Module Specification - University of Leicester · 2015-08-03 · At the end of this module, typical students should be able to compute limits of sequences and functions, compute derivatives

Module Specification

No. Assessment Description Weight % Exam Hours Ass't Group Alt Reass't

001 Exam 60 2002 Skills Test (Qualifying Element) 20 1003 Coursework 20101 Exam 100 2 Y

Period: Semester 1Occurence: ACoordinator: Katrin LeschkeMark Scheme: UG Pass for Credit


001 Exam 60 2002 Skills Test (Qualifying Element) 20 1003 Coursework 20101 Exam 100 2 Y

Period: Semester 1Occurence: BCoordinator: Katrin LeschkeMark Scheme: UG Pass for Credit

Academic Year: 2013/4Module Level: Year 1Scheme: UGDepartment: MathematicsCredits: 20

Intended Learning OutcomesAt the end of this module, typical students should be able to compute limits of sequences and functions, compute derivativesof standard functions, apply Taylor's formula, compute basic integrals, interpolate functions.Students should know the definitions and should be able to work with the key concepts introduced in this module, like realnumbers, sequences and limits, continuity and differentiability of functions. Students should be able to understand andreproduce main results and proofs of this module. Construct basic VBA computer programs for the numerical solution of basic problems

Teaching and Learning MethodsLectures, Tutorials, Surgeries, Directed reading, Computer practical classes, Computer-aided learning, Example sheets,

Assessment MethodsFormal written examination (January), Computer-based exercises, Competency-based assessment (qualifying element),Coursework exercisesSkills test is a qualifying element (40%)

Pre-Requisites

Co-Requisites

Lectures 32Seminars

Practical Classes & Workshops 10Tutorials 10

FieldworkProject Supervision

Guided Independent Study 88Demonstration

Supervised time in studio/workshop 10Work Based Learning

PlacementYear Abroad

Total Module Hours 150

Student Workload (hours)

MA1012 #MULTIVALUE

Last Published: 3 August 2015


Excluded Combinations-

MA1012 #MULTIVALUE




001 COURSEWORK 20002 SKILLS TEST (QULAIFYING ELEMENT ) 20003 EXAM (Final) 60 2103 EXAM (Final) 100 2 Y

Period: Semester 2Occurence: ACoordinator: Andrea CangianiMark Scheme: UG Pass for Credit


Intended Learning Outcomes"Comprehend Basic Mathematical Modelling principles and be able to solve basic differential equations Analyse infinite series convergence properties and know the series of all elementary functionsKnow the rigorous definition of Multivariable differential calculus concepts. Apply rigorous mathematical analysis argumentations writing skills.Apply differential calculus to the solution of integration, optimisation, and zero-finding problems via Excel spreadsheet.Construct basic VBA computer programs for the numerical solution of basic problems. "


Assessment MethodsFormal written examination (June), Computer-based exercises, Competency-based assessment (qualifying element),Coursework exercisesSkills test is a qualifying element (40%)

Pre-Requisites

Co-Requisites


Lectures 18Seminars








MA1013 CALCULUS AND ANALYSIS 2




001 Coursework 20002 Examination (Final) 80 2102 Examination (Final) 100 2 Y

Period: Semester 2Occurence: ACoordinator: Andrey MorozovMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo know how classical mechanics conceptualises problems. To be able to write down equations of motionand initial conditions for some representative problems, and to use elementary mathematical techniquesto solve problems and to interpret the solutions. Students will have improved their ability to solve problems usingpencil and paper, and will have improved their ability to write mathematical to solve problems and to interpret the solutions.Students will have improved their ability to solve problems using pencil andpaper, and will have improved their ability to write mathematical arguments.

Teaching and Learning MethodsLectures, optional surgeries, problem classes.

Assessment MethodsMarked problem sheets, examination.

Pre-Requisites

Co-Requisites


Lectures 18Seminars




Supervised time in studio/workshopWork Based Learning




MA1051 Introduction to Newtonian Dynamics




001 Coursework 20002 SKILLS TEST (QUALIFYING ELEMENT) 20003 Examination (Final) 60 2103 Examination (Final) 100 2 Y

Period: Semester 1Occurence: ACoordinator: Sibylle SchrollMark Scheme: UG Pass for Credit


Intended Learning Outcomes1. To understand the concept of a probabilistic model for an experiment with a finite number of outcomes (finite probabilityspace). ; sample space, algebras of events/sigma algebra, probability and its properties. 2. To be able to compute probabilities for events defined on a sample space of equally likely outcomes.3. To understand and be able to work with the concept of conditional probability and independence (Bayes' theorem, totalprobability theorem and multiplication formula).4. To understand and be able to work with the concept of random variable and the differences between discrete andcontinuous random variables. 5. To understand and be able to calculate the notions of expectation and variance of random variables and their basicproperties. 6. To understand what a probability distribution and density function are, and to be able to apply the appropriate methods forcomputing probabilities, expectations and variances. 7. To understand the genesis of the binomial, geometric and Poisson distributions. 8. To understand the normal distribution, its ubiquity, its parameters and their interpretations, the general shape of itsprobability density function and finding probabilities using standard tables. 9. To be able to use Poisson tables.10. To understand the content and consequences of the DeMoivre-Laplace and Central Limit theorems and to eb able toapply. 11. To be able to solve problems and present their answers in written communication

Teaching and Learning MethodsLectures, Surgeries, Problem solving classes, Computer practical classes, Computer-aided learning.

Assessment MethodsComputer assessed test(s) and homework will be used as continuous assessment. There will be a written examination.Skills test is a qualifying element (40%)

Pre-Requisites

Co-Requisites


Lectures 18Seminars








MA1061 Probability




001 COURSEWORK (Final) 100

Period: Semester 2Occurence: ACoordinator: Frank NeumannMark Scheme: UG Pass for Credit


Intended Learning OutcomesUpon completing the module, the student should be able to: define what a prime number is, state the fundamental theorem ofarithmetic, construct proofs using mathematical induction, apply Euclid's algorithm, solve basic Diophantine equations, knowand be able to apply Fermat's Little theorem and Euler's theorem

Teaching and Learning MethodsLectures, surgeries, problem classes.

Assessment MethodsMarked problem sheets.

Pre-Requisites

Co-Requisites


Lectures 18Seminars








MA1104 ELEMENTS OF NUMBER THEORY




001 COURSEWORK 20002 SKILLS TEST (QULAIFYING ELEMENT) 20 1003 EXAM (Final) 60 2103 EXAM (Final) 100 2 Y

Period: Semester 1Occurence: ACoordinator: Emmanuil GeorgoulisMark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents should demonstrate ability to work with real and complex numbers, to understand the representation of complexnumbers on the complex plane, to be able to undertand and manipulate vectors, to be able to solve simple linear systems ofequations with Gaussian ellimination, to write linear systems in matrix-vector form, to use LU and Cholesky factorisations forthe solution of linear systems in matrix form and implement them in the computer (using VBA), to be able to manipulate anduse determinants.


Assessment MethodsFormal written examination (January), Computer-based exercises, Competency-based assessment, Coursework exercisesSkills test is a qualifying element (40%)

Pre-Requisites

Co-Requisites


Lectures 18Seminars








MA1112 LINEAR ALGEBRA 1




001 SKILLS TEST (QUALIFYING ELEMENT) 20002 COURSEWORK 20003 EXAM (Final) 60 2103 EXAM (Final) 100 2 Y

Period: Semester 2Occurence: ACoordinator: Alexander ClarkMark Scheme: UG Pass for Credit


Intended Learning Outcomes"Upon completing the module, students should be able to: understand linear transformations between vector spaces andperform related calculations with matrices, calculate the inner product of vectors and interpret these calculationsgeometrically in both the real and complex vector space setting, find orthogonal bases for vector spaces using the Gram-Schmidt Orthogonalization process, calculate and define eigenvalues and eigenvectors of matrices.In the tutorials, students will be asked to present their own solutions to problems to develop their oral and presentation skills. "

Teaching and Learning MethodsLectures, Tutorials, Surgeries, Directed reading, Computer practical classes, Computer-aided learning, Example sheets.

Assessment MethodsWritten examination, Computer-based exercises, Competency-based assessment, Coursework exercisesSkills Test is a qualifying element (40%)

Pre-RequisitesMA1112

Co-Requisites


Lectures 32Seminars








MA1113 LINEAR ALGEBRA 2




001 SKILLS TEST (QUALIFYING ELEMENT) 20002 COURSEWORK 20003 EXAM (Final) 60 2103 EXAM (Final) 100 2 Y

Period: Semester 2Occurence: ACoordinator: Zahir HussainMark Scheme: UG Pass for Credit


Intended Learning Outcomes"Students should know what is meant by an estimate, an estimator, and asampling distribution; understand what is meant by an unbiased estimator; know the mean and varianceof the sampling distribution of the sample mean; know how to write down a likelihood function and finda maximum likelihood estimate for simple models. Students should have an informal understanding ofthe process of hypothesis testing and the meaning of P-values and know what is meant by a confidenceinterval and the relationship between confidence intervals and hypothesis tests."

Teaching and Learning MethodsLectures, Tutorials, Surgeries, Computer practical classes, Computer-aided learning, Example sheets,

Assessment MethodsFormal written examination, Computer-based exercises, Competency-based assessment, Coursework exercisesSkills test is a qualifying element (40%)

Pre-Requisites

Co-Requisites


Lectures 18Seminars








MA1202 INTRODUCTORY STATISTICS




006 Computer Test 100 3

Period: Semester 1Occurence: ACoordinator: Cancer Studies (Generic Code for HESA)Mark Scheme: UG Pass for Credit


Intended Learning OutcomesAn understanding of the way mathematics has developed; an appreciation of both the practical roots ofmathematics and the study of mathematics for its own sake; an appreciation of how mathematics can evolve very differently indifferent cultures; and an improved understanding of the relationships between different aspects of mathematics.

Teaching and Learning MethodsCase studies, optional consultations, reading, electronic search.Module Convenor: Clive Rix

Assessment MethodsComputer test.

Pre-Requisitesnone

Co-Requisitesnone


Lectures 8Seminars 3

Practical Classes & WorkshopsTutorials

Fieldwork 8Project Supervision






MA1253 Mathematics and Society




001 TEST (final) 40 1002 COURSEWORK 60

Period: Semester 1Occurence: ACoordinator: John HuntonMark Scheme: UG Pass for Credit


Intended Learning OutcomesUpon completing the module, the student should be able to: construct basic proofs using the classical axioms of geometry,determine and prove when two triangles are congruent, calculate the basic trigonometric functions and apply Heron'stheorem, apply Ptyolemy's theorem, use analytic techniques and coordinates to solve geometric problems.

Teaching and Learning MethodsSeminar, Group presentations.

Assessment MethodsGroup projects, tests and coursework.

Pre-Requisites

Co-Requisites


Lectures 20Seminars

Practical Classes & Workshops 10Tutorials







MA1272 PLANE GEOMETRY




001 Coursework 20002 Skills test 20003 Examination (Final) 60 2103 Examination (Final) 100 2 Y

Period: Semester 2Occurence: ACoordinator: Ivan TyukinMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo be able to:1) understand both the analytic and the geometric interpretation of differential equations 2) distinguish between classes of differential equations (autonomous, non-autonomous, linear, non-linear, homogeneous,inhomogeneous)3) analyze initial value problems in order to determine whether or not they have unique solutions 4) state and prove basic existence and uniqueness results (Peano existence theorem, Osgood’s uniqueness theorem,Cauchy existence anduniqueness theorem, Picard’s theorem)5) use and apply methods for finding general solutions of general ODEs of the first-order in normal form6) solve linear homogeneous and inhomogeneous equations with constant coefficients7) use and write programs for finding numerical solutions of ordinary differential equations (involving both explicit and implicitprocedures).

Teaching and Learning MethodsLectures, Problem Classes, Computer Classes, automated computer assignments

Assessment MethodsComputer test, exam

Pre-Requisites

Co-RequisitesMA1051


Lectures 33Seminars








MA2021 Differential Equations and Dynamics




003 Examination (Final) 100 2

Period: Semester 2Occurence: ECoordinator: Ivan TyukinMark Scheme: UG Pass for Credit


LecturesSeminars



Guided Independent StudyDemonstration



Total Module Hours


MA2022 Differential Equations and Dynamics




001 Examination (Final) 60 2002 Coursework 20003 Skills Test (Qualifying Element) 20 1101 Examination (Final) 100 2 Y

Period: Semester 1Occurence: ACoordinator: Jeremy LevesleyMark Scheme: UG Pass for Credit


Intended Learning OutcomesUpon completing the module, students should be able to: differentiate and integrate vector valued functions, apply Fubini'stheorem and learn to calculate iterated integrals, use Jacobians to calculate change of variables, learn how to use multi-dimensional linear interpolation for approximations, apply the theorems of Stoke and Green, calculate with basic Fourierseries and use Pareval's theorem.

Teaching and Learning MethodsLectures, Tutorials, Computer practical classes, Computer-aided learning, Example sheets.

Assessment MethodsWritten examination, Computer-based exercises, weekly written homework, Skills Test (qualifying element) pass mark 40%

Pre-RequisitesMA1012, MA1013

Co-Requisites


Lectures 32Seminars








MA2032 Calculus and Analysis 3




001 Exam 60 2002 Coursework 40003 Exam 100 2 Y



Intended Learning OutcomesUpon completing the module, students should be able to: define topology and continuity in the general setting and to relatethese notions to the analogues they will have seen in analysis; apply the quotient construction to create new spaces, includingsurfaces, from more basic spaces; visualise the abstract concepts developed in topology and present in poster form theresults of their visualisation.

Through the written assignments, students should develop their ability to think critically, to analyse and to write cleararguments. Through the poster presentation (worked on in small groups) the students should develop team working skills andoral presentation skill when presenting the poster.

Teaching and Learning MethodsLectures, Problem solving classes, Poster presentation.

Assessment MethodsWritten examination, written assignments and poster presentation.

Pre-Requisites

Co-Requisites


Lectures 18Seminars

Practical Classes & WorkshopsTutorials 5







MA2104 Elements of Topology




001 Examination (Final) 60 2002 Skills Test (qualifying element) 20 1003 Coursework 20101 Examination (Final) 100 2 Y

Period: Semester 1Occurence: ACoordinator: Alexander BaranovMark Scheme: UG Pass for Credit


Intended Learning OutcomesUpon completing the module, students should be able to: define and calculate the basis of a subspace of a vector space andto calculate a change of basis, diagonalise matrices and understand when this is possible, to find the minimal polynomial of amatrix and to interpret the meaning of this polynomial, manipulate quadratic forms.

Teaching and Learning MethodsLectures, Tutorials, Directed reading, Computer practical classes, Computer-aided learning, Example sheets.

Assessment MethodsWritten examination, Computer-based exercises, Competency-based assessment, Coursework exercises. The skills test is aqualifying element.


Co-Requisites


Lectures 18Seminars








MA2132 Linear Algebra 3




001 Coursework 20002 Exam 80 2003 Exam 100 2 Y

Period: Semester 2Occurence: ACoordinator: Teimuraz PirashviliMark Scheme: UG Pass for Credit


002 Exam (Final) 100 2

Period: Semester 2Occurence: ECoordinator: Teimuraz PirashviliMark Scheme: UG Pass for Credit


Intended Learning OutcomesThe module aims to provide students the foundation required for further study in algebra and to provide the knowledgeessential to be able to use algebra as it occurs in other areas. At the same time, students will see ample applications ofalgebra, for example in the study of symmetry, and students should develop the ability to see how to apply algebra in thosesituations to which it naturally applies. Students will be introduced to groups, rings and fields and students should be able toperform basic calculations in each of these contexts. The students will learn how the notions of homomorphisms andisomorphisms apply to all these contexts and should be able to perform related calculations. Students should be able to applythe quotient construction in the context of groups and rings to construct new groups and rings. Students should be able todefine the various types of factorisation in rings and be able to identify the class to which various rings belong. Studentsshould be able to define what a maximal ideal is and to be able to use maximal ideals to construct fields.

Through the weekly written assignments, students should develop their ability to think critically, to analyse and to write cleararguments.

Teaching and Learning MethodsLectures, Problem solving classes

Assessment MethodsContinuous assessment based on written homework. Written exam.

Pre-Requisites

Co-Requisites

Lectures 30Seminars








MA2133 Algebra




MA2133 Algebra




001 Exam 80 2002 Coursework 20003 Exam 100 2 Y

Period: Semester 1Occurence: ACoordinator: Ruslan DavidchackMark Scheme: UG Pass for Credit


Intended Learning OutcomesThe module is designed to introduce students to the basics of data representation in computers, algorithmic thinking, andprogramming simple numerical methods. Students will gain practical experience of working with Matlab.Drawing theflowcharts of computer programs is also required.

Teaching and Learning MethodsLectures, computer lab sessions, and problem classes

Assessment MethodsSolutions of problem sheets, 2h written examination

Pre-Requisites

Co-Requisites


Lectures 20Seminars








MA2252 Introduction to Computing




001 Coursework 20002 Examination 80 3003 Exam 100 3 Y

Period: Semester 2Occurence: ACoordinator: Simona PaoliMark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents should know the distributions of the least squares estimators for parameters of the simple linear regression model,be able to calculate confidence intervals and prediction intervals and use hypothesis tests for model parameters. Studentsshould be able to perform hypothesis tests using an analysis of variance (ANOVA) table and to understand how it is used toexplain variation, and be able to assess the lack of fit of a linear model using repeated observations.

Teaching and Learning MethodsClass sessions with some handouts.

Assessment MethodsMarked problem sheets and examination.


Co-Requisitesnone

Excluded CombinationsCannot be taken with MA2262



Fieldwork 0Project Supervision 0

Guided Independent Study 110Demonstration 0

Supervised time in studio/workshop 0Work Based Learning 0

Placement 0Year Abroad 0



MA2261 Linear Statistical Models




001 Coursework 20002 Examination 80 1.5003 Exam 100 1.5 Y



Intended Learning OutcomesStudents should know the distributions of the least squares estimators for parameters of the simple linear regression model,be able to calculate confidence intervals and prediction intervals and use hypothesis tests for model parameters. Studentsshould be able to perform hypothesis tests using an analysis of variance (ANOVA) table and to understand how it is used toexplain variation, and be able to assess the lack of fit of a linear model using repeated observations.


Assessment Methods Marked problem sheets and examination.


Co-Requisitesnone

Excluded Combinations-Cannot be taken with MA2261. Normally this module should be taken along with MA2511.









MA2262 Linear Statistical Models




001 Exam 70 2002 Computational Tasks 30003 Exam 100 2 Y

Period: Semester 2Occurence: ACoordinator: Stephen GarrettMark Scheme: UG Pass for Credit


001 Exam 70 2002 Coursework 30

Period: Semester 2Occurence: BCoordinator: Dalia ChakrabartyMark Scheme: UG Pass for Credit


Intended Learning Outcomes-Students will learn statistical methods relevant to the actuarial industry.-Develop problem-solving skills in the statistical context. -Practical use of relevant software such as R and Excel/VBA will be explored.

-Explain need for statistical methods in finance-Explain the need for and construct simple models of reinsurance models. Reproduce underlying mathematics.-Explain the need for and compute ruin probabilities. Reproduce underlying mathematics-Implement computational models of the above in standard situations.

Full syllabus from http://www.actuaries.org.uk/students/pages/syllabus-exams (CT6 to (iv))

Teaching and Learning MethodsStudents will be provided with material written specifically for the module. Three lectures per week will be used to teach thedetails of the material. Students are further supported with 1 problem solving skills/computational session and 1 problem classper week.

Assessment Methods2 hour written examination intended to assess technical skills.Fortnightly computational tasks are marked.

Pre-Requisites

Co-Requisites









MA2266 Applied Statistics




MA2266 Applied Statistics




001 Exam 70 2002 Problem sheets 30003 Exam 100 2 Y



Intended Learning OutcomesThe syllabus is taken from the Actuarial Profession's CT1 module (from item (v)): http://www.actuaries.org.uk/research-and-resources/documents/subject-ct1-models-core-technical-syllabus-2013-exams.A successful student will be able to-Describe fundamental financial terms. -Begin to understand the role of actuaries in the financial sector-Form cashflow descriptions of financial and business scenarios. -Demonstrate the ability to manipulate use standard actuarial notation.-Explain the use and function of basic financial products.-Reproduce standard criticisms of fixed-interest models, and have an appreciation of mathematical issues arising fromstochastic models.-Demonstrate basic skills in the interpretation of financial problems.

Teaching and Learning MethodsStudents will be provided with material written specifically for the module. Three lectures per week will be used to teach thedetails of the material. Students are further supported with 1 problem solving skills supervision session and 1 problem classper week.

Assessment Methods2 hour written examination intended to assess technical skills.Fortnightly problem sheets of exam standard are marked.

Pre-Requisites

Co-Requisites










MA2401 Cash-flow Analysis and Interest




001 Exam 70 2002 Project 30



Intended Learning OutcomesThe module aims to give students a solid grounding in the basics of finance and accounting.The syllabus is taken from theActuarial Profession's CT2 module: http://www.actuaries.org.uk/research-and-resources/documents/subject-ct2-finance-and-financial-reporting-syllabus-2013-exams.

Students will be able to discuss the fundamental framework of UK finance and be able to write/interpret company accounts.Tax and the international perspective are also considered.

Students will also address the challenges of communicating financial and business solutions to less mathematical members ofthe sector.

Teaching and Learning MethodsStudents will be provided with material written specifically for self study which will be paced across the semester. Threelectures will be given per week. One problem solving class per week will be given to go through regular (non assessedcoursework). To support students in the preparation of their case-study report, fortnightly skills sessions will also be given.

Assessment Methods2 hour written examination intended to assess technical skills.An independent case-study report. This is an individual, open-ended task which requires students to demonstrate self-direction in tackling a realistic business problem and communicating their conclusions in an appropriate manner.

Pre-Requisites

Co-Requisites


Lectures 30Seminars








MA2402 Finance and Financial Reporting




001 Exam 70 2002 Computational Tasks 30003 Exam 100 2 Y



Intended Learning OutcomesStudents will be introduced to the need and theory of mortality modelling in the actuarial context. The syllabus is taken fromthe Actuarial Profession's CT4 module (items (i)-(iv)): http://www.actuaries.org.uk/research-and-resources/documents/subject-ct4-models-core-technical-syllabus-2013-exams, namely1. Describe the principles of actuarial modelling.2. Describe the general principles of stochastic processes, and their classification into different types.3. Define and apply a Markov chain.4. Define and apply a Markov process.Furthermore, students will be required to develop practical skills in VBA.

Teaching and Learning MethodsStudents will be provided with material written specifically for the module. Three lectures per week will be used to teach thedetails of the material. Students are further supported with 1 computing session and 1 problem class per week. The studentswill be required to work through pre-set computational tasks in each computing session.

Assessment Methods2 hour written examination intended to assess technical skills.Fortnightly computational tasks are marked.

Pre-Requisites

Co-Requisites










MA2404 The Principles of Financial Modelling




001 Exam 70 2002 Problem Sheets 30003 Exam 100 2 Y

Period: Semester 1Occurence: ACoordinator:Mark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents will be introduced to the need and theory of mortality modelling in the actuarial context. The syllabus is taken fromthe Actuarial Profession's CT4 module (from item (v)): http://www.actuaries.org.uk/research-and-resources/documents/subject-ct4-models-core-technical-syllabus-2013-exams, namely1. Explain the concept of survival models.2. Describe estimation procedures for lifetime distributions.3. Derive maximum likelihood estimators for the transition intensities in models of transfers between states with piecewiseconstant transition intensities.4. Describe the Binomial model of mortality, derive a maximum likelihood estimator for the probability of death and comparethe Binomial model with the multiple state models.5. Describe how to estimate transition intensities depending on age, exactly or using the census approximation.6. Describe how to test crude estimates for consistency with a standard table or a set of graduated estimates, and describethe process of graduation.

Teaching and Learning MethodsStudents will be provided with material written specifically for the module. Three lectures per week will be used (over half thesemester) to teach the details of the material. Students are further supported with 1 problem class per week.

Assessment Methods2 hour written examination intended to assess technical skills.Weekly problem sheets of exam standard are marked.


Co-RequisitesMA2404










MA2414 Mortality Modelling




001 Coursework (Final) 100 0003 Written report 100 Y



002 Coursework (Final) 100 0

Period: Semester 1Occurence: ECoordinator: John HuntonMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo write a clear and logical presentation of their topic based on the given notes and work programme.To give oral explanations of some of their solutions.To reflect on problem-solving skills used.To develop self study skillsTo develop oral communication skills by presenting solutions and making group presentation.To develop team working skills by working in groups on the group presentations and poster presentation ."

Teaching and Learning Methods"Seminars based on topic of students choice from a list of topics. Seminars based on the topic of students choice from a list oftopics. Poster presentation, group presentation and a written report on the module.

Assessment MethodsGroup poster presentation, group presentation to larger group of peers and staff and individual written report.

Pre-Requisitesnone

Co-Requisitesnone

Excluded Combinations-Certain students taking MA2510 cannot take MA2511 - those on the following degrees may only choose one or the other: Maths with Astronomy, Maths with Computer Science









MA2510 Investigations in Mathematics




001 Presentations and reports (Final) 100 0003 Report and presentation 100 1 Y



002 Presentations and reports (Final) 100 0

Period: Semester 2Occurence: ECoordinator:Mark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents will be able to: apply mathematical techniques to practical business problems; compile reports relating to thebusiness case studies; understand the importance of articulating their academic skills for graduate employment; understandhow to prepare and apply for a year in industry; produce an effective CV targeted towards a jobs advertisement/personspecification; make an oral presentation reflecting on their experience of the topics covered.

Teaching and Learning MethodsModule convenor: Clive RixSeminars, lectures.

Assessment MethodsCase study written report; Case study presentation; Production of an effective CV; Reflective presentation and job interviewassessment.

Pre-Requisitesnone

Co-Requisitesnone










MA2511 Business Applications of Mathematics




001 Computer demonstration 50002 Group work and report 50003 Written report 100 Y



Intended Learning OutcomesDemonstrate flexible application of basic statistical methods.Selection of appropriate methodology for real world data.Demonstration of appropriate use of solutions to inform business decisions.Demonstration of knowledge of advanced functionality in EXCEL, and knowledge of statistical add-ons. Basic statistical programming using VBA and VBA for implementation of statistical methods, and appropriate selection ofinformation for presentation of results to a variety of audiences, including oral and written presentation.

Teaching and Learning MethodsModule convenor: Clive RixLecturesComputer practicalGroup workshop

Assessment MethodsComputer demonstrationWritten reportGroup work

Pre-Requisites

Co-Requisites


Lectures 12Seminars








MA2512 APPLIED ECONOMETRICS




001 Year abroad 100



Intended Learning OutcomesRefer to Department for further details

Teaching and Learning MethodsRefer to Department for further details

Assessment MethodsRefer to Department for further details

Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2992 Year Abroad




001 Year abroad 100



001 Year abroad 100101 Alt reassessment using MA2022 exam paper 100 Y

Period: Semester 1Occurence: BCoordinator:Mark Scheme: UG Pass for Credit





Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2993 Year Abroad




001 Year abroad 100



001 Year abroad 100101 Alternate reassessment using paper for MA2133 100 Y






Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2994 Year Abroad




001 Year abroad 100






Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2995 Year Abroad




001 Year abroad 100






Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2996 Year Abroad




001 Year abroad 100



001 Year abroad 100101 Alternate reassessment using paper for MA2032 100 Y






Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2997 Year Abroad




001 Year abroad 100






Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2998 Year Abroad




001 Year abroad 100






Pre-Requisites

Co-Requisites


LecturesSeminars






Total Module Hours


MA2999 Year Abroad




001 Weekly Exercises 20002 Examination (Final) 80 3005 Exam 100 3 Y

Period: Semester 2Occurence: ACoordinator: Nikolai BrilliantovMark Scheme: UG Pass for Credit



Period: Semester 2Occurence: BCoordinator: Nikolai BrilliantovMark Scheme: UG Pass for Credit


003 Weekly Exercises 20004 Examination 80 3

Period: Semester 2Occurence: ECoordinator: Nikolai BrilliantovMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo use the classification of linear partial differential equations, in order to apply the basic methodsof its solution for one, two and three dimensions. To apply the concepts of eigenfunctions, eigenvalues, and a Green functionin solution of partial differntial equation of hyperbolic, parabolic and elliptic types. To use the Fourierseries and some special functions in solving partial differential equation on domains of different geometry. To derive somebasic equation of matematical physics of hyperbolic, parabolic and analyse the limits of its applications.

Teaching and Learning MethodsLectures, problem classes

Assessment MethodsThere will be an intermediate 1 hour test based on the weekly problem sheets and 3 hour Summer examination. It will have 4questions with full marks obtained by correctly answering 4 of them.









MA3002 Equations of Mathematical Physics




Co-RequisitesMA1051


MA3002 Equations of Mathematical Physics




001 Coursework 30002 Examination (Final) 70 2005 Exam (Final) 100 2 Y

Period: Semester 1Occurence: ACoordinator: Ruslan DavidchackMark Scheme: UG Pass for Credit


003 Coursework 30004 Examination (Final) 70 2

Period: Semester 1Occurence: ECoordinator: Ruslan DavidchackMark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents should be able to use advanced methods of scientific computing in order to solve linear systems of equations, solvenonlinear equations and systems of equations, interpolateand approximate functions by polynomials, calculate function derivatives and quadratures, solve optimization problems in theleast squares sense, find numerical solutions of ordinary differential equations, and use fast Fourier transform for Fourieranalysis of signals.

Teaching and Learning MethodsLectures, problem classes, instructor-assisted computer lab sessions, revision problem sheets.

Assessment Methods1. Computer assignments designed to develop understanding of numerical algorithms and learn how to implement them in acomputer program (within Matlab). 2. Revision Problem Sheets for assessing students' understanding of theoretical material.3. Two hour January examinationof numerical algorithms and learn how to implement them in a computer program (within Matlab).There will be weekly instructor-assisted computer lab sessions.The 2 hour January examination will have 4 questions, with full marks obtained by correctly answering3 of them.


Co-Requisites

Lectures 20Seminars








MA3012 Scientific Computing




MA3012 Scientific Computing





Period: Semester 1Occurence: ACoordinator: Zahir HussainMark Scheme: UG Pass for Credit



Period: Semester 1Occurence: ECoordinator: Zahir HussainMark Scheme: UG Pass for Credit


Intended Learning OutcomesOn completion of this module, a diligent student will know the basic concepts and instruments of financial market, the mainconcepts of probability and stochastic processes, will be able to use the knowledge of probability & stochastics to analysedifferent models of financial market.

Teaching and Learning MethodsClass sessions with some handouts

Assessment Methods3 hour written examination


Co-Requisitesnone










MA3071 Introduction to Financial Mathematics







002 Examination 100 3

Period: Semester 1Occurence: ECoordinator: Stephen GarrettMark Scheme: UG Pass for Credit






Period: Semester 2Occurence: ECoordinator: Stephen GarrettMark Scheme: UG Pass for Credit


Intended Learning OutcomesOn completion of this module, a diligent student will be able to apply cashflow models to financial and business scenarios,and be able to understand standard actuarial notation and fundamental financial concepts. The student will have a clearunderstanding of the role of actuaries in the financial sector.

The student will also practice the ability to self study - an important skill for lifelong learning in any chosen profession.









MA3074 Introduction to Actuarial Mathematics



Teaching and Learning MethodsStudents will be provided with material written specifically for self study which will be paced across the semester. One lecturewill be given per week and the onus is on self study. This study will be supported via electronic means on blackboard. Oneexamples class per week will be given to go through regular (non-assessed) coursework.

Assessment MethodsThe assessment for this module will consist of a 3hr examination on unseen questions.


Co-Requisitesnone


MA3074 Introduction to Actuarial Mathematics




001 Coursework 50002 Examination (Final) 50 2005 Examination 100 2 Y

Period: Semester 2Occurence: ACoordinator: Ivan TyukinMark Scheme: UG Pass for Credit


001 Coursework 50002 Examination (Final) 50 2005 Examination 100 2 Y

Period: Semester 2Occurence: ECoordinator: Ivan TyukinMark Scheme: UG Pass for Credit


Intended Learning OutcomesThe students will be able to recognize, formulate, and classify linear and nonlinear optimization problems. With regards tolinear optimization (programming), they will be able to apply the theory of the simplex method, and be able to use the methodfor solving problems with linear cost functions and constraints in the form of a convex polyhedron. In addition, the studentswill apply techniques and methods for solving one-dimensional and multi-dimensional constrained and unconstrainednonlinear optimization problems. The students will be able to solve shortest path and minimal-tree problems, and shouldknow basic notions and concepts from the theory of games. Application of programming skills to production of algorithms inVBA.

Teaching and Learning MethodsLectures, problem classes, computer practicals, automated computer assignments, plus optional VBA classes in semester 1

Assessment MethodsClass tests, written reports on computer practicals, final exam, computer demonstration. Class computer test on linearprogramming and networks.

Pre-Requisites

Co-Requisites


Lectures 33Seminars








MA3077 Operations Research




001 Poster Presentation 10002 Examination (Final) 90 2005 Exam 100 2 Y



003 Poster Presentation 10004 Examination (Final) 90 2

Period: Semester 1Occurence: ECoordinator: Sibylle SchrollMark Scheme: UG Pass for Credit


Intended Learning OutcomesDemonstrate ability to construct and work with factor rings. Demonstrate ability to prove and to use tests for irreducibility. Demonstrate ability to relate irreducible elements and maximal ideal in the ring of polynomials over a field. Demonstrate ability to explain the significance and properties of the minimal polynomial.Demonstrate ability to construct extension fields and use the concept of the degree of an extension. Demonstrate ability to apply the concepts introduced in the course to ruler and compass constructions. Demonstrate ability to solve the three classical Greek questions discussed in this moduels.

Teaching and Learning MethodsLectures and problem classes

Assessment MethodsExamination and group project with poster presentation.


Co-Requisitesnone


Lectures 33Seminars








MA3101 Irreducible Polynomials and Squaring the Circle




001 Examination (Final) 80 3002 Group presentation 20005 Exam 100 3 Y

Period: Semester 1Occurence: ACoordinator: Dimitrina StavrovaMark Scheme: UG Pass for Credit


003 Exam 80 3004 Group Presentation 20

Period: Semester 1Occurence: ECoordinator: Dimitrina StavrovaMark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents should know and be able to apply the key concepts of this module:Analytic functions, path integrals, Taylor and Laurent series, singularities and residues of complex functions. Students shouldbe able to explain the main proofs given in the lectures and be able todetermine whether a complex function is differentiable, define and evaluate path integrals, find Taylor and Laurent expansionsof complex functions, calculate residues and use the residue theorem to evaluate real integrals and sums of real series.

Teaching and Learning MethodsLectures and problem classes, coursework.

Assessment MethodsWritten examination and group presentations.

Pre-Requisites

Co-Requisitesnone










MA3121 Complex Analysis




001 Examination (Final) 90 2002 Coursework 10005 Exam 100 2 Y

Period: Semester 2Occurence: ACoordinator: Alexander BaranovMark Scheme: UG Pass for Credit


003 Examination 90 2004 Coursework 10

Period: Semester 2Occurence: ECoordinator: Alexander BaranovMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo understand the concepts of symmetries, direct symmetries and isometries;To know classification of finite groups of isometries in R2 and R3;To use the concepts of homomorphisms, normal subgroups and quotient groups and their relevance to the structure of agroup;To understand the concept of a group action and to use group actions for enumeration and to prove fundamental results suchas the Sylow theorems;To calculate using generators and relations and to understand the idea of a group presentation in order to study a group;To know the properties of permutations and of symmetric and alternating groups;To understand the idea of simple groups as the basic building blocks of group theory;To understand and be able to use the main Sylow theorems for finite groups;To understand and be able to use the main Structure Theorem for finitely generated abelian groups.

Teaching and Learning MethodsLectures and problem classes.

Assessment MethodsExamination, marked problem sheets


Co-Requisitesnone









MA3131 Groups and Symmetry




MA3131 Groups and Symmetry




001 Group Project (Final) 30002 Skills test 40003 Class test 30007 Exam 100 2 Y

Period: Semester 2Occurence: ACoordinator: Katrin LeschkeMark Scheme: UG Pass for Credit


004 Group Project 30005 Skills test 40006 Class test 30

Period: Semester 2Occurence: ECoordinator: Katrin LeschkeMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo know the definitions and the key concepts of curves and surfaces. To be able to reproduce and apply the main results and proofs given in the module. To demonstrate familiarity with the topic and to be able to solve routine problems. To know how to connect visual information with geometric properties.To be able to produce mathematical exhibits and to communicate mathematical content to non-experts.

Teaching and Learning MethodsLectures, example classes, example sheets, group project

Assessment MethodsWritten skills test, computer tests, group project


Co-Requisitesnone


Lectures 33Seminars








MA3152 Curves and Surfaces



MA3152 Curves and Surfaces




001 Examination (Final) 90 2002 Group Work 10005 Exam 100 2 Y



003 Examination 90 2004 Group Work 10

Period: Semester 1Occurence: ECoordinator: Frank NeumannMark Scheme: UG Pass for Credit





003 Examination 90 2004 Group Work 10

Period: Semester 2Occurence: ECoordinator: Frank NeumannMark Scheme: UG Pass for Credit


Intended Learning OutcomesTo know the definitions and the key concepts of elementary number theory and to be able to reproduce and apply the mainresults and proofs given in the module. To know how to formulate number theoretical problems in rigorous mathematicallanguage. To demonstrate familiarity with the topic and to be able to solve routine problems.

Lectures 33Seminars








MA3153 Number Theory



Teaching and Learning MethodsLectures, example classes, example sheets, group work

Assessment MethodsMarked problem sheets, written examination

Pre-Requisites

Co-Requisitesnone


MA3153 Number Theory




001 Coursework 20002 Examination (Final) 80 3005 Exam 100 3 Y



003 Coursework 20004 Examination (Final) 80 3

Period: Semester 1Occurence: ECoordinator: Simona PaoliMark Scheme: UG Pass for Credit


Intended Learning OutcomesStudents should know the assumptions made in using the generalized linear regression model and be able to calculateconfidence intervals and use hypothesis tests for model parameters. Also be able to assess the fit of a log-linear modelusing a nested hierarchy of log-linear models.


Assessment MethodsMarked problem sheets and examination.

Pre-RequisitesMA1061, MA2201, MA2261

Co-Requisitesnone


Lectures 30Seminars








MA3201 Generalized Linear Models




001 Written assignments 30002 Group Project 20003 Examination (Final) 50 2004 Exam 100 2 Y



001 Written assignments 30002 Group Project 20003 Examination (Final) 50 2004 Exam 100 2 Y

Period: Semester 2Occurence: ECoordinator:Mark Scheme: UG Pass for Credit


Intended Learning OutcomesTo understand the key developments in the history of mathematics; to appreciate the issues surrounding the interpretation ofhistorical mathematical texts; to have an improved understanding of the relationships between different aspects ofmathematics and how they evolved.

Teaching and Learning MethodsLectures, seminar, field trip, optional consultations, online resources, reading, electronic search

Assessment MethodsMarked essays, poster presentation, written examination

Pre-RequisitesA deep felt interest in the history of mathematics and a general familiarity with mathematical concepts at about second yearundergraduate level

Co-Requisitesnone

Excluded Combinationscannot be taken with MA3511



Fieldwork 9Project Supervision






MA3501 History of Mathematics




001 Coursework (Final) 100

Period: Semester 2Occurence: ACoordinator: Nicole SnashallMark Scheme: UG Pass for Credit


Intended Learning Outcomes1. presentation skills,2. the ability to select information appropriately for presentation to a target audience,3. skills in analysing mathematical information from books or journals,4. writing skills,5. the ability to work effectively in a team setting,6. the ability to apply knowledge in ways that are relevant the school environment,7. to critically evaluate communication skills within a classroom setting.

Teaching and Learning MethodsSeminars and in school experience.

Assessment MethodsThe UAS component of the coursework will be assessed via your written evaluation of your special project, and anassessment by the teacher with whom you worked. In total this counts for 55% of the mark. The university component counts for 45% and will be assessed via written work, an oral presentation, contribution to adiscussion board, and groupwork.

Pre-Requisites{IMPORTANT NOTE}: Any student who wishes to take this module MUST complete an application form prior to beinginterviewed and accepted. This is part of the requirement for the module being run under the Undergraduate AmbassadorScheme (UAS). Electronic application forms will sent directly to students who have chosen the module by the central Schooland College Services team. It is expected that interviews will take place before the end of term in June 2013. CRB checks andtraining must be completed in semester 1 in preparation for placement in schools in semester 2.

Co-Requisitesnone

Excluded Combinations-Students may NOT take this module in combination with MA3501

Lectures 20Seminars




Supervised time in studio/workshopWork Based Learning 60




MA3511 Communicating Mathematics




001 Continuous assessment 100

Period: Semester 2Occurence: ACoordinator: Jeremy LevesleyMark Scheme: UG Honours Level



Period: Semester 2Occurence: ECoordinator: Jeremy LevesleyMark Scheme: UG Honours Level


Intended Learning OutcomesTo write short reports on a range of research topics.To write more detailed report on one research topic.To deliver a presentation based on their report for an audience of peers

Teaching and Learning MethodsLectures to stimulate research into each of the research areas.Report writing workshop.Presentation skills workshop.Individual supervision of final longer report.

Assessment Methods20% short reports50% longer report30% presentation

Pre-Requisites

Co-Requisites

Excluded CombinationsCannot be taken alongside MA3501, MA3511, MA3513

LecturesSeminars








MA3512 Mathematics Research Project







Intended Learning OutcomesStudents will be able to identify and mathematically model a problemin business. They will learn to do simple programming in Visual Basic. They will be able to implement a mathematicalalgorithm for solving the problem if appropriate. They will be able to test and evaluate the end product. They will be able todocument the process. The will present their findings as to a directors of a company.They will develop employability skills, and go through the process of applying for a job with a CV and accompanying letter ofapplication.Successful students will complete a project with a supervisor from local business.

Teaching and Learning MethodsVisual basic lectures.Employability skills seminar.Individual supervision.

Assessment Methods20% Busines game10% Visual basic skills30% Written project report30% project presentation10% problem statement

Pre-RequisitesTwo years UG maths

Co-Requisites






Supervised time in studio/workshopWork Based Learning 20




MA3513 Mathematics Business Project




001 Coursework 100 0

Period: Semester 2Occurence: ACoordinator: Alexander GorbanMark Scheme: UG Pass for Credit


LecturesSeminars






Total Module Hours


MA3521 Computational Mathematics Project




001 Continuous assessment 100 0

Period: Academic YearOccurence: ACoordinator: Jeremy LevesleyMark Scheme: UG Honours Level


Intended Learning OutcomesTo manage other students in delivering a project.Do take part in a business game.To experience some components of setting up a business of their own.To develop IT skills relevent to the commercial world.Pursue a course of self-study with guidance from a member of staff.Write a structured project report on a computational mathematical topic.Receive instruction on making a formal oral presentation.Give an oral and visual presentation to a group of peers and staff.

Teaching and Learning MethodsStudents will be able to identify and mathematically model the business problem. They will be able to implement amathematical algorithm for solving the problem if appropriate.They will be able to test and evaluate the end product. They will be able to document the process.

Assessment MethodsOral presentation.Written presentation.IT product.Teamwork.Business gameBusiness plan

Pre-Requisites2 years UG maths

Co-Requisitesnone

Excluded Combinations-Cannot be taken with MA3562

LecturesSeminars








MA3561 Mathematics With Management Project





Period: Academic YearOccurence: ACoordinator: Jeremy LevesleyMark Scheme: UG Honours Level


Intended Learning OutcomesTo manage other students in delivering a project.Do take part in a business game.To experience some components of setting up a business of their own.To develop IT skills relevent to the commercial world.Pursue a course of self-study with guidance from a member of staff.Write a structured project report on a computational mathematical topic.Receive instruction on making a formal oral presentation.Give an oral and visual presentation to a group of peers and staff.

Teaching and Learning MethodsStudents will be able to identify and mathematically model the business problem. They will be able to implement amathematical lgorithm for solving the problem if appropriate.They will be able to test and evaluate the end product. They will be able to document the process.

Assessment MethodsOral presentation.Written presentation.IT product.Teamwork.Business planBusiness game

Pre-Requisites2 years UG maths

Co-Requisitesnone

Excluded Combinations-Cannnot be taken with MA3561

LecturesSeminars








MA3562 Mathematics With Management Project




001 Oral Presentation 30002 Written report and documented software 70



Intended Learning OutcomesStudents will be able to identify and mathematically model diverse problems in finance and economics. They will be able toimplement a mathematical algorithm for solving the problem if appropriate. They will be able to test and evaluate the endproduct. They will be able to document the process. Students will also receive training in Visual Basic for Applications whichthey will then use to implement numerical methods relevant to their project.

Teaching and Learning MethodsStudents will be able to identify and mathematically model the business problem including a numerical component. They willbe able to implement a mathematical algorithm for solving the problem using their VBA training. They will be able to test andevaluate the end product. They will be able to document the process.

Assessment MethodsBusiness GameVisual Basic SkillsWritten project reportProject presentationProblem statement

Pre-Requisites

Co-Requisites


LecturesSeminars








MA3580 Financial Mathematics Project




001 Oral presentation 30002 Written report and documented software 70



Intended Learning OutcomesStudents will be able to identify and mathematically model diverse problems in finance and economics. They will be able toimplement a mathematical algorithm for solving the problem if appropriate. They will be able to test and evaluate the endproduct. They will be able to document the process. Students will also receive training in Visual Basic for Applications whichthey will then use to implement numerical methods relevant to their project."

Teaching and Learning MethodsStudents will be able to identify and mathematically model the business problem including a numerical component. They willbe able to implement a mathematical algorithm for solving the problem using their VBA training. They will be able to test andevaluate the end product. They will be able to document the process."

Assessment MethodsBusiness GameVisual Basic SkillsWritten Project ReportProject presentationProblem Statement

Pre-Requisites

Co-Requisitesnone


LecturesSeminars








MA3581 Financial Mathematics Project




001 Presentation (final) 60 0002 Coursework 40



Intended Learning OutcomesRead and assess his own understanding of a topic in basic Functional Analysis Develop reporting and presentation skills of mathematical topics

Teaching and Learning MethodsReadings, group work, students presentations through supervision.

Assessment MethodsOral presentations and problem sheets, essay writing and oral examination

Pre-RequisitesThis module is only available to third year students on MMath degrees

Co-Requisitesnone

Excluded Combinations-Students may not take both MA3701 and MA3702. Third year M.Math. students must take one of MA3701 or MA3702.

Lectures 20Seminars








MA3701 Readings in Mathematics 1




001 Coursework 40002 Oral examination (Final) 60



Intended Learning Outcomes1. Read and assess his own understanding of a topic in Special Realativity 2. Develop reporting and presentation skills of mathematical topics

Teaching and Learning MethodsReadings, group work, students presentations through supervision.

Assessment MethodsOral presentations and problem sheets, essay writing and oral examination

Pre-RequisitesThis module is only available to third year students on MMath degrees

Co-Requisitesnone

Excluded Combinations-Students may not take both MA3701 and MA3702. Third year M.Math.students must take one of MA3701 or MA3702.

Lectures 20Seminars








MA3702 Readings in Mathematics 2




001 Computer Practicals 20002 Examination (Final) 80 2003 Exam 100 2 Y

Period: Semester 2Occurence: ACoordinator: Andrea CangianiMark Scheme: UG Pass for Credit


Intended Learning Outcomes"Students will understand the basics from mathematical physics, including the knowledge of many classical PDEs, derivationof some of them, and their properties. Moreover, they will be familiar with basic concepts and methods from numericalanalysis, such as writing a discretised scheme for a PDE, numerical approximation, eigenvalue problems, and consistency,stability, and convergence analysis, focusing on finite element methods. Finally, students will be able to implement thesenumerical methods in MATLAB.

Teaching and Learning MethodsClass sessions/lectures, computer labs and problem classes.

Assessment MethodsThe coursework will consist of regularly assigned exercise sheets, including problem sets and computer assignments. Asubstantial amount of individual work will be required for a student to grasp thetheoretical material (problem sets) and to get enough computational practice (computer exercises) to be able to solve PDEsnumerically. The June examination will have 5 questions, and it will be possible toobtain a full mark by answering any 4 of them correctly.

Pre-RequisitesODEs, calculus and MATLAB

Co-Requisitesnone


Lectures 31Seminars








MA4011 Finite Element Theory and Applications




001 Examination (Final) 50 2002 Coursework 20003 Computational Tasks 30004 Exam 100 3 Y

Period: Semester 2Occurence: ACoordinator: Alexander GorbanMark Scheme: UG Pass for Credit


001 Examination (Final) 50 2002 Coursework 20003 Computational Tasks 30004 Exam 100 3 Y

Period: Semester 2Occurence: ECoordinator: Alexander GorbanMark Scheme: UG Pass for Credit


Intended Learning OutcomesRepresent the structure of the data mining process and explain the basic notions and operation:data preprocessing, datacleaning. dimensionality reduction, binning, sampling, supervisind and unsupervising learning, classification, clustering,regression, probability distribution estimation, entropy, information, information gain, independence and conditionalindependence, time series, stationary time series (in strong and in weak sense).Analyze a data mining problem, recognize its type and select the adequate approach to solution, from evaluation and cleaningof the dataset to selection of the algorithms for data analysis. Analyze and validate the results.Apply the basic methods and algorithms to data analysis, in particular: for classification kNN and Decision tree algorithms, forclustering k-means, hierarchical clustering and density based algorithms, for prediction multivariate regression (linearregression and the kernel trick), for probability distribution estimation Bayes networks, for dimension reduction principalcomponent analysis, for time series use the basic models( white noise, random walk, moving average processes,autoregressive processes, integrated and ARIMA processes), apply mean filter and median filter, analyze trend and performsegmentation. Construct basic neural networks for data analysis (Hopfield, Kohonen, cascade correlation and back-propagation of errors).

Teaching and Learning MethodsLectures, problem classes, computer practicals.

Assessment MethodsMarked fortnightly work, computer logs, written examination.









MA4022 Data Mining and Neural Networks




Co-Requisites


MA4022 Data Mining and Neural Networks




001 Examination (Final) 90 3002 Class test 10003 Exam 100 3 Y

Period: Semester 1Occurence: ACoordinator: Sergei PetrovskiyMark Scheme: UG Pass for Credit


Intended Learning OutcomesThe student is required to demonstrate knowledge of the main principles of model building and analysis in population biologyand ecology.

Teaching and Learning MethodsLectures, seminars.

Assessment MethodsContinuous assessment is achieved through regular assessment of the student’s work at problem classes. Summativeassessment is also based on the results of written examination


Co-Requisites










MA4061 Topics in Mathematical Biology





Period: Semester 2Occurence: ACoordinator: Sergey UtevMark Scheme: UG Pass for Credit



Period: Semester 2Occurence: ECoordinator: Sergey UtevMark Scheme: UG Pass for Credit


Intended Learning OutcomesBy the end of this module a student should be able to define the main concepts of financial market instruments; the studentshould be able to apply the martingale technique and stochastic analysis to option pricing."

Teaching and Learning MethodsLectures, example classes, problem classes.

Assessment MethodsThe final assessment of this module will consist of 100% from a three hour examination.


Co-Requisites

Excluded Combinations-Only available to MMath degree Year 4 students only









MA4072 Financial Mathematics II




001 Examination (Final) 90 3002 Programming Test 10003 Exam 100 3 Y

Period: Semester 2Occurence: ACoordinator: Sergei LevendorskiyMark Scheme: UG Pass for Credit


Intended Learning OutcomesBy the end of the course students should have a general understanding of the language, concepts, main objects and groupsof methods for pricing contingent claims (derivatives) of various kind, including equity derivatives, interest rate derivatives,credit risk derivatives, commodity derivatives, which will allow them understand new developments in the rapidly changingand expanding huge field worth several hundred trillion dollars, develop new variations and write corresponding programs.

Teaching and Learning MethodsLectures and problem classes

Assessment MethodsThe final assessment of this module will consist of 10% from test of programming skills in applications to finance and 90%from a three hour examination during the May-June exam period. The examination paper will contain 4 questions with fullmarks on the paper obtainable from 4 complete answers"

Pre-RequisitesMA1061, MA1152, MA2021 or MA2022, MA3121

Co-Requisites

Excluded Combinations-Only open to MMath 4th years.









MA4078 Advanced Methods in Derivative Pricing




001 Exam 90 3002 Group Project 10 3003 Exam 100 3 Y



Intended Learning OutcomesStudents will learn core materials in representation theory based on the representation theory of finite groups. They will obtaina working knowledge of the subject, based on a group characters and construct character tables for smaller groups. Aparticular emphasis will be on the symmetric group. The students will be able to connnect the representation theory of finitegroups to applications in other disciplines such as chemistry. In guided group projects, students will select topics of the courseto present. This will be focused on character tables and applications of the representation theory to other mathematicalsubjects suc as dynamics or combinatorics and to other disciplines such as chemistry or physics.

Teaching and Learning Methods30 hours of lectures with unassessed problem sheets and assignments. 12 problem or revision classes. Poster presentations.

Assessment Methods2 hour exam and assessed group project poster.

Pre-Requisites

Co-Requisites


Lectures 30Seminars








MA4142 Representation Theory of Finite Groups




001 COURSEWORK 80002 Presentation 20



Intended Learning OutcomesAfter finishing this module a student should have working knowledge of the notion of a differentiable manifold, includingvarious advanced concepts and methods of mutivariable calculus, such as the implicit function theorem and, inverse functiontheorem, various examples of manifoldsassociated with matrix groups and their homogeneous spaces. Among morespecialized topics are: integration on manifolds, Stokes' theorem and the de Rham cohomology, including the calculation ofde Rham cohomology of spheres, homogeneous spaces and homotopy invariance of the de Rham cohomology.

Teaching and Learning MethodsLectures and problem classes.

Assessment MethodsCoursework and presentations.

Pre-Requisites

Co-Requisites










MA4143 GEOMETRY AND TOPOLOGY




001 Exam 90 2002 Group Project 10003 Exam 100 2 Y



Intended Learning OutcomesStudents will learn core material in homotopy theory, identifying and distinguishing global, topological phenomena in a varietyof mathematical systems, and will obtain a working knowledge of some of the classical tools for analysing and utlising suckinformation. In guided group projects, students will slect, work through in detail, and present examples if important current ofclassical applications of homotopy theory in a variety of possible areas of mathematics and related disciplines, such asgeometry, algebra, dynamics, data analysis, economics or biology.

Teaching and Learning Methods30 hours of lectures with unassessed problem sheets and assignments. 12 problem or revision classes. Guided group work inprojects.

Assessment Methods2 hour exam and group project work assessed by presentation and written report.

Pre-Requisites

Co-Requisites




FieldworkProject Supervision 2






MA4144 Topology and its Applications




001 Examination (Final) 50 3002 Test 50



Intended Learning OutcomesTo enable student to: Understand and define the Galois Group of a field extension and the Galois group of a polynomial.Understand and prove the Galois correspondence, including the relationship between normal subject structure of the Galoisgroupd and normality of the intermediate extensions.Understand the definition of a solvable group and be able to determine whether or not a group of reasonable size is solvable.Appreciate the significance of the Galois group of a polynomial as a group of permutations of the roots.Prove that the alternating group of degree at least 5 is simple.Understand the definition of a radical extension and prove that such an extension has a solvable Galois group.Understand that the symmetric group is the Galois group of the general polynomial.Be able to construct polynomials whose Galois group is not solvable.Be able to apply Galois Theory for certain transcendence proofs in Number Theory.

Teaching and Learning MethodsLectures, Problem classes

Assessment Methodswo exams - one take-home during the Easter break and one during the Midsummer Examinations


Co-Requisitesnone










MA4161 Galois Theory










Intended Learning OutcomesThe student will establish the lines of enquiry to be followed and produce a final thesis and presentation on this planned work.

Teaching and Learning MethodsWeekly supervisions and independent study.

Assessment MethodsProject description document, diary, presentation, written thesis.

Pre-Requisites

Co-Requisitesnone

Excluded CombinationsThis module is available only to final year MMath Mathematics with Astronomy students and it may not be taken in the samesemester as PA4970.

LecturesSeminars








MA4501 Mathematics Project





Period: Academic YearOccurence: ACoordinator: Alexander BaranovMark Scheme: UG Pass for Credit


Intended Learning OutcomesThe student will establish the lines of enquiry to be followed and produce an interim report at the end of the first semester,demonstrating both progress to date and a detailed plan of the further steps needed to complete the work. In the secondsemester, the student will complete the project work planned and produce a substantial Mathematics dissertation.

Teaching and Learning MethodsWeekly supervisions and independent study

Assessment MethodsProject description document, diary, presentations, written thesis.

Pre-RequisitesOnly 4th year students on the M.Math. Mathematics and M.Math. Mathematics with Astronomy degreesdegree are allowed to take this module.

Co-Requisites

Excluded Combinations-This module cannot be taken in combination with the 20-credit project MA4501.Mathematics with Astronomy students may not take this module in combination with PA4970.

Lectures 28Seminars








MA4504 Mathematics Project





Period: Semester 1Occurence: ACoordinator: Alexander ClarkMark Scheme: UG Pass for Credit


Intended Learning OutcomesAt the end of this module, typical students should be able to demonstrate knowledge and understanding of the chosen topicstudied in this reading module, and have communicated this through seminar discussions, written work and an oralpresentation.

Teaching and Learning MethodsSeminars, guided reading, problems/project.

Assessment MethodsSeminar, written problems/project, oral examination.

Pre-RequisitesThis module is only available to fourth year M.Math. students as three years of undergraduate mathematics are required.

Co-Requisites

Excluded Combinations- Students may not take both MA4701 and MA4702

LecturesSeminars 22








MA4701 Advanced Readings in Mathematics







Intended Learning OutcomesAt the end of this module, typical students should be able to demonstrate knowledge and understanding of the chosen topicstudied in this reading module, and have communicated this through seminar discussions, written work and an oralpresentation.

Teaching and Learning MethodsSeminars, guided reading, problems/project.

Assessment MethodsSeminar, written problems/project, oral examination.

Pre-RequisitesThis module is only available to fourth year M.Math. students as three years of undergraduate mathematics are required.

Co-Requisites

Excluded Combinations- Students may not take both MA4701 and MA4702

LecturesSeminars 10








MA4702 Advanced Readings in Mathematics


Documents

Module Specification - University of Leicester · 2015-08-03 · At the end of this module, typical students should be able to compute limits of sequences and functions, compute derivatives