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pThis free course accommodates an introduction to rings and polynomials. We see that polynomial rings have many properties in common with the integers; for instance, we will outline a division algorithm, and this permits us to develop the analogue of the best common issue for 2 polynomials. Section 2 evaluations concepts of conditional possibilities and introduces Bayes’ theorem and its use in updating beliefs a couple of proposition, when data are noticed, or information turns into out there. This free course consolidates and builds on group principle studied at OU level 2 or equal. Section 1 describes the method to assemble a gaggle known as the direct product of two given teams, after which describes sure conditions beneath which a group can be thought to be the direct product of its subgroups. Section 1 offers a quick introduction to the sorts of problem that come up in Number Theory./p