A Level Requirements
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see all requirements
Full time 4 Year(s)
Lancaster’s joint Spanish Studies and Mathematics degree is taught by the Department of Languages and Cultures in conjunction with the Mathematics and Statistics Department. The Complete University Guide 2017 ranked Spanish Studies 5th and Mathematics 10th in the UK.
Your Spanish Studies programme gives you the opportunity to acquire high-level language skills while gaining a thorough understanding of the country’s historical, cultural, social and political background in a global context. In Maths, you’ll study in-depth mathematical theory and practice and have the option to specialise in pure mathematics or statistics.
Your first year comprises an exploration of the Spanish language and its cultural context, core modules in calculus and probability, and selected modules in topics such as ‘Linear Algebra’ and ‘Discrete Mathematics’. Alongside these, you will study a minor subject of your choice.
Building on your language skills in Year 2, you will study the culture, politics and history of the Spanish-speaking world in more depth, as well as selecting modules which are international in scope and promote a comparative understanding of Europe and beyond. You will combine these with Mathematics modules such as ‘Groups and Rings’ and ‘Real Analysis’.
Spending your third year abroad in a Spanish-speaking country makes a major contribution to your command of the language, while deepening your intercultural sensitivity. You can study at a partner institution or conduct a work placement.
In your final year, you consolidate your Spanish language skills, and study specialist culture and comparative modules, such as ‘Translation as a Cultural Practice’. You will also select Mathematics modules such as ‘Differential Equations’, ‘Combinatorics’, or ‘Geometry of Curves and Surfaces’.
A Level AAB including A level Mathematics or Further Mathematics grade A OR ABB including A level Mathematics and Further Mathematics, at least one of which at grade A. See below for language requirements.
Required Subjects In addition to the Mathematics requirements above, A level Spanish, or if this is to be studied from beginners’ level, AS grade B or A level grade B in another foreign language, or GCSE grade A in a foreign language. Native Spanish speakers will not be accepted onto this scheme.
IELTS 6.5 overall with at least 5.5 in each component. For other English language qualifications we accept, please see our English language requirements webpages.
International Baccalaureate 35 points overall with 16 points from the best 3 Higher Level subjects including 6 in Mathematics HL and appropriate evidence of language ability
BTEC May be accepted alongside A level Mathematics and Further Mathematics, and evidence of language ability
Access to HE Diploma May occasionally be accepted
We welcome applications from students with a range of alternative UK and international qualifications, including combinations of qualification. Further guidance on admission to the University, including other qualifications that we accept, frequently asked questions and information on applying, can be found on our general admissions webpages.
Contact Admissions Team + 44 (0) 1524 592028 or via firstname.lastname@example.org
Many of Lancaster's degree programmes are flexible, offering students the opportunity to cover a wide selection of subject areas to complement their main specialism. You will be able to study a range of modules, some examples of which are listed below.
This module provides the student with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. We introduce examples of functions and their graphs, and techniques for building new functions from old. We then consider the notion of a limit and introduce the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and be introduced to rational functions and their partial fractions.
The exponential function is defined by means of a power series which is subsequently extended to the complex exponential function of an imaginary variable, so that students understand the connection between analysis, trigonometry and geometry. The trigonometric and hyperbolic functions are introduced in parallel with analogous power series so that students understand the role of functional identities. Such functional identities are later used to simplify integrals and to parametrise geometrical curves.
This module extends the theory of calculus from functions of a single real variable to functions of two real variables. Students will learn more about the notions of differentiation and integration and how they extend from functions defined on a line to functions defined on the plane. We see how partial derivatives help us to understand surfaces, while repeated integrals enable us to calculate volumes. Students will also investigate complex polynomials and use De Moivre’s theorem to calculate complex roots.
In mathematical models, it is common to use functions of several variables. For example, the speed of an airliner can depend upon the air pressure, temperature and wind direction. To study functions of several variables, we introduce rates of change with respect to several quantities. We learn how to find maxima and minima. Applications include the method of least squares. Finally, we investigate various methods for solving differential equations of one variable.
Introducing the theory of matrices together with some basic applications, students will learn essential techniques such as arithmetic rules, row operations and computation of determinants by expansion about a row or a column.
The second part of the module covers a notable range of applications of matrices, such as solving systems of simultaneous linear equations, linear transformations, characteristic equation and eigenvectors and eigenvalues.
This module is designed for students who have already completed an A-level in Spanish or whose Spanish is of a broadly similar standard. The language element aims to enable students both to consolidate and improve their skills in spoken and written Spanish. A further aim is to provide students with an introduction to the historical and cultural development of Spain in the twentieth century, and also to contemporary institutions and society.
There are three language classes per week, of which at least one is normally conducted by a Spanish native speaker. Tutorials are based on a textbook, and emphasis is placed on the acquisition of vocabulary and a firm grasp of Spanish grammatical structures. Listening and speaking skills are developed under the guidance of Spanish native speakers using audio and video materials.
The culture programme consists of a combination of lectures and seminars over 20 weeks. The module looks at how key moments in Spanish history have shaped contemporary Spanish culture (films, plays, novels etc.).
This module is designed for students having little or no knowledge of the Spanish language. Consequently, a substantial part of the module is devoted to intensive language teaching aimed at making the student proficient in both written and spoken Spanish. At the same time, students will be introduced to aspects of Spanish history, culture and society in the twentieth century.
There are four language classes per week, of which at least one is normally conducted by a Spanish native speaker. Tutorials are based on a textbook, and emphasis is placed on the acquisition of vocabulary and a firm grasp of Spanish grammatical structures. Listening and speaking skills are developed under the guidance of Spanish native speakers using audio and video materials.
Probability theory is the study of chance phenomena, the concepts of which are fundamental to the study of statistics. This module will introduce students to some simple combinatorics, set theory and the axioms of probability.
Students will become aware of the different probability models used to characterise the outcomes of experiments that involve a chance or random component. The module covers ideas associated with the axioms of probability, conditional probability, independence, discrete random variables and their distributions, expectation and probability models.
To enable students to achieve a solid understanding of the broad role that statistical thinking plays in addressing scientific problems, the module begins with a brief overview of statistics in science and society and then moves on to the selection of appropriate probability models to describe systematic and random variations of discrete and continuous real data sets. Students will learn to implement statistical techniques and to draw clear and informative conclusions.
The module will be supported by the statistical software package ‘R’, which forms the basis of weekly lab sessions. Students will develop a strategic understanding of statistics and the use of associated software, and this underpins the skills needed for all subsequent statistical modules of the degree.
This module provides a rigorous overview of real numbers, sequences and continuity. Covering bounds, monotonicity, subsequences, invertibility, and the intermediate value theorem, among other topics, students will become familiar with definitions, theorems and proofs.
Examining a range of examples, students will become accustomed to mathematical writing and will develop an understanding of mathematical notation. Through this module, students will also gain an appreciation of the importance of proof, generalisation and abstraction in the logical development of formal theories, and develop an ability to imagine and ‘see’ complicated mathematical objects.
In addition to learning and developing subject specific knowledge, students will enhance their ability to assimilate information from different presentations of material; learn to apply previously acquired knowledge to new situations; and develop their communication skills.
Students are introduced to the basic ideas and notations involved in describing sets and their functions. The module helps students to formalise the idea of the size of a set and what it means to be finite, countably infinite or uncountably finite. For finite sets, we can say that one is bigger than another if it contains more elements. What about infinite sets? Are some infinite sets bigger than others? We develop the tools to answer these questions and other counting problems, such as those involving recurrence relations, e.g. the Fibonacci numbers.
Rather than counting objects, we might be interested in connections between them, leading to the study of graphs and networks – collections of nodes joined by edges. There are many applications of this theory in designing or understanding properties of systems, such as the infrastructure powering the internet, social networks, the London Underground and the global ecosystem.
The main focus of this course is vectors in two and three-dimensional space. We start off with the definition of vectors and we see some applications to finding equations of lines and planes. We then consider some different ways of describing curves and surfaces via equations or parameters, and we use partial differentiation to determine tangent lines and planes, as well as using integration to calculate the length of a curve.
In the second half of the course, we study functions of several variables. When attempting to calculate an integral over one variable, we often substitute one variable for another more convenient one; here we will see the equivalent technique for a double integral, where we have to substitute two variables simultaneously. We also investigate some methods for finding maxima and minima of a function subject to certain conditions.
Finally, we discuss how to calculate the areas of various surfaces and the volumes of various solids.
Building on MATH113, this module explores the familiar topics of integration, series and differentiation, and develops them further. Taking a different approach, students will learn about the concept of integrability of continuous functions; improper integrals of continuous functions; the definition of differentiability for functions; and the algebra of differentiation.
Applying the skills and knowledge gained from this module, students will tackle questions such as: “Can you sum up infinitely many numbers and get a finite number?”. Students will also enhance their knowledge and understanding of the fundamental theorem of calculus.
This module introduces the student to logic and mathematical proofs, with emphasis placed on proving general theorems than on performing calculations. This is because a result which can be applied to many different cases is clearly more powerful than a calculation that deals only with a single specific case.
We take a look at the language and structure of mathematical proofs in general, emphasising how logic can be used to express mathematical arguments in a concise and rigorous manner. These ideas are then applied to the study of number theory, establishing several fundamental results such as Bezout’s Theorem on highest common factors and the Fundamental Theorem of Arithmetic on prime factorisations.
The concept of congruence of integers is introduced to students and they study the idea that a highest common factor can be generalised from the integers to polynomials.
Probability provides the theoretical basis for statistics and is of interest in its own right.
You’ll revisit basic concepts from the first year probability module, and extend these to encompass continuous random variables, investigating several important continuous probability distributions.
You’ll 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 core module is divided into three topic areas comprising of the following: (1) Power and Resistance in Spanish America from the Colony to the 21st Century; (2) War, Dictatorship and Transition in Spain in the 20th and 21st Century; (3) Culture and Resistance in Catalunya in the 20th and 21st Century. The students will study texts which both encourage an engaged reading of Spanish and open up alternative avenues towards traditional fields of study in Hispanism (empire and colonialism, nineteenth-century nation-building, revolution, dictatorship, Francoism, regionalism, neo-liberalism and globalisation.) These disparate fields of study are conceptually unified and made more accessible for the students in two ways. Firstly, we refer students to the theme of power and resistance which concerns them all in various ways. Secondly, we divide the module by geographical region which, given the array of varying cultures and histories in the Spanish-speaking world, represents the least mystifying and most logical method of study. We will employ a text-based approach in which the texts chosen allow us to operate within certain very specific historical and geographical parameters whilst never losing sight of the main theme. Throughout, students will be encouraged to interrogate the meanings of terms such as colony, revolution, rebellion, republic, empire, dictatorship and democracy with close readings of cultural texts which themselves question the assumptions which underpin these terms.
DELC200 is a non-credit bearing module. All major students going abroad in their second or third year are enrolled on it during the year prior to their departure, and timetabled to attend the events. These include: introduction to the Year Abroad 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 Year Abroad; research skills and questionnaire design; teaching abroad; curriculum writing and employability skills; welfare and wellbeing; Year Abroad Preparation Week in the Summer Term. Materials are uploaded on the DELC200 Moodle pages.
This module comprises of both oral and aural skills, to be taken alongside the Written Skills module. It builds upon skills gained in the first year.
This module aims to enhance students’ linguistic proficiency in spoken Spanish 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.
By the end of this module, students should have enhanced their comprehension of the spoken language, as used in both formal speech, and in everyday life situations including those that they may encounter in Spanish-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. 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 Spanish 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 Spanish-speaking societies, politics and culture, and contemporary issues and institutions in order to prepare them for residence abroad in their 3rd year.
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 students’ proficiency in the writing of Spanish (notes, reports, summaries, essays, projects, etc.) including translation from and into Spanish; and the systematic study of Spanish lexis, grammar and syntax.
The module aims to enhance students' 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.
The module aims to enhance students’ proficiency in understanding spoken Spanish, as well as in the writing of Spanish (notes, reports, summaries, essays, projects, etc.) including translation from and into Spanish; and the systematic study of Spanish lexis, grammar and syntax.
This module builds on the binary operations studies in previous modules, such as addition or multiplication of numbers and composition of functions. Here you’ll select a small number of properties which these and other examples have in common, and use them to define a group.
You’ll also consider the elementary properties of groups. It turns out that several surprisingly elegant results can be proved fairly simply! By looking at maps between groups which 'preserve structure' you’ll discover a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same'.
Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives us 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, but you’ll meet several less familiar examples too.
Complex Analysis has its origins in differential calculus and the study of polynomial equations.
In this module you’ll consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. You’ll use integral calculus of complex functions to find elegant and important results, including the fundamental theorem of algebra, and you’ll also use classical theorems to evaluate real 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:
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.
What is world literature? How have writers engaged with the concept? How have they explored their role as a writer in the 20th century?
This module explores a range of texts written in a range of languages and genres, examining the engagement of writers with their role in different social, political and historical contexts. Lectures will provide an introduction to the genre being studied and address the question of the role of the writer in the context of world literatures. Workshops will focus on a range of set and optional texts of global importance, which will be considered as examples of the literary genre and in relation to material covered in the lecture.
The module is divided into five sections, each focusing on a specific genre. Each section will comprise three texts, two of which are optional. All texts explore the role of the writer in different social, political and historical contexts of the 20th century, and the ways their writing engages with these contexts.
This module explores how post-war economic change has affected European societies, and how socio-political factors in turn have influenced the patterns and outcomes of economic development, over the second half of the twentieth and the beginning of the twenty first century.
The module is structured on the basis of three country-specific modules (France, Germany and Spain), examining how these countries have confronted key moments of economic change, and what the longer-term consequences of that change have been. While the module emphasis is on broad national developments, discussion also covers examples relating to particular industries and major companies.
In lectures, workshops and seminars we will explore the context of reconstruction after World War II and the pattern of subsequent economic development; the relationship between social and economic policies; the development of the three country's economies; the changes of the 1980s and their impact on subsequent years; and the consequences of specific momentous events, such as the re-unification of Germany and how the financial crisis of 2008 affected, and still affects, France, Germany and Spain.
This module will introduce second-year students to the role that the language used by institutions plays in shaping individual perceptions of identity. It will provide them with a basic theoretical framework that allows them to understand the relationship between language and power as reflected in current language policies at regional, national, and supranational levels. It will enable them to recognise forms of prestige and stigma associated with varieties of the three main languages under study. It will therefore 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 and ‘Gastarbeiter’ language and policies; regional variations of France: Linguistic Diversity: A threat to French National Identity?; The languages and language attitudes of Spain (Castilian Spanish, Catalan, Basque, Galician).
This module is taught in English.
This module will give you the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.
You’ll 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 your study will also involve looking at the concepts of length and angle with regard to vector spaces.
This module seeks to support students to apply their linguistic and cultural understanding in a specific professional context. Students will 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. Students will typically spend between 25-30 hours over a period of 10 weeks engaging with a placement organisation in Lent. Alternatively students may undertake a 'block' placement over a two to three week period during the Easter vacation (this will allow placements abroad). We have developed a number of local work placements and students can also source placements (subject to departmental approval). There will be some preparation for the module before Lent. This will consist of short interviews and the sourcing and confirmation of placements. For students undertaking schools placements, there will also be some training. Workshops in Lent will provide preparation for placements and guidance on reflective 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:
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.
In this module you’ll take a thorough look at the limits of sequences and convergence of series. You’ll 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.
You’ll spend time studying the Intermediate Value Theorem and the Mean Value Theorem, and will discover that they have many applications of widely differing kinds. 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 we put the notion of integration under the microscope. Once it’s properly defined (via limits), you’ll learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. You’ll 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 like terrorism, immigration, resistance and city life? Do they entertain viewers, instruct them, or both?
This module explores European and Latin American films in their social and historical contexts. 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.
To these ends, there will be introductory lectures on cinema and society and on film aesthetics and content in the first week of the module. The connections mentioned will be the focus of seminars and presentations within the four core topic areas: terrorism, migration, the city and resistance.
The module consists of four two-week strands on cinema and society: Terrorism, Migration and Hybrid identities, The City and Collaboration/Resistance.
Each strand will be introduced with a lecture and followed by seminars on the set films. Students will give a presentation on a short sequence within their allocated film.
Statistics is the science of understanding patterns of population behaviour from data.
In this module we approach this problem by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.
You’ll focus on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and also considering linear regression techniques within the statistical modelling framework.
This module aims to give students 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 Year Abroad is compulsory for Single and Joint Honours Language students, who must spend at least eight months abroad in their third year.
The module also aims to enhance and develop students' language skills, with all assessments being written in the target language.
Students who started a language as a beginner in Part I must spend a minimum of four months in a country where that language is spoken.
Joint Honours students studying two languages may choose to spend the year in either of the two countries concerned or, if appropriate arrangements can be made, can spend a semester in each country.
This module is a half unit and is integrated with the Spanish Language: Written Skills module.
This module together with the written skills module consists of three hours tuition per week. Both the oral and the written language modules focus on particular topics of cultural and contemporary interest. The general aim of these half unit modules is to develop the abilities the students gained during their second year and the year abroad.
By the end of this module, students should have developed an informed interest in the society and culture of the Spanish-speaking world. They should also have acquired almost native-speaker abilities in both spoken and written language.
This module is a half unit and is integrated with the Spanish Language: Oral Skills module.
This module together with the oral skills module consists of three hours tuition per week.
This module has two main aims. The first one is to enhance students’ linguistic proficiency with emphasis on understanding of spoken and written Spanish, the speaking of Spanish (prepared and spontaneous) in both formal and informal settings, the writing of Spanish, and the systematic study of Spanish lexis, grammar and syntax. The second aim is to increase students’ awareness, knowledge and understanding of contemporary Spain.
By the end of this module, students should have developed an informed interest in the society and culture of the Spanish -speaking world. They should also have acquired almost native-speaker abilities in both spoken and written language.
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?
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 you’ll 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). You’ll also explore important practical applications of the results and methods.
This module introduces students to major themes that shape the experience of contemporary city dwellers: gender, social inequality, and practices of citizenship. These interlinking themes will be introduced through novels, poetry and films on 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, Berlin, and Los Angeles.
Each topic will be covered though an introductory lecture and a core text, followed by a range of additional texts for students to analyse. During workshops students will share their findings and opinions, emphasizing on identifying links between the topics studied, aiming to encourage discussion.
The format of the module encourages cross-referencing between the themes of the module (for example, gender and sexuality are relevant to an analysis of social inequality, and vice versa).
This module considers questions relating to linear ordinary differential equations. 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 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:
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.
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. The other two restrictions on topic choice are: it must be capable of and approached from a serious academic angle and it falls within the range of expertise of a member of the Department’s staff.
Each student gets assigned a supervisor - one of the lecturers from the Department, who will provide 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.
This module is based on the comparison of masterpieces of Spanish poetry from the 13th-20th century with the events of the current TV show Game of Thrones.
The purpose of this comparison is to consider how patterns and stereotypes related to the past, some of which are achieving success in both the TV show and the contemporary novels by Martin, have also been responsible for the success of a number of works that today are considered as classics of Spanish poetry. Students do not have to be familiar with the TV show or the novels in order to be successful in this module. Fragments of this show will be introduced in class, before drawing comparisons with the assigned readings in order to enhance general understanding.
Students on this module will engage in the study of the socio-historical events and features of Spanish society, as well as the literary mechanisms of each one of the texts. It is essential to understand the dynamic of these events in order to better understand the texts read.
This module is an introduction to smooth curves and surfaces in three-dimensional space. You’ll encounter various geometrical properties of these objects, such as length, area, torsion and curvature, and will have the opportunity to explore the meaning of these quantities. You’ll use a variety of examples to calculate their values, and will use them to apply techniques from calculus and linear algebra.
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.
In this module you’ll develop the knowledge of groups that you’ve gained in second year. You’ll study ‘direct products’ which are used to construct new groups, while any finite group is shown to ‘factor’ into ‘simple’ pieces. You’ll also consider situations 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.
This module aims at exploring the nature of the relationship between the individual and society, notions of progress and economic justice, as these are still widely debated topics in contemporary Europe in light of the current economic and political crisis.
This module will use the concepts of utopia, dystopia and ideology as a forum for discussion on the relationship between individual imagination and social discourse in the nineteenth century, as well as the relationship between fiction and political discourse. Students will look at the major intellectual debates which influenced the contemporary European thought after the French Revolution.
Students will explore the development of major ideologies and cultural movements such as Romanticism, Marxism, Socialism and Positivism, spanning from the period immediately following the French Revolution to the middle of the nineteenth century.
This module aims to provide students with a grasp of both the historical contexts for violence and masculinities as they are depicted in Spanish and Latin American film as well as an understanding of theoretical approaches, enabling rich analyses of such violence and evolving masculinities.
The module seeks to pluralise violence so that it is understood by students in its many forms. It will also ensure students have the terminology to discuss relevant contexts and approaches in relation to specific films in a coherent and intellectually appropriate framework.
Students will be required to view films set in historical contexts highlighting key themes. They will be encouraged to observe and analyse structural violence in various forms in these films and to understand its relationship with such categories as hegemonic, protest and patriarchal masculinities. The module will then question the 'invisible' nature of domestic violence, violence as a means (or not) of providing 'cheap shocks' and different aesthetic approaches towards the depiction of state violence.
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.
The aim of this module is to provide third year students with more options of applicable topics which draw upon second year pure mathematics courses 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 course shows how to reduce certain linear systems of differential equations to systems of matrix equations and thus solve them. Linear algebra enables us 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 stabilize a (A,B,C,D) system.
This module is designed to give you an opportunity to consider key issues in the teaching and learning of mathematics. Whilst it is an academic study of mathematics education and not a training course for teachers, it does provide an excellent foundation for a PGCE especially in preparing students to write academically.
Having studies Mathematics for many years, you are well-placed to reflect upon that experience and attempt to make sense of it in the light of theoretical frameworks developed by researchers in the field. Within this course we hope to help you with this process so that as a Mathematics graduate you will be able to contribute knowledgeably to future debate about the ways in which your subject is treated within the education system.
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.
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 furthers your knowledge of commutative rings from your second year study.
You’ll be introduced to two new classes of integral domains called Euclidean domains, where you have a counterpart of the division algorithm, and unique factorization domains, in which an analogue of the Fundamental Theorem of Arithmetic holds.
You’ll also explore how well-known concepts from the integers such as the highest common factor, the Euclidean algorithm, and factorization of polynomials, carry over to this new setting.
This module covers Mexican political history and committed writing since 1968. Students will be presented with several important and politically defining events in Mexican contemporary history: the student movement of 1968, the guerrilla movements and the guerra sucia of the 1970s, the emergence of civil society after the earthquake of 1985, the Zapatista Uprising in 1994, and the Oaxaca Uprising in 2006.
These movements and events are explored through lectures on the political context of each movement, and through a combination of fictional and non-fictional texts from a variety of genres, such as testimonial literature, the documentary novel, and communiqués. Students will be analysing texts written by the most important contemporary Mexican writers and public intellectuals such as Paco Ignacio Taibo II, Elena Poniatowska, Carlos Monsivais, Carlos Montemayor, and the Subcomandante Insurgente Marcos.
This module is taught in English and all texts are available in English.
What makes a good translation and how do translations do good? This module helps 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 (philosophical essays on the craft of translation from French, German and Hispanic authors of the 19th and 20th centuries), representative fictional texts reflecting on translation processes, and contemporary documents from the EU directorate on translation, PEN and the Translators' Association. We will also make considerable use of contemporary online resources as exemplified by Anglophone advocates of intercultural exchange such as Words Without Borders. 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.
This module will explore the relationship between witchcraft, heresy and inquisition in regard to the prosecution of the 'otherness', focusing specifically on their literary representation in medieval and Renaissance Europe. Students will engage in the study of the socio-historical events and features of European society from the 14th to the 17th centuries, as well as the literary mechanisms utilised by authors of each one of the texts under study. The course will cover texts and events occurred in Germany, France, Italy, Spain, and England. Specific authors, such as Dante Alighieri, François Villon and Miguel de Cervantes, and masterpieces such as 'The Divine Comedy', 'La Celestina', and 'Don Quijote de La Mancha', will be analysed together with genres such as 'Geisslerlieder', balade, and drama. In addition, we will have a special week studying our neighbours, the Lancashire witches, and how the successful trial from 1612 is still perceived all along our city.
This module consists of 20 hours over the course of 10 weeks, comprising of a mixture of informal lectures and workshops, and independent showings of films.
The module aims at reviewing a series of narratives by 21st century European-born authors: writers, cinematographers, anthropologists and documentary makers. It not only introduces students to the historical contexts within which each of the narratives is situated, but also explores contemporary theories of identity and writing.
Students are presented with autobiographical accounts, semi-fictional stories, films and documentaries in order to understand the experience of being caught between cultures as a result of travel or involuntary displacement resulting from war or social upheaval. They reflect upon the issues of identity, problems associated with cross-cultural analysis and the relationship between history and personal destiny, border-crossing, cultural fragmentation and continuity. The focus of the module lies on the historical relationship between countries within Europe, and between Europe and other parts of the world; mainly India, North Africa and America.
Lancaster University offers a range of programmes, some of which follow a structured study programme, and others which offer the chance for you to devise a more flexible programme. We divide academic study into two sections - Part 1 (Year 1) and Part 2 (Year 2, 3 and sometimes 4). For most programmes Part 1 requires you to study 120 credits spread over at least three modules which, depending upon your programme, will be drawn from one, two or three different academic subjects. A higher degree of specialisation then develops in subsequent years. For more information about our teaching methods at Lancaster visit our Teaching and Learning section.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.
As well as language and subject-related skills, a degree in languages develops rich interpersonal, intercultural, cognitive and transferable skills that can be utilised across a variety of careers such as accountancy, IT, business development, civil service, events management, finance, journalism, publishing, research and sales, as well as teaching and translating both in the UK and abroad.
Mathematics is a very versatile degree, developing logical thinking, analytical working and problem solving skills that are highly transferable and much sought after by employers. Recent graduates are pursuing career paths as actuaries, analysts, clinical and medical statisticians, software developers, accountants, and teachers.
For the last ten years, languages graduates from Lancaster have been in the top ten universities in the country in terms of their employment prospects. The Complete University Guide 2017 ranked Spanish Studies 1st and Mathematics 7th in the UK for graduate prospects.
Many graduates continue their studies at Lancaster, making the most of our excellent postgraduate research facilities. We offer Masters degrees in Translation and Languages and Cultures, as well as in a variety of statistical and related fields.
We set our fees on an annual basis and the 2018/19 entry fees have not yet been set.
As a guide, our fees in 2017 were:
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Students also need to consider further costs which may include books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation it may be necessary to take out subscriptions to professional bodies and to buy business attire for job interviews.
Average time in lectures, seminars and similar
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