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...course contains an introduction to metric spaces and continuity. The key idea is to use three particular properties of the Euclidean distance as the basis for defining what is meant by a general distance function, a metric. Section 1 introduces the idea of a metric space and shows how this concept allows us to generalise the notion of continuity. Section 2 develops the...

...course, Analytical science: secrets of the Mary Rose, teaches you about the analytical techniques that are used in the research and investigation of historical objects using the case study of the Mary Rose. It covers the use of sonar to locate shipwrecks, and the analysis of the artefacts found on the ship, and the crew and their remains...This free course, Analytical...

...course looks at point estimation, that is, the estimation of the value of the parameter of a statistical model by a single number, a point estimate for the parameter. Section 1 develops some aspects of maximum likelihood estimation. In particular, you will find out how to obtain the maximum likelihood estimator of an unknown parameter, using calculus. You will need to do...

...course looks at a number of the basic properties of statistical models. Section 1 is concerned with the distributions of continuous random variables which are described by their probability density functions (pdfs) and cumulative distribution functions (cdfs). Section 2 is concerned with moments and covers, the concept of expectation or expected value, the familiar notion...