This module comprises of both oral and aural skills, to be taken alongside the corresponding Written Language module. It builds upon skills gained in the first year.

The module aims to enhance students’ linguistic proficiency in spoken Chinese in a range of formal and informal settings (both spontaneous and prepared). Specific attention will be given to developing good, accurate pronunciation and intonations as well as fluency, accuracy of grammar, and vocabulary when speaking the language.

This module also aims at broadening students’ knowledge about different aspects of modern Chinese-speaking societies, politics and culture, and contemporary issues and institutions.

By the end of this module, we hope you will have enhanced your comprehension of the spoken language, as used in both formal speech, and in everyday life situations including those that they may encounter in Chinese-speaking countries.

This module comprises of both oral and aural skills, to be taken alongside the corresponding Written Language module. It builds upon skills gained in the first year of the Intensive course. Students who have taken the Intensive language course in their first year, normally follow this course throughout the second year.

The module aims to enhance students’ linguistic proficiency in spoken Chinese in a range of formal and informal settings (both spontaneous and prepared). Specific attention will be given to developing good, accurate pronunciation and intonations well as fluency, accuracy of grammar, and vocabulary when speaking the language.

This module also aims at broadening students’ knowledge about different aspects of modern society, politics and culture, and contemporary issues and institutions in order to prepare them for residence abroad in their 3rd year.

By the end of this module, students will have had the opportunity to enhance their comprehension of the spoken language, as used in both formal speech, and in everyday life situations including those that they may encounter in Chinese-speaking countries.

This module comprises of reading and writing skills to be taken alongside the Oral Skills module.

This module aims to consolidate skills gained by students in the first year of study, and enable them to build a level of competence and confidence required to familiarise themselves with the culture and society of countries where their studied language is spoken.

The module aims to enhance your proficiency in understanding written Chinese, as well as in the writing of Chinese (notes, reports, summaries, essays, projects, etc.) including translation from and into Chinese; and the systematic study of Chinese lexis, grammar and syntax.

The module aims to enhance your linguistic proficiency, with particular emphasis on reading a variety of sources and on writing fluently and accurately in the language, in a variety of registers.

This module comprises of reading and writing skills to be taken alongside the Oral Skills module.

This module aims to consolidate skills you have developed in the first year of study, and enable you to build a level of competence and confidence required to familiarise yourselves with the culture and society of countries where your studied language is spoken.

The module aims to enhance your proficiency in understanding spoken Chinese, as well as in the writing of Chinese (notes, reports, summaries, essays, projects, etc.) including translation from and into Chinese; and the systematic study of Chinese lexis, grammar and syntax.

The module aims to enhance your linguistic proficiency, with particular emphasis on reading a variety of sources and on writing fluently and accurately in the language, in a variety of registers.

This module is a non-credit bearing module. If you are a major student going abroad in your second or third year you are enrolled on it during the year prior to your departure, and timetabled to attend the events. These include: introduction to the International Placement Year and choice of activities; British Council English Language Assistantships and how to apply; introduction to partner universities and how they function; working in companies abroad; finance during the International Placement Year; research skills and questionnaire design; teaching abroad; curriculum writing and employability skills; and welfare and wellbeing.

This modules focuses on the ‘must-know’ historical moments, political events and aesthetic movements that shaped Chinese and Sinophone cultures in the 19th, 20th and 21st centuries.

You will hone your skills in cultural analysis via diverse media as we explored four topics:

• Revolutions and Reforms
• Dreams and Futures
• Walls and Spaces
• Identities and Relationships

During the module, you'll consider themes such as power, resistance, trauma, aspirations, wellbeing, urbanisation, the urban/rural divide, migration, individualisation, collectivisation, gender, sexuality, ethnicity, class, and family. Texts, films and art will be studied in historical and cultural contexts, with due regard to relevant global trends such as imperialism, colonialism, postcolonialism, democracy, neoliberalism and nationalism.

During your journey through moments and movements across two centuries of Chinese cultural history, you'll encounter some of the most radical thinkers, writers, filmmakers and creative artists that make the Chinese-language intellectual tradition so distinctive and fascinating. You'll discover a stimulating range of cultural forms and learn how to reflect critically on them as expressions of multi-faceted, nuanced societies.

This module builds on the binary operations studies in previous modules, such as addition or multiplication of numbers and composition of functions. Here, students will select a small number of properties which these and other examples have in common, and use them to define a group.

They will also consider the elementary properties of groups. By looking at maps between groups which 'preserve structure', a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same' will be discovered.

Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives students a way to abstractly model various number systems, proving results that can be applied in many different situations, such as number theory and geometry. Familiar examples of rings include the integers, the integers modulation, the rational numbers, matrices and polynomials; several less familiar examples will also be explored.

Complex Analysis has its origins in differential calculus and the study of polynomial equations. In this module, students will consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. They will use integral calculus of complex functions to find elegant and important results and will also use classical theorems to evaluate real integrals.

The first part of the module reviews complex numbers, and presents complex series and the complex derivative in a style similar to calculus. The module then introduces integrals along curves and develops complex function theory from Cauchy's Theorem for a triangle, which is proved by way of a bisection argument. These analytic ideas are used to prove the fundamental theorem of algebra, that every non-constant complex polynomial has a root. Finally, the theory is employed to evaluate some definite integrals.The module ends with basic discussion of harmonic functions, which play a significant role in physics.

Students will gain a solid understanding of computation and computer programming within the context of maths and statistics. This module expands on five key areas:

• Programming and R
• Numerical solutions of equations
• Numerical differentiation and integration
• Monte Carlo methods
• Numerical solutions to ODEs

Under these headings, students will study a range of complex mathematical concepts, such as: data structures, fixed-point iteration, higher dimensions, first and second derivatives, non-parametric bootstraps, and modified Euler methods.

Throughout the module, students will gain an understanding of general programming and algorithms. They will develop a good level of IT skills and familiarity with computer tools that support mathematical computation.

Over the course of this module, students will have the opportunity to put their knowledge and skills into practice. Workshops, based in dedicated computing labs, allow them to gain relatable, practical experience of computational mathematics.

The humanities were once regarded as having an intrinsic value. As disciplines devoted to the study of cultures and societies, the humanities enjoyed prestige as areas of inquiry that were uniquely placed to probe the human condition. But do the humanities still have a role to play in a world where science and technology appear to be driving political and social agendas? Can they help us address global challenges?

This module encourages you to engage with these questions by examining the history of the humanities in different linguistic and cultural contexts, by exploring the connection between the humanities and other disciplines across time and space, and by engaging with the tradition of critical thinking that is central to the identity of the discipline.

You will explore the intersection between the humanities and other disciplines with the aim of understanding what other disciplines can bring to study of art and, conversely, the value of art in our contemporary, outcome-driven world.

In this module, students learn how the language used by institutions shapes individual perceptions of identity. It aims to provide a basic theoretical framework for understanding the relationship between language and power as reflected in current language policies at regional, national, and supranational levels. It gives you the opportunity to recognise forms of prestige and stigma associated with varieties of the three main languages under study. We aim to raise critical awareness of the portrayal and representation of linguistic variations in the media and in the sphere of literature.

The main topics covered in the course include language and power; European language policies; German as a pluricentric language; regional variations of France: linguistic diversity and French national identity; the languages and language attitudes of Spain (Castilian Spanish, Catalan, Basque, Galician); language and power in the Sinophone world.

Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.

They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

Probability provides the theoretical basis for statistics and is of interest in its own right.

Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.

Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

This module seeks to support you to apply your linguistic and cultural understanding in a specific professional context. This module gives you the opportunity to spend time on a work-based placement in the UK or abroad. You will be given the opportunity to develop, reflect on and articulate both the range of competences and the linguistic and cross-cultural skills that enhance employability by working in language-related professional contexts and reflecting on key issues in relation to their placement organisation. There is the opportunity to join a local work placement developed by the department, or for you to source your own placements (subject to departmental approval). Workshops before and during the placement will provide preparation and guidance on sourcing, confirming and then reflecting on academic work. Students will share their experiences and learning with each other by means of end-of-module presentations.

Project Skills is a module designed to support and develop a range of key technical and professional skills that will be valuable for all career paths. Covering five major components, this module will guide students through and explore:

• Mathematical programmes
• Scientific writing
• Communication and presentation skills
• Individual projects
• Group projects

Students will gain an excellent grasp of LaTeX, learning to prepare mathematical documents; display mathematical symbols and formulae; create environments; and present tables and figures.

Scientific writing, communication and presentations skills will also be developed. Students will work on short and group projects to investigate mathematical or statistical topics, and present these in written reports and verbal presentations.

A thorough look will be taken at the limits of sequences and convergence of series during this module. Students will learn to extend the notion of a limit to functions, leading to the analysis of differentiation, including proper proofs of techniques learned at A-level.

Time will be spent studying the Intermediate Value Theorem and the Mean Value Theorem, and their many applications of widely differing kinds will be explored. The next topic is new: sequences and series of functions (rather than just numbers), which again has many applications and is central to more advanced analysis.

Next, the notion of integration will be put under the microscope. Once it is properly defined (via limits) students will learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. They will also explore some applications of integration that are quite different from the ones in A-level, such as estimations of discrete sums of series.

Further possible topics include Stirling's Formula, infinite products and Fourier series.

How do films deal with topics such as immigration, environment, the posthuman and gender? Do they entertain viewers, instruct them, or both?

This module explores European, Latin American, and Chinese films in their social and historical contexts; the topics mentioned are the focus of key lectures and seminars. The module begins with introductory lectures on cinema and society and on film aesthetics and content. The main aim is to make connections between the films and such contexts, not only on the level of narrative, characterisation and dialogue, but also on that of form and technique.

Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.

The focus will be on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.

Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.

This module explores cultural and theoretical approaches to queerness and LGBTQIA+ lives, identities, and politics across diverse linguistic and cultural contexts. It includes texts and artworks by philosophers, writers, filmmakers, and artists from the LGBTQIA+ community around the globe, asking how different queer voices and cultures have approached questions such as:

• What does it mean to be queer or LGBTQIA+ today?
• How are human experiences of gender, sexuality, and queer identity conceptualised and expressed?
• How do queer people stand up against oppression and violence, and how have they in the past?
• What might queer tomorrows look like?
• How do LGBTQIA+ people and communities imagine the future?

The module explores key theoretical approaches in queer theory, and gender and sexuality studies, typically spanning cutting-edge fields such as queer environmentalism, postcolonial queer studies, transgender studies, intersex studies, and the queer medical humanities.

This module aims to give you a background to and insight into the diversity of twentieth and twenty-first century thought and contemporary definitions of culture.

Some key questions explored on the module include: What is 'culture' and how does it work? How do 'art' and 'culture' relate to each other? What do we mean when we talk about the production and consumption of culture? Why does popular culture arouse conflicting responses? What role does the body play in our understanding of culture? How does culture define who we are? Can a work of culture be an act of resistance?

With these questions in mind, this module focuses on texts which raise questions about class, race, gender, and subcultures.

The module encourages intercultural dialogue between students from different backgrounds and specifically welcomes Visiting and International students.

As part of The International Placement Year you will normally spend at least eight months abroad in your third year. You will have the opportunity to:

• analyse the contemporary relevance of a tradition, contemporary social, political or economic issue, or a living part of the regional culture.
• reflect critically on cultural differences observed in everyday life such as social relationships, politics, attitudes to food, drink, religion, etc., explaining them in the context of various historical, social and cultural developments.
• think analytically about your intercultural position and understanding of the relevant culture(s).
• reflect on language use (different registers, varieties of pronunciation and accents, dialects, vocabulary and idiomatic expressions, and aspects of grammar) and the process of the acquisition of skills in the relevant language(s).

The module also aims to enhance and develop your language skills, with all assessments being written in the target language. If you have started a language as a beginner in year one you will spend a minimum of four months in a country where that language is spoken. If you are a joint honours student who is studying two languages, you may choose to spend the year in either of the two countries concerned or, if appropriate arrangements can be made, you can spend a semester in each country.

Lancaster University will make reasonable endeavours to place students at an approved overseas partner. Students conduct either a study placement at a partner University, a teaching assistantship placement with the British Council or an appropriate working placement with a vetted employer abroad or a combination of placements (please note that there are some restrictions on British Council placements which usually last for the whole of the academic year).

Joint honours degrees

If you are a joint honours student who is combining a language with a non-language subject, your placement year will provide the opportunity to develop your language skills and cultural awareness, but will not necessarily relate to the non-language aspect of your degree.

Lancaster University cannot accept responsibility for any financial aspects of your International Placement Year.

This module includes authentic texts only slightly adapted from the originals, with a special focus on contemporary Chinese society and institutions. You will have the opportunity to learn how to communicate comprehensively and systematically using the appropriate expressions and language norms in the right context.

You’ll have the opportunity to develop your skills in understanding and joining political, academic and journalistic discussions using advanced Chinese language skills. An aim of this module is for you to be able to translate between English and Chinese and develop an idiomatic style of formal writing.

It’s not necessary to have studied the Part I, Chinese Language 2 or 3 modules in order to continue on to this module. However you must have reached a CEFR (Common European Framework of Reference for Languages) B1-B2 level of Chinese proficiency.

This module is integrated with the Chinese Language 4 module.

This module has two main aims. The first one is to enhance your linguistic proficiency with emphasis on understanding of spoken and written Chinese, the speaking of Chinese (prepared and spontaneous) in both formal and informal settings, the writing of Chinese, and the systematic study of Chinese lexis, grammar and syntax. The second aim is to increase your awareness, knowledge and understanding of contemporary China.

By the end of this module we aim for you to have an informed interest in the society and culture of the Chinese-speaking world. You should also have acquired almost native-speaker abilities in both spoken and written language.

This is a non-credit bearing module aimed at preparation for coursework and employability. If you are a major student you will be timetabled to attend the events. These include areas such as returning to Lancaster, academic writing after the year abroad, careers information on graduate schemes and postgraduate study opportunities.

Students will be given a solid foundation in the basics of algebraic geometry. They will explore how curves can be described by algebraic equations, and learn how to use abstract groups in dealing with geometrical objects (curves). The module will present applications and results of the theory of elliptic curves and provide a useful link between concepts from algebra and geometry.

Students will also gain an understanding of the notions and the main results pertaining to elliptic curves, and the way that algebra and geometry are linked via polynomial equations. Finally, they will learn to perform algebraic computations with elliptic curves.

This module will consider different ways in which the concept of ‘dictatorship’ has been understood and critiqued throughout the twentieth century. Considering examples from Argentina, the Dominican Republic, Germany, Guinea, Italy, Kenya, Uganda and Zimbabwe, students will explore the differences between the Latin American caudillo, European dictators, and the ‘Big Men’ of Africa. Selected critical and theoretical sources will be drawn upon to develop a more critical understanding of dictatorship, including the work of Hannah Arendt, Roberto González Echevarría and Achille Mbembe.

The module will also examine relationships between dictatorship and cultural production. How have dictators represented themselves in their writing, speeches and literature? To what extent have they controlled cultural production and to what end? How, in turn, have they been represented in cultural production? What role do writers, artists and intellectuals play in evaluating and critiquing dictatorship? In turn, can the writer, artist or intellectual be considered to be a dictator in the particular world view he/she projects and/or the rhetoric he/she adopts?

Bayesian statistics provides a mechanism for making decisions in the presence of uncertainty. Using Bayes’ theorem, knowledge or rational beliefs are updated as fresh observations are collected. The purpose of the data collection exercise is expressed through a utility function, which is specific to the client or user. It defines what is to be gained or lost through taking particular actions in the current environment. Actions are continually made or not made depending on the expectation of this utility function at any point in time.

Bayesians admit probability as the sole measure of uncertainty. Thus Bayesian reasoning is based on a firm axiomatic system. In addition, since most people have an intuitive notion about probability, Bayesian analysis is readily communicated.

Combinatorics is the core subject of discrete mathematics which refers to the study of mathematical structures that are discrete in nature rather than continuous (for example graphs, lattices, designs and codes). While combinatorics is a huge subject - with many important connections to other areas of modern mathematics - it is a very accessible one.

In this module, students will be introduced to the fundamental topics of combinatorial enumeration (sophisticated counting methods), graph theory (graphs, networks and algorithms) and combinatorial design theory (Latin squares and block designs). They will also explore important practical applications of the results and methods.

Students’ knowledge of commutative rings as gained from their second year of study in Rings and Linear Algebra will be built upon, and an introduction to the fourth year Galois Theory module will be provided.

They will be introduced to two new classes of integral domains called Euclidean domains, where they have a counterpart of the division algorithm, and unique factorisation domains, in which an analogue of the Fundamental Theorem of Arithmetic holds.

How well-known concepts from the integers such as the highest common factor, the Euclidean algorithm, and factorisation of polynomials, carry over to this new setting, will also be explored.

This module introduces you to major themes that shape the experience of contemporary city dwellers: gender, social inequality, and practices of citizenship. These interlinking themes are introduced through novels, poetry and films and typically covers the following European, North American (with the emphasis on immigrant communities within its cities) and Latin American cities: New York, Mexico City, Santiago de Chile, Barcelona, and Berlin.

The combination of lectures, workshops and textual analysis encourages cross-referencing between the themes; students are encouraged to identify links between the topics studied (for example, gender and sexuality are relevant to an analysis of social inequality, and vice versa).

Questions relating to linear ordinary differential equations will be considered during this module. Differential equations arise throughout the applications of mathematics, and consequently the study of them has always been recognised as a fundamental branch of the subject. The module aims to give a systematic introduction to the topic, striking a balance between methods for finding solutions of particular types of equations, and theoretical results about the nature of solutions.

While explicit solutions can only be found for special types of equations, some of the ideas of real analysis allow us to answer questions about the existence and uniqueness of solutions to more general equations, as well as allowing us to study certain properties of these solutions.

This module is assessed entirely through coursework. Students are given a chance of pursuing a topic of their own interest, which is not covered in taught options. A dissertation consists of approximately 10,000 words written in English. The topic of dissertation must relate to French/German/Spanish language, or a comparison between two or more, or a general European issue. Any topic is subject to approval and must fall within the range of expertise of a member of staff.

Each student is assigned a supervisor, who provides regular supervision, and feedback on the first draft of the completed dissertation. The topic is agreed and discussed with the supervisor in the Summer Term of the second year, and preparatory research should begin during the Year Abroad.

The topic of smooth curves and surfaces in three-dimensional space is introduced. The various geometrical properties of these objects, such as length, area, torsion and curvature, will be explored and students will have the opportunity to discover the meaning of these quantities. They will then use a variety of examples to calculate these values, and will use those values to apply techniques from calculus and linear algebra.

A number of well-known concepts will be encountered, such as length and area, and some new ideas will be introduced, including the curvature and torsion of a curve, and the first and second fundamental forms of a surface. Students will learn how to compute these quantities for a variety of examples, and in doing so will develop their geometric intuition and understanding.

The study of graphs - mathematical objects used to model pairwise relations between objects - is a cornerstone of discrete mathematics. As a result, students will develop an appreciation for a range of discrete mathematical techniques while undertaking this module.

Throughout the module, students will also learn about structural notions, such as connectivity, and will explore trees, minor closed families of graphs, matrices related to graphs, the Tutte polynomial of small graphs, and planar graphs and analogues.

While studying these areas, students will gain experience of following and constructing mathematical proofs, and correctly and coherently using mathematical notation.

Students will develop the knowledge of groups that they gained in second year during the Groups and Rings module. ‘Direct products’, which are used to construct new groups, will be studied, while any finite group will be shown to ‘factor’ into ‘simple’ pieces.

Situations will be considered in which a group ‘acts’ on a set by permuting its elements; this powerful idea is used to identify the symmetries of the Platonic solids, and to help study the structure of groups themselves.

Finally, students will prove some interesting and important results, known as 'Sylow’s theorems', relating to subgroups of certain orders.

Students will examine the notion of a norm, which introduces a generalised notion of ‘distance’ to the purely algebraic setting of vector spaces. They will learn several quite natural ways to do this, both for vectors of any dimension and for functions. Focus will then be on the more special notion of an inner product which generalises angles at the same time as distances.

Once these concepts have been established, students will have the opportunity to study geometrical ideas like orthogonality, which can be seen to apply to much more general spaces than Euclidean spaces of three (or even n) dimensions, notably to infinite dimensional spaces of functions. For example, Hilbert space theory shows how Fourier series are really another case of expressing an element in terms of a basis, and how people can use orthogonality to find best approximations to a given function by functions of a prescribed type. Finally, students will look at some of the main results of linear algebra, which generalise very nicely to linear operators between Hilbert spaces.

What makes a good translation and how do translations do good? This module aims to help you understand the practice of translation as it has evolved historically from the 18th century to the present across European and American societies.

The materials we study include historical textual sources as well as contemporary documents. Our aim is to look at translation as both a functional process for getting text in one language accurately into another and a culturally-inflected process that varies in its status and purpose from one context to another.

We will pay particular attention to the practical role that literary translators play within the contemporary global publishing industry and consider the practicalities of following a career in literary translation in the Anglophone world.

Introducing the Lebesgue integral for functions on the real line, this module features a classical approach to the construction of Lebesgue measure on the line and to the definition of the integral. The bounded convergence theorem is used to prove the monotone and dominated convergence theorems, and the results are illustrated in classical convergence problems including Fourier integrals.

Among the range of topics addressed on this module, students will become familiar with Lebesgue's definition of the integral, and the integral of a step function. There will be an introduction to subsets of the real line, including open sets and countable sets. Students will measure of an open set, and will discover measurable sets and null sets. Additionally, the module will focus on integral functions, along with Lebesgue's integral of a bounded measurable function, his bounded convergence theorem and the integral of an unbounded function. Dominated convergence theorem; monotone convergence theorem.

Other topics on the module will include applications of the convergence theorems and Wallis's product for P. Gaussian integral, along with some classical limit inversion results and the Fourier cosine integral. Students will develop an understanding of Dirichlet's comb function, Archimedes' axiom and Cantor's uncountability theorem, and will learn to prove the structure theorem for open sets. In addition, students will be able to prove covering lemmas for open sets, as well as understanding the statement of Heine—Bore theorem, as well as understanding the concept and proving basic properties of outer measure. As well as understanding inner measure. Finally, students will be expected to prove Lebesgue's theorem on countable additivity of measure.

Statistical inference is the theory of the extraction of information about the unknown parameters of an underlying probability distribution from observed data. Consequently, statistical inference underpins all practical statistical applications.

This module reinforces the likelihood approach taken in second year Statistics for single parameter statistical models, and extends this to problems where the probability for the data depends on more than one unknown parameter.

Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?

The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

The aim of this module is to provide third year students with more options of applicable topics which draw upon second year pure mathematics modules and provide opportunities for further study. The theory of linear systems is engineering mathematics.

In the mid nineteenth century, the engineer Watt used a governor to control the amount of steam going into an engine, so that the input of steam reduced when the engine was going too quickly, and the input increased when the engine was going too slowly. Maxwell then developed a theory of controllers for various mechanical devices, and identified properties such as stability. The crucial idea of a controller is that the output can be fed back into the system to adjust the input.

Many devices can be described by linear systems of differential and integral equations which can be reduced to a standard (A,B,C,D) model. These include electrical appliances, heating systems and economic processes. The module shows how to reduce certain linear systems of differential equations to systems of matrix equations and thus solve them. Linear algebra enables students to classify (A,B,C,D) models and describe their properties in terms of quantities which are relatively easy to compute.

The module then describes feedback control for linear systems. The main result describes all the linear controllers that stabilise a (A,B,C,D) system.

Ideas about modern manhood have had significant influence around the world since the ‘globalisation’ wrought by colonisation and imperialism in the nineteenth century.

This module focuses on the search for new icons of masculinity in a modernising China, introducing students to key discursive notions such as “Mr Science” and “Mr Democracy” in the Republican era; the worker-soldier-peasant triad in the Mao era; the peasant heroes of the immediate post-Mao years; and the “explosive” nouveau riche, white-collar, migrant worker, and “little fresh meat” masculinities of the market-infused postsocialist era. Students analyse how cultural products present and critique notions of Chinese masculinities. Material is considered for its significance in key debates about masculinities, and may include novels, short stories, essays, graphic posters, art, music, films, TV drama series and reality shows, online dramas, websites, as well as secondary literature from a range of academic disciplines.

Using the classical problem of data classification as a running example, this module covers mathematical representation and visualisation of multivariate data; dimensionality reduction; linear discriminant analysis; and Support Vector Machines. While studying these theoretical aspects, students will also gain experience of applying them using R.

An appreciation for multivariate statistical analysis will be developed during the module, as will an ability to represent and visualise high-dimensional data. Students will also gain the ability to evaluate larger statistical models, apply statistical computer packages to analyse large data sets, and extract and evaluate meaning from data.

This module formally introduces students to the discipline of financial mathematics, providing them with an understanding of some of the maths that is used in the financial and business sectors.

Students will begin to encounter financial terminology and will study both European and American option pricing. The module will cover these in relation to discrete and continuous financial models, which include binomial, finite market and Black-Scholes models.

Students will also explore mathematical topics, some of which may be familiar, specifically in relation to finance. These include:

• Conditional expectation
• Filtrations
• Martingales
• Stopping times
• Brownian motion
• Black-Scholes formula

Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated risk-neutral probability; performing calculations with the Black-Scholes formula; and proving various steps in the derivation of the Black-Scholes formula. They will also be able to describe basic concepts of investment strategy analysis, and perform price calculations for stocks with and without dividend payments.

In addition, to these subject specific skills and knowledge, students will gain an appreciation for how mathematics can be used to model the real-world; improve their written and oral communication skills; and develop their critical thinking.

The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.

Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.

They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

An introduction to the key concepts and methods of metric space theory, a core topic for pure mathematics and its applications, is given during this module. Studying this module will give students a deeper understanding of continuity as well as a basic grounding in abstract topology. With this grounding, they will be able to solve problems involving topological ideas, such as continuity and compactness.

They will also gain a firm foundation for further study of many topics including geometry, Lie groups and Hilbert space, and learn to apply their knowledge to areas including probability theory, differential equations, mathematical quantum theory and the theory of fractals.

Number theory is the study of the fascinating properties of the natural number system.

Many numbers are special in some sense, eg. primes or squares. Which numbers can be expressed as the sum of two squares? What is special about the number 561? Are there short cuts to factorizing large numbers or determining whether they are prime (this is important in cryptography)? The number of divisors of an integer fluctuates wildly, but is there a good estimation of the ‘average’ number of divisors in some sense?

Questions like these are easy to ask, and to describe to the non-specialist, but vary hugely in the amount of work needed to answer them. An extreme example is Fermat’s last theorem, which is very simple to state, but was proved by Taylor and Wiles 300 years after it was first stated. To answer questions about the natural numbers, we sometimes use rational, real and complex numbers, as well as any ideas from algebra and analysis that help, including groups, integration, infinite series and even infinite products.

This module introduces some of the central ideas and problems of the subject, and some of the methods used to solve them, while constantly illustrating the results with exercises and examples involving actual numbers.

This module is ideal for students who want to develop an analytical and axiomatic approach to the theory of probabilities.

First the notion of a probability space will be examined through simple examples featuring both discrete and continuous sample spaces. Random variables and the expectation will be used to develop a probability calculus, which can be applied to achieve laws of large numbers for sums of independent random variables.

Students will also use the characteristic function to study the distributions of sums of independent variables, which have applications to random walks and to statistical physics.

Students will cover the basics of ordinary representation theory. Two approaches are presented: representations as group homomorphisms into matrix groups, and as modules over group algebras. The correspondence between the two will be discussed.

The second part is an introduction to the ordinary character theory of finite groups, intrinsic to representation theory. Students will learn the concepts of R-module and of group representations, the main results pertaining to group representations, and will handle basic applications in the study of finite groups.

They will also learn to perform computations with representations and morphisms in a selection of finite groups

The question at the heart of Sinophone Studies is “What is Chineseness in the modern world?” This question has played out in different fashions across the various Sinophone cultures.

Sinophone cultural production offers crucial counterpoints to the depictions of Chinese identity in mainland Chinese, Han-centric creative works. Drawing from the work of scholars in the nascent field of Sinophone studies, this course understands Sinophone cultures as existing in the “minority nationalities” of China; in Hong Kong, Taiwan, Malaysia, Singapore and other locations in the East Asian “Sinosphere”; and in the significant Sinitic-language immigrant populations of the Americas, Australasia, and elsewhere. It recognises Sinophone cultural production as multilingual and multi-ethnic.

This module introduces key Sinophone literary works and films including novels, short stories, and films. Discussion focuses on the diverse ways in which Chineseness is imagined, negotiated, or resisted in these works, and the alternative cultural identities that they put forward.

DELC338 Spirits in the Material World: Cultures and Sciences

This module lives in the space between the here-and-now and a future made possible by science. You’ll explore perceptions of science across different languages and cultures, from Asia to Europe to the Americas, and explore relationships between the spiritual and the material.

You’ll look at some intriguing questions about science and the twenty-first century human condition such as: Where is AI taking humanity and are we already robots? Are science fiction writers a form of contemporary shaman? What possibilities do modern medical advances offer for transformative queer and trans healthcare?

You’ll find out about differing views on these and other topics from a wide range of source materials, such as speculative fiction, graphic novels, film, philosophical essays, and online talks. Themes typically cover Spirit and Matter, Speculative Fiction, The Post-Human, Philosophy, Art and Neuroscience, Biomedicine and the Hospital.

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The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).

Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.

As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).

The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

Modern statistics is characterised by computer-intensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.

Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.

Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.

Lastly,students will spend time looking at Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.

This module covers key debates on how television shows are consumed both nationally and transnationally, the appeal of crime dramas, cultural translation, and in particular the concept of domestication. Theoretical frameworks are applied to examples from television series produced in languages that are taught to degree level at Lancaster and are available in English via dubbing or subtitling. Selected case studies are devoted to the exploration of a particular theme. Typically, such themes may include aspects such as the sympathetic perpetrator, setting, local colour and exoticism, gender, race and ethnicity.