# French and Mathematics BA (Joint Hons)

• Offers a Year in China

## Key information

• Course length: 4 years
• UCAS code: GR11
• Year of entry: 2020
• Typical offer: A-level : ABB / IB : 33 / BTEC : Applications considered

### Programme Year One

In Year One you will take three core and one optional module in Mathematics, as well as two core modules in modern French language, and two core modules in French Studies.

After passing the first year, you have the flexibility of transferring to G100 if you wish, subject to approval.

#### Year One Compulsory Modules

• ##### Calculus I (MATH101)
Level 1 15 First Semester 70:30 1. To introduce the basic ideas of differential and integral calculus, to develop the basic skills required to work with them and to apply these skills to a range of problems.2. To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.3. To introduce the notions of sequences and series and of their convergence. (LO1) Differentiate and integrate a wide range of functions;(LO2) Sketch graphs and solve problems involving optimisation and mensuration(LO3) Understand the notions of sequence and series and apply a range of tests to determine if a series is convergent(S1) Numeracy
• ##### Calculus II (MATH102)
Level 1 15 Second Semester 80:20 - To discuss local behaviour of functions using Taylor’s theorem.- To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals. (LO1) Use Taylor series to obtain local approximations to functions(LO2) Obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables.(LO3) Evaluate double integrals using Cartesian and Polar Co-ordinates.
• ##### Math103 - Introduction to Linear Algebra (MATH103)
Level 1 15 First Semester 60:40 • To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors. • To develop geometrical intuition in 2 and 3 dimensions. • To introduce students to the concept of subspace in a concrete situation. • To provide a foundation for the study of linear problems both within mathematics and in other subjects (LO1) Manipulate complex numbers and solve simple equations involving them solve arbitrary systems of linear equations(LO2) Understand and use matrix arithmetic, including the computation of matrix inverses(LO3) Compute and use determinants(LO4) Understand and use vector methods in the geometry of 2 and 3 dimensions(LO5) Calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics.(LO6) calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics(S2) Numeracy
• ##### Beginners French 1+2 (FREN112)
Level 1 15 First Semester 0:100 Develop all the skills necessary to begin to communicate confidently in spoken and written French, including basic competence in reading and listening;Provide students with a sound understanding of the basic structures of the French grammar;Encourage students to explore some aspects of contemporary French culture through the medium of French;Develop useful language learning strategies and a reflective approach as well as the ability to work collaboratively and independently. (LO1) Apply basic listening, reading, writing and speaking skills in the target language.(LO2) Communicate in the target language in everyday contexts using basic formal and informal registers.(LO3) Demonstrate a knowledge and understanding of the structures, registers and appropriate varieties of the target languages.(LO4) Critically reflect on and effectively apply language learning strategies.(LO5) Demonstrate knowledge and understanding of the culture and linguistic contexts of the country of the target language. (S1) Communication skills – basic reading, writing, speaking and listening skills in the target language(S2) Global citizenship – cultural awareness(S3) Improving own learning/performance – Self-awareness/self-analysis
• ##### Elementary French 3+4, Year 1 (FREN134)
Level 1 15 Second Semester 0:100 Continue to develop all the skills necessary to communicate confidently in spoken and written French within a range of topics, including reading and listening competences;Consolidate existing knowledge of French language while learning even more complex structures;Encourage students to explore more aspects of contemporary French culture through the medium of French;Develop useful language learning strategies and a reflective approach as well as the ability to work collaboratively and independently. (LO1) Consolidate listening, reading, writing and speaking skills in the target language.(LO2) Communicate in the target language in a wider variety of contexts using appropriate register. (LO3) Demonstrate knowledge and understanding of the structures, registers and appropriate varieties of the target language. (LO4) Critically reflect on and effectively apply language learning strategies. (LO5) Demonstrate a knowledge and understanding of the culture and linguistic contexts of the country of the target language. (S1) Communication skills – basic reading, writing, speaking and listening skills in the target language(S2) Global citizenship – cultural awareness(S3) Improving own learning/performance – Self-awareness/self-analysis
• ##### Intermediate French 5, Year 1 (FREN105)
Level 1 15 First Semester 60:40 To consolidate skills acquired during the period of ‘A’ level tuition in secondary school, in particular the knowledge of grammar and the written and oral practice of the French language;Will introduce students to different registers of French: Standard, informal, argotique, encourage the production of accurate, authentic and fluent French, both written and spoken, in different formats;(Re)familiarise students with important cultural and historical references as part of a wider appreciation of the French language, develop students’ active and passive vocabulary;To enhance their competence in listening in the target language and will encourage students to take charge of their own language learning and to use the available resources for improving their command of the target language. (LO1) Demonstrate a knowledge and understanding of the structures, registers and, as appropriate, varieties of the target language.(LO2) Understand and improve knowledge and manipulation of the variety of registers in the target language.(LO3) Improve their listening, speaking, reading and writing skills in the target language and their knowledge of basic grammar.(LO4) Understand important cultural and historical references pertinent to French culture and demonstrate a knowledge of the cultures and linguistic contexts of the country of the target language.(LO5) Express themselves more fluently and accurately, and communicate more effectively in the target language.(LO6) Improve their listening and comprehension skills of authentic and more complex audio clips and videos.(LO7) Improve their understanding of how to assess strengths and weaknesses and apply learning strategies to improve performance.(S1) Communication (oral, written and visual) - Presentation skills – oral(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written, visual) – foreign language skills(S4) Communication (oral, written and visual) - Listening skills(S5) Improving own learning/performance - Reflective practice(S6) Global citizenship - Cultural awareness(S7) Working in groups and teams - Listening skills
• ##### Intermediate French 6, Year 1 (FREN106)
Level 1 15 Second Semester 60:40 To consolidate both the skills acquired during the period of ‘A’ level tuition in secondary school, in particular grammar and written and oral French language practice, and the skills acquired in FREN105;To introduce students to different registers of French: standard, informal, argotique;To encourage the production of accurate, authentic and fluent French, both written and spoken, in different formats;To (re)familiarise students with important cultural and historical references as part of a wider appreciation of the French language;To continue developing students' active and passive vocabulary;To provide students with enhanced competence in listening in the target language;To encourage students to take charge of their own language learning and to use the available resources for improving their command of the target language. (LO1) Demonstrate a knowledge and understanding of the structures, registers and, as appropriate, varieties of the target language.(LO2) Understand and improve knowledge and manipulation of the variety of registers in the target language.(LO3) Improve their listening, speaking, reading and writing skills in the target language and their knowledge of basic grammar. (LO4) Understand important cultural and historical references pertinent to French culture and demonstrate a knowledge of the cultures and linguistic contexts of the country of the target language. (LO5) Express themselves more fluently and accurately, and communicate more effectively in the target language.(LO6) Improve their listening and comprehension skills of authentic and more complex audio clips and videos. (LO7) Improve their understanding of how to assess strengths and weaknesses and apply learning strategies to improve performance.(S1) Communication (oral, written and visual) - Presentation skills – oral(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written, visual) - foreign language skills(S4) Communication (oral, written and visual) - Listening skills(S5) Improving own learning/performance - Reflective practice(S6) Global citizenship - Cultural awareness(S7) Working in groups and teams - Listening skills
• ##### Language Awareness (MODL105)
Level 1 15 First Semester 0:100 Develop students' awareness of and explicit knowledge about language; Introduce students to key concepts of linguistics; Enhance students' skills of critical analysis of language, including hypothesis testing and rule formation; Develop students' understanding of similarities and differences between human languages; Develop students' awareness of and explicit knowledge about language learning that will help them become more efficient language learners. (LO1) Manage language learning processes more efficiently.(LO2) Understand key aspects of phonetics, phonology, morphology, syntax, semantics and pragmatics which are relevant for language learners.(LO3) Talk about and describe language using the correct terminology.(LO4) Reflect critically on selected language-related issues.(LO5) Relate knowledge about text features to the translation of text.(LO6) Communicate more efficiently in the first and foreign language.(S1) Improving own learning/performance - Reflective practice(S2) Improving own learning/performance - Self-awareness/self-analysis(S3) Improving own learning/performance - Personal action planning(S4) Communication (oral, written and visual) - Presentation skills - written(S5) Critical thinking and problem solving - Problem identification(S6) Critical thinking and problem solving - Creative thinking(S7) Time and project management - Personal organisation

#### Year One Optional Modules

• ##### Newtonian Mechanics (MATH122)
Level 1 15 Second Semester 80:20 To provide a basic understanding of the principles of Classical Mechanics and their application to simple dynamical systems. Learning Outcomes:After completing the module students should be able to analyse real world problems involving:- the motions of bodies under simple force systems- conservation laws for momentum and energy- rigid body dynamics using centre of mass, angular momentum and moments of inertia (LO1) the motions of bodies under simple force systems(LO2) conservation laws for momentum and energy(LO3) rigid body dynamics using centre of mass, angular momentum and moments(LO4) oscillation, vibration, resonance(LO5) oscillation, vibration, resonance(S1) Representing physical problems in a mathematical way(S2) Problem Solving Skills
• ##### Numbers, Groups and Codes (MATH142)
Level 1 15 Second Semester 80:20 - To provide an introduction to rigorous reasoning in axiomatic systems exemplified by the framework of group theory.- To give an appreciation of the utility and power of group theory as the study of symmetries.- To introduce public-key cryptosystems as used in the transmission of confidential data, and also error-correcting codes used to ensure that transmission of data is accurate. Both of these ideas are illustrations of the application of algebraic techniques. (LO1) Be able to apply the Euclidean algorithm to find the greatest common divisor of a pair of positive integers, and use this procedure to find the inverse of an integer modulo a given integer.(LO2) Be able to solve linear congruences and apply appropriate techniques to solve systems of such congruences.(LO3) Be able to perform a range of calculations and manipulations with permutations.(LO4) Recall the definition of a group and a subgroup and be able to identify these in explicit examples.(LO5) Be able to prove that a given mapping between groups is a homomorphism and identify isomorphic groups.(LO6) To be able to apply group theoretic ideas to applications with error correcting codes.(LO7) Engage in group project work to investigate applications of the theoretical material covered in the module.
• ##### Introduction to Statistics (MATH162)
Level 1 15 Second Semester 80:20 •To introduce topics in Statistics and to describe and discuss basic statistical methods. •To describe the scope of the application of these methods. (LO1) To know how to describe statistical data.(LO2)  To be able to use the Binomial, Poisson, Exponential and Normal distributions.(LO3) To be able to perform simple goodness-of-fit tests.(LO4) To be able to use an appropriate statistical software package to present data and to make statistical analysis.(S1) Numeracy(S2) Problem solving skills(S3) IT skills(S4) Communication skills

### Programme Year Two

You will continue to take two language modules in order to develop your language skills, as well as two other optional modules in French alongside modules in Maths.

#### Year Two Compulsory Modules

• ##### Advanced French 7, Year 2 (FREN207)
Level 2 15 First Semester 60:40 To provide students with enhanced competence in reading, writing, listening and speaking in French, building on the skills acquired in the year one language modules;To provide students with a greater understanding of the grammar, syntax and idioms of French;To prepare students for their period of study in France, focusing on the world of work and applying for internships in a French speaking country;To explore aspects of French culture, topical issues and changes affecting French society;To increase students' confidence in the manipulation of language;   To develop translation and interpreting skills;To develop students' language learning strategy use and a reflective approach towards language learning. (LO1) At the end of this module students should be able to improve their language skills and be able to cope with longer, more difficult texts and videos, express themselves more fluently and accurately in French.(LO2) Apply the rules of syntax and grammar in their written work, using a wider range of lexis and idioms.(LO3) Produce a CV and supporting statement; communicate effectively during an interview.(LO4) Identify some of the changes affecting French society, discuss topical issues and identify cultural differences.(LO5) Select important information from a document and reformulate the main ideas in a summary.(LO6) Demonstrate an understanding of the structures, lexis, registers of the target language and translate them into English.(LO7) Assess strengths and weaknesses and apply learning strategies to improve performance.(S1) Communication (oral, written and visual) - foreign language skills(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written and visual) - Presentation skills – oral(S4) Global citizenship - Cultural awareness(S5) Improving own learning/performance - Reflective practice(S6) Critical thinking and problem solving - Synthesis(S7) Communication (oral, written and visual) - Influencing skills – argumentation(S8) Working in groups and teams - Listening skills(S9) Commercial awareness - ability to use language for professional purpose
• ##### Advanced French 7, Year 2 (FREN207)
Level 2 15 First Semester 60:40 To provide students with enhanced competence in reading, writing, listening and speaking in French, building on the skills acquired in the year one language modules;To provide students with a greater understanding of the grammar, syntax and idioms of French;To prepare students for their period of study in France, focusing on the world of work and applying for internships in a French speaking country;To explore aspects of French culture, topical issues and changes affecting French society;To increase students' confidence in the manipulation of language;   To develop translation and interpreting skills;To develop students' language learning strategy use and a reflective approach towards language learning. (LO1) At the end of this module students should be able to improve their language skills and be able to cope with longer, more difficult texts and videos, express themselves more fluently and accurately in French.(LO2) Apply the rules of syntax and grammar in their written work, using a wider range of lexis and idioms.(LO3) Produce a CV and supporting statement; communicate effectively during an interview.(LO4) Identify some of the changes affecting French society, discuss topical issues and identify cultural differences.(LO5) Select important information from a document and reformulate the main ideas in a summary.(LO6) Demonstrate an understanding of the structures, lexis, registers of the target language and translate them into English.(LO7) Assess strengths and weaknesses and apply learning strategies to improve performance.(S1) Communication (oral, written and visual) - foreign language skills(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written and visual) - Presentation skills – oral(S4) Global citizenship - Cultural awareness(S5) Improving own learning/performance - Reflective practice(S6) Critical thinking and problem solving - Synthesis(S7) Communication (oral, written and visual) - Influencing skills – argumentation(S8) Working in groups and teams - Listening skills(S9) Commercial awareness - ability to use language for professional purpose
• ##### Intermediate French 5+6, Year 2 (FREN256)
Level 2 15 First Semester 0:100 Develop further all the skills necessary to communicate confidently and effectively in spoken and written French, including reading and listening competences;Consolidate existing knowledge of French language while learning more complex structures;Enable students to develop further language learning strategies and fosters a reflective approach as well as the ability to work collaboratively and independently;Encourage students to explore aspects of contemporary French culture and to reflect on some current French issues in preparation for the Year Abroad. (LO1) At the end of this module students should be able to improve their language skills and be able to cope with longer, more difficult texts and videos / audio documents, express themselves more fluently and accurately in French.(LO2) Communicate more effectively in the target language in a wider variety of contexts. (LO3) Demonstrate a deeper knowledge and understanding of the culture and linguistic contexts of the country of the target language. (LO4) Demonstrate an increased understanding of the structures, lexis, registers of the target language and apply these to improve writing and speaking skills.(LO5) Apply research skills and produce well-structured essays and presentations.(LO6) Recognise the various registers of French, use them in appropriate situations. (S1) Communication (oral, written and visual): foreign language skills(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Global citizenship - Cultural awareness(S4) Information skills - Information accessing: [Locating relevant information] [Identifying and evaluating information sources](S5) Improving own learning/performance - Reflective practice
• ##### Advanced French 7+8 (FREN278)
Level 2 15 Second Semester 0:100 Develop further all the skills necessary to communicate confidently and effectively in spoken and written French, including reading and listening competences; Continue to consolidate existing knowledge of French language while learning more complex structures; Enable students to develop further language learning strategies and fosters a reflective approach as well as the ability to work collaboratively and independently; Encourage students to further explore aspects of contemporary French culture and to reflect on some current French issues in preparation for the Year Abroad. (LO1) At the end of this module students should be able to improve their language skills and be able to cope with longer, more difficult texts and videos / audio documents, express themselves more fluently and accurately in French.(LO2) Communicate more effectively in the target language in a wider variety of contexts. (LO3) Demonstrate a deeper knowledge and understanding of the culture and linguistic contexts of the country of the target language. (LO4) Demonstrate an increased understanding of the structures, lexis, registers of the target language and apply these to improve writing and speaking skills.(LO5) Apply research skills and produce well-structured essays and presentations.(LO6) Recognise the various registers of French, use them in appropriate situations. (S1) Communication (oral, written and visual): foreign language skills(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Global citizenship - Cultural awareness(S4) Information skills - Information accessing: [Locating relevant information] [Identifying and evaluating information sources](S5) Communication (oral, written and visual) - Presentation skills – oral(S6) Improving own learning/performance - Reflective practice
• ##### Math201 - Ordinary Differential Equations (MATH201)
Level 2 15 First Semester 75:25 •To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations.•To illustrate the breadth of applications of ODEs and fundamental importance of related concepts. (LO1) To understand the basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions.(LO2) To know the elementary techniques for the solution of ODEs.(LO3) To understand the idea of reducing a complex ODE to a simpler one.(LO4) To be able to solve linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix.(LO5) To understand a range of applications of ODE.(S1) Problem solving skills(S2) Numeracy
• ##### Complex Functions (MATH243)
Level 2 15 First Semester 80:20 •To introduce the student to a surprising, very beautiful theory having intimate connections with other areas of mathematics and physical sciences, for instance ordinary and partial differential equations and potential theory. (LO1) To understand the central role of complex numbers in mathematics;.(LO2) To develop the knowledge and understanding of all the classical holomorphic functions.(LO3) To be able to compute Taylor and Laurent series of standard holomorphic functions.(LO4) To understand various Cauchy formulae and theorems and their applications.(LO5) To be able to reduce a real definite integral to a contour integral.(LO6) To be competent at computing contour integrals.(S1) Problem solving skills(S2) Numeracy(S3) Adaptability

#### Year Two Optional Modules

• ##### Art and VIolence: VIsual Cultures and the Media in Modern France (FREN220)
Level 2 15 First Semester 40:60 To equip students with the analytical tools and critical vocabulary necessary to 'read' any still image in terms of its aesthetic qualities. The images studied will include: advertising (both commercial and public information advertising) commercial logotypes, bande dessinee and selected fine art images. Many of the images will be challenging depicting or suggesting violence;To give students an 'image bank' by introducing them to the diversity of social and cultural contexts in which images are important carriers of meaning in France;To introduce students to the critical vocabulary of semiology as far as it is useful for the analysis of images. These tools and vocabulary used during the module are intended to be useful in the world beyond the module;To give students the confidence to think critically and independently about images and to be aware of the partisan uses to which they are frequently put. (LO1) On successful completion of this module students will be able to: Quickly and cogently analyse an image both orally and in writing.(LO2) Ask informed questions about the cultural context and possible functions of a given image.(LO3) Appreciate a selection of the most influential images in France (and of France) from a range of different non-fictional and fictional contexts: advertising, the bande dessinee, company logotypes and satirical cartoons.(LO4) Appreciate a selection of the different discourses which have been used in France to analyse the image such as semiology and modern art criticism.(LO5) Interact constructively with other students in the electronic discussion and project fora WIKIS associated with the module content.(LO6) Select and apply relevant French-language secondary materials to enrich their interpretations of images.(LO7) Understand the fundamental differences between the French and English-speaking traditions of image analysis: Barthes, Jakobson, Pierce, David Scott.(S1) Communication (oral, written and visual) - Presentation skills - written(S2) Commercial awareness - Relevant understanding of organisations(S3) Communication (oral, written and visual) - Media analysis
• ##### Paris: Capital Cultures? (FREN223)
Level 2 15 First Semester 50:50 To introduce students to Paris as a diverse, global city from a historical and theoretical perspective; To develop students' ability to apply theoretical approaches or critical secondary literature to the study of cities in general, and to Paris, its arrondissements and banlieues in particular; To enhance students' skills of critical analysis and independent thinking and research. (LO1) Understand the diversity of Paris and its culture as a capital city both across time and at individual periods in its history.(LO2) Apply theoretical approaches or critical secondary literature to the analysis of a range of sources in different textual forms and visual media, and from diverse periods in French history, both individually and comparatively.(LO3) Show an awareness of concepts and debates relating to the study of the city in general as a cultural, multilingual, and historically marked space.(LO4) Successfully carry out a piece of individual research.(S1) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S2) Communication (oral, written and visual) - Presentation skills - visual(S3) Critical thinking and problem solving - Critical analysis(S4) Global citizenship - Cultural awareness(S5) Personal attributes and qualities - independence
• ##### Manger! Food and French Culture (FREN230)
Level 2 15 Second Semester 0:100 Recognised by UNESCO in 2010 as part of humanity's intangible cultural heritage, the French 'gastronomic meal' has been one of the gifts the French feel they have given the world. This is the first module in French Studies globally that aims to give students both a historically grounded understanding of the discourses of food in France and a critical understanding of how French cuisine functions as a national myth; The wider context for this module's aims is the opportunity to offer our students content and teaching and learning unique in UK French Studies. The module capitalizes on the research expertise of 90% of members of staff at Liverpool; T his module aims to familiarize students with authentic documents written in French from different time periods from the Middle Ages onwards; This module aims to encourage students to apply the theoretical concepts, historical understanding and specialist French vocabulary that they have learnt to the understanding and analysis of real-life situations ; This module aims to encourage students to make learnig and assessment choices which play to their strengths as independent learners. (LO1) On completion of this module, students will have an understanding of the development of the significance of food for French society from the Middle Ages to the end of the twentieth century.(LO2) On completion of this module, students will have acquired and internalized the core vocabulary in French for describing French food and its modes of presentation on the table and in a menu.(LO3) On completion of this module, students will understand the role played by the absence and presence of food at specific moments in the history of France. (LO4) Students will know the names of the principal individuals who have shaped French culinary tradition and understand the importance of food in terms of the relation between Paris and the provinces of France and between France and the UK(S1) Global citizenship - Cultural awareness(S2) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S3) Demonstrate a knowledge and understanding of the cultures, linguistic contexts, history, politics, geography, and social and economic structures of the societies of the country of the target language(S4) Apply theoretical approaches or critical secondary literature to the analysis of real-world situations.
• ##### Introduction to French Cinema (FREN236)
Level 2 15 Second Semester 0:100 To introduce students to the basic language of film analysis; To introduce students to the rich cultural field which the cinema has represented in France through study of selected films from particularly significant periods, giving them a background of reference points and an understanding of how cinema has developed in France; To cultivate habits of close visual analysis and careful structuring of such analysis ; To increase confidence in class discussion and presentation. (LO1) Students should be able to give an intelligent and informed account of how any film (from whatever culture) is put together, the ways in which it engages its audience and the messages it conveys.(LO2) Students will develop thorough and perceptive powers of observation and interpretation of the elements of a cinematic text both visual and aural(LO3) Students will be able to explain their observations in a structured way, in written analyses and also orally in front of a class, in the latter case using visual aids when appropriate.(LO4) Students will be able to insert their detailed observations into a thematic or historical context in order to show how a particular film deals with larger issues, and to construct a well-written essay to explain their ideas. (LO5) Students should have a basic overview of major directors and trends in the history of the cinema in France, which will enable them to see other French films in their historical and artistic context.(S1) Demonstrate a knowledge and understanding of the cultures, linguistic contexts, history, politics, geography, and social and economic structures of the societies of the country of the target language(S2) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S3) Communication (oral, written and visual) - Communicating for audience(S4) Critical thinking and problem solving - Critical analysis(S5) Working in groups and teams - Group action planning(S6) Successfully apply a close reading to a text of the target language(S7) Global citizenship - Cultural awareness(S8) Working in groups and teams - Listening skills(S9) Personal attributes and qualities - Willingness to take responsibility(S10) Communication (oral, written and visual) - Influencing skills – argumentation
• ##### Multilingual Liverpool: Reading the City (MODL234)
Level 2 15 Second Semester 70:30 To introduce students to core theoretical topics in sociolinguistics;To encourage critical awareness of multilingualism and language practices;To apply decoding approaches to texts publicly available in Liverpool. (LO1) Read critically public texts, both in English and in the target language.(LO2) Decode signs into the target language, bearing in mind the principles of semiotics, audience, design and other linguistic landscape theories.(LO3) Develop an understanding of multilingualism.(S1) Communication (oral, written and visual) - Presentation skills - oral(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written and visual) - Academic writing (including referencing skills)(S4) Critical thinking and problem solving - Critical analysis(S5) Working in groups and teams - Group action planning(S6) Global citizenship - Cultural awareness
• ##### Math201 - Ordinary Differential Equations (MATH201)
Level 2 15 First Semester 75:25 •To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations.•To illustrate the breadth of applications of ODEs and fundamental importance of related concepts. (LO1) To understand the basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions.(LO2) To know the elementary techniques for the solution of ODEs.(LO3) To understand the idea of reducing a complex ODE to a simpler one.(LO4) To be able to solve linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix.(LO5) To understand a range of applications of ODE.(S1) Problem solving skills(S2) Numeracy
• ##### Vector Calculus With Applications in Fluid Mechanics (MATH225)
Level 2 15 First Semester 85:15 •To provide an understanding of the various vector integrals, the operator’s div, grad and curl and the relations between them.•To give an appreciation of the many applications of vector calculus to physical situations.•To provide an introduction to the subjects of fluid mechanics and electromagnetism. (LO1) After completing the module students should be able to: - Work confidently with different coordinate systems. - Evaluate line, surface and volume integrals. - Appreciate the need for the operators div, grad and curl together with the associated theorems of Gauss and Stokes. - Recognise the many physical situations that involve the use of vector calculus. - Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow. All learning outcomes are assessed by both examination and course work.
• ##### Mathematical Models: Microeconomics and Population Dynamics (MATH227)
Level 2 15 First Semester 90:10 •To provide an understanding of the techniques used in constructing, analysing, evaluating and interpreting mathematical models.•To do this in the context of two non-physical applications, namely microeconomics and population dynamics. •To use and develop mathematical skills introduced in Year 1 - particularly the calculus of functions of several variables and elementary differential equations. (LO1) After completing the module students should be able to: - Use techniques from several variable calculus in tackling problems in microeconomics. - Use techniques from elementary differential equations in tackling problems in population dynamics. - Apply mathematical modelling methodology in these subject areas. All learning outcomes are assessed by both examination and course work.
• ##### Metric Spaces and Calculus (MATH241)
Level 2 15 First Semester 80:20 To introduce the basic elements of the theory of metric spaces and calculus of several variables. (LO1) After completing the module students should: Be familiar with a range of examples of metric spaces. Have developed their understanding of the notions of convergence and continuity. Understand the contraction mapping theorem and appreciate some of its applications. Be familiar with the concept of the derivative of a vector valued function of several variables as a linear map. Understand the inverse function and implicit function theorems and appreciate their importance. Have developed their appreciation of the role of proof and rigour in mathematics.(S1) Problem solving skills
• ##### Complex Functions (MATH243)
Level 2 15 First Semester 80:20 •To introduce the student to a surprising, very beautiful theory having intimate connections with other areas of mathematics and physical sciences, for instance ordinary and partial differential equations and potential theory. (LO1) To understand the central role of complex numbers in mathematics;.(LO2) To develop the knowledge and understanding of all the classical holomorphic functions.(LO3) To be able to compute Taylor and Laurent series of standard holomorphic functions.(LO4) To understand various Cauchy formulae and theorems and their applications.(LO5) To be able to reduce a real definite integral to a contour integral.(LO6) To be competent at computing contour integrals.(S1) Problem solving skills(S2) Numeracy(S3) Adaptability
• ##### Linear Algebra and Geometry (MATH244)
Level 2 15 First Semester 80:20 To introduce general concepts of linear algebra and its applications in geometry and other areas of mathematics. (LO1) To understand the geometric meaning of linear algebraic ideas.(LO2) To know the concept of an abstract vector space and how it is used in different mathematical situations.(LO3) To be able to apply a change of coordinates to simplify a linear map.(LO4) To be able to work with matrix groups, in particular GL(n), O(n) and SO(n),.(LO5) To understand bilinear forms from a geometric point of view.(S1) Problem solving skills(S2) Numeracy(S3) Adaptability
• ##### Introduction to Methods of Operational Research (MATH261)
Level 2 15 First Semester 70:30 The aims of the module are to develop an understanding of how mathematical modelling and operational research techniques are applied to real-world problems and to gain an understanding of linear and convex programming, multi-objective problems, inventory control and sensitivity analysis. (LO1) To understand the operational research approach.(LO2) To be able to apply standard methods of operational research to a wide range of real-world problems as well as to problems in other areas of mathematics.(LO3) To understand the advantages and disadvantages of particular operational research methods.(LO4) To be able to derive methods and modify them to model real-world problems.(LO5) To understand and be able to derive and apply the methods of sensitivity analysis.(LO6) To understand the importance of sensitivity analysis.(S1) Adaptability(S2) Problem solving skills(S3) Numeracy(S4) Self-management readiness to accept responsibility (i.e. leadership), flexibility, resilience, self-starting, initiative, integrity, willingness to take risks, appropriate assertiveness, time management, readiness to improve own performance based on feedback/reflective learning
• ##### Group Project Module (MATH206)
Level 2 15 Second Semester 0:100 ·         To give students experience of working effectively in small groups. ·         To train students to write about mathematics. ·         To give students practice in delivering presentations. ·         To develop students’ ability to study independently. ·         To prepare students for later individual project work. ·         To enhance students’ understanding of the connections between different areas of mathematics. ·         To encourage students to discuss mathematics with each other. Work effectively in groups, and delegate common tasks.​Write substantial mathematical documents in an accessible form. ​ ​Give coherent verbal presentations of more advanced mathematical topics.  ​Understand how mathematical techniques can be applied in a variety of different contexts.
• ##### Introduction to the Methods of Applied Mathematics (MATH224)
Level 2 15 Second Semester 90:10 •To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics.•To introduce some of the basic tools (Fourier Series) used in the solution of differential equations and other applications of mathematics. (LO1) After completing the module students should: - be fluent in the solution of basic ordinary differential equations, including systems of first order equations:- be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations:- be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations: - be able to solve simple first order partial differential equations: - be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.
• ##### Classical Mechanics (MATH228)
Level 2 15 Second Semester 90:10 To provide an understanding of the principles of Classical Mechanics and their application to dynamical systems. (LO1) To understand the variational principles, Lagrangian mechanics, Hamiltonian mechanics.(LO2) To be able to use Newtonian gravity and Kepler's laws to perform the calculations of the orbits of satellites, comets and planetary motions.(LO3) To understand the motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravity over the Earth's surface.(LO4) To understand the connection between symmetry and conservation laws.(LO5) To be able to work with inertial and non-inertial frames.(S1) Applying mathematics to physical problems(S2) Problem solving skills
• ##### Math247 - Commutative Algebra (MATH247)
Level 2 15 Second Semester 90:10 To give an introduction to abstract commutative algebra and show how it both arises naturally, and is a useful tool, in number theory. (LO1) After completing the module students should be able to: • Work confidently with the basic tools of algebra (sets, maps, binary operations and equivalence relations). • Recognise abelian groups, different kinds of rings (integral, Euclidean, principal ideal and unique factorisation domains) and fields. • Find greatest common divisors using the Euclidean algorithm in Euclidean domains. • Apply commutative algebra to solve simple number-theoretic problems.
• ##### Geometry of Curves (MATH248)
Level 2 15 Second Semester 90:10 To introduce geometric ideas and develop the basic skills in handling them.To study the line, circle, ellipse, hyperbola, parabola, cubics and many other curves.To study theoretical aspects of parametric, algebraic and projective curves.To study and sketch curves using an appropriate computer package. (LO1) After completing this module students should be able to use a computer package to study curves and their evolution in both parametric and algebraic forms.(LO2) After completing this module students should be able to determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.(LO3) After completing this module students should be able to determine the position and shape of some algebraic curves including conics.(S1) Problem solving skills(S2) Numeracy(S3) IT skills(S4) Adaptability
• ##### Financial Mathematics (MATH260)
Level 2 15 Second Semester 0:0 To introduce geometric ideas and develop the basic skills in handling them.To study the line, circle, ellipse, hyperbola, parabola, cubics and many other curves.To study theoretical aspects of parametric, algebraic and projective curves.To study and sketch curves using an appropriate computer package. (LO1) Understand the assumptions of CAMP, explain the no riskless lending or borrowing and other lending and borrowing assumptions, be able to use the formulas of CAMP, be able to derive the capital market line and security market line(LO2) Describe the Arbitrage Theory Model (APT) and explain its assumptions, perform estimating and testing in APT(LO3) Be able to explain the terms long/short position, spot/delivery/forward price, understand the use of future contracts, describe what a call/put option (European/American) is and be able to makes graphs and explain their payouts, describe the hedging for reducing the exposure to risk, be able to explain arbitrage, understand the mechanism of short sales(LO4) Explain/describe what arbitrage is, and also the risk neutral probability measure, explain/describe and be able to use (perform calculation) the binomial tree for European and American style options(LO5) Understand the probabilistic interpretation and the basic concept of the random walk of asset pricing(LO6) Understand the concepts of replication, hedging, and delta hedging in continuous time(LO7) Be able to use Ito's formula, derive/use the Black‐Scholes formula, price contingent claims (in particular European/American style options and forward contracts), be able to explain the properties of the Black‐Scholes formula, be able to use the Normal distribution function in numerical examples of pricing(LO8) Understand the role of Greeks , describe intuitively what Delta, Theta, Gamma is, and be able to calculate them in numerical examples.
• ##### Statistical Theory and Methods I (MATH263)
Level 2 15 Second Semester 85:15 To introduce statistical methods with a strong emphasis on applying standard statistical techniques appropriately and with clear interpretation.  The emphasis is on applications. (LO1) To have a conceptual and practical understanding of a range of commonly applied statistical procedures.(LO2) To have developed some familiarity with an appropriate statistical software package.(S1) Problem solving skills(S2) Numeracy(S3) IT skills(S4) Communication skills
• ##### Statistical Theory and Methods II (MATH264)
Level 2 15 Second Semester 90:10 To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory. (LO1) To have an understanding of basic probability calculus.(LO2) To have an understanding of a range of techniques for solving real life problems of probabilistic nature.(S1) Problem solving skills(S2) Numeracy
• ##### Math266 - Numerical Methods for Applied Mathematics (MATH266)
Level 2 15 Second Semester 90:10 To provide an introduction to the main topics in Numerical Analysis and their relation to other branches of Mathematics (LO1) To strengthen students’ knowledge of scientific programming, building on the ideas introduced in MATH111.(LO2) To provide an introduction to the foundations of numerical analysis and its relation to other branches of Mathematics.(LO3) To introduce students to theoretical concepts that underpin numerical methods, including fixed point iteration, interpolation, orthogonal polynomials and error estimates based on Taylor series.(LO4) To demonstrate how analysis can be combined with sound programming techniques to produce accurate, efficient programs for solving practical mathematical problems.(S1) Numeracy(S2) Problem solving skills
• ##### Operational Research: Probabilistic Models (MATH268)
Level 2 15 Second Semester 90:10 To introduce a range of models and techniques for solving under uncertainty in Business, Industry, and Finance. (LO1) The ability to understand and describe mathematically real-life optimization problems.(LO2) Understanding the basic methods of dynamical decision making.(LO3) Understanding the basics of forecasting and simulation.(LO4) The ability to analyse elementary queueing systems.(S1) Problem solving skills(S2) Numeracy

### Programme Year Four

You will continue to take two language modules in order to further develop and consolidate your language skills after the year abroad, as well as two other optional modules in French alongside modules in Maths.

#### Year Four Compulsory Modules

• ##### Proficient French 11 (FREN311)
Level 3 15 First Semester 50:50 To provide students with advanced competence in reading, writing, listening and speaking in French, building on the skills acquired in the Year 2 language modules and during the Year Abroad in Year 3;To increase students' linguistic confidence;To equip students with the speaking skills necessary in a professional and social context;To equip students with the writing skills necessary in a professional and social context;To develop students' cultural understanding of France. (LO1) Ability to communicate in both spoken and written French with near-native fluency.(LO2) Ability to use the necessary linguistic and cultural tools to deal with realistic and complex situations of the world of work.(LO3) Ability to operate as an effective inter-cultural communicator.(LO4) Attainment of a sophisticated level of linguistic and cultural awareness.(S1) Communication (oral, written and visual) - Presentation skills – oral(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written and visual) - Listening skills(S4) Global citizenship - Cultural awareness
• ##### Proficient French 12 (FREN312)
Level 3 15 Second Semester 50:50 To provide students with advanced competence in reading, writing, listening and speaking in French, building on the skills acquired in the year two language modules, in year three during the Year Abroad and in semester one of year four in FREN311;To further increase students linguistic confidence;To equip students with the speaking skills necessary in a professional and every day context;To equip students with the writing skills necessary in a professional and every day context;To develop students cultural understanding of France. (LO1) Ability to communicate in both spoken and written French with near-native fluency.(LO2) Ability to use the necessary linguistic and cultural tools to deal with realistic and complex situations of the world of work(LO3) Ability to operate as an effective inter-cultural communicator(LO4) Attainment of a sophisticated level of linguistic and cultural awareness(S1) Communication (oral, written and visual) - Presentation skills – oral(S2) Communication (oral, written and visual) - Presentation skills - written(S3) Communication (oral, written and visual) - Listening skills(S4) Global citizenship - Cultural awareness

#### Year Four Optional Modules

• ##### Representing China in Twentieth-century French and Francophone Cultures (FREN313)
Level 3 15 Second Semester 50:50 This option will introduce students to a variety of literary, historical, ideological and cultural issues raised by representations of China in a range of twentieth-century literary texts (and other related material) written in French. Whilst providing a general overview of Franco-Chinese relations in the modern and contemporary period, the module will concentrate on the prescribed texts (two travelogues, two bandes dessinées, a novel and a cinematic adaptation) to consider how these works illuminate the international contexts from which they emerge. The texts have been selected to reflect issues relating to representation and identity across a period of almost a century, and will allow students to develop an intercultural sensitivity to the material under consideration. As a result of the module, students will have improved their ability to: •     read unfamiliar and challenging literary texts, showing specific knowledge about the contexts in which those texts were produced (considering in particular issues of exoticism, alterity, Orientalism, politics and travel); •      appreciate the diversity of French-language material that represents China, by considering a variety of differing approaches to representations of a specific continental zone; •      evaluate critical approaches to representations of China, and select those likely to be pertinent and fruitful, explaining and defending choices when asked to do so either by other students or the course tutors; •     discuss the problems involved in tackling relatively unfamiliar value-systems, literary conventions, socio-cultural contexts and ideas; •      understand the various societies and historical contexts from which the prescribed texts emerge and to which their authors belong; •      contribute to and (where appropriate) lead tutorial discussion, analysing material with regard to their broad themes, significant detail, and literary, socio-cultural, historical and ideological context; •     detect affinities between the prescribed texts by analysing common themes whilst making cross comparisons between authors and contexts; •       complete coherent, focused and structured assignments on topics related to the set texts; •     make competent use of secondary literature and achieve the proper integration of such material into an original argument; •     demonstrate an awareness of the intercultural sensitivity required for a successful understanding of the material and themes under consideration.
• ##### From Sheepskin to E-reader: Books and Publishing in France (FREN331)
Level 3 15 First Semester 0:100 To provide students with a good understanding of the main developments of the history of the book in France from the medieval period and the Ancien Régime;To introduce students to the study and description of old printed and hand-written books;To encourage students to reflect on the interaction between text and non-textual elements (illustrations, layout, typography);To develop an understanding of the importance of the printing press for shaping of popular culture. (LO1) After having completed this module students will have a good understanding of the main developments of the history of the book in France from the medieval period to the present day.(LO2) Students will have been introduced to the study and description of old printed and hand-written books and will be able to use the appropriate technical vocabulary to describe and analyse features of layout, typography and physical appearance.(LO3) They will have reflected on the interaction between text and non-textual elements (illustrations, layout, typography) and have developed an understanding of the importance of the printing press for shaping of popular culture.(LO4) Through the project they will have learned to identify suitable research topics, formulate research questions in relation to these topics, collect relevant primary and secondary sources and report on their findings in oral and written form.(S1) Communication, listening and questioning respecting others, contributing to discussions, communicating in a foreign language, influencing, presentations(S2) Research management developing a research strategy, project planning and delivery, risk management, formulating questions, selecting literature, using primary/secondary/diverse sources, collecting & using data, applying research methods, applying ethics(S3) Information literacy online, finding, interpreting, evaluating, managing and sharing information(S4) Adaptability
• ##### French Travellers in the New World (FREN332)
Level 3 15 Second Semester 0:100 To provide an understanding of the historical and cultural contexts of the discovery of the New World; To introduce students to the language, style and themes of sixteenth-century French texts; To give students an insight into the diversity and contrasts in representations of the New World in French Renaissance literature; To encourage students to reflect on the issues presented by the texts in the light of recent theories developed to conceptualise travel, cultural exchange, cultural difference and 'otherness', such as postcolonial theory and psychoanalysis; To develop students' subject-specific and transferable skills such as the ability to read in French; the ability to use electronic resources such as the internet; presentational, organisational, analytical, time management, problem-solving, research and writing skills. (LO1) The ability to read and understand French Renaissance texts.(LO2) Comment on the historical and cultural factors pertinent to the discovery of the New World and its representation French Renaissance writing.(LO3) Identify and discuss the stylistic and thematic features of the works studied.(LO4) Compare and contrast the set works and the stylistic and thematic issues they present.(LO5) Read and understand theories of 'otherness' and apply them to the prescribed material where appropriate.(LO6) Use electronic resources such as the internet to further their understanding of the issues raised by the course, particularly digitised texts.(LO7) Evaluate critical approaches to the issues discussed and select those likely to be pertinent and fruitful, explaining and defending choices when asked to do so either by other students or the course tutors.(LO8) Contribute to tutorial discussion, analysing material with regard to its broad themes, significant detail, and socio-cultural, historical and ideological context.(LO9) Complete coherent, focused and structured assignments on topics related to the set texts.(LO10) Make competent use of secondary literature and achieve the proper integration of such material into an original argument.(LO11) Use library and bibliographical skills to find secondary literature relating to the chosen texts, including that available on the internet.(S1) Teamwork(S2) Adaptability(S3) Ethical awareness(S4) Lifelong learning skills(S5) International awareness(S6) IT skills(S7) Communication skills(S8) Organisational skills
• ##### The Sociolinguistics of Modern French (FREN333)
Level 3 15 Second Semester 50:50 Deepen students’ understanding of language policy in general, and French language policy in particular (from the reign of François I to François Hollande ); Explore the social situation in France with regard to the use of language;Consider aspects of variation in language across France (both European and overseas territories);Introduce students to the methodology of research in sociolinguistics. (LO1) Understand the ways in which language is appropriate for social purposes.(LO2) Read and use unfamiliar texts, including journal articles(LO3) Evaluate critical approaches to sociolinguistic issues in France(LO4) Contribute to seminar discussion, exploiting their own increased understanding of the issues at play(S1) Communication (oral, written and visual) - Presentation skills – oral(S2) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S3) Critical thinking and problem solving - Critical analysis(S4) Global citizenship - Cultural awareness
• ##### French Identities: France, Europe and the World, C. 1720-1830 (FREN334)
Level 3 15 Second Semester 50:50 To introduce students to the range of literature which explores French cultural contact with the wider world during the ''long'' eighteenth century; To explore how representations of the ''other'' problematize the French ''self'', under the the Bourbon monarchy, the Revolutionary and Napoleonic wars, and the Restoration;To encourage students to challenge homogeneous views of ''Frenchness'' through the analysis of texts written by fictional ''marginal’ characters; To encourage students to reflect on themes raised by the texts using recent theories developed by postcolonialism, psychoanalysis and feminism which conceptualize alterity; To provide an understanding of  key periods in French history (the Bourbon monarchy, the Enlightenment, the Revolutionary and Napoleonic Wars) while simultaneously encouraging students to reflect upon the problem of traditional periodization in French historical writings;To develop students'' analytical and critical skills (in both oral and written form). Understand a pre-modern text (of the target language if read in French) within its broader, historical, cultural and social context​Successfully apply a close-reading to a pre-modern text (of the target language if read in French)​Demonstrate a knowledge and understanding of the cultures, history and politics of France and its contact with the wider world under the Bourbon monarchy, the Revolution, the Revolutionary and Napoleonic Wars, and the Restoration Apply theoretical approaches (e.g., postcolonial, Marxist, feminist) to the analysis of primary textsDemonstrate a knowledge and understanding of the cultural and intellectual relationship between France, Europe and the world during a period of history which has had a profound effect on modern-day France ​
• ##### French Dressing: Six Centuries of Clothing and Cultural History in France (FREN335)
Level 3 15 Second Semester 0:100 To introduce students to the ways in which French cultural productions from the fifteenth to the twentieth centuries (e.g. paintings, lifestyle journalism) using clothing to convey and shape identity; To develop students' ability to apply theoretical approaches or critical secondary literature to the study of clothing; To enhance students' skills of critical analysis and independent thinking. (LO1) Ability to evaluate critically the role and significance of fashion in French culture from the late Middle Ages to the twentieth century.(LO2) Apply theoretical approaches or critical secondary literature to the analysis of a range of artefacts in different visual media and from diverse periods in French history, both individually and comparatively.(LO3) Understand concepts and approaches relating to the history of fashion and consumption, especially in relation to individual and group identity.(S1) Critical thinking and problem solving - Critical analysis(S2) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S3) Global citizenship - Cultural awareness(S4) Critical thinking and problem solving - Problem identification(S5) Personal attributes and qualities - Independence
• ##### Resistance and Collaboration: the French Legacy (FREN343)
Level 3 15 Second Semester 60:40 To introduce students to a range of key post-1945 French responses to the issues of resistance and collaboration during the wartime Occupation of France (printed, film and video); To explore the different ways in which those materials engage with the complex issues of history, memory and responsibility; To develop students’ ability to read materials critically, and to draw conclusions across these by comparing and contrasting; To encourage reflection and discussion on the ongoing questions surrounding France’s engagement with her past;   To support students’ ability to produce coherent and focussed writing on the module themes. (LO1) As a result of the module, students should have improved their ability to: read/view unfamiliar and challenging literary, historical and cinematic materials, showing specific knowledge about the contexts in which those texts were produced(LO2) Appreciate the diversity of historical, literary and cinematic material available on the topic, by considering a variety of differing approaches to common themes, in order to evaluate representations of the Occupation years(LO3) Understand the society and historical context from which the prescribed materials emerge and to which their authors belong(LO4) Contribute to seminar discussion, analysing materials with regard to their broad themes, significant detail, and socio-cultural, historical and ideological context; and detecting affinities between the prescribed materials by analysing common themes whilst making cross comparisons between authors and contexts(LO5) Demonstrate an awareness of the intercultural sensitivity required for a successful understanding of the material and themes under consideration (S1) Critical thinking and problem solving - Critical analysis(S2) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S3) Global citizenship - Cultural awareness(S4) Personal attributes and qualities: ability to work independently
• ##### Chaos and Dynamical Systems (MATH322)
Level 3 15 First Semester 100:0 To develop expertise in dynamical systems in general and study particular systems in detail. (LO1) After completing the module students will be able to understand the possible behaviour of dynamical systems with particular attention to chaotic motion;(LO2) After completing the module students will be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;(LO3) After completing the module students will understand how fractal sets arise and how to characterise them.(S1) Problem solving skills(S2) Numeracy
• ##### Further Methods of Applied Mathematics (MATH323)
Level 3 15 First Semester 100:0 •To give an insight into some specific methods for solving important types of ordinary differential equations.•To provide a basic understanding of the Calculus of Variations and to illustrate the techniques using simple examples in a variety of areas in mathematics and physics.•To build on the students'' existing knowledge of partial differential equations of first and second order. (LO1) After completing the module students should be able to: - use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ordinary differential equations.- solve simple integral extremal problems including cases with constraints;- classify a system of simultaneous 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases;- classify 2nd-order linear partial differential equations and, in appropriate cases, find general or specific solutions.  [This might involve a practical understanding of a variety of mathematics tools; e.g. conformal mapping and Fourier transforms.]
• ##### Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)
Level 3 15 First Semester 100:0 To provide an introduction to the mathematical theory of viscous fluid flows and solid elastic materials. Cartesian tensors are first introduced. This is followed by modelling of the mechanics of continuous media. The module includes particular examples of the flow of a viscous fluid as well as a variety of problems of linear elasticity. (LO1) To understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations.(LO2) To apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.(S1) Problem solving skills(S2) Numeracy(S3) Adaptability
• ##### Quantum Mechanics (MATH325)
Level 3 15 First Semester 90:10 The aim of the module is to lead the student to an understanding of the way that relatively simple mathematics (in modern terms) led Bohr, Einstein, Heisenberg and others to a radical change and improvement in our understanding of the microscopic world. (LO1) To be able to solve Schrodinger's equation for simple systems.(LO2) To have an understanding of the significance of quantum mechanics for both elementary systems and the behaviour of matter.(S1) Problem solving skills(S2) Numeracy
• ##### Relativity (MATH326)
Level 3 15 First Semester 100:0 To impart(i) a firm grasp of the physical principles behind Special and General Relativity and their main consequences;(ii) technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;(iii) knowledge of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;(iv)basic concepts of black holes and (if time) relativistic cosmology. (LO1) After completing this module students should understand why space-time forms a non-Euclidean four-dimensional manifold.(LO2) After completing this module students should be proficient at calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols.(LO3) After completing this module students should understand the arguments leading to the Einstein's field equations and how Newton's law of gravity arises as a limiting case.(LO4) After completing this module students should be able to calculate the trajectories of bodies in a Schwarzschild space-time.
• ##### Group Theory (MATH343)
Level 3 15 First Semester 100:0 To introduce the basic techniques of finite group theory with the objective of explaining the ideas needed to solve classification results. (LO1) Understanding of abstract algebraic systems (groups) by concrete, explicit realisations (permutations, matrices, Mobius transformations).(LO2) The ability to understand and explain classification results to users of group theory.(LO3) The understanding of connections of the subject with other areas of Mathematics.(LO4) To have a general understanding of the origins and history of the subject.(S1) Problem solving skills(S2) Logical reasoning
• ##### Combinatorics (MATH344)
Level 3 15 First Semester 90:10 To provide an introduction to the problems and methods of Combinatorics, particularly to those areas of the subject with the widest applications such as pairings problems, the inclusion-exclusion principle, recurrence relations, partitions and the elementary theory of symmetric functions. (LO1) After completing the module students should be able to: understand of the type of problem to which the methods of Combinatorics apply, and model these problems; solve counting and arrangement problems; solve general recurrence relations using the generating function method; appreciate the elementary theory of partitions and its application to the study of symmetric functions.
• ##### Applied Probability (MATH362)
Level 3 15 First Semester 100:0 To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of probabilistic model building for ‘‘dynamic" events occurring over time. To familiarise students with an important area of probability modelling. (LO1) 1. Knowledge and Understanding After the module, students should have a basic understanding of: (a) some basic models in discrete and continuous time Markov chains such as random walk and Poisson processes (b) important subjects like transition matrix, equilibrium distribution, limiting behaviour etc. of Markov chain (c) special properties of the simple finite state discrete time Markov chain and Poisson processes, and perform calculations using these.2. Intellectual Abilities After the module, students should be able to: (a) formulate appropriate situations as probability models: random processes (b) demonstrate knowledge of standard models (c) demonstrate understanding of the theory underpinning simple dynamical systems 3. General Transferable Skills (a) numeracy through manipulation and interpretation of datasets (b) communication through presentation of written work and preparation of diagrams (c) problem solving through tasks set in tutorials (d) time management in the completion of practicals and the submission of assessed work (e) choosing, applying and interpreting results of probability techniques for a range of different problems.
• ##### Linear Statistical Models (MATH363)
Level 3 15 First Semester 70:30 - To understand how regression methods for continuous data extend to include multiple continuous and categorical predictors, and categorical response variables.- To provide an understanding of how this class of models forms the basis for the analysis of experimental and also observational studies.- To understand generalized linear models.- To develop skills in using the computer package SPSS. (LO1) Be able to understand the rationale and assumptions of linear regression and analysis of variance.(LO2) Be able to understand the rationale and assumptions of generalized linear models.(LO3) Be able to recognise the correct analysis for a given experiment.(LO4) Be able to carry out and interpret linear regressions and analyses of variance, and derive appropriate theoretical results.(LO5) Be able to carry out and interpret analyses involving generalised linear models and derive appropriate theoretical results.(LO6) Be able to perform linear regression, analysis of variance and generalised linear model analysis using the SPSS computer package.(S1) Be able to perform linear regression, analysis of variance and generalised linear model analysis using the SPSS computer package.
• ##### Networks in Theory and Practice (MATH367)
Level 3 15 First Semester 100:0 •To develop an appreciation of network models for real world problems.•To describe optimisation methods to solve them.•To study a range of classical problems and techniques related to network models. (LO1) After completing the module students should be able to model problems in terms of networks and be able to apply effectively a range of exact and heuristic optimisation techniques.
• ##### Statistical Physics (MATH327)
Level 3 15 Second Semester 80:20 1. To develop an understanding of the foundations of Statistical Physics normally including statistical ensembles and related extensive and intrinsic quantities.2. To develop an understanding of the properties of classical and quantum gases and an appreciation of their applications to concepts such as the classical equation of state or the statisticaltheory of photons.3. To obtain a reasonable level of skill in using computer simulations for describing diffusion and transport in terms of stochastic processes.4. To knowledge the laws of thermodynamics and thermodynamical cycles.5. To obtain a reasonable understanding of interacting statistical systems and related phenomenons such as phase transitions. (LO1) Demonstrate understanding of the microcanonical, canonical and grand canonical ensembles, their relation and the derived concepts of entropy, temperature and particle numberdensity.(LO2) Understand the derivation of the equation-of-state for non-interacting classical or quantum gases.(LO3) Demonstrate numerical skills to understand diffusion from an underlying stochastic process.(LO4) Know the laws of thermodynamics and demonstrate their application to thermodynamic cycles.(LO5) Be aware of the effect of interactions including an understanding of the origin of phase transitions.(S1) Problem solving skills(S2) Numeracy(S3) Adaptability(S4) Communication skills(S5) IT skills(S6) Organisational skills(S7) Teamwork
• ##### Mathematical Economics (MATH331)
Level 3 15 Second Semester 100:0 · To explore, from a game-theoreticpoint of view, models which have been used to understand phenomena in whichconflict and cooperation occur.· To see the relevance of the theorynot only to parlour games but also to situations involving humanrelationships, economic bargaining (between trade union and employer, etc),threats, formation of coalitions, war, etc..· To treat fully a number ofspecific games including the famous examples of "The Prisoners'' Dilemma"and "The Battle of the Sexes".· To treat in detail two-personzero-sum and non-zero-sum games.· To give a brief review of n-persongames.· In microeconomics, to look atexchanges in the absence of money, i.e. bartering, in which two individualsor two groups are involved. To see how the Prisoner''s Dilemmaarises in the context of public goods. (LO1) After completing the module students should: Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences. .Be able to formulate, in game-theoretic terms, situations of conflict and cooperation. ·Be able to solve mathematically a variety of standard problems in the theory of games. ·To understand the relevance of such solutions in real situations.
• ##### Population Dynamics (MATH332)
Level 3 15 Second Semester 100:0 •To provide a theoretical basis for the understanding of population ecology•To explore the classical models of population dynamics•To learn basic techniques of qualitative analysis of mathematical models (LO1) The ability to relate the predictions of the mathematical models to experimental results obtained in the field.(LO2) The ability to  recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.(LO3) The ability to use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems.(S1) Problem solving skills(S2) Numeracy
• ##### Number Theory (MATH342)
Level 3 15 Second Semester 100:0 To give an account of elementary number theory with use of certain algebraic methods and to apply the concepts to problem solving. (LO1) To understand and solve a wide range of problems about integers numbers.(LO2) To have a better understanding of the properties of prime numbers.(S1) Problem solving skills(S2) Numeracy(S3) Communication skills
• ##### The Magic of Complex Numbers: Complex Dynamics, Chaos and the Mandelbrot Set (MATH345)
Level 3 15 Second Semester 90:10 1. To introduce students to the theory of the iteration of functions of one complex variable, and its fundamental objects;2. To introduce students to some topics of current and recent research in the field;3. To study various advanced results from complex analysis, and show how to apply these in a dynamical setting;4. To illustrate that many results in complex analysis are "magic", in that there is no reason to expect them in a real-variable context, and the implications of this in complex dynamics;5. To explain how complex-variable methods have been instrumental in questions purely about real-valued one-dimensional dynamical systems, such as the logistic family.6. To deepen students' appreciations for formal reasoning and proof. After completing the module, students should be able to: 1. understand the compactification of the complex plane to the Riemann sphere, and use spherical distances and derivatives. 2. use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems. 3. state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties. 4. determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set. 5. apply advanced results from complex analysis in the setting of complex dynamics. 6. determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not. (LO1) To understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives.(LO2) To be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.(LO3) To be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.(LO4) To be able to determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.(LO5) To know how to apply advanced results from complex analysis in a dynamical setting.(LO6) To be able to determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.(S1) Problem solving/ critical thinking/ creativity analysing facts and situations and applying creative thinking to develop appropriate solutions.(S2) Problem solving skills
• ##### Topology (MATH346)
Level 3 15 Second Semester 100:0 1. To introduce students to the mathematical notions of space and continuity.2. To develop students’ ability to reason in an axiomatic framework.3. To provide students with a foundation for further study in the area of topology and geometry, both within their degree and subsequently.4. To introduce students to some basic constructions in topological data analysis.5. To enhance students’ understanding of mathematics met elsewhere within their degree (in particular real and complex analysis, partial orders, groups) by placing it within a broader context.6. To deepen students’ understanding of mathematical objects commonly discussed in popular and recreational mathematics (e.g. Cantor sets, space-filling curves, real surfaces). (IM1) An understanding of the ubiquity of topological spaces within mathematics.(IM2) Knowledge of a wide range of examples of topological spaces, and of their basic properties.(IM3) The ability to construct proofs of, or counter-examples to, simple statements about topological spaces and continuous maps.(IM4) The ability to decide if a (simple) space is connected and/or compact.(IM5) The ability to construct the Cech and Vietoris-Rips complexes of a point set in Euclidean spac. e(IM6) The ability to compute the fundamental group of a (simple) space, and to use it to distinguish spaces.
• ##### Differential Geometry (MATH349)
Level 3 15 Second Semester 85:15 This module is designed to provide an introduction to the methods of differential geometry, applied in concrete situations to the study of curves and surfaces in euclidean 3-space.  While forming a self-contained whole, it will also provide a basis for further study of differential geometry, including Riemannian geometry and applications to science and engineering. (LO1) 1a. Knowledge and understanding: Students will have a reasonable understanding of invariants used to describe the shape of explicitly given curves and surfaces.(LO2) 1b. Knowledge and understanding: Students will have a reasonable understanding of special curves on surfaces.(LO3) 1c. Knowledge and understanding: Students will have a reasonable understanding of the difference between extrinsically defined properties and those which depend only on the surface metric.(LO4) 1d. Knowledge and understanding: Students will have a reasonable understanding of the passage from local to global properties exemplified by the Gauss-Bonnet Theorem.(LO5) 2a. Intellectual abilities: Students will be able to use differential calculus to discover geometric properties of explicitly given curves and surfaces.(LO6) 2b. Intellectual abilities: Students will be able to understand the role played by special curves on surfaces.(LO7) 3a. Subject-based practical skills: Students will learn to compute invariants of curves and surfaces.(LO8) 3b. Subject-based practical skills: Students will learn to interpret the invariants of curves and surfaces as indicators of their geometrical properties.(LO9) 4a. General transferable skills: Students will improve their ability to think logically about abstract concepts,(LO10) 4b. General transferable skills: Students will improve their ability to combine theory with examples in a meaningful way.(S1) Problem solving skills(S2) Numeracy
• ##### Applied Stochastic Models (MATH360)
Level 3 15 Second Semester 100:0 To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of stochastic model building for 'dynamic' events occurring over time or space. To enable further study of the theory of stochastic processes by using this course as a base. (LO1) To understans the theory of continuous-time Markov chains.(LO2) To understans the theory of diffusion processes. (LO3) To be able to solve problems arising in epidemiology, mathematical biology, financial mathematics, etc. using the theory of continuous-time Markov chains and diffusion processes. (LO4) To acquire an undertanding of the standard concepts and methods of stochastic modelling.(S1) Problem solving skills(S2) Numeracy
• ##### Theory of Statistical Inference (MATH361)
Level 3 15 Second Semester 90:10 To introduce some of the concepts and principles which provide theoretical underpinning for the various statistical methods, and, thus, to consolidate the theory behind the other second year and third year statistics options. (LO1) To acquire a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference.(LO2) To acquire an understanding of the blossoming area of Bayesian approach to inference.(S1) Problem solving skills(S2) Numeracy
• ##### Medical Statistics (MATH364)
Level 3 15 Second Semester 100:0 The aims of this module are to:•Demonstrate the purpose of medical statistics and the role it plays in the control of disease and promotion of health •Explore different epidemiological concepts and study designs •Apply statistical methods learnt in other programmes, and some new concepts, to medical problems and practical epidemiological research •Enable further study of the theory of medical statistics by using this module as a base. (LO1) identify the types of problems encountered in medical statistics(LO2) demonstrate the advantages and disadvantages of different epidemiological study designs(LO3) apply appropriate statistical methods to problems arising in epidemiology and interpret results(LO4) explain and apply statistical techniques used in survival analysis(LO5) critically evaluate statistical issues in the design and analysis of clinical trials(LO6) discuss statistical issues related to systematic review and apply appropriate methods of meta-analysis(LO7) apply Bayesian methods to simple medical problems.(S1) Problem solving skills
• ##### Mathematical Risk Theory (MATH366)
Level 3 15 Second Semester 100:0 •To provide an understanding of the mathematical risk theory used in the study process of actuarial interest• To provide an introduction to mathematical methods for managing the risk in insurance and finance (calculation of risk measures/quantities)• To develop skills of calculating the ruin probability and the total claim amount distribution in some non‐life actuarial risk models with applications to insurance industry• To prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CT6 subject of the Institute of Actuaries (MATH366 covers 50% of CT6 in much more depth). (LO1) After completing the module students should be able to: (a) Define the loss/risk function and explain intuitively the meaning of it, describe and determine optimal strategies of game theory, apply the decision criteria's, be able to decide a model due to certain model selection criterion, describe and perform calculations with Minimax and Bayes rules. (b) Understand the concept (and the mathematical assumptions) of the sums of independent random variables, derive the distribution function and the moment generating function of finite sums of independent random variables.(c) Define and explain the compound Poisson risk model, the compound binomial risk model, the compound geometric risk model and be able to derive the distribution function, the probability function, the mean, the variance, the moment generating function and the probability generating function for exponential/mixture of exponential severities and gamma (Erlang) severities, be able to calculate the distribution of sums of independent compound Poisson random variables. (d) Understand the use of convolutions and compute the distribution function and the probability function of the compound risk model for aggregate claims using convolutions and recursion relationships.(e) Define the stop‐loss reinsurance and calculate the (mean) stop‐loss premium for exponential and mixtures of exponential severities, be able to compare the original premium and the stoploss premium in numerical examples.(f) Understand and be able to use Panjer's equation when the number of claims belongs to theR(a, b, 0) class of distributions, use the Panjer's recursion in order to derive/evaluate the probability function for the total aggregate claims.(g) Explain intuitively the individual risk model, be able to calculate the expected losses (as well as the variance) of group life/non‐life insurance policies when the benefits of the each person of the group are assumed to have deterministic variables.(h) Derive a compound Poisson approximations for a group of insurance policies (individual risk model as approximation), (i) Understand/describe the classical surplus process ruin model and calculate probabilities of the number of the risks appearing in a specific time period, under the assumption of the Poisson process.(j) Derive the moment generating function of the classical compound Poisson surplus process, calculate and explain the importance of the adjustment coefficient, also be able to make use of Lundberg's inequality for exponential and mixtures of exponential claim severities.(k) Derive the analytic solutions for the probability of ruin, psi(u), by solving the corresponding integro‐differential equation for exponential and mixtures of exponential claim amount severities, (l) Define the discrete time surplus process and be able to calculate the infinite ruin probability, psi(u,t) in numerical examples (using convolutions). (m) Derive Lundberg's equation and explain the importance of the adjustment coefficient under the consideration of reinsurance schemes.(n) Understand the concept of delayed claims and the need for reserving, present claim data as a triangle (most commonly used method), be able to fill in the lower triangle by comparing present data with past (experience) data.(o) Explain the difference and adjust the chain ladder method, when inflation is considered.(p) Describe the average cost per claim method and project ultimate claims, calculate the required reserve (by using the claims of the data table).(q) Use loss ratios to estimate the eventual loss and hence outstanding claims.(r) Describe the Bornjuetter‐Ferguson method (be able to understand the combination of the estimated loss ratios with a projection method). Use the aforementioned method to calculate the revised ultimate losses (by making use of the credibility factor).