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...course contains an introduction to rings and polynomials. We see that polynomial rings have many properties in common with the integers; for example, we can define a division algorithm, and this enables us to develop the analogue of the highest common factor for two polynomials. Section 1 explores the abstract definitions of a ring and a field. Sections 2 and 3 define...

...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...