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4434Statistics - an intuitive introduction : standard deviation
http://www.merlot.org/merlot/viewMaterial.htm?id=490961
A standard way of measuring statistical variability: standard deviation and the associated concepts of variance and degrees of freedom.Beyond infinity
http://www.merlot.org/merlot/viewMaterial.htm?id=490945
This popular maths talk gives an introduction to various different kinds of infinity, both countable and uncountable. These concepts are illustrated in a somewhat informal way using the notion of Hilbert's infinite hotel. In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should learn that many apparently different types of infinity are really the same size. However, there are genuinely "more" real numbers than there are positive integers, as is shown in the more challenging final section, using Cantor's diagonalization argument.Functional analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=490995
As taught in 2006-2007 and 2007-2008. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include: – norm topology and topological isomorphism; – boundedness of operators; – compactness and finite dimensionality; – extension of functionals; – weak*-compactness; – sequence spaces and duality; – basic properties of Banach algebras. Suitable for: Undergraduate students Level Four Dr Joel F. Feinstein School of Mathematical Sciences Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.How and why we do mathematical proofs
http://www.merlot.org/merlot/viewMaterial.htm?id=490979
This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009/10 The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs. In particular, the student will learn the following: * proofs can help you to really see why a result is true; * problems that are easy to state can be hard to solve (e.g. Fermat's Last Theorem); * sometimes statements which appear to be intuitively obvious may turn out to be false (e.g. Simpson's paradox); * the answer to a question will often depend crucially on the definitions you are working with; * how to start proofs; * how and when to use definitions and known results. The module is organised into three sections: Why; How (Part I); How (Part II) With practice, students should become fluent in these routine aspects of writing proofs, and this will allow them to focus instead on the more creative and interesting aspects of constructing proofs. A practice sheet is included after students have completed all three sections. Each section is suitable for a different level of audience, as described below: Suitable for: Foundation, undergraduate year one and undergraduate year two students Section 1: Why: Anyone with a knowledge of elementary algebra and prime numbers, as may be obtained by studying A level mathematics. (Foundation) Section 2: How (Part I) – Suitable for anyone with a knowledge of elementary algebra (including odd numbers, multiples of eight and the binomial theorem for expanding powers of (a+b)), and functions from the set of real numbers to itself (odd functions, even functions, multiplication and composition of functions). (Undergraduate year one) Section 3: How (Part II) – Requires some background knowledge of convergence and divergence of series of real numbers. A revision sheet is available. (Undergraduate year two) Dr Joel Feinstein, School of Mathematical Sciences Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this areaIntroduction to compact operators
http://www.merlot.org/merlot/viewMaterial.htm?id=490947
The aim of this session is to cover the basic theory of compact linear operators on Banach spaces. This includes definitions and statements of the background and main results, with illustrative examples and some proofs. Target audience: This material is accessible to anyone who has a basic knowledge of metric space topology, and who knows what a bounded linear operator on a Banach space is. It is most likely to be suitable for postgraduate students or final year undergraduates.Levels of measurement
http://www.merlot.org/merlot/viewMaterial.htm?id=490954
Aimed at statistics beginners, this learning object describes, and gives examples of, the four levels of measurement of data: nominal, ordinal, interval and ratio.Mathematical analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=490999
This is a module framework. It can be viewed online or downloaded as a zip file. It is as taught in 2009-2010. This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associated theory, with a strong emphasis on rigorous proof. This module is suitable for study at undergraduate level 2. Dr Joel Feinstein, School of Mathematical Sciences Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.Number for Nurses: Division
http://www.merlot.org/merlot/viewMaterial.htm?id=490914
The Number for Nurses Computer Assisted Learning Package begins with a basic principles section which is followed by application to nursing practice. The basic principles section deals with addition, subtraction, multiplication, division, S.I. units and scales and gauges. In each area a variety of methods are used to enable the student to understand these principles, through interactive tutorials and consolidate learning through exercises. The aim of the division section is to help the student become competent both in the recognition of factors in fractions, and the ability to transfer simple fractions into long division format. These skills are particularly relevant during clinical practice as the nurse will be expected to utilise these methods to accurately calculate the drug dose to be administered to a patient. The package can be accessed from the first year of the course and it is expected that the student will work through the basic principles section first. The application section will support the student through the second and third years of the course, as they become involved in the more complex elements of nursing skills. By the end of the third year the package should have enabled the student to gain the competency in application of number skills which will facilitate the transfer to qualified nurse status.Quantum field theory
http://www.merlot.org/merlot/viewMaterial.htm?id=490980
This is a module framework. It can be viewed online or downloaded as a zip file. Last taught in Spring Semester 2006 A compilation of fourteen lectures in PDF format on the subject of quantum field theory. This module is suitable for 3rd or 4th year undergraduate and postgraduate level learners. Suitable for year 3/4 undergraduate and postgraduate study. Dr Kirill Krasnov, School of Mathematical Sciences Dr Kirill Krasnov is a Lecturer at the University of Nottingham. After studying physics in Kiev, Ukraine, he carried out research for his doctorate at Pennsylvania State University, USA and then held post-doctoral positions at University of California, Santa Barbara and Max Planck Institute for Gravitational Physics, Germany. His main research interest is in the field of quantum gravity. Dr Krasnov is a holder of an EPSRC Advanced Fellowship.Regularity conditions for Banach function algebras
http://www.merlot.org/merlot/viewMaterial.htm?id=490972
In June 2009 the Operator Algebras and Applications International Summer School was held in Lisbon. Dr Joel Feinstein taught one of the four courses available on Regularity conditions for Banach function algebras. He delivered four 90 minute lectures on and this learning object contains the slides, handouts, annotated slides and audio podcasts from each session. Banach function algebras are complete normed algebras of bounded, continuous, complex-valued functions defined on topological spaces.