We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. Whatever your background, you should assess your suitability for this MSc in Mathematics module by trying our diagnostic quiz.Īll teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. Mathematical methods, models and modelling (MST210) (or the discontinued module MST209), and/or Pure mathematics (M208) (or the discontinued module M203) and some study of mathematics at third year honours level should provide adequate preparation. You should have a sound working knowledge of undergraduate calculus and have studied the elements of vector spaces. Students already registered for a qualification of which M820 is a constituent part will normally be admitted to M820.
Non-graduates will not normally be admitted to M820 unless as part of another Open University qualification.
If you do not have such a qualification, your application will be considered and you may be asked to complete an entry test. You should normally have a minimum of a 2:2 honours degree in mathematics or a 2:1 honours degree in a subject with a high mathematical content. You must declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention. Note you must complete this module if you wish to take the ‘Variational methods applied to eigenvalue problems’ topic for your Dissertation in mathematics (M840). This module and Analytic number theory 1 (M823) are entry-level modules for the MSc in Mathematics (F04), and normally you should have studied one of them before progressing to the intermediate and advanced intermediate modules in the degree. Successful study of this module should enhance your skills in understanding complex mathematical texts, communicating solutions to problems clearly and interpreting mathematical results in real-world terms. Applications will be discussed but you are not expected to have a detailed understanding of the underlying physical ideas. Throughout, the emphasis is on the mathematical ideas and one aim is to illustrate the need for mathematical rigour. The module also contains some more advanced material, such as an analysis of the second variation and of discontinuous solutions it ends with a discussion of the general properties of the solutions of an important class of linear differential equations, namely Sturm–Liouville systems. Many of the simple applications of calculus of variations are described and, where possible, the historical context of these problems is discussed. This module provides an introduction to the central ideas of variational problems, as well as some of the mathematical background necessary for the subject. The calculus of variations also provides useful methods of approximating solutions of linear differential equations furthermore, variational principles also provide the theoretical underpinning for the coordinate-free formulations of many laws of nature. Problems such as the determination of the shortest curve between two points on a given smooth surface and the shapes of soap films are most easily formulated using ideas from the calculus of variations.
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