark and comment on your written work, and whom you can ask for advice and guidance.

Assessment

The assessment details can be found in the facts box above.

You will be expected to submit your TMAs online using the eTMA system, unless there are some difficulties which prevent you from doing so. In these circumstances, you must negotiate with your tutor to get their agreement to submit your assignment on paper. We strongly recommend that you submit these TMAs electronically.

There is no examination. The final assignment, the dissertation (or EMA), should be typeset and must be submitted electronically.

Course work includes

3 Tutor-marked assignments (TMAs)

End-of-module assessment

No residential school

Course satisfaction survey

See the satisfaction survey results for this course.

Future availability

Dissertation in mathematics (M840) starts once a year – in October. This page describes the module that will start in October 2019. We expect it to start for the last time in October 2025.

Regulations

As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

Entry requirements

This module is a dissertation and assumes a high level of mathematical maturity.

To study this module you must:

declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention
have successfully completed at least four other modules in the MSc in Mathematics (F04).

The ‘Advances in approximation theory’ topic builds on the material in Advanced mathematical methods (M833) and Approximation theory (M832). Normally, you should have completed both these modules to be accepted to study this topic.

To study the 'Variational methods applied to eigenvalue problems' topic, normally, you should have completed Calculus of variations and advanced calculus (M820).

The number of students on each topic may be limited so you are advised to register early, noting that you may not be offered your first choice of topic.

All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.

If you have any doubt about the suitability of the module, please speak to an adviser.

Register

Start	End	Fee	Register
03 Oct 2020	Jun 2021	Not yet available	Registration closes 10/09/20 (places subject to availability) Register
This module is expected to start for the last time in October 2021.

Future availability

Dissertation in mathematics (M840) starts once a year – in October. This page describes the module that will start in October 2019. We expect it to start for the last time in October 2025.

Additional costs

Study costs

There may be extra costs on top of the tuition fee, such as a laptop, travel to tutorials, set books and internet access.

Study weekend

This module normally includes an optional study weekend. For each day you choose to attend, you must pay an additional charge of around £60 to cover tuition and refreshments during the day. You’ll pay this charge when you book, after you’ve registered on the module. You must also pay for your travel to and from the venue and your accommodation if you need it.

Ways to pay

We know there’s a lot to think about when choosing to study, not least how much it’s going to cost and how you can pay.

That’s why we keep our fees as low as possible and offer a range of flexible payment and funding options, including a postgraduate loan, if you study this module as part of an eligible qualification. To find out more, see Fees and funding.

Study materials

What's included

Module notes, other printed materials.

You will need

You will need to buy the set book relevant for your topic (see 'Materials to buy' section).

Computing requirements

A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

A desktop or laptop computer with Windows 7 or higher
The screen must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.

Materials to buy

Set books

de Boor, C. A Practical Guide to Splines (Revised edn) Springer £64.99 - ISBN 9780387953663 Advances in approximation theory option set book.
Gray, J. Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century Springer £29.99 - ISBN 9780857290595 History of modern geometry option set book. Please ensure you purchase the December 2010 edition.
Godsil, C. & Royle, G. Algebraic Graph Theory Springer £36.99 - ISBN 9780387952208 Algebraic graph theory option set book.

Note: All of these books are Print on Demand, please allow at least 2 weeks for receipt following order.

If you have a disability

The material contains small print and diagrams, which may cause problems if you find reading text difficult. Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader and mathematical materials may be particularly difficult to read in this way. Alternative formats of the study materials may be available in the future.

If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Visit our Disability support website to find more about what we offer.

Dissertation in mathematics

Qualifications

Module

What you will study

History of modern geometry

Advances in approximation theory

Variational methods applied to eigenvalue problems

Algebraic graph theory

You will learn

Teaching and assessment

Support from your tutor

Assessment

Course work includes

Course satisfaction survey

Future availability

Regulations

Entry requirements

Register

Future availability

Additional costs

Study costs

Study weekend

Ways to pay

Study materials

What's included

You will need

Computing requirements

Materials to buy

Set books

If you have a disability

The Open University

OU Community

OU Students Community

Support

Study

Policy

What you will study

History of modern geometry

Advances in approximation theory

Variational methods applied to eigenvalue problems

Algebraic graph theory

You will learn

Teaching and assessment

Support from your tutor

Assessment

Course work includes

Course satisfaction survey

Future availability

Regulations

Entry requirements

Register

Future availability

Additional costs

Study costs

Study weekend

Ways to pay

Study materials

What's included

You will need

Computing requirements

Materials to buy

Set books

If you have a disability

Where do you live?