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This is a structured module, partly delivered by self-study and partly by lectures, designed for MMath students in their fourth year.

A semigroup is a non-empty set on which is defined an associative binary operation. Unlike a group, a semigroup needn't contain an identity element nor inverses for each element. For example, the natural numbers N with the operation of addition + is a semigroup as is the set T(X) of all maps from a set X to itself with operation of composition of maps. As another example consider the set of all nxn matrices with real coefficients with the binary operation of matrix multiplication. We already know that matrix multiplication is associative and this set forms a semigroup.

In some respects we can think of a semigroup as an abstraction of a group but on the other hand it is sometimes useful to compare the theory of semigroups with that of rings (the 'multiplicative part' of a ring is just a semigroup) and many of the historical developments in the theory of semigroups owe much to these two theories. However recent work has highlighted strong connections with, for example, many aspects of theoretical computer science (automata theory, theory of codes and formal language theory) as well as with other areas of mathematics such as the theory of ordered structures and (partial) symmetries.

This module is focused on developing the basics of Signals, Control and Communications:
• To introduce the underpinning elements of signal processing.
• To develop an approach to the modelling of dynamic electromechanical and electronic systems
• To introduce the basic concepts and applications of communications.

This module is focused on developing the basics of Signals, Control and Communications:
• To introduce the underpinning elements of signal processing.
• To develop an approach to the modelling of dynamic electromechanical and electronic systems
• To introduce the basic concepts and applications of communications.

This module will develop understanding of how to quantitatively analyse data in the social sciences, building on the foundations from the research methods modules in the first year. It will be focused around the common methods for data analysis that are needed within the social science and will prepare students for conducting their own research in their dissertations. The module will also satisfy the requirements of the British Psychological Association (BPA) for those who need this in their degree.

The module will use real-world examples to illustrate the methods, giving participants insight into different studies that will be of interest, with examples coming from all disciplinary areas involved, including Psychology. The methods will be taught through flipped learning, with instructional videos placed online, supplemented by lectures and tutorials were problem sets will be considered. A range of further examples, as worksheets and recorded lectures, will be placed online in order to create a comprehensive resource for the methods, with the online material further tailored to different disciplines.

The module will follow the BPA requirements, including the use of the APA style of referencing.

This module will develop understanding of how to quantitatively analyse data in the social sciences, building on the foundations from the research methods modules in the first year. It will be focused around the common methods for data analysis that are needed within the social science and will prepare students for conducting their own research in their dissertations. The module will also satisfy the requirements of the British Psychological Association (BPA) for those who need this in their degree.

The module will use real-world examples to illustrate the methods, giving participants insight into different studies that will be of interest, with examples coming from all disciplinary areas involved, including Psychology. The methods will be taught through flipped learning, with instructional videos placed online, supplemented by lectures and tutorials were problem sets will be considered. A range of further examples, as worksheets and recorded lectures, will be placed online in order to create a comprehensive resource for the methods, with the online material further tailored to different disciplines.

The module will follow the BPA requirements, including the use of the APA style of referencing.

This module is designed to provide you with a broad introduction to the diverse cultures and histories of Spain, Latin America and the Portuguese-speaking or 'Lusophone' world. By studying various types of primary and secondary sources, you will become familiar with a wide range of themes, events and ideas from those regions.

All materials will be available in English, allowing students with little or no knowledge of Spanish and Portuguese to engage with the module.

This module is designed to provide you with a broad introduction to the culture, history and language of Spain, Latin America and the Spanish speaking World. By studying various types of primary and secondary sources, you will become familiar with a wide range of themes, events and ideas from the regions.

All materials will be available in English, allowing students with little or no knowledge of the Spanish language to engage with the module.

This module is designed to provide you with a broad introduction to the culture, history and language of Spain, Latin America and the Spanish speaking World. By studying various types of primary and secondary sources, you will become familiar with a wide range of themes, events and ideas from the regions.

All materials will be available in English, allowing students with little or no knowledge of the Spanish language to engage with the module.

This prepares you for the rest of the programme and so it is intended to support you in concurrent and subsequent modules by developing your skills with the statistical analyses that are used in quantitative approaches to research. You will develop your understanding of how to plan statistical analyses, how to carry out a bivariate statistical analysis, and how to use the results of a statistical analysis to advance scientific knowledge in a given area. You will use all of this knowledge to complete a partially written research report by carrying out a statistical analysis of a real-world educational dataset and then writing-up the results of this analysis in a critical manner.

This prepares you for the rest of the programme and so it is intended to support you in concurrent and subsequent modules by developing your skills with the statistical analyses that are used in quantitative approaches to research. You will develop your understanding of how to plan statistical analyses, how to carry out a bivariate statistical analysis, and how to use the results of a statistical analysis to advance scientific knowledge in a given area. You will use all of this knowledge to complete a partially written research report by carrying out a statistical analysis of a real-world educational dataset and then writing-up the results of this analysis in a critical manner.