msc in mathematics - the open university · 2013. 3. 7. · approximation theory (m832) credits: 30...

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MSc in MathematicsDistance learning degree qualification

QUALIFICATION LEAFLET

The modules may well be of interest to mathematically inclined scientists and engineers as well as to mathematicians.

Career relevance and employabilityMathematics is at the heart of advances in science, engineering and technology, as well as being an indispensable problem-solving and decision-making tool in many other areas of life. It is no surprise therefore that mathematics postgraduates can be found throughout industry, business and commerce, in the public and private sectors. Employers value the intellectual rigour and reasoning skills that mathematics students can acquire, their familiarity with numerical and symbolic thinking and the analytic approach to problem-solving which is their hallmark.There are a variety of reasons for studying mathematics at postgraduate level. You may want a postgraduate qualification in order to distinguish yourself from an increasingly large graduate population. You may find, particularly if you are a professional programmer or work in finance, that your undergraduate mathematical knowledge is becoming insufficient for your career requirements, especially if you are hoping to specialise in one of the more mathematical areas, which are becoming more sought after by employers. The extent of opportunities is vast and mathematics postgraduates are equipped with skills and knowledge required for jobs in fields such as finance, education, engineering, science and business, as well as mathematics and mathematical science research.

Credit for previous study elsewhereFor this qualification, we do not allow you to count credit for study you have already done elsewhere.

ModulesFor this 180-credit masters degree you require:

150 credits from the following optional modules:

Postgraduate compulsory module CreditsAdvanced mathematical methods (M833)

30

Analytic number theory I (M823) 30

Anaytic number theory II (M829) 30

Applied complex variables (M828) 30

Approximation theory (M832) 30

Calculus of variations and advanced calculus (M820)

30

Coding theory (M836) 30

Fractal geometry (M835) 30

Functional analysis (M826) 30

Nonlinear ordinary differential equations (M821)

30

And 30 credits from the following compulsory module:

Postgraduate compulsory module CreditsDissertation in mathematics (M840) 30

Qualification detailsThe MSc in Mathematics course has been designed for students who want to continue their mathematics studies by delving more deeply into particular aspects of pure and applied mathematics.

1 QUALIFICATION LEAFLET MSc in Mathematics (F04) 2

For more information and to register go to www.openuniversity.edu, or call +44 845 241 6555 For more information and to register go to www.openuniversity.edu, or call +44 845 241 6555

For a full list of modules available, please refer to our website, www.openuniversity.edu.

Assessment keyEMA = End-of-module assessment

iCMA = Interactive computer marked assessment

TMA = Tutor-marked assignment

Advanced mathematical methods (M833)

Credits: 30 at Postgraduate

Assessment: 4 TMAs, 1 Examination

This course teaches advanced mathematical methods with the aid of Maple, an algebraic computing language with graphics and numerical capabilities, which you’ll be taught how to use. Although the emphasis is on mathematical methods, you’ll use Maple partly to extend the use of these methods, partly to help you to visualise the mathematics and partly to enable you to combine conventional analytic techniques with numerical analysis. You’ll explore various forms of approximations, perturbation expansions, accelerated convergence methods including Padé approximants, asymptotic expansions of integrals and some eigenvalue problems.

Analytic number theory I (M823)



Number theory has its roots in ancient history but particularly since the seventeenth century, it has undergone intensive development using ideas from many branches of mathematics. In spite of the subject’s maturity, there are still unsolved problems that are easy to state and understand – for example, is every even number greater than two the sum of two primes? In this course, (and in Analytic number theory II (M829)) you’ll study number theory using techniques from analysis, in particular, the convergence of series and the calculus of residues.

Analytic number theory II (M829)



This module continues to explore number theory and is based on the readings from T.M. Apostol’s Introduction to Analytic Number Theory.

Applied complex variables (M828)



This course is based on Applied Complex Variables by J. W. Dettman (reprinted by Dover, 1984), and will appeal to scientists and engineers as well as to mathematicians. Complex variable theory pervades a wide variety of important subjects and this course teaches topics that are both useful in the theoretical sciences and of interest in their own right.

Approximation theory (M832)



Approximation theory is concerned with approximating functions of a given class using functions from another, usually more elementary, class. A simple example is the problem of approximating a function such as ex by means of polynomial functions. The efficient solution of such problems is of great importance for computing, and this course will give you a general introduction to the mathematical theory behind many approximation methods in common use. The course is based on the set book Approximation Theory and Methods by M. J. D. Powell.

Calculus of variations and advanced calculus (M820)



The calculus of variations, which plays an important role in both pure and applied mathematics, dates from the time of Newton. Development of the subject started mainly with the work of Euler and Lagrange in the eighteenth century and still continues. This course, which for most students begins the MSc in Mathematics programme, develops the theory of the calculus of variations. It also introduces other topics including the calculus of functions of several real variables; and ideas of convergence, particularly of sequences of functions and normed vector spaces – a working knowledge of which is required both in this and other modules in the MSc in Mathematics programme.

Coding theory (M836)



This course deals with the theory of error-detecting and error-correcting codes. In particular, it investigates their constraints and bounds, and introduces a wide variety of linear and nonlinear codes – together with associated encoding and decoding procedures. You’ll analyse the structure and properties of these codes,

Modules

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investigate links between the theory of error-correcting codes and other mathematical structures, and examine the applicability of codes to real situations. You’ll also look at the concepts of optimal and perfect codes, and examine a wide variety of codes, including some constructed from other mathematical structures.

Fractal geometry (M835)



There has recently been an explosion of interest in the mathematics of fractals – sets whose geometry cannot easily be described in classical terms. There’s no simple definition but all fractals have a highly intricate structure. Many fractals contain copies of themselves at many different scales, and computer pictures have shown that such sets (which are often very beautiful) are a very good representation of shapes of natural phenomena such as clouds, mountains and ferns. This course deals with the theory of fractals and their geometry, and looks at examples to which the theory can be applied.

Functional analysis (M826)



Modern mathematics places emphasis on classes of functions, rather than special properties of individual functions. Functions are considered as elements of a set and these sets can usually be given the additional structure of a linear and topological space. The interplay of these structures gives the subject its characteristic flavour. Along with the set of functions, this course considers sets of mappings from the set into various other sets, particularly, linear mappings onto the set itself (operators) and into complex numbers (linear functionals).

Nonlinear ordinary differential equations (M821)



Relevant to scientists and engineers as well as mathematicians, this introduction to basic theory and simpler approximation schemes covers systems with two degrees of freedom. It introduces the geometric aspects of the two-dimensional phase space, the importance of fixed points and how they can be classified, and the notion of a limit cycle. You’ll develop schemes to approximate the solutions of autonomous and non-autonomous equations to understand how these solutions behave. Periodically forced nonlinear oscillators and nonlinear oscillators with periodically time-varying parameters leading to parametric resonances are discussed, along with the stability of these solutions and tests for obtaining stability.

Dissertation in mathematics (M840)


Assessment: 2 TMAs, 1 EMA

This course 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.

For more information and to register go to www.openuniversity.edu, or call +44 845 241 6555

3 QUALIFICATION LEAFLET

Can I study in any country?This course is approved for study in most countries. Please use the Course Finder menu at www.openuniversity.edu to see if it is available in your country.

Is the OU course recognised in my country?An OU degree is equal in academic standard to a degree from any other British university. The University is subject to the same quality assurance procedures, through the Quality Assurance Agency (QAA), as all other British universities, and uses external assessors and examiners to ensure comparability of standard and level in its courses.A leaflet is available on how you can apply for formal recognition in your country. Please contact us to receive a copy.

What tutor support will I receive?The OU excels in its unrivalled support for students. You’ll have email and online support from a tutor and you will be able to discuss your study in online tutor group discussions, using our customised learning environment. Our community websites Platform and OpenLearn offer a different perspective on your subject, and a huge range of OU resources on YouTube and iTunes U can expand your understanding. In addition, you can tap into a range of enthusiastic and welcoming OU social network groups on Facebook, Twitter and LinkedIn.

Are there any entry requirements?To gain entry to our postgraduate programmes you’ll normally need an undergraduate degree or equivalent. However, your previous work experience and study, or

qualifications from other higher-education institutions, may all count towards programme entry.As part of the registration process, however, you will be asked to confirm your proficiency in English. (If you are unsure, you can take a short online test, which you will find when completing the online registration form.)

Can I count previous study towards an OU qualification?For this qualification, we do not allow you to count credit for study you have already done elsewhere.

How do you work towards a qualification? We measure the size of our qualifications in credits - you need 60 credits for the certificate, 120 credits for the diploma and 180 credits for the masters degree.

How long does it take? Our qualifications are designed to be flexible. So if you want to vary the amount of time you spend studying, you can. The table below is a guide on the time required, but call us today to discuss how you can vary the study intensity and therefore the time taken to complete your course.

Postgraduate qualifications

Credits required

Time required to complete1

Certificate 60 1 year part-time studyDiploma 120 2 years part-time studyMasters degree 180 3-4 years part-time study

1For illustrative purposes only – in most cases you can vary the number of credits taken per year and therefore the time taken to complete the course.

FAQs


MSc in Mathematics (F04) 4




How much will it cost?You pay for your postgraduate studies module by module, rather than for an entire programme up front. Therefore, the total cost of a qualification may vary according to which modules you choose and how long you take to complete your degree. The EU fee for this qualification in 2012/13 is:

£7115

Please note: prices are approximate and subject to change. Please check our website or call us for latest details.

For information please go to www.openuniversity.edu and view the details on the Courses pages.

When can I start?To give you more opportunities to start, most qualifications have two intakes a year – October and February for this qualification.

Can I meet and network with other students?Definitely – when you start with the OU you automatically become a member of the Open University Student Association (OUSA). OUSA also runs a popular student forum site. For more information, go to www.ousa.org.uk. Once you have gained your qualification, you can join the OU Alumni Association, our vibrant and active alumni community with 280,000 members worldwide. You will enjoy many membership benefits, including regular newsletters, good networking opportunities and access to the alumni website.

How is my privacy protected?We record your personal information when you contact us and use this to manage registration, study, examination and other services. When you register, we’ll tell you more about how we process and use your personal information.

When should I apply?Apply as early as you can – particularly if you wish to claim for credit for previous study. Registration open dates are shown in the Courses section on each qualification page at www.openuniversity.edu.

Go to www.openuniversity.edu, select the Courses section and the degree you require. You will then be asked to select your first module to register.

Alternatively call us on +44 845 241 6555.

Don’t worry, you don’t need to pay anything at this stage.

As soon as you have registered you’ll get an email confirmation which contains your login details.

What do I need to do next?

It takes just 2 simple steps.Begin the process to secure your place. Here's how easy it is.

Before you start studying you will need to choose and register on your first modules and arrange payment; instructions for this will be emailed to you. Once complete you will officially be an Open University student – welcome!


2. Choose your first module, make payment to enrol

1. Register now

5 QUALIFICATION LEAFLET MSc in Mathematics (F04) 6



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The Open University is incorporated by Royal Charter (RC 000391), an exempt charity in England and Wales and a charity registered in Scotland (SC 038302).While we have done everything possible to make sure the information in this publication is accurate, it may change due to regulations or policy, or because of financial or other reasons.

Copyright © 2013 The Open University.

All details shown in this leaflet are correct as at February 2013, but are subject to change. Please call +44 845 241 6555 for the latest details.

msc in mathematics - the open university · 2013. 3. 7. · approximation theory (m832) credits: 30...

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