# Mathematics and Philosophy BA (Joint Hons)

- Course length: 3 years
- UCAS code: GV15
- Year of entry: 2019
- Typical offer: A-level : ABB / IB : 33 including 6 in HL Mathematics with no score less than 4 / BTEC : Applications considered

## Honours Select

×This programme offers Honours Select combinations.

## Honours Select 100

×This programme is available through Honours Select as a Single Honours (100%).

## Honours Select 75

×This programme is available through Honours Select as a Major (75%).

## Honours Select 50

×This programme is available through Honours Select as a Joint Honours (50%).

## Honours Select 25

×This programme is available through Honours Select as a Minor (25%).

## Study abroad

×This programme offers study abroad opportunities.

## Year in China

×This programme offers the opportunity to spend a Year in China.

## Accredited

×This programme is accredited.

### Module details

### Programme Year One

Students take four modules from the Philosophy Year One programme.

Philosophy modules:

- Reading and Writing Philosophy 1
- Reading and Writing Philosophy 2 Critical, Analytical, and Creative Thinking
- Symbolic Logic 1

Students take the core foundation modules from the Mathematics Year One programme:

- Foundation Module I: Calculus
- Foundation Module II: Complex Numbers and Linear Algebra
- Foundation Module III: Multivariable Calculus

And one of the following:

- Numbers, Groups and Codes
- Mathematical Reasoning and Problem Solving

#### Year One Compulsory Modules

##### Calculus I (MATH101)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **Aims**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.

**Learning Outcomes**differentiate and integrate a wide range of functions;

sketch graphs and solve problems involving optimisation and mensuration

understand the notions of sequence and series and apply a range of tests to determine if a series is convergent

##### Introduction to Linear Algebra (MATH103)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **Aims**- 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.

**Learning Outcomes**manipulate complex numbers and solve simple equations involving them

solve arbitrary systems of linear equations

understand and use matrix arithmetic, including the computation of matrix inverses

compute and use determinants

understand and use vector methods in the geometry of 2 and 3 dimensions

calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics

##### Mind, Knowledge and Reality (PHIL103)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**To introduce students to some of the main topics in metaphysics: God, the mind/body problem, personal identity, time and free will.

To introduce students to the philosophical system of Rene Descartes.**Learning Outcomes**Students will be able to distinguish between sound and unsound arguments.

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.

Students will be able to extract an argument from text, render it into standard form, and critically evaluate its premises.

Students will be able to explain Descartes'' philosophical system.

Students will be able explain the basic issues, and the standard views, pertaining to five topics in contemporary metaphysics: God, personal identity, consciousness, free will and time.

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.

Students will be able to discuss reality in the partially abstract manner distinctive of metaphysical thought.

##### Reading and Writing Practical Philosophy (PHIL107)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**- Tointroduce the academic skills and knowledge necessary for the critical readingand writing of philosophy.
- Tofoster in students an appreciation of the value of philosophy.
- Toenable students to read effectively and to takes notes efficiently.
- Todevelop students'' skill in presenting complex ideas to an audience and inpracticing the intellectual virtues associated with philosophical discussion.
- Topromote students'' skill in writing rigorously argued, well-written andwell-presented philosophical essays.
- To developstudents'' research skills.
- Toincrease students'' awareness of the importance of feedback, review andreflection and to encourage them to use feedback, review and reflection toshape their approach to future work.

**Learning Outcomes**Students will be able to explain and evaluate some work relevant to a selected specialist topic in ethics. (This topic may vary from year to year. Examples include: human treatment of animals; ethics and the environment.)

Students will be able to explain and evaluate some central work about political liberty.

Students will be able to give structured seminar presentations and to conduct discussion in a manner that displays the intellectual virtues associated with philosophy.

Students will be able to write essays that embody a philosophically-informed approach to argumentation.

Students will be able to use the Harvard referencing system.

Students will be able to conduct independent research in support of their work, using appropriate print and online resources (including the Routledge Encyclopedia of Philosophy and the Philosopher''s Index). Students will be able to explain and evaluate some work in aesthetics and the philosophy of art.

##### Calculus II (MATH102)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**· To discuss local behaviour of functions using Taylor’s theorem.

· To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

**Learning Outcomes**use Taylor series to obtain local approximations to functions;

obtain partial derivaties and use them in several applications such as, error analysis, stationary points change of variables

evaluate double integrals using Cartesian and Polar Co-ordinates

##### Reading and Writing Theoretical Philosophy (PHIL108)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**To consolidate the academic skills and knowledge necessary for the critical reading and writing of philosophy.

To consolidate students'' appreciation of the value of philosophy.

To consolidate students'' ability to read and take notes effectively.

To consolidate students'' skill in presenting complex ideas to an audience and in practising the intellectual virtues associated with philosophical discussion.

To consolidate students'' skill in writing rigorously argued, well-written and well-presented essays.

To consolidate students'' research skills.

To consolidate students'' appreciation of, and ability to use, forward-facing feedback and review.

**Learning Outcomes**Students will be able to explain and evaluate some central work from the early modern period, covering the following topics: (i) perception; (ii) personal identity; (iii) freedom and determinism.

Students will develop greater skill and confidence in giving structured seminar presentations and in conducting discussion in a manner that displays the intellectual virtues associated with philosophy.

Students will develop greater skill and confindence in writing essays that embody a philosophically-informed approach to argumentation.

Students will be able to use the Harvard system of referencing.

Students will be able to conduct independent research in support of their work, using appropriate print and online resources (including the Routledge Encyclopedia of Philosophy and the Philosopher''s Index).

##### Introduction to Logic (PHIL127)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**To introduce students to the concepts, a language of, and the methods of, classical sentential logic.

To introduce students to a language of classical quantificational logic.**Learning Outcomes**Students will be able to explain and apply the basic concepts of classical sentence logic.

Students will be able to translate from English into sentence logic and vice versa.

Students will be able to construct and use truth tables.

Students will be able to construct proofs in natural deduction for sentence logic.

Students will be able to translate from English into quantificational logic and vice versa.

#### Year One Optional Modules

##### Newtonian Mechanics (MATH122)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**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**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

oscillation, vibration, resonance

##### Numbers, Groups and Codes (MATH142)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**· 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.

**Learning Outcomes** Use the division algorithm to construct the greatest common divisor of a pair of positive integers;

Solve linear congruences and find the inverse of an integer modulo a given integer;

Code and decode messages using the public-key method

Manipulate permutations with confidence

Decide when a given set is a group under a specified operation and give formal axiomatic proofs;

Understand the concept of a subgroup and use Lagrange''s theorem;

Understand the concept of a group action, an orbit and a stabiliser subgroup

Understand the concept of a group homomorphism and be able to show (in simple cases) that two groups are isomorphic;

##### Introduction to Statistics (MATH162)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**To introduce topics in Statistics and to describe and discuss basic statistical methods.

To describe the scope of the application of these methods.

**Learning Outcomes**to describe statistical data;

to use the Binomial, Poisson, Exponential and Normal distributions;

to perform simple goodness-of-fit tests

to use the package Minitab to present data, and to make statistical analysis

### Programme Year Two

Students choose modules to the value of four units from the Philosophy Year Two programme and four from Mathematics.

#### Year Two Compulsory Modules

##### Ordinary Differential Equations (MATH201)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**75:25 **Aims**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.

**Learning Outcomes**After completing the module students should be:

- familiar with elementary techniques for the solution of ODE''s, and the idea of reducing a complex ODE to a simpler one;

- familiar with basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions;

- well versed in the solution of linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix;

- aware of a range of applications of ODE.

##### Linear Algebra and Geometry (MATH244)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**To introduce general concepts of linear algebra and its applications in geometry and other areas of mathematics.

**Learning Outcomes**After completing the module students should be able to:

• appreciate the geometric meaning of linear algebraic ideas,

• appreciate the concept of an abstract vector space and how it is used in different mathematical situations,

• apply a change of coordinates to simplify a linear map,

• manipulate matrix groups, in particular GL(n), O(n) and SO(n),

• understand bilinear forms from a geometric point of view.

##### Logic (PHIL207)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**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. **Learning Outcomes**Students will be able to explain and apply the basic concepts of classical quantificational logic.

Students will consolidate their skill in translating from English into quantificational logic and vice versa.

Students will be able to construct proofs in natural deducation for valid sequents of quantificational logic.

Students will be able to test sets of formulas for consistency using trees and to assess sequents of sentence logic and sequents of quantificational logic for validity using trees.

Students will be able to explain Russell''s theory of definite descriptions and formally to represent sentences that use definite descriptions in a Russellain manner using the notation of quantificational logic.

Students will be able to define, both formally and informally, some formal properties of relations (i.e., reflexivity, symmetry, transitivity and related properties) and to represent these properties using diagrams.

#### Year Two Optional Modules

##### Uses, Misuses and Abuses of Language (PHIL276)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**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.

**Learning Outcomes**Students will be able to explain different accounts of the meaning and function of referring expressions.

Students will be able to understand and apply the distinction between semantics and pragmatics.

Students will be able to discuss competing philosophical accounts of the relation between meaning and use.

Students will be able to explain and critically assess Grice’s theory of meaning and/or Austin’s speech-act theory.

Students will be able to apply theoretical tools from philosophy of language to questions about free speech and harm in political philosophy.

##### Philosophy of Religion (PHIL215)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**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.**Learning Outcomes**Students will be able to engage with key debates and arguments in the philosophy of religion, primarily in the Western tradition. Students will be able to reflect on methodological issues that arise in the philosophy of religion, such as the relationship between faith and reason.

Students will be able to assess challenges to the coherence of the concept of God.

Students will be able to discuss and evalate arguments for the existence of God.Students will be able to reflect critically on the significance and implications of the problem of evil for religious thought.

##### Metaphysics (PHIL228)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**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.

**Learning Outcomes**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.Students will be able to explain the main strengths and weaknesses of these positions. Students will be able to identify the historical contexts of some of these positions.

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.

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.Students will be able to think more creatively about metaphysical issues.

Students will be able to explain the competing positions in contemporary meta-metaphysics.

##### Business Ethics (PHIL272)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**40:60 **Aims**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.**Learning Outcomes**Studentswill be able to discuss the main theories concerning the placeof ethics in business.

Student will be able to explain assess the main approaches to normative ethics.Students will be able to state and discuss the broad ethical principles concerning costs and benefits, the challenge posed by uncertainty, professional roles, profits and the right of shareholder interests, and affirmative action.Students will be able to state and discuss the broad ethical principles concerning the obligations of complex organizations with respect to loyalty and whistle-blowing, insider trading, customer responsibility, and corporate responsibility.

Students will be able to state and discuss the broad ethical principles concerning social justice and executive compensation.

Students will be able to consider an ethical approach as a basis for sustainable marketing.

##### Numbers, Groups and Codes (MATH142)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**· 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.

**Learning Outcomes** Use the division algorithm to construct the greatest common divisor of a pair of positive integers;

Solve linear congruences and find the inverse of an integer modulo a given integer;

Code and decode messages using the public-key method

Manipulate permutations with confidence

Decide when a given set is a group under a specified operation and give formal axiomatic proofs;

Understand the concept of a subgroup and use Lagrange''s theorem;

Understand the concept of a group action, an orbit and a stabiliser subgroup

Understand the concept of a group homomorphism and be able to show (in simple cases) that two groups are isomorphic;

##### Introduction to the Methods of Applied Mathematics (MATH224)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics.

To introduce some of the basic tools (Fourier Series) used in the solution of differential equations and other applications of mathematics.

**Learning Outcomes**After completing the module students should:

- be fluent in the solution of basic ordinary differential equations, including systems of first order equations;

- be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations;

- be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations;

- be able to solve simple first order partial differential equations;

- be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.

##### Classical Mechanics (MATH228)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To provide an understanding of the principles of Classical Mechanics and their application to dynamical systems.

**Learning Outcomes**Understanding of variational principles, Lagrangian mechanics, Hamiltonian mechanics.

Newtonian gravity and Kepler''s laws, including calculations of the orbits of satellites, comets and planetary motions

Motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravity over the Earth''s surface

Connection between symmetry and conservation laws

Inertial and non-inertial frames.

##### Commutative Algebra (MATH247)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To give an introduction to abstract commutative algebra and show how it both arises naturally, and is a useful tool, in number theory.

**Learning Outcomes**After completing the module students should be able to:

• Work confidently with the basic tools of algebra (sets, maps, binary operations and equivalence relations).

• Recognise abelian groups, different kinds of rings (integral, Euclidean, principal ideal and unique factorisation domains) and fields.

• Find greatest common divisors using the Euclidean algorithm in Euclidean domains.

• Apply commutative algebra to solve simple number-theoretic problems.

##### Geometry of Curves (MATH248)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce geometric ideas and develop the basic skills in handling them.

To study the line, circle, ellipse, hyperbola, parabola, cubics and many other curves.

To study theoretical aspects of parametric, algebraic and projective curves.

To study and sketch curves using an appropriate computer package.

**Learning Outcomes**After completing this module students should be able to:

- use a computer package to study curves and their evolution in both parametric and algebraic forms.

-determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.

-calculate envelopes and evolutes.

- solve the position and shape of some algebraic curves including conics.

The first learning outcome is assessed by coursework, the others by both coursework and examination.

##### Statistical Theory and Methods I (MATH263)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**85:15 **Aims**To introduce statistical methods with a strong emphasis on applying standard statistical techniques appropriately and with clear interpretation. The emphasis is on applications.

**Learning Outcomes**After completing the module students should have a conceptual and practical understanding of a range of commonly applied statistical procedures. They should have also developed some familiarity with the statistical package MINITAB.

##### Statistical Theory and Methods II (MATH264)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory.

**Learning Outcomes**After completing the module students should understand basic probability calculus. They should be familiar with a range of techniques for solving real life problems of the probabilistic nature.

##### Numerical Methods (MATH266)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To provide an introduction to the main topics in Numerical Analysis and their relation to other branches of Mathematics

**Learning Outcomes**After completing the module students should be able to:

• write simple mathematical computer programs in Maple,

• understand the consequences of using fixed-precision arithmetic,

• analyse the efficiency and convergence rate of simple numerical methods,

• develop and implement algorithms for solving nonlinear equations,

• develop quadrature methods for numerical integration,

• apply numerical methods to solve systems of linear equations and to calculate eigenvalues and eigenvectors,

• solve boundary and initial value problems using finite difference methods.

##### Operational Research: Probabilistic Models (MATH268)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce a range of models and techniques for solving under uncertainty in Business, Industry, and Finance.

**Learning Outcomes**The ability to understand and describe mathematically real-life optimization problems.

Understanding the basic methods of dynamical decision making.

Understanding the basics of forecasting and simulation.

The ability to analyse elementary queueing systems.

### Programme Year Three

Students choose modules to the value of four units from the Philosophy Year Three programme and four Mathematics modules. Students may choose to undertake a project as one of the Mathematics options – this may be on a topic related to Philosophy.

#### Year Three Optional Modules

##### Philosophy Dissertation (PHIL306)

**Level**3 **Credit level**30 **Semester**Whole Session **Exam:Coursework weighting**0:100 **Aims**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 supervison of the supervisor to whom they have been allocated.

**Learning Outcomes**The student will produce a systematic piece of written work, organised in chapters/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.

##### School of the Arts Work Placements Module (SOTA300)

**Level**3 **Credit level**30 **Semester**Whole Session **Exam:Coursework weighting**0:100 **Aims**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.

**Learning Outcomes**To demonstrate an ability to develop materials and/or undertake tasks, according to a given specification and requirement, within a practical or vocational context.

To reflect on and evaluate the efficacy of the materials developed and/or the tasks undertaken.

To identify the connection between academic and/or theoretical knowledge and its practical or vocational application.

To identify, reflect and report on a range of personal/employability skills.

##### Further Methods of Applied Mathematics (MATH323)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**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.

**Learning Outcomes**After completing the module students should be able to:

- use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ordinary differential equations.

- solve simple integral extremal problems including cases with constraints;

- classify a system of simultaneous 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases;

- classify 2nd-order linear partial differential equations and, in appropriate cases, find general or specific solutions. [This might involve a practical understanding of a variety of mathematics tools; e.g. conformal mapping and Fourier transforms.]

##### Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**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.

**Learning Outcomes**After completing the module, students should be able to understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, and apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.

##### Quantum Mechanics (MATH325)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**The development of Quantum Mechanics, requiring as it did revolutionary changes in our understanding of the nature of reality, was arguably the greatest conceptual achievement of all time. The aim of the module is to lead the student to an understanding of the way that relatively simple mathemactics (in modern terms) led Bohr, Einstein, Heisenberg and others to a radical change and improvement in our understanding of the microscopic world.

**Learning Outcomes**After completing the module students should be able to solve Schrodinger''s equation for simple systems, and have some intuitive understanding of the significance of quantum mechanics for both elementary systems and the behaviour of matter.

##### Relativity (MATH326)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To impart

(i) a firm grasp of the physical principles behind Special and General Relativity and their main consequences;

(ii) technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;

(iii) knowledge of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;

(iv) basic concepts of black holes and (if time) relativistic cosmology.

**Learning Outcomes**After completing this module students should

(i) understand why space-time forms a non-Euclidean four-dimensional manifold;

(ii) be proficient at calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols.

(iii) understand the arguments leading to the Einstein''s field equations and how Newton''s law of gravity arises as a limiting case.

(iv) be able to calculate the trajectories of bodies in a Schwarzschild space-time.

##### Population Dynamics (MATH332)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**- 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

**Learning Outcomes**The ability to relate the predictions of the mathematical models to experimental results obtained in the field.The ability to recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.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. ##### Group Theory (MATH343)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**To introduce the basic techniques of finite group theory with the objective of explaining the ideas needed to solve classification results.

**Learning Outcomes**Understanding of abstract algebraic systems (groups) by concrete, explicit realisations (permutations, matrices, Mobius transformations).

The ability to understand and explain classification results to users of group theory.

The understanding of connections of the subject with other areas of Mathematics.

To have a general understanding of the origins and history of the subject.

##### Combinatorics (MATH344)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**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.

**Learning Outcomes**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.

##### Analysis and Number Theory (MATH351)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To provide an introduction to uniform distribution modulo one as a meeting ground for other branches of pure mathematics such as topology, analysis and number theory.

To give an idea of how these subjects work together in this context to shape modern analysis by focusing on one particular rich context.

**Learning Outcomes**After completing the module students should be able to:

understand completions and irrationality;

understand diophantine approximation and its relation to uniform distribution;

appreciate that analysis has a complex unity and to have a feel for basic computations in analysis.

calculate rational approximations to real and p adic numbers and to put this to use in number theoretic situations.

calculate approximations to functions from families of simpler functions e.g. continuous functions by polynomials and step functions by trigonometric sums.

work with basic tools from analysis, like Fourier series and continuous functions to prove distributional properties of sequences of numbers.

##### Linear Statistical Models (MATH363)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**· 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 familiarity with the computer package SPSS.

**Learning Outcomes**After completing the module students should be able to:

understand the rationale and assumptions of linear regression and analysis of variance.

· understand the rationale and assumptions of generalized linear models.

· recognise the correct analysis for a given experiment.

· carry out and interpret linear regressions and analyses of variance, and derive appropriate theoretical results.

· carry out and interpret analyses involving generalised linear models and derive appropriate theoretical results.

· perform linear regression, analysis of variance and generalised linear model analysis using the SPSS computer package.

##### Measure Theory and Probability (MATH365)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**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.

**Learning Outcomes**After completing the module students should be ableto:

master the basic results about measures and measurable functions;

master the basic results about Lebesgue integrals and their properties;to understand deeply the rigorous foundations ofprobability theory;

to know certain applications of measure theoryto probability, random processes, and financial mathematics.

##### Networks in Theory and Practice (MATH367)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**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.

**Learning Outcomes**After completing the module students should

. be able to model problems in terms of networks.

· be able to apply effectively a range of exact and heuristic optimisation techniques.

##### Chaos and Dynamical Systems (MATH322)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To develop expertise in dynamical systems in general and study particular systems in detail.

**Learning Outcomes**After completing the module students will be able to understand the possible behaviour of dynamical systems with particular attention to chaotic motion;

After completing the module students will be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;

After completing the module students will understand how fractal sets arise and how to characterise them.

##### Relativity (MATH326)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To impart

(i) a firm grasp of the physical principles behind Special and General Relativity and their main consequences;

(ii) technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;

(iii) knowledge of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;

(iv) basic concepts of black holes and (if time) relativistic cosmology.

**Learning Outcomes**After completing this module students should

(i) understand why space-time forms a non-Euclidean four-dimensional manifold;

(ii) be proficient at calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols.

(iii) understand the arguments leading to the Einstein''s field equations and how Newton''s law of gravity arises as a limiting case.

(iv) be able to calculate the trajectories of bodies in a Schwarzschild space-time.

##### Mathematical Economics (MATH331)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**· 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.

**Learning Outcomes**After completing the module students should:

· Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences.

· Be able to formulate, in game-theoretic terms, situations of conflict and cooperation.

· Be able to solve mathematically a variety of standard problems in the theory of games.

· To understand the relevance of such solutions in real situations.

##### Riemann Surfaces (MATH340)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To introduce to a beautiful theory at the core of modern mathematics. Students will learn how to handle some abstract geometric notions from an elementary point of view that relies on the theory of holomorphic functions. This will provide those who aim to continue their studies in mathematics with an invaluable source of examples, and those who plan to leave the subject with the example of a modern axiomatic mathematical theory.

**Learning Outcomes**Students should be familiar with themost basic examples of Riemann surfaces: the Riemann sphere, hyperelliptic Riemann surfaces, and smooth plane algebraic curves.

Students should understand and be able to use the abstract notions used to build the theory: holomorphic maps, meromorphic differentials, residues and integrals, Euler characteristic and genus.

##### Number Theory (MATH342)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To give an account of elementary number theory with use of certain algebraic methods and to apply the concepts to problem solving.

**Learning Outcomes**After completing this module students should be able to understand and solve a wide range of problems about the integers, and have a better understanding of the properties of prime numbers.

##### The Magic of Complex Numbers: Complex Dynamics, Chaos and the Mandelbrot Set (MATH345)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**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.**Learning Outcomes**will understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives

will be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems

will be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties

will be able to determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set

will know how to apply advanced results from complex analysis in a dynamical setting

will be able to determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not

##### Differential Geometry (MATH349)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**85:15 **Aims**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.

**Learning Outcomes**1. Knowledge and understanding

After the module, students should have a basic understanding of

a) invariants used to describe the shape of explicitly given curves and surfaces,

b) special curves on surfaces,

c) the difference between extrinsically defined properties and those which depend only on the surface metric,

d) understanding the passage from local to global properties exemplified by the Gauss-Bonnet Theorem.

2. Intellectual abilities

After the module, students should be able to

a) use differential calculus to discover geometric properties of explicitly given curves and surface,

b) understand the role played by special curves on surfaces.

3. Subject-based practical skills

Students should learn to

a) compute invariants of curves and surfaces,

b) interpret the invariants of curves and surfaces as indicators of their geometrical properties.

4. General transferable skills

Students will improve their ability to

a) think logically about abstract concepts,

b) combine theory with examples in a meaningful way.

##### Applied Stochastic Models (MATH360)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**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.

**Learning Outcomes**After completing the module students should have a grounding in the theory of continuous-time Markov chains and diffusion processes. They should be able to solve corresponding problems arising in epidemiology, mathematical biology, financial mathematics, etc.

##### Theory of Statistical Inference (MATH361)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**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.

**Learning Outcomes**After completing the module students should have a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference.

The students should also gain an appreciation of the blossoming area of Bayesian approach to inference

##### Medical Statistics (MATH364)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**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.

**Learning Outcomes**identify the types of problems encountered in medical statistics

demonstrate the advantages and disadvantages of different epidemiological study designs

apply appropriate statistical methods to problems arising in epidemiology and interpret results

explain and apply statistical techniques used in survival analysis

critically evaluate statistical issues in the design and analysis of clinical trials

discuss statistical issues related to systematic review and apply appropriate methods of meta-analysisapply Bayesian methods to simple medical problems.

##### Mathematical Risk Theory (MATH366)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims** 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).

**Learning Outcomes**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 the

R(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).

##### Modal Logic (PHIL301)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**To introduce students to some systems of pure and applied modal logic and to some associated philosophical issues.

**Learning Outcomes**Students will be able to construct proofs in a system of propositional logic not studied on previous modules.

Students will be able to explain the distinction between primitive and derived rules of inference and prove, of derived rules, that they are derived.

Students will be able to explain the relationships between necessity, possibility, impossibility and contingency.

Students will be distinguish between the systems

**K**,**M**,**B**,**S4**and**S5**and to construct proofs in these systems.Students will be able to explain the working of the system of deontic logic

**D**, an applied modal logic dealing with moral/legal obligation and permissibility and to construct proofs in**D**.Students will be able to explain and employ concepts from model-theoretical semantics for modal logics.

Students will be able to explain the the relationships between various systems in terms of the properties of the accessibility relation.

Students will be able to assess sequents for validity in modal systems using trees, to construct counter-models for invalid sequents and to verify counter-models by appeal to model-theoretical considerations.

##### Frontiers of Ethics (PHIL302)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**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.**Learning Outcomes**Students will be able to distinguish between some of the main concepts involved in philosophical debates arising from matters of current global concern. Students will be able to distinguish between different ways of understanding concepts in philosophical debates arising from from matters of global concern.

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.Students will be able to analyse concepts and arguments relating to current ethical issues.

Students will be able to identify philosophical assumptions underlying ethical claims.

Students will be able to structure a philosophical discussion of current ethical issues.Students will be able to speak with confidence and clarity on current ethical issues.Students will be able to explain details of texts shaping current philosophical debates about matters of global concern.Students will be able to articulate and defend positions in current philosophical debates about matters of global concern.

Students will be able to write coherently and rigorously about abstract philosophical issues raised by current ethical controversies.##### Mind, Brain and Consciousness (PHIL309)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**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.**Learning Outcomes**Students should be able to explain the history of twentieth century analytic philosophy of mind.

Students should be able to explain cutting edge contemporary debates on (i) the place of consciousness in nature, (ii) the relationship between thought and consciousness, (iii) artificial intelligence.

Students should be able to build a case for a specific view concerning (i) the place of consciousness in nature, (ii) the relationship between thought and consciousenss, (iii) aritificial intelligence.

Students should be able to explain the main strengths and weaknesses of dominent theories on these three things in the philosophical literature.

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.

Students should be able to think more creatively about the relationship between thought, consciousness and the physical world.

##### Philosophy of Language (PHIL310)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**To study some of the main issues in the contemporary philosophy of language.

**Learning Outcomes**Students will be able to explain the point of compositional theories of meaning. Students will be able to explain the nature and purpose of Frege''s sense-reference distinction.

Students will be able to explain Russell''s Theory of Descriptions.

Students will be able to explain the difference between extensionality and intensionality and be able to evaluate some of the problems connected with these notions.

Students will be able to explain and evaluate sceptical approaches to meaning, such as Quine''s and Kripke''s.

Students will be able to explain and evaluate Davidson''s programme of radical interpretation.

Students will be able to explain rival theories of truth and evaluate their relative merits.

Students will be able to explain the connections between the notions of truth and meaning, and be able to evaluate the debate between realists and anti-realists.

##### Existentialism (PHIL332)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**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.

**Learning Outcomes**Students will be able to explain and evaluate some of the main theories in existentialism.Students will be able to analyse key concepts and arguments relating to existentialism.Students will be able to structure discussion of issues around existentialist metaphysics and ethics.Students will be able to identify the relevance of existentialist philosophy to their own lives.

Students will be able to present their ideas with clarity and confidence.

Students will be able to write coherent, structured and informative accounts on abstract philosophical issues.##### Philosophy of Play and the VIrtual (PHIL343)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**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.

**Learning Outcomes**Students will be able to explain the importance of play as a topic for study.

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.

Students will be able to identify philosophical issues ariding from specific games/instances of play.

Students will be able to explain some of the philosophical literature around play, make-believe, choice and responsibility, and virtual worlds.

Students will be able to trace connections between surface controversies and deeper philosophical concerns.

Students will develop their ability to reflect on their own preconceptions and how these contribute to both philosophical and popular discourse.##### Classical Chinese Philosophy (PHIL367)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**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.**Learning Outcomes**Students will be able to engage in informed discussions about the concepts and categories in which philosophical discussions were conducted in ancient China.

Students will develop abilities in developing and contextualising new information about other worldviews.

Students will be enabled to assimilate alternative cultural perspectives from which to view their own traditions.

Students will be able to explain and evaluate some of the main theories propounded in the classical period of Chinese thought.

Students will be able to discuss the problem of cultural relativism informed by an understanding of a particular alien pattern of thinking.

Students will be able to relate classical Chinese thought to European philosophical interests.

##### Philosophy of the Future (PHIL312)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**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.**Learning Outcomes**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.Students will be able to explain the main strengths and weaknesses of these positions.Students will be able to explain the relevance of metaphysical and ethical considerations to debates concerning these issues. Students will be able to think more creatively about philosophical issues.

Students will be able to structure philosophical arguments relating issues raised by future technological developments.

Students will be able to articulate and defend specific positions in current philosophical debates concerning likely future developments in science and technology.

Students will be able to write coherently and rigourously about the philosophical issues raised by future technological developments.

##### Mythologies of Transhumanism (PHIL313)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**50:50 **Aims**This module aims to familiarise students with key transhumanist concepts and arguments, their history and philosophical context. Participants will improve their ability to analyze arguments, criticize texts, write well-argued essays, and question received ideas. At the end of the module, they will, with limited guidance, be able to construct and evaluate as well as formulate and express ideas at an intermediate level of abstraction, and assess and criticize the views of others.

**Learning Outcomes**Students will be able to distinguish between different ways of understanding concepts in philosophical debates about human enhancement.

Students will be able to explain and evaluate some of the main theories in debates about human enhancement.

Students will be able to analyse concepts and arguments relating to debates about human enhancement.

Students will be able to identify philosophical assumptions underlying ethical claims.

Students will be able to structure a philosophical discussion of current ethical issues.##### Indian Philosophy (PHIL326)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**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.

**Learning Outcomes**Students will be able to engage in informed discussions identifying and evaluating the concepts and categories in which philosophical discussions were conducted in India. Students will able to be enabled to assimilate a differentview Western philosophical traditions from the perspective of Indian philosohical traditions.

Students will be able to contextualise information about the Indian worldviews under discussion.

Students will be able to think more imaginatively by empathising with unfamiliar outlooks on life.

Students will be able to engage in debate informed by an awareness of the particularity and peculiarities of Western philosophical positions.

##### Philosophy and Literature (PHIL327)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**Students will be introduced to arguments of some of the most important philosophers on literature, such as Plato, Aristotle, Schelling and Derrida.

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.

**Learning Outcomes**Students will be able to explain and evaluate some of the theories central to philosophy and literature. Students will be able to analyse key concepts and arguments relating to philosophy of literature.

Students will be able to structure discussion of issues in philosophy and literature.

Students will be able to interrogate literature through philosophy and vice versa.

Students will be able to articulate and defend positions in philosophy of literature.

Students will be able to present their ideas with clarity and confidence.

Students will be able to develop in writing coherent, structured and informative accounts on philosophical issues.

##### Wittgenstein (PHIL340)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**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.

**Learning Outcomes**Students will be able to explain how the Tractatus influenced Wittgenstein''s later philosophy.

Students will be able to explain and assess both the Augustinian picture of language and Wittgenstein''s criticism of it.

Students will be able to explain the rule-following considerations and their importance to Wittgenstein and contemporary philosophy of language.

Students will be able to explain and assess the private language argument and its importance to contemporary philosophy of mind.

Students will be able to explain and assess Wittgenstein''s technical notion of ''criterion'' and its philosophical significance.

Students will be able to explain and assess Wittgenstein''s later epistemology.

##### Philosophical Approaches to Conflict (PHIL365)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**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.**Learning Outcomes**Students will show a capacity to analyse and evaluate, from a philosophical point of view, competing legal and moral rights. Students will be able to form considered and philosophically defensible judgements about appropriate resolution when rights clash in the public sphere.

Students will be able to apply theoretical resources to conflictual issues of contemporary socio-political and/or legal concern.Students will be able to articulate philosophical debates emerging from analysis of complex and sensitive scenarios.

Students will be able to defend positions in relation to competing socio-political perspectives.

Students will be able to be able to write with philosophical rigour about socio-political and/or legal conflicts.

##### Hellenistic and Neoplatonic Philosophy (PHIL368)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**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.**Learning Outcomes**Students will be able to explain and evaluate some of the main theories in Hellenistic and Neoplatonic philosophy.Students will be able to analyse concepts and arguments relating to classic ethical, epistemological and/or metaphysical issues.Students will be able to structure a discussion of central issues in Hellenistic and Neoplatonic philosophyStudents will be able to identify points of agreement and disagreement between different philosophies.Students will be able to engage dialectically with positions in ancient and/or medieval philosophy and articulate their implications.Students will be able to present their ideas with clarity and confidence.Students will be able to develop in writing coherent, structured and informative accounts of abstract philosophical issues.

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 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).