# Mathematics and Philosophy BA (Joint Hons)

## Key information

### Module details

Due to the impact of COVID-19 we're changing how the course is delivered.

### Programme Year One

Students take seven required modules: four from Philosophy, and three core foundation modules from the Mathematics Year 1 programme. Students will also choose one optional module from Mathematics.

#### Year One Compulsory Modules

• ##### Calculus I (MATH101)
Level 1 15 First Semester 50:50 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) Understand the key definitions that underpin real analysis and interpret these in terms of straightforward examples.(LO2) Apply the methods of calculus and real analysis to solve previously unseen problems (of a similar style to those covered in the course).(LO3) Understand in interpret proofs in the context of real analysis and apply the theorems developed in the course to straightforward examples.(LO4) Independently construct proofs of previously unseen mathematical results in real analysis (of a similar style to those demonstrated in the course).(LO5) Differentiate and integrate a wide range of functions;(LO6) Sketch graphs and solve problems involving optimisation and mensuration(LO7) Understand the notions of sequence and series and apply a range of tests to determine if a series is convergent(S1) Numeracy
• ##### Introduction to Linear Algebra (MATH103)
Level 1 15 First Semester 45:55 • 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.(S1) Numeracy
• ##### Mind, Knowledge and Reality (PHIL103)
Level 1 15 First Semester 0:100 To introduce students to modern metaphysics in its historical context, with a particular focus on the systems of Descartes and Locke and their influences in the present day. (LO1) Students will be able to distinguish between sound and unsound arguments.(LO2) Students will be able to build a case for a specific metaphysical position, by weighing theoretical virtues, such as Occam's razor, and metaphysical principles, such as the conceivability principle and the principle of sufficient reason.(LO3) Students will be able to prepare an argument for presentation in a piece of long-form writing, with a clear understanding of argumentative structure and the use of citations for support.(LO4) Students will be able to explain philosophical systems, including those of Descartes and Locke, in their historical and intellectual context.(LO5) Students will be able explain the basic issues, and the standard views, pertaining to Descartes’ essentialism, Locke’s account of the self, and the contemporary philosophy of mind.(LO6) Students will be able to able to argue for a specific view pertaining to five issues in contemporary metaphysics: God, personal identity, consciousness, free will and time.(LO7) Students will be able to discuss reality in the partially abstract manner distinctive of metaphysical thought.(S1) Critical thinking and problem solving - Critical analysis(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop the ability to perform bibliographical searches, to include (to professional standard) citations and bibliographies in their work and to plan, organise and produce presentations and essays.(S7) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.(S8) Students will develop their ability to work independently.(S9) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S10) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.
• ##### Philosophy Toolkit (PHIL105)
Level 1 15 First Semester 0:100 To introduce and develop the academic skills and knowledge necessary for the successful practice of philosophy.To help prepare students for future academic or professional work by honing core essential reading, writing and presenting skills.To foster in students an appreciation of the value of philosophy, and the value of the skills developed through studying philosophy.To introduce students to three central philosophical topics, and to promote understanding, considered reflection, and independent thinking with respect to these topics.To develop effective critical reading skills.To develop the ability to present complex ideas orally and in writing.To enable and promote the practicing of the intellectual virtues associated with philosophical discussion.To promote the skills involved in producing clear, accurate and concise summaries of philosophical views, arguments and positions.To further develop the skills involved in writing well-structured, rigorously argued, clearly-written and well-presented philosophical essays.To expand upon students’ research skills, and provide guidance on assessing the reliability of online resources.To increase students’ awareness of the importance of feedback, and to provide guidance on understanding and learning from that feedback to develop and improve their future work. (LO1) Students will be able to explain and evaluate some work relevant to three topics in philosophy (animal ethics, lying and bullshit (epistemology), aesthetics).(LO2) Students will be able to conduct discussions in a manner that displays the intellectual virtues associated with philosophy.(LO3) Students will be able to write successful executive summaries of key texts.(LO4) Students will be able to write essays that embody a philosophically-informed approach to argumentation.(LO5) Students will be able to conduct independent research in support of their work, and make use of the Harvard Referencing System.(LO6) Students will have the skills required to successfully present their work using a variety of digital and non-digital formats.(LO7) Students will be able to understand how to develop their work in light of feedback received.(LO8) Students will be able to apply their knowledge and understanding to real world situations (particularly with respect to the first topic covered – animal ethics).(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop the ability to perform bibliographical searches, to include (to professional standard) citations and bibliographies in their work and to plan, organise and produce presentations and essays.(S7) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.(S8) Students will develop their ability to work independently towards enquiry-led research goals.(S9) Students will develop their ability to quickly identify the most relevant and important information in a text.(S10) Students will develop their digital fluency through using a variety of technologies and software.(S11) Students will develop the ability to write to a professional standard, using word-processing software.(S12) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S13) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S14) Through developing their analytical and critical skills and observing good standards of academic practice, students will develop their intellectual honesty.(S15) Students will develop their ability to consider the real world application of the views, positions and arguments discussed.
• ##### Calculus II (MATH102)
Level 1 15 Second Semester 0:100 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.
• ##### Introduction to Logic (PHIL127)
Level 1 15 Second Semester 100:0 To introduce students to the concepts, language and methods of classical sentential logic. To introduce students to a language of classical quantificational logic. (LO1) Students will be able to explain and apply the basic concepts of classical sentence logic.(LO2) Students will be able to translate from English into sentence logic and vice versa.(LO3) Students will be able to construct and use truth tables.(LO4) Students will be able to construct proofs in natural deduction for sentence logic.(LO5) Students will be able to translate from English into quantificational logic and vice versa.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to marshal arguments and present them orally and in writing.(S4) Students will develop their ability to work independently.(S5) Students will develop their problem-solving skills.(S6) Improving own learning and performance; personal action planning.(S7) Communication; oral, written and visual; listening skills.(S8) Communication oral, written and visual, following instructions, protocols and procedures.(S9) Communication oral, written and visual, influencing skills and argumentation.(S10) Personal attributes and qualities; resilience.
• ##### Philosophical Insights (PHIL106)
Level 1 15 Second Semester 0:100 To consolidate the academic skills and knowledge necessary for the critical reading and writing of philosophy.To acquaint students with some well-known philosophical quotations, and to introduce key insights, ideas and debates in the history of philosophy via these philosophical quotations.To enable students to understand and explain the meaning and context of these quotations.To equip students with the skills to evaluate these quotations.To consolidate students’ research skills.To enhance students’ team-working skills.To consolidate students' appreciation of, and ability to use, forward-facing feedback and review. (LO1) Students will be able to understand and explain some well-known philosophical quotations.(LO2) Students will understand how these quotations relate to key insights, ideas and debates in the history of philosophy.(LO3) Students will be able to critically engage with these philosophical quotations.(LO4) Students will be able to write a blogpost, and compile a list of wiki entries on a series of related topics.(LO5) Students will be able to conduct independent research in support of their work, using appropriate print and online resources.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop the ability to perform bibliographical searches, and (to include to professional standard) citations and bibliographies in their work.(S7) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.(S8) Students will develop their ability to work independently.(S9) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S10) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.(S11) Students will develop the ability to write to a professional standard.(S12) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S13) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S14) Through developing their analytical and critical skills and observing good standards of academic practice, students will develop their intellectual honesty.

#### Year One Optional Modules

• ##### Introduction to Statistics Using R (MATH163)
Level 1 15 Second Semester 50:50 1. Use software R to display and analyse data, perform tests and demonstrate basic statistical concepts.2. Describe statistical data and display it using variety of plots and diagrams.3. Understand basic laws of probability: law of total probability, independence, Bayes’ rule.4. Be able to estimate mean and variance.5. Be familiar with properties of some probability distributions and relations between them: Binomial, Poisson, Normal, t, Chi-squared.6. To perform simple statistical tests: goodness-of-fit test, z-test, t-test.7. To understand and be able to interpret p-values.8. To be able to report finding of statistical outcomes to non-specialist audience.9. Group work will help students to develop transferable skills such as communication, the ability to coordinate and prioritise tasks, time management and teamwork. (LO1) An ability to apply statistical concepts and methods covered in the module's syllabus to well defined contexts and interpret results.(LO2) An ability to understand, communicate, and solve straightforward problems related to the theory and derivation of statistical methods covered in the module's syllabus.(LO3) An ability to understand, communicate, and solve straightforward theoretical and applied problems related to probability theory covered in the syllabus.(LO4) Use the R programming language fluently in well-defined contexts. Students should be able to understand and correct given code; select appropriate code to solve given problems; select appropriate packages to solve given problems; and independently write small amounts of code.
• ##### Newtonian Mechanics (MATH122)
Level 1 15 Second Semester 50:50 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(S1) Representing physical problems in a mathematical way(S2) Problem Solving Skills
• ##### Numbers, Groups and Codes (MATH142)
Level 1 15 Second Semester 50:50 - 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.

### Programme Year Two

In each Semester, students must take 30 credits from Mathematics and 30 credits from Philosophy (SOTA260 counts towards Philosophy credits and is compulsory if you choose to study this programme with a Year in Industry).

MATH142 may be taken in Year 2 only by students that did not take it in Year 1.

#### Year Two Compulsory Modules

• ##### Logic (PHIL207)
Level 2 15 First Semester 0:100 To introduce students to the language and methods of classical quantificational logic.To enable students to use trees for both sentence logic and quantificational logic. To relate quantificational logic to the philosophy of language. (LO1) Students will be able to explain and apply the basic concepts of classical first-order logic.(LO2) Students will consolidate their skill in translating from English into first-order logic and vice versa.(LO3) Students will be able to construct proofs in natural deduction for valid sequents of first-order logic.(LO4) Students will be able to test sets of formulas for consistency using trees and to assess sequents of truth-functional logic and sequents of first-order logic for validity using trees.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will enhance their ability to marshal arguments and present them orally and in writing.(S5) Students will develop their ability to work independently.(S6) Students will develop their problem solving skills.(S7) Improving own learning and performance; personal action planning.(S8) Communication oral, written and visual; following instructions, protocols and procedures.(S9) Communication oral, written and visual; influencing skills, argumentation.(S10) Personal attributes and qualities; resilience.
• ##### Differential Equations (MATH221)
Level 2 15 Second Semester 0:100 •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

#### Year Two Optional Modules

• ##### Complex Functions (MATH243)
Level 2 15 First Semester 0:100 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
• ##### Knowledge and Epistemic Justice (PHIL212)
Level 2 15 First Semester 50:50 To introduce students to contemporary epistemology and to prepare them for more advanced study in this area.To enable students to address traditional issues in epistemology, such as the nature and sources ofknowledge.To enable students to engage with cutting-edge research in contemporary epistemology, including on topics (e.g., bias, epistemic justice, fake news) that are of wide social significance.To enable students to critically reflect on their own practices and methods of enquiry, in particular on how they access information online. (LO1) Students will be able to discuss some of the main traditional philosophical questions concerning knowledge and its sources.(LO2) Students will be able to discuss some topics in contemporary epistemology that are of wide social significance.(LO3) Students will be able to discuss some philosophical issues relating to scientific and social-scientific knowledge.(LO4) Students will be able to explain, and competently to employ, key terminology and concepts from traditional and contemporary epistemology.(LO5) To enable students to critically reflect on their own practices and methods of enquiry, in particular how they access information online.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop their ability to work independently.(S7) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S8) Students will develop their problem-solving skills.(S9) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S10) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.
• ##### Linear Algebra and Geometry (MATH244)
Level 2 15 First Semester 50:48 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
• ##### Professional and Career Development (SOTA260)
Level 2 15 First Semester 0:100 The module aims to prepare students for a smooth transition into a year in industry and, more broadly, to develop lifelong skills, attitudes and behaviours that will help students lead flexible, fulfilling careers working as professionals in their field, and enable them to contribute meaningfully to society. (LO1) Students will analyse a range of employment and enterprise opportunities in an industry of their choosing.(LO2) Students will compare the process of applying for two placements/internships/jobs including researching industries and opportunities, and evaluating application and selection processes.(LO3) Students will evaluate the development of their professional skills, attitudes and behaviours using reflective thinking and writing.(LO4) Students will propose an authentic solution to a commercial or cultural challenge experienced by an employer.(S1) Career and identity management online: managing digital reputation and online identity.(S2) Communication, listening and questioning: Communication, listening and questioning respecting others, contributing to discussions, influencing, presentations.(S3) Information literacy online.(S4) Positive attitude/ self-confidence. A can-do approach, a readiness to take part and contribute; openness to new ideas and the drive to make these happen.(S5) Problem solving/ critical thinking/ creativity analysing facts and situations and applying creative thinking to develop appropriate solutions.(S6) 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.(S7) 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.
• ##### Statistics and Probability I (MATH253)
Level 2 15 First Semester 50:50 Use the R programming language fluently to analyse data, perform tests, ANOVA and SLR, and check assumptions.Develop confidence to understand and use statistical methods to analyse and interpret data; check assumptions of these methods.Develop an awareness of ethical issues related to the design of studies. (LO1) An ability to apply advanced statistical concepts and methods covered in the module's syllabus to well defined contexts and interpret results.(LO2) Use the R programming language fluently for a broad selection of statistical tests, in well-defined contexts.(S1) Problem solving skills(S2) Numeracy(S3) IT skills(S4) Communication skills
• ##### Vector Calculus With Applications in Fluid Mechanics (MATH225)
Level 2 15 First Semester 70:30 To provide an understanding of the various vector integrals, the operators 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.
Level 2 15 Second Semester 60:40 To introduce and explain major contemporary perspectives on corporate behaviours.To introduce moral perspectives as they relate to managerial decision-making and corporate structures.To make students familiar with a range of recurrent ethical problems arising in business.To improve students' skills in identifying and analyzing ethical issues that managers and employees face.To give students practice in formulating, defending, and planning the implementation of action plans managing ethical dilemmas. (LO1) Students will be able to discuss the main theories concerning the place of ethics in business.(LO2) Student will be able to explain assess the main approaches to normative ethics.(LO3) Students will be able to state and discuss the relationship between ethical theory and business practice. And use theory to decide on moral courses of action in business scenarios.(S1) Students will enhance their ability to identify the issues that underlie debates.(S2) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S3) Students will enhance their ability to marshal arguments and present them orally and in writing.(S4) Students will develop their ability to work in groups.(S5) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S6) Students will develop their problem-solving skills.(S7) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S8) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S9) Communication (oral, written and visual) - Influencing skills – argumentation(S10) Critical thinking and problem solving - Critical analysis(S11) Communication (oral, written and visual) - Presentation skills - written(S12) Communication (oral, written and visual) - Influencing skills – persuading(S13) Working in groups and teams - Listening skills(S14) Communication (oral, written and visual) - Report writing(S15) Critical thinking and problem solving - Synthesis(S16) Working in groups and teams - Group action planning(S17) Working in groups and teams - Negotiation skills(S18) Skills in using technology - Information accessing(S19) Skills in using technology - Using common applications (work processing, databases, spreadsheets etc.)
• ##### Classical Mechanics (MATH228)
Level 2 15 Second Semester 50:50 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
• ##### Commutative Algebra (MATH247)
Level 2 15 Second Semester 50:50 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.
• ##### Financial Mathematics (MATH260)
Level 2 15 Second Semester 50:50 To provide an understanding of basic theories in Financial Mathematics used in the study process of actuarial/financial interest.To provide an introduction to financial methods and derivative pricing financial instruments in discrete time set up. (LO1) Know how to optimise portfolios and calculating risks associated with investment.(LO2) Demonstrate principles of markets.(LO3) Assess risks and rewards of financial products.(LO4) Understand mathematical principles used for describing financial markets.
• ##### Metaphysics (PHIL228)
Level 2 15 Second Semester 60:40 To provide an introduction to some of the most significant debates in contemporary metaphysics;  topics include:  change and persistence, objects and properties, space and time. (LO1) Students will be able to identify the main issues and positions in contemporary metaphysical discussions of space, time, persistence, properties, substance, persons, modality and existence.(LO2) Students will be able to explain the main strengths and weaknesses of these positions.(LO3) Students will be able to identify the historical contexts of some of these positions.(LO4) Students will be able to construct a positive case for a specific metaphysical position, by appealing to theoretical virtues, e.g. simplicity, metaphysical principles, e.g. the principle of sufficient reason and thought experiments which evoke powerful intuitions.(LO5) Students will further develop their abilities to extract arguments from texts, render them in standard form, and assess the soundness of their premises and the validity of their structures.(LO6) Students will be able to think more creatively about metaphysical issues.(LO7) Students will be able to explain the competing positions in contemporary meta-metaphysics.(S1) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S2) Students will enhance their ability to identify the issues with truly underlie debates.(S3) Students will enhance their ability to think creatively in constructing solutions to problems.(S4) Students will develop their ability to marshal arguments, and present them orally and in writing.(S5) Students will develop and enhance their ability to work effectively and independently.(S6) Students will become more self-disciplined, and intellectually self-sufficient.
• ##### Metric Spaces and Calculus (MATH242)
Level 2 15 Second Semester 50:50 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.(LO2) Understand the contraction mapping theorem and appreciate some of its applications.(LO3) Be familiar with the concept of the derivative of a vector valued function of several variables as a linear map.(LO4) Understand the inverse function and implicit function theorems and appreciate their importance.(LO5) Have developed their appreciation of the role of proof and rigour in mathematics.(S1) problem solving skills
• ##### Numbers, Groups and Codes (MATH142)
Level 1 15 Second Semester 50:50 - 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.
• ##### Numerical Methods for Applied Mathematics (MATH226)
Level 2 15 Second Semester 20:80 To demonstrate how these ideas can be implemented using a high-level programming language, leading to accurate, efficient mathematical algorithms. (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 (MATH269)
Level 2 15 Second Semester 50:50 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
• ##### Philosophy of Religion (PHIL215)
Level 2 15 Second Semester 65:35 To introduce the current state of discussion concerning the concept of God. To introduce the major arguments for, and the major arguments against, the existence of God. To enable students to clarify and develop their own views on whether God exists and, if so, what God is like. (LO1) Students will be able to engage with key debates and arguments in the philosophy of religion, primarily in the Western tradition.(LO2) Students will be able to reflect on methodological issues that arise in the philosophy of religion, such as the relationship between faith and reason.(LO3) Students will be able to assess challenges to the coherence of the concept of God.(LO4) Students will be able to discuss and evaluate arguments for the existence of God.(LO5) Students will be able to reflect critically on the significance and implications of the problem of evil for religious thought.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and reconstructing and evaluating arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop their ability to work independently.(S7) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S8) Students will develop their problem-solving skills.(S9) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S10) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.
• ##### Statistics and Probability II (MATH254)
Level 2 15 Second Semester 50:50 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
• ##### Uses, Misuses and Abuses of Language (PHIL276)
Level 2 15 Second Semester 0:100 To introduce students to key concepts and figures in the project of understanding natural language. To introduce students to the distinction between semantics and pragmatics and to speech-act theory. To introduce students to some contemporary applications of speech-act theory to topics in political philosophy. (LO1) Students will be able to explain different accounts of the meaning and function of referring expressions.(LO2) Students will be able to understand and apply the distinction between semantics and pragmatics.(LO3) Students will be able to discuss competing philosophical accounts of the relation between meaning and use.(LO4) Students will be able to explain and critically assess Grice’s theory of meaning and/or Austin’s speech-act theory.(LO5) Students will be able to apply theoretical tools from philosophy of language to questions about free speech and harm in political philosophy.(S1) Problem solving/ critical thinking/ creativity analysing facts and situations and applying creative thinking to develop appropriate solutions.(S2) Communication, listening and questioning respecting others, contributing to discussions, communicating in a foreign language, influencing, presentations(S3) Information literacy online, finding, interpreting, evaluating, managing and sharing information(S4) Literacy application of literacy, ability to produce clear, structured written work and oral literacy - including listening and questioning(S5) Problem solving/ critical thinking/ creativity analysing facts and situations and applying creative thinking to develop appropriate solutions.(S6) 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(S7) Problem solving skills(S8) Organisational skills(S9) Communication skills

### Programme Year Three

In each Semester, students must take 30 credits of Mathematics and 30 credits of Philosophy. Whole Year modules weighted at 30 credits count as 15 credits per semester. SOTA300 counts as a Philosophy module (students who have completed a Year in Industry may not take SOTA300).

Students must take at least one of PHIL306, SOTA300, PHIL311 or PHIL365, but may not take both PHIL306 and PHIL311. Students must consult with their academic advisor before taking both PHIL306 and SOTA300.

#### Year Three Optional Modules

• ##### Applied Probability (MATH362)
Level 3 15 First Semester 50:50 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.
• ##### Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)
Level 3 15 First Semester 50:50 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
• ##### Chaos and Dynamical Systems (MATH322)
Level 3 15 First Semester 50:50 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
• ##### Classical Chinese Philosophy (PHIL367)
Level 3 15 First Semester 60:40 To investigate what is distinctive about classical Chinese approaches to questions of ontology, social harmony, personal morality and soteriology. To examine the ways in which philosophy in Classical Chinese civilisation develops in the Hundred Schools period, with particular attention to the dialogue between Confucians and Daoists. (LO1) Students will be able to engage in informed discussions about the concepts and categories in which philosophical discussions were conducted in ancient China.(LO2) Students will develop abilities in developing and contextualising new information about other worldviews.(LO3) Students will be enabled to assimilate alternative cultural perspectives from which to view their own traditions.(LO4) Students will be able to explain and evaluate some of the main theories propounded in the classical period of Chinese thought.(LO5) Students will be able to discuss the problem of cultural relativism informed by an understanding of a particular alien pattern of thinking.(LO6) Students will be able to relate classical Chinese thought to European philosophical interests.(S1) Students will develop abilities to read and understand ancient texts in English translation.(S2) Students will improve their ability to identify the issues that underlie debates.(S3) Students will develop the confidence to consider previously unfamiliar ideas and approaches.(S4) Students will develop their ability to identify presuppositions and to reflect critically upon them.(S5) Students will develop a facility to compare and evaluate categories of thought from different cultures.(S6) Students will enhance their written and communication skills.(S7) Students will develop their ability to work independently.(S8) Students will develop an ability to write in a manner that accords with professional standards and expectations.
• ##### Combinatorics (MATH344)
Level 3 15 First Semester 50:50 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.
• ##### Existentialism (PHIL332)
Level 3 15 First Semester 40:60 To consider the theories and arguments of some of the most important existentialist philosophers, such as Kierkegaard, Nietzsche and Sartre. To analyse some of the main themes of existentialist philosophy, such as absurdity, ethics, authenticity and 'truth'. To relate the philosophical issues raised by existentialism to lived practice and to concrete examples. (LO1) Students will be able to explain and evaluate some of the main theories in existentialism.(LO2) Students will be able to analyse key concepts and arguments relating to existentialism.(LO3) Students will be able to structure discussion of issues around existentialist metaphysics and ethics.(LO4) Students will be able to identify the relevance of existentialist philosophy to their own lives.(LO5) Students will be able to articulate and defend positions relating to existentialist themes.(LO6) Students will be able to present their ideas with clarity and confidence.(LO7) Students will be able to write coherent, structured and informative accounts on abstract philosophical issues.(S1) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.(S2) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S3) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S4) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S5) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S6) Students will enhance their ability to identify and reflect critically upon the issues that underlie debates.(S7) Students will develop confidence in considering previously unfamiliar ideas and approaches.(S8) Students will enhance their ability to marshal arguments and present them orally and in writing.(S9) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.
• ##### Frontiers of Ethics (PHIL302)
Level 3 15 First Semester 0:100 To consider conceptual and ethical issues arising from matters of global concern, such as international justice, humanitarian intervention and the environmental crisis. To consider arguments and assumptions underlying a range of claims concerning such issues as disability, global citizenship, climate change and the ethical status of nature. To examine difficulties for traditional philosophical approaches raised by such issues and recent theoretical developments relevant to them. (LO1) Students will be able to distinguish between some of the main concepts involved in philosophical debates arising from matters of current global concern.(LO2) Students will be able to distinguish between different ways of understanding  concepts in philosophical debates arising from matters of global concern.(LO3) Students will be able to explain and evaluate some of the main theories in debates about matters of disability, global justice, just war, environmental justice and environmental ethics.(LO4) Students will be able to analyse concepts and arguments relating to current ethical issues.(LO5) Students will be able to identify philosophical assumptions underlying ethical claims.(LO6) Students will be able to structure a philosophical discussion of current ethical issues.(LO7) Students will be able to speak with confidence and clarity on current ethical issues.(LO8) Students will be able to explain details of texts shaping current philosophical debates about matters of global concern.(LO9) Students will be able to articulate and defend positions in current philosophical debates about matters of global concern.(LO10) Students will be able to write coherently and rigorously about abstract philosophical issues raised by current ethical controversies.(S1) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.(S2) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S3) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S4) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S5) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S6) Students will enhance their ability to identify and reflect critically upon the issues that underlie debates.(S7) Students will develop confidence in considering previously unfamiliar ideas and approaches.(S8) Students will enhance their ability to marshal arguments and present them orally and in writing.(S9) Students will develop the ability to research a philosophical topic, perform bibliographical searches, to include (to professional standard) citations and bibliographies in their work and to plan, organise and produce presentations and essays.(S10) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.
• ##### Further Methods of Applied Mathematics (MATH323)
Level 3 15 First Semester 50:50 •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.]
• ##### Group Theory (MATH343)
Level 3 15 First Semester 50:50 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
• ##### Linear Statistical Models (MATH363)
Level 3 15 First Semester 40:60 - 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 an appropriate statistical software package. (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 an appropriate statistical software package.
• ##### Measure Theory and Probability (MATH365)
Level 3 15 First Semester 50:50 The main aim is to provide a sufficiently deepintroduction to measure theory and to the Lebesgue theory of integration. Inparticular, this module aims to provide a solid background for the modernprobability theory, which is essential for Financial Mathematics. (LO1) After completing the module students should be ableto:(LO2) master the basic results about measures and measurable functions;(LO3) master the basic results about Lebesgue integrals and their properties;(LO4) to understand deeply the rigorous foundations ofprobability theory;(LO5) to know certain applications of measure theoryto probability, random processes, and financial mathematics.(S1) Problem solving skills(S2) Logical reasoning
• ##### Mind, Brain and Consciousness (PHIL309)
Level 3 15 First Semester 60:40 To give students an understanding of the main developments in twentieth century analytic philosophy of mind: dualism, behaviourism, identity theory and functionalism. To give students a grasp of cutting-edge debates in philosophy of mind concerning (i) the place of consciousness in nature, (ii) the relationship between consciousness and thought, (iii) artificial intelligence. (LO1) Students should be able to explain the history of twentieth century analytic philosophy of mind.(LO2) Students should be able to explain cutting edge contemporary debates on, the place of consciousness in nature, the relationship between thought and consciousness, artificial intelligence.(LO3) Students should be able to build a case for a specific view concerning, the place of consciousness in nature, the relationship between thought and consciousness, artificial intelligence. (LO4) Students should be able to explain the main strengths and weaknesses of dominant theories on these three things in the philosophical literature.(LO5) Students should further develop their abilities to extract arguments from texts, render them in schematic form, and assess the soundness of their premises and the validity of their structures.(LO6) Students should be able to think more creatively about the relationship between thought, consciousness and the physical world.(S1) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S2) Students will enhance their ability to identify the issues that underlie debates.(S3) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S4) Students will enhance their ability to marshal arguments and present them orally and in writing.(S5) Students will develop the ability to perform bibliographical searches, to include to professional standard, citations and bibliographies in their work and to plan, organise and produce presentations and essays.(S6) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.(S7) Students will develop their ability to work independently.(S8) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S9) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.
• ##### Networks in Theory and Practice (MATH367)
Level 3 15 First Semester 50:50 •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.
• ##### Philosophy of Play and the VIrtual (PHIL343)
Level 3 15 First Semester 0:100 To introduce students to the main contemporary issues around play and games. To develop students understanding of the relationships between play, labour and virtuality. To enable students to reflect on their own preconceptions of play and value. (LO1) Students will be able to explain the importance of play as a topic for study.(LO2) Students will be able to analyse common topics of discourse around play and games, especially digital games: violence, addiction, therapeutic and educational effects, and gamification.(LO3) Students will be able to identify philosophical issues arising from specific games/instances of play.(LO4) Students will be able to explain some of the philosophical literature around play, make-believe, choice and responsibility, and virtual worlds.(LO5) Students will be able to trace connections between surface controversies and deeper philosophical concerns.(LO6) Students will develop their ability to reflect on their own preconceptions and how these contribute to both philosophical and popular discourse.(S1) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S2) Students will enhance their ability to identify unifying philosophical issues in everyday discussions and mass-media environments.(S3) Students will develop confidence in considering previously unfamiliar ideas and approaches.(S4) Students will develop their ability to identify their own presumptions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop the ability to perform bibliographical searches, use and reference academic sources, and to plan, organise and produce presentations and essays.(S7) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.(S8) Students will develop their ability to work independently.(S9) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S10) Students will develop their skills in making appropriate use of information technology, including online sources, video and screen capture and editing, and visual presentation aids.
• ##### Quantum Mechanics (MATH325)
Level 3 15 First Semester 50:50 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 50:50 (i) To introduce the physical principles behind Special and General Relativity and their main consequences;(ii) To develop the competence in the mathematical framework of the subjects - Lorentz transformation and Minkowski space-time, semi-Riemannian geometry and curved space-time, symmetries and conservation laws, Variational principles.(iii) To develop the understanding of the dynamics of particles and of the Maxwell field in Minkowski space-time, and of particles in curved space-time(iv) To develop the knowledge of tests of General Relativity, including the classical tests (perihelion shift, gravitational deflection of light)(v) To understand the basic concepts of black holes and (time permitting) relativistic cosmology and gravitational waves. (LO1) To be proficient at calculations involving Lorentz transformations, the kinematical and dynamical quantities associated to particles in Minkowski space-times, and the application of the conservation law for the four-momentum to scattering processes.(LO2) To know the relativistically covariant form of the Maxwell equations .(LO3) To know the action principles for relativistic particles, the Maxwell field and the gravitational field.(LO4) To be proficient at calculations in semi-Riemannian geometry as far as needed for General Relativity, including calculations involving general coordinate transformations, tensor fields, covariant derivatives, parallel transport, geodesics and curvature.(LO5) To understand the arguments leading to the Einstein's field equations and how Newton's law of gravity arises as a limiting(LO6) To be able to calculate the trajectories of bodies in a Schwarzschild space-time.(S1) problem solving skills(S2) numeracy
• ##### Applied Stochastic Models (MATH360)
Level 3 15 Second Semester 50:50 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 understand the theory of continuous-time Markov chains.(LO2) To understand 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 understanding of the standard concepts and methods of stochastic modelling.(S1) Problem solving skills(S2) Numeracy
• ##### Differential Geometry (MATH349)
Level 3 15 Second Semester 50:50 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
• ##### Digital Inquiry Project (PHIL311)
Level 3 15 Second Semester 0:100 The module aims to integrate the production of academic knowledge within a student’s field of study and skills of digital presentation for non-academic audiences.It seeks to foster skills in independent research, communication and digital fluency, thus contributing to employability and the development of aptitudes transferable to broader personal, professional and public contexts. (LO1) Students will show the capacity to undertake independent research into a selected topic, identifying an area for investigation and developing arguments towards a reasoned conclusion.(LO2) Students will show the ability to present their research as a piece of systematic academic writing.(LO3) Students will show the ability to present their research on a digital platform as if to a specified non-academic target audience.(LO4) Students will show the ability to present material effectively in a way appropriate to the selected digital medium.(LO5) Students will show an awareness of copyright and accessibility issues in the production of material for public dissemination.(LO6) Students will show the capacity to engage in critical self-reflection.(S1) Students will develop their digital fluency skills, both through competency in information retrieval and through the effective digital presentation of work.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to marshal arguments and present them in writing and via a selected digital platform.(S4) Students will develop their ability to work independently.(S5) Students will enhance their digital lifelong learning skills for continuing personal and professional development.(S6) Students will develop skills in effective communication in a way sensitive to specified target audiences.(S7) Students will develop their skills in presentation of independently researched material.(S8) Students will develop skills in peer-to-peer assessment and feedback.(S9) Students will develop skills of personal reflection in relation to work undertaken and challenges faced.
• ##### Game Theory (MATH331)
Level 3 15 Second Semester 50:50 To explore, from a game-theoretic point of view, models which have been used to understand phenomena in which conflict and cooperation occur. To see the relevance of the theory not only to parlour games but also to situations involving human relationships, economic bargaining (between trade union and employer, etc), threats, formation of coalitions, war, etc. To treat fully a number of specific games including the famous examples of "The Prisoners' Dilemma" and "The Battle of the Sexes". To treat in detail two-person zero-sum and non-zero-sum games. To give a brief review of n-person games. In microeconomics, to look at exchanges in the absence of money, i.e. bartering, in which two individuals or two groups are involved.To see how the Prisoner's Dilemma arises in the context of public goods. (LO1) To extend the appreciation of the role of mathematics in modelling in Economics and the Social Sciences.(LO2) To be able to formulate, in game-theoretic terms, situations of conflict and cooperation.(LO3) To be able to solve mathematically a variety of standard problems in the theory of games and to understand the relevance of such solutions in real situations.
• ##### Hellenistic and Neoplatonic Philosophy (PHIL368)
Level 3 15 Second Semester 0:100 To consider the theories and arguments of some of the most important philosophers of the Hellenistic and Neoplatonic periods. To study key ethical, epistemological and metaphysical concepts and their interconnections. To enable students to analyse and practise the dialectical skills portrayed in the texts examined. (LO1) Students will be able to explain and evaluate some of the main theories in Hellenistic and Neoplatonic philosophy.(LO2) Students will be able to analyse concepts and arguments relating to classic ethical, epistemological and/or metaphysical issues.(LO3) Students will be able to structure a discussion of central issues in Hellenistic and Neoplatonic philosophy(LO4) Students will be able to identify points of agreement and disagreement between different philosophies.(LO5) Students will be able to engage dialectically with positions in ancient and/or medieval philosophy and articulate their implications.(LO6) Students will be able to present their ideas with clarity and confidence.(LO7) Students will be able to develop in writing coherent, structured and informative accounts of abstract philosophical issues.(S1) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.(S2) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S3) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S4) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S5) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S6) Students will enhance their ability to identify and reflect critically upon the issues that underlie debates.(S7) Students will develop confidence in considering previously unfamiliar ideas and approaches(S8) Students will enhance their ability to marshal arguments and present them orally and in writing.(S9) Students will develop the ability to perform bibliographical searches, to include (to professional standard) citations and bibliographies in their work and to plan, organise and produce presentations and essays.(S10) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.
• ##### Indian Philosophy (PHIL326)
Level 3 15 Second Semester 60:40 To examine the ways in which philosophy in Classical India develops as a dialogue between thinkers of Buddhist and Brahminical persuasions and to relate fundamental Indian metaphysical concepts to Western counterparts. To investigate what is distinctive about Indian approaches to questions of ontology, soteriology, social harmony, and morality. (LO1) Students will be able to engage in informed discussions identifying and evaluating the concepts and categories in which philosophical discussions were conducted in India.(LO2) Students will able to be enabled to assimilate a different view Western philosophical traditions from the perspective of Indian philosophical traditions.(LO3) Students will be able to contextualise information about the Indian worldviews under discussion.(LO4) Students will be able to think more imaginatively by empathising with unfamiliar outlooks on life.(LO5) Students will be able to engage in debate informed by an awareness of the particularity and peculiarities of Western philosophical positions.(S1) Students will develop the confidence to consider previously unfamiliar ideas and approaches.(S2) Students will enhance their abilities to read and understand texts from non-European cultural traditions.(S3) Students will improve their ability to identify the issues that underlie debates.(S4) Students will develop their ability to identify presuppositions and to reflect critically upon them.(S5) Students will develop a facility to compare and evaluate categories of thought from other civilisations.(S6) Students will enhance their written and oral communication skills.(S7) Students will develop their ability to work independently.(S8) Students will develop an ability to write in a manner that accords with professional standards and expectations.
• ##### Mathematical Risk Theory (MATH366)
Level 3 15 Second Semester 50:50 •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).
• ##### Medical Statistics (MATH364)
Level 3 15 Second Semester 50:50 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
• ##### Number Theory (MATH342)
Level 3 15 Second Semester 35:65 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
• ##### Numerical Methods for Ordinary and Partial Differential Equations (MATH336)
Level 3 15 Second Semester 50:50 Many real-world systems in mathematics, physics and engineering can be described by differential equations. In rare cases these can be solved exactly by purely analytical methods, but much more often we can only solve the equations numerically, by reducing the problem to an iterative scheme that requires hundreds of steps. We will learn efficient methods for solving ODEs and PDEs on a computer. (LO1) Demonstrate an advanced knowledge of the analysis of ODEs and PDEs underpinning the scientific programming within our context.(LO2) Demonstrate an extended understanding of scientific programming and its application to numerical analysis and to other branches of Mathematics.(LO3) Continuous engagement with putting practical problems into mathematical language.(S1) Numeracy(S2) Problem solving skills(S3) Programming skills
• ##### Philosophical Approaches to Conflict (PHIL365)
Level 3 15 Second Semester 0:100 To introduce students to the philosophical analysis of conflict. To help students to think through for themselves the just solution to various conflicts between societies and within society. To help students to think through for themselves the appropriateness or otherwise of the various ways in which present-day societies solve, or attempt to solve, conflicts. To help students to think through for themselves the relationship between state and individual, and between different groups in the state. (LO1) Students will show a capacity to analyse and evaluate, from a philosophical point of view, competing legal and moral rights.(LO2) Students will be able to form considered and philosophically defensible judgements about appropriate resolution when rights clash in the public sphere.(LO3) Students will be able to apply theoretical resources to conflictual issues of contemporary socio-political and/or legal concern.(LO4) Students will be able to articulate philosophical debates emerging from analysis of complex and sensitive scenarios.(LO5) Students will be able to defend positions in relation to competing socio-political perspectives.(LO6) Students will be able to be able to write with philosophical rigour about socio-political and/or legal conflicts.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop their ability to work independently.(S7) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S8) Students will develop their problem-solving skills.(S9) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S10) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S11) Students will exercise skills in the digital sharing of their work and peer comment.
• ##### Philosophy and Literature (PHIL327)
Level 3 15 Second Semester 60:40 Students will be introduced to arguments of some of the most important philosophers on literature, such as Plato, Aristotle, Du Bois, Benjamin, Derrida and Nussbaum.Students will consider key concepts and theories that deal with specific themes surrounding philosophical and literary production, such as the nature of emotion, narrative, metaphor and language.Students will be encouraged to make connections with works of literature from different historical periods and cultural contexts. (LO1) Students will be able to explain and evaluate some of the theories central to philosophy and literature.(LO2) Students will be able to analyse key concepts and arguments relating to philosophy of literature.(LO3) Students will be able to structure discussion of issues in philosophy and literature.(LO4) Students will be able to interrogate literature through philosophy and vice versa.(LO5) Students will be able to articulate and defend positions in philosophy of literature.(LO6) Students will be able to present their ideas with clarity and confidence.(LO7) Students will be able to develop in writing coherent, structured and informative accounts on philosophical issues.(S1) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.(S2) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S3) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S4) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S5) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S6) Students will enhance their ability to identify and reflect critically upon the issues that underlie debates.(S7) Students will develop confidence in considering previously unfamiliar ideas and approaches.(S8) Students will enhance their ability to marshal arguments and present them orally and in writing.(S9) Students will develop the ability to perform bibliographical searches, to include to professional standard citations and bibliographies in their work and to plan, organise and produce presentations and essays.(S10) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.
• ##### Philosophy of the Future (PHIL312)
Level 3 15 Second Semester 60:40 To provide an introduction to debates concerning the philosophical implications of foreseeable future technological innovations. To examine the relevance of metaphysical and ethical considerations to future technological and scientific developments. (LO1) Students will be able to identify the main issues and positions in contemporary philosophical discussions of issues such as human enhancement, existential risks, teleportation, time travel, the technological singularity, the simulation argument, the feasibility and desirability of uploading into virtual worlds.(LO2) Students will be able to explain the main strengths and weaknesses of these positions.(LO3) Students will be able to explain the relevance of metaphysical and ethical considerations to debates concerning these issues. (LO4) Students will be able to think more creatively about philosophical issues.(LO5) Students will be able to structure philosophical arguments relating issues raised by future technological developments.(LO6) Students will be able to articulate and defend specific positions in current philosophical debates concerning likely future developments in science and technology.(LO7) Students will be able to write coherently and rigorously about the philosophical issues raised by future technological developments.(S1) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S2) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S3) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S4) Students will enhance their ability to identify the issues with truly underlie debates.(S5) Students will develop their ability to marshal arguments, and present them orally and in writing.(S6) Students will develop and enhance their ability to work effectively and independently.(S7) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S8) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.
• ##### Population Dynamics (MATH332)
Level 3 15 Second Semester 50:50 - 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
• ##### Statistical Physics (MATH327)
Level 3 15 Second Semester 50:50 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 know 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
• ##### The Magic of Complex Numbers: Complex Dynamics, Chaos and the Mandelbrot Set (MATH345)
Level 3 15 Second Semester 50:50 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
• ##### Themes From Wittgenstein (PHIL340)
Level 3 15 First Semester 60:40 To study the later Wittgenstein. Topics will include: background in the Tractatus; the limits of language and the nature of ethical and religious discourse; rule following and the private; the limits of language and the nature of ethical and religious discourse; rule following and the private language argument; the nature and prospects of philosophy; epistemology and certainty. (LO1) Students will be able to explain how the Tractatus influenced Wittgenstein's later philosophy.(LO2) Students will be able to explain and assess both the Augustinian picture of language and Wittgenstein's criticism of it.(LO3) Students will be able to explain the rule following considerations and their importance to Wittgenstein and contemporary philosophy of language.(LO4) Students will be able to explain and assess the private language argument and its importance to contemporary philosophy of mind.(LO5) Students will be able to explain and assess Wittgenstein's technical notion of 'criterion' and its philosophical significance.(LO6) Students will be able to explain and assess Wittgenstein's later epistemology.(S1) Students will enhance their ability to read complex texts.(S2) Students will develop their analytical skills.(S3) Students will enhance their ability to construct arguments.(S4) Students will enhance their ability to work independently.(S5) Students will develop the ability to make appropriate use of library resources and the internet.
• ##### Theory of Statistical Inference (MATH361)
Level 3 15 Second Semester 50:50 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
• ##### Topology (MATH346)
Level 3 15 Second Semester 50:50 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). (BH1) An understanding of the ubiquity of topological spaces within mathematics.(BH2) Knowledge of a wide range of examples of topological spaces, and of their basic properties.(BH3) The ability to construct proofs of, or counter-examples to, simple statements about topological spaces and continuous maps.(BH4) The ability to decide if a (simple) space is connected and/or compact.(BH5) The ability to construct the Cech and Vietoris-Rips complexes of a point set in Euclidean spac. e(BH6) The ability to compute the fundamental group of a (simple) space, and to use it to distinguish spaces.
• ##### Philosophy Dissertation (PHIL306)
Level 3 30 Whole Session 0:100 The aim is for the student to choose a topic of special interest in philosophy and conduct research into this area of interest via reading and private study under the supervision of the supervisor to whom they have been allocated. (LO1) The student will produce a systematic piece of written work, organised in chapters and sections in the manner of professional and published work in philosophy, so as to show that the research referred to in the Aims has been mastered in a way appropriate to someone with a grasp of the practice of professional philosophy.(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.(S3) Students will enhance their ability to identify the issues that underlie debates.(S4) Students will develop confidence in considering previously unfamiliar ideas and approaches, and their ability to identify presuppositions and to reflect critically upon them.(S5) Students will enhance their ability to marshal arguments and present them orally and in writing.(S6) Students will develop the ability to perform bibliographical searches, to include to professional standard citations and bibliographies in their work and to plan, organise and produce presentations a dissertation.(S7) Students will enhance their oral and written communications skills and develop skill in explaining complex material in a precise manner.(S8) Students will develop their ability to work independently.(S9) Students will develop their ability to sift through information, assessing the relevance and importance of the information to what is at issue.(S10) Students will develop their skills in making appropriate use of information technology, information on the World Wide Web and reference works and databases relevant to the discipline.(S11) Students will develop the ability to write to a professional standard, using word processing software.(S12) Students will enhance their capacity to participate, in a dispassionate and respectful manner, in debates about controversial and profound matters.(S13) Students will develop their willingness critically to evaluate and reflect upon arguments, beliefs, proposals and values, both their own and those of others.(S14) Through developing their analytical and critical skills and observing good standards of academic practice, students will develop their intellectual honesty.
• ##### School of the Arts Work Placements Module (SOTA300)
Level 3 30 Whole Session 0:100 To develop materials and/or undertake tasks within a practical or vocational context. To apply within that practical or vocational context professional, pedagogical, theoretical and other knowledge relevant to the development and delivery of the placement materials and/or tasks. To apply academic and/or theoretical knowledge within a practical context, and reflect and report on the relationship between the two. To develop and identify a range of personal/ employability skills, and reflect and report on this development. (LO1) To demonstrate an ability to develop materials and/or undertake tasks, according to a given specification and requirement, within a practical or vocational context.(LO2) To reflect on and evaluate the efficacy of the materials developed and/or the tasks undertaken.(LO3) To identify the connection between academic and/or theoretical knowledge and its practical or vocational application.(LO4) To identify, reflect and report on a range of personal/employability skills.(S1) Commercial awareness - Relevant understanding of organisations(S2) Improving own learning/performance - Self-awareness/self-analysis(S3) Improving own learning/performance - Personal action planning(S4) Improving own learning/performance - Record-keeping(S5) Communication (oral, written and visual) - Presentation skills – oral(S6) Communication (oral, written and visual) - Academic writing (inc. referencing skills)(S7) Communication (oral, written and visual) - Report writing(S8) Critical thinking and problem solving - Critical analysis(S9) Skills in using technology - Using common applications (work processing, databases, spreadsheets etc.)

The programme detail and modules listed are illustrative only and subject to change.

#### Teaching and Learning

In studying Philosophy you will learn how to defend your views with reasoned arguments, and to assess the arguments of others. Argumentative skills are learned through attending lectures and reading philosophical texts, developed by group seminar discussions, and formally assessed through essays and exams. You will complete modules to the value of 120 credits per year, from a wide range of options available. Most modules employ a blend of lectures, seminars and online support materials. You will learn by reading and studying outside class time, by attending and participating in classes, by doing coursework and, for dissertations, via one-to-one meetings with a supervisor. There is also scope, both formally in the placement module and informally, for you to develop practical skills by volunteering.

#### Assessment

Philosophy employs a mixture of modes of assessment: exams and coursework in many different varieties including essays, oral presentations, dissertations, exercises, and supported independent work (eg in the placement module).