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HERIOT-WATT UNIVERSITYDEPARTMENT OF MATHEMATICS

Information Guide for Students for the Session 2000-2001

KEEP FOR FUTURE REFERENCE

Contents

1. Introduction.........................................................................................................................1.1 This Guide......................................................................................................................1.2 Departmental Aims........................................................................................................1.3 Other Sources of Information.........................................................................................

2. General Information............................................................................................................2.1 Lectures and Tutorials....................................................................................................2.2 Teaching, Revision and Exam Weeks.............................................................................2.3 Attendance.....................................................................................................................

3. Departmental Support Structures.........................................................................................3.1 Mentors..........................................................................................................................3.2 Year Directors of Study..................................................................................................3.3 Staff-Student Committee................................................................................................3.4 The Head of Department................................................................................................

4. Communication within the Department...............................................................................4.1 Your Responsibilities.....................................................................................................4.2 How we will contact you................................................................................................4.3 Computing Facilities......................................................................................................

5. Mathematics Degrees and their Modular Structure..............................................................5.1 Mathematics Degrees Offered........................................................................................5.2 The Module System.......................................................................................................5.3 Direct Entry....................................................................................................................5.4 Transfer Between Courses and Modules.........................................................................5.5 Common Assessment and Progression System (CAPS)..................................................5.6 Resitting Modules..........................................................................................................

6. First Year Course Information.............................................................................................6.1 General Information about First Year.............................................................................6.2 First Year Modules.........................................................................................................6.3 First Year Module Summaries........................................................................................6.4 Assessment, Exams and Progress to Year 2....................................................................

7. Second Year Course Information.........................................................................................7.1 General Information about Second Year.........................................................................7.2 Second Year Modules.....................................................................................................7.3 Second Year Module Summaries....................................................................................7.4 Assessment, Exams and Progress to Year 3....................................................................

8. Third Year Course Information...........................................................................................8.1 General Information about Third Year...........................................................................8.2 Third Year Modules.......................................................................................................8.3 Third Year Module Summaries......................................................................................

8.4 Assessment and Exams...................................................................................................9. Fourth Year Course Information..........................................................................................

9.1 General Information about Fourth Year..........................................................................9.2 Fourth Year Courses.......................................................................................................9.3 Examinations..................................................................................................................9.4 Classification of Honours Degrees.................................................................................

10. Staff and How to Contact Them........................................................................................11. Course Structures For All Mathematics Courses................................................................

11.1 B.Sc. in Mathematics (Honours) / General Mathematics (Ordinary).............................11.2 B.Sc. in Mathematics (Hons.) / General Mathematics (Ord.) with Physics...................11.3 B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Economics........................11.4 B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Education..........................11.5 B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Applied Mechanics...........11.6 B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Computer Science.............11.7 B.Sc. in Mathematics (Honours) with a European Language........................................11.8 B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Statistics...........................11.9 B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Finance.............................

12. Appendix A : Other course options....................................................................................

1 INTRODUCTION 3

1Introduction

1.1This GuideThese notes have been prepared primarily for the guidance of students in the Department of Mathematics. The guide provides an outline of courses taught by the Department and gives a summary of University and Departmental regulations. While we try to make this guide as accurate as possible, you should note that the detailed University and Department regulations take precedence over this guide.

1.2Departmental AimsThe Department of Mathematics has a very broad mission in the University, comprising undergraduate education for mathematics students, service mathematics education, research and graduate education, and various outreach programmes. Each year, over one thousand students study a course taught by the Mathematics Department.

The goals of the Department of Mathematics are to deliver the highest quality teaching of mathematics to all students who take classes in mathematics, and, through its research, to contribute to the advancement of mathematics and its applications. In the recent teaching assessment in Scotland we were rated “highly satisfactory” (the second highest rating) while in the UK Research Assessment Exercise we were rated “5”, the top grade for Applied Mathematics in Scotland.

For our mathematics students, the aim of the curriculum is to ensure that our graduates have a sound knowledge of mathematics so that they can successfully pursue careers in industry, commerce, education and scientific research.

We offer honours and ordinary degrees in mathematics and also in mathematics combined with a variety of subjects. These subjects are currently: statistics, physics, economics, education, applied mechanics, computer science, European language, finance. More details are given below in Section 5.1.

1.3Other Sources of InformationFurther information is available in: General Information for First Degree Students which contains a summary of relevant University regulations. All students are given a copy of this booklet as part of the registration process. Information on modules and on course structure is also available on the WWW.

2 GENERAL INFORMATION 4

2General Information

2.1Lectures and TutorialsClasses in mathematics are either lectures or tutorials. A lecture consists mainly of listening, understanding and making notes of the topics being taught. Tutorials will give you an opportunity to ask questions about material which you have not understood and to find out how to solve problems which you were unable to do in the examples sheets which are given at lectures.

Classes begin at 9.20 a.m., 10.20 a.m. etc and are scheduled so that students can change rooms if necessary for the start of the next class.

If you have problems after reading your notes and attempting the tutorial examples, please ask for help. You should do this at the tutorial classes or by going to see the lecturer teaching the course. To avoid fruitless searches, you can make an appointment at the end of a lecture or a tutorial. Lecturers can also be contacted via the secretary, Ms I Fraser, in the Departmental Office, M3.19A or by e-mail. (addresses in Section 10)

2.2Teaching, Revision and Exam WeeksThe academic year consists of 30 weeks divided into three 10-week terms. Each term students study four modules. In the first and second year there will normally be eight weeks teaching followed by one week of revision with an examination in the last week of term. Some courses (e.g. Languages) have opted for one examination at the end of the academic year. For such courses, a student can opt to exit the module at the end of any term in which case an end of term examination will be set so that the appropriate credit can be obtained. A student wishing to do this should notify their Mentor by week 7 of the module.

For third year mathematics modules, there are examinations in December and June. For fourth year mathematics modules, all examinations are held in June.

Detailed exam timetables are posted on the departmental notice board and on the main University notice board in the entrance complex.

2.3AttendanceIn order to satisfy the course requirements in each module, a satisfactory record of attendance at lectures and tutorials is required and course work must be handed in by the stipulated dates. Students who, in the opinion of the Head of Department, fail to satisfy these requirements for any of the modules for which they are registered may, after due warning, be disallowed from presenting themselves for examination in those modules. In this case they will be deemed to have failed those modules.

Students with medical and other problems which cause them to miss classes for more than a few days, or which are likely to affect their exam performance should inform their mentor as soon as possible. Self certification is required for periods of incapacity from work of four days or less, and a doctor's certificate is required for longer periods. Doctor's certificates are essential when illness causes absence from examinations or difficulties with continuous assessment.

Self certification forms should be collected from the Departmental Office. Self and Doctor's Certificates should be submitted to the Departmental Office, room M3.19A.

3 DEPARTMENTAL SUPPORT STRUCTURES 5

3Departmental Support Structures

3.1MentorsYou will be allocated a mentor when you arrive in the University and, normally, you will retain the same mentor while you are registered in the Department. The mentor/student relationship serves various functions:

At the beginning of the session you register for courses and choose classes with the help of your mentor and at the same time, you also provide personal information such as term and home addresses and telephone numbers. Your mentor should be informed of any changes to your chosen course or in your personal information so that our records can be kept up to date.

Your mentor is usually the person in the department who knows you and your work best and so is well placed to provide job (and other) references when the time comes.

If you have personal problems the mentor can often help with a sympathetic chat or by putting you in touch with the appropriate University support service (Medical Centre, Accommodation and Welfare, Students Union or Chaplaincy).

It is important that you see your mentor regularly. We have a Departmental requirement that students should see their mentors at the start of each term but more frequent meetings are often appropriate. These meetings serve two purposes. They enable the Department to keep an eye on how you are doing and, just as important, they allow the personal side of the mentor/student relationship to develop. These meetings are particularly important in first year. The mentor is there to help you - do not hesitate to contact him or her if you need help. (See Section10.) If you have any difficulty contacting your mentor, Ms I Fraser, in the Departmental Office M3.19A will be pleased to arrange an appointment.

3.2Year Directors of StudyFor each of the four years of study the department has appointed a Year Director of Studies whose has the responsibility of ensuring the overall smooth functioning of that year. The directors of study will take an overview of all the material taught to the year, should be aware of difficulties which are occurring in any of the courses, will arrange that continual assessment is carried out in an appropriate manner and will deal with the collation of examination marks.

Name Room Telephone0131-451-

e-mailZ=ma.hw.ac.uk

1st Year Director of Studies Dr G.R. McGuire 2.04 -3235 G.R.Mcguire@Z

2nd Year Director of Studies Dr B.P. Rynne 1.01 -3243 B.P.Rynne@Z3rd Year Director of Studies Dr A.R. Prince 2.07 -3232 A.R.Prince@Z4th Year Director of Studies Dr D.B. Duncan 2.09 -3244 D.B.Duncan@Z

3.3Staff-Student CommitteeThe Staff-Student Committee is a forum for notification and discussion of various issues affecting undergraduate courses and provides valuable feedback to the Department. Typical issues raised include organisational problems encountered by students (e.g. too many tutors in some tutorials and not enough in others) and discussion of proposed changes in course structures. It is composed of two student and one staff representative for each year of the mathematics course. Directors of Studies represent the staff and the student representatives

3 DEPARTMENTAL SUPPORT STRUCTURES 6

are elected by the class. You will be asked to select representatives for this committee early in the first term. The committee meets once each term. Details of the discussion at this Committee are posted along with the other departmental notices on the notice board on the second floor of the Mathematics Building.

3.4The Head of DepartmentWe hope that all your problems both personal and academic can be resolved with the help of mentors, year directors of study and the staff-student committee. If, however, for any reason you find that you cannot resolve a difficulty by these means you should consult with the Head of Department, Professor Ken Brown.

4 COMMUNICATION WITHIN THE DEPARTMENT 7

4Communication within the Department

4.1Your Responsibilities So that we can communicate easily with you and so that we can make sure that you are appropriately registered for modules and examinations it is necessary that you : (i) notify your mentor about any changes in address or telephone number (ii) notify your mentor of any change of course or elective (in fact s/he must arrange for a form to be completed to authorize such a change) (iii) around week 3 of each term check the list of modules for which you are registered - you will be provided with such a list and failure to report any errors on the list can lead to a £10 fine by our central administration. (iv) keep your mentor informed about any illnesses or other problems.

4.2How we will contact you If we have to contact you during term time we will use e-mail and/or the student mail boxes on the second floor of the Mathematics Department. These mail boxes are also used for mail delivered to students c/o the department.

In some circumstances we will also use your term-time address. In emergencies we will use e-mail and/or telephone. Outside term time, we will write to your home address.

As noted in Section 4.1, it is important to let us know of any changes to your term and/or home addresses as soon as possible.

Details of how to contact us by phone, fax, letter and e-mail are given in Section 10.

4.3Computing FacilitiesAll students are issued with accounts on the PC Caledonia network. Word-processing, the Minitab for Windows statistics package and spreadsheet facilities are available on the Caledonia network. Computer lab sessions are held in the CALM lab (G13), which is also open for student use when lab sessions are not in progress. The Learning Skills manual, given to all new students, includes details of how to access PC Caledonia and the use of e-mail.

You are expected to check your e-mail regularly (at least once a week). General announcements from lecturers and specific announcements from mentors will be sent to you by e-mail, and you are responsible for keeping up to date with them.

Students are expected to use the computing facilities in an appropriate and considerate way. Abuse of the facilities is subject to various disciplinary measures, ranging from a ban on access to the facilities to, in extreme and flagrant cases, expulsion from the university. Examples of abuse include monopolizing a terminal for non-academic related purposes, running excessively long or inappropriate print jobs, and displaying circulating or printing offensive material on or from the Internet. Computer games and relay chat are specifically forbidden. Further information on University policy regarding the abuse of computing facilities is available from the Computing Centre.

5 MATHEMATICS DEGREES AND THEIR MODULAR STRUCTURE 8

5Mathematics Degrees and their Modular Structure

5.1Mathematics Degrees OfferedA full listing of the mathematics degrees on offer is given here. Where “n” appears in the Code, it should be replaced by the year of study. For example, the code for the 2nd year of the Honours Mathematics with Education degree is 11.261 and for the 4th year it is 11.461.

Honours DegreesCode Title11.n11 Degree of B.Sc. in Mathematics11.n41 Degree of B.Sc. in Mathematics with Physics11.n51 Degree of B.Sc. in Mathematics with Economics11.n61 Degree of B.Sc. in Mathematics with Education11.n71 Degree of B.Sc. in Mathematics with Applied Mechanics11.n81 Degree of B.Sc. in Mathematics with Computer Science11.n91 Degree of B.Sc. in Mathematics with a European Language11.nA1 Degree of B.Sc. in Mathematics with Statistics11.nB1 Degree of B.Sc. in Mathematics with Finance

Replace “n” in the Code by the year of study.

Ordinary DegreesCode Title11.n12 Degree of B.Sc. in General Mathematics11.n42 Degree of B.Sc. in General Mathematics with Physics11.n52 Degree of B.Sc. in General Mathematics with Economics11.n62 Degree of B.Sc. in General Mathematics with Education11.n72 Degree of B.Sc. in General Mathematics with Applied Mechanics11.n82 Degree of B.Sc. in General Mathematics with Computer Science11.nA2 Degree of B.Sc. in General Mathematics with Statistics11.nB2 Degree of B.Sc. in General Mathematics with Finance

Replace “n” in the Code by the year of study.

Study for an honours degree normally takes four years and for an ordinary degree three years. Honours degrees are classified into 1st class, upper second (2.1), lower second (2.2) and third class. An ordinary degree may be awarded at the end of the fourth year of the honours degree if the average mark is below 40% (see Section 9.4). The general structure of each year of the courses is outlined in Sections 6-9 of this guide.

5.2The Module SystemA credit-based modular system is the common structure of degree courses offered by the University. Normally students study 4 modules per term giving a total of 12 modules per year.

This system has a number of advantages for students. Each module is of equal length so that we can ensure that all students have a reasonable workload. Credit transfers between institutions is easier since many universities now operate a modular scheme. By having shorter courses, students are examined on smaller amounts of material more frequently, thus giving them a better indication of how they are progressing. For some


degrees, modules increase the flexibility of course choice and enables alternative choices to be made earlier.

The assessment may be by written examination or by continuous assessment or by a mixture of the two methods. Further information on assessment methods can be found in the year sections in this booklet.

The University requirements for the number of modules passed for the award of an ordinary or honours degree are given below. In the terms used in the University regulations, the Degree of B.Sc. in Mathematics is subject to the requirements for a specialist departmental degree; all other degrees are subject to the requirements for a core degree.

Degree OrdinaryCore Degree

Honours B.Sc.in Maths with X

Honours B.Sc. in Maths

Normal Study Period 3 years 4 years 4 yearsModules taken 36 48 48

Module passes required 32 44 46

5.3Direct EntryStudents who come directly into the second or third year of the degree course are credited with module passes for the time they have missed.

5.4Transfer Between Courses and ModulesIf you want to change any of the modules for which you are registered, then see your mentor or the year Director of Studies.

Transfer between the various degree courses is possible under certain circumstances; for example, at the beginning of the second and third years, students studying one of the joint degrees may switch to the Degree of B.Sc. in Mathematics. At some stages in your course it might also be possible to transfer to the Department of Combined Studies to study a broader range of subjects.

5.5Common Assessment and Progression System (CAPS)Assessment at Heriot-Watt is based on the CAPS (Common Assessment and Progression System). Traditionally we used a % based system with a pass-mark set at 40%. In CAPS your exam result for each module will be presented in the form of a letter grade (A - F) where

A= approximately 70% - 100%B = approximately 60% - 70%C = approximately 50% - 60%D= approximately 40% - 50%

An ‘E’ grade will indicate a mark of somewhat less than 40% and is awarded when you have done enough to be given credit points in the subject but you have not done enough to be allowed to study the same topic at a higher level. Thus an ‘E’ should be considered as a rather unsatisfactory pass; an ‘F’ indicates a fail for which no credit points are given towards your degree. In general in order to be allowed to proceed to the next year of an Honours course you will need to obtain passes in all modules with at least 9 of these passes at ‘D’ or better. It should be stressed, however, that 9 D’s and 3 E’s is very much the minimal level acceptable. If you hope to flourish in the later years of an Honours course you should be aiming for ‘C’ passes or better in all modules in earlier years.


More details about progression are given in the information about the various years later in this guide

5.6Resitting ModulesIf you do not pass a module at the first attempt you are entitled to a further attempt in late August at the diet of resit exams. Note that there are no resits in exams in years 3 and 4 which count towards the classification of your Honours degree; also continuous assessment work carried out during the original course is not counted in the resit mark.

If you fail modules (or do not obtain a sufficient number of D passes ) in earlier years, success in resit examinations is vital for progress. You must be available for such examinations,

i.e., IF YOU DO NOT PERFORM SUFFICIENTLY WELL IN EXAMINATIONS DURING THE YEAR, DO NOT BOOK HOLIDAYS OR ASSUME WORK COMMITMENTS DURING THE RESIT PERIOD.

6 FIRST YEAR COURSE INFORMATION 11

6First Year Course Information

6.1General Information about First YearDirector of Studies: Dr G.R. McGuire, Room 2.04

Each term you have to study 4 modules (making a total of 12 modules in the year), two of which will be mathematics courses, one a statistics course and the other class given by one of the other departments.

The two streams of modules in mathematics, algebra and calculus, start a deeper study of two familiar areas of mathematics which will be continued and extended in subsequent years. In the statistics module stream the first module introduces probability theory and the second introduces data analysis and also associated computing, IT and report writing skills.

6.2First Year Modules

Term Module No. Title Lecturer1 11.1MA1

11.1MB117.1YA1

Algebra 1Calculus 1Statistics 1Option/Joint Degree Subject

N.D. GilbertG.R. McGuireD. Mollison

2 11.1MC211.1MD217.1YB2

Algebra 2Calculus 2Statistics 2Option/Joint Degree Subject

R.J. SzaboM.A. YoungsonS. Zachary

3 11.1ME311.1MF317.1YC3

Algebra 3Math. ModellingStatistics 3Option/Joint Degree Subject

N.D. GilbertJ. KristensenJ. Hansen

Notes

· For some degrees the modules that you take are fixed. e.g. For the Mathematics with Physics degree, the joint degree subject in the table above would normally be Physics.

· Other courses such as the Mathematics Degree allow students to choose from a number of options. Students who need to choose three optional modules should pick them from the same group e.g. Moral and Social Philosophy (32.1MS1, 32.1MT2, 32.1MU3). It may be possible to switch options at the end of the first or second term but the choice then is likely to be restricted.


6.3First Year Module SummariesA brief outline for each of these mathematics and statistics modules is given below; a detailed syllabus for each module together with information about textbooks you may wish to read or buy will be handed out at the start of the term in which the module is given.

TERM 1

Algebra 1. Sets and functions, binomial expansion, complex numbers, solution of recurrence relations.

Calculus 1. Limits, differential calculus, applications.

Statistics 1. Probability Theory: Sample spaces and events, conditional probability, independence of events, discrete random variables, expectations and distributions, joint distributions.

TERM 2

Algebra 2. Algebra of linear systems, matrices, determinants, vectors.

Calculus 2. Integration, solution of first order differential equations, applications.

Statistics 2. Data Analysis: Descriptive, exploratory and graphical techniques for the analysis of data, introduction to appropriate statistical analysis packages.

TERM 3

Algebra 3. Mathematical reasoning and proof, introduction to algebraic structures.

Mathematical Modelling. Solution of second order differential equations, modelling, introduction to mechanics.

Statistics 3. An introduction to the statistics of inference; introduction to computer algebra using MAPLE


6.4Assessment, Exams and Progress to Year 2· All mathematics and statistics modules (except Statistics 2) are structured similarly; 8

weeks of teaching (7 in term 3) is followed by one week of revision, followed by an exam week (2 weeks in term 3). The assessment for Statistics 2 is project based.

· All first year mathematics modules have a two hour examination at the end of the term in which they are taught.

· In general, students passing all 12 modules with 9 passes at ‘D’ or better (at first attempt or at resit) proceed to second year of an Honours course. In addition ‘D’ passes must be obtained to satisfy the prerequisites for the modules you intend to study in year 2. In mathematics and statistics this is quite a minor restriction - all that is required is a ‘D’ pass in one algebra module, in one calculus/mathematical modelling module and in one statistics module. In other subjects studied by students on joint degrees there may be more stringent prerequisite requirements.

· Students on the General Mathematics and General Mathematics with Another Subject degrees need to pass at least 10 modules out of 12 with 6 passes at ‘D’ or better (at first attempt or at resit) and obtain D’s in appropriate prerequisites in order to proceed.

· Students who have not passed the required number of modules will receive advice from the First Year Director of Studies.

7 SECOND YEAR COURSE INFORMATION 14

7Second Year Course Information

7.1General Information about Second YearDirector of Studies: Dr B.P. Rynne, Room 1.01

Each term you must study four modules. In the first term three of these modules are mathematics modules and the other will be given by another department. If you are on a joint degree this module will be in the appropriate subject area but otherwise you may choose from a list of electives. In the latter case it is important that you take the elective module very seriously; failure in it will lead to a resit examination in August before you are allowed into Honours Mathematics in Year 3 even if you have done well in all your mathematical modules.

In each of terms two and three again three mathematics modules are available as well as modules in statistics and modules linked to particular joint degrees.

Three main themes occur in the mathematics modules. Firstly your knowledge of calculus will be extended by studying functions of several variables in term 1 and by courses in real analysis in terms 2 and 3 in which you will consider in much greater depth than before the basic concepts of calculus. Secondly there are two modules on algebra; in term 1 a module on linear algebra in which you will learn more about matrices and systems of equations and in term 3 a course on abstract algebra where you will learn more about group theory. In term 2 there is a course on computer assisted mathematics. Finally there are three modules on applied mathematics. In term 1 a module on mathematical methods introduces the various (mainly vector) tools needed for modules in mechanics in terms 2 and 3.

Two Statistics modules are on offer in term 3. Most students will probably choose to study the module 17.2XB3 (Statistics for the Environment). If you wish to study statistics in more depth you must choose module 17.2SE3 (Statistics 5) as this is a prerequisite for more advanced statistics courses; otherwise you may choose to study the module 17.2XB3 (Statistics for the Environment).

7.2Second Year ModulesThe following mathematics modules are available to mathematics students in second year. Individual module choices vary with the degree you have chosen to follow. See notes above and below for more details.

Term Module No. Title Lecturer1 11.2MG1

11.2MH111.2MJ1

Advanced CalculusLinear AlgebraMath. Methods

M.A. YoungsonD.G. WilkinsonB.P. Rynne

2 11.2MK211.2ML211.2MM2

Real Analysis 2Computer Assisted MathsParticle Dynamics

B.P. RynneA.R. WhiteC. Noble

3 11.2MN311.2MP311.2MQ3

Real Analysis 2Abstract AlgebraRigid Body Dynamics

M.A. YoungsonD.E.R. ClarkD.A. Johnston


Notes

· Direct entrants to second year of the BSc in Mathematics course may choose as their term 1 elective module 11.2DE1 ‘Mathematics for Direct Entrants’ aimed at bridging the gap between school and second year mathematics.

· For some joint degree courses not all of the above listed mathematics modules will be taken.

· Statistics modules and those given by other departments and taken by maths students as an option in term 1, or as a joint degree subject are not shown. Consult the course structures guide for your degree course in Section 11 and the guide to elective modules for that information.

7.3Second Year Module SummariesA brief outline for each of these mathematics modules is given below; a detailed syllabus for each module together with information about textbooks you may wish to read or buy will be handed out at the start of the term in which the module is given.

TERM 1

Advanced Calculus. Calculus for functions of several variables, i.e., partial derivatives and multiple integrals.

Linear Algebra. Solution of systems of equations; vector spaces, linear independence, basis; linear transformations; eigenvalues and eigenvectors.

Mathematical Methods. Vector analysis; vector geometry; vector differentiation; line, surface and volume integrals; vector integral theorems.

TERM 2

Real Analysis 1. Introduction to analysis by means of a detailed study of the notion of limit; convergence of sequences; continuity of functions.

Computer Assisted Maths. More advanced use of MAPLE as a computer tool in mathematics; symbolic and numerical calculations; graphical representation. Introduction to the MATLAB numerical analysis, programming and graphics package.

Three Dimensional Particle Dynamics. Newton's laws and their applications: solution of problems in mechanics including damped and undamped simple harmonic motion, projectiles and rocket motion. Statistics 4. Continuous probability theory, i.e., distributions, expectation, variance etc. for continuous random variables; Central Limit Theorem; weak law of large numbers.


TERM 3

Real Analysis 2. Continuation of Real Analysis 1 ; applications of analysis to calculus.

Abstract Algebra. Introduction to abstract algebraic structures; elementary group theory.

Rigid Body Dynamics. Circular and planetary motion; centre of mass, conservation laws, general motion and geometry of a rigid body. Statistics 5. Statistical inference, i.e., theory of the methods of estimation, confidence intervals and statistical testing; Neyman-Pearson Lemma; likelihood ratio tests.

Statistics for the Environment. Statistical inference and regression, design and analysis of environmental studies - case studies.

7.4Assessment, Exams and Progress to Year 3· The Computer Assisted Mathematics module 11.2ML2 is continuously assessed.

· All other second year mathematics modules have a two hour examination at the end of the term in which they are taught. 15% of the final mark will come from work carried out during the term.

· In general, students passing all 12 modules with 9 passes at ‘D’ or better (at first attempt or at resit) proceed to the third year of an Honours course. In addition ‘D’ passes must be obtained to satisfy the prerequisites for the modules you intend to study in year 3. In general in mathematics these prerequisites are not very stringent - D passes in Advanced Calculus and Linear Algebra - would satisfy the requirements for four of the five maths options on offer in year 3. In other subjects studied by students on joint degrees there may be more stringent prerequisite requirements.

· Students on the General Mathematics and General Mathematics with Another Subject degrees need to have passed at least 20 modules in total over their first two years with 6 passes at ‘D’ or better in year 2 (at first attempt or at resit) and obtain D’s in appropriate prerequisites in order to proceed.

· The options for students who have not passed the required number of modules are complicated, and they should contact the 2nd Year Director of Studies.

8 THIRD YEAR COURSE INFORMATION 17

8Third Year Course Information

8.1General Information about Third YearDirector of Studies: Dr. A.R. Prince, Room 2.07

The structure of mathematics modules in year three is different from the previous two years, although you always study 4 modules in each term. In the first term, each module has eight weeks of teaching then one week of revision followed by an exam week. In terms 2 and 3 you study double modules which are assessed by a three hour examination at the end of term 3. As an example, the second term module Algebra and Analysis 1 and the third term module Algebra and Analysis 2 have a single examination at the end of term 3.

It is important to note that the Honours degree assessment is based on examinations held in both the third and fourth years (See Section 9.4 on Degree Classification in this guide for more details). All the mathematics modules in third year count towards the degree assessment with a weighting of 40% on third year results and 60% on fourth year. Students on the Mathematics with a European Language degree spend their third year studying abroad, and so there are special arrangements for them.

8.2Third Year ModulesIndividual module choices vary with the degree you have decided to follow, but the mathematics courses will be chosen from the following modules.

Year 3 Honours Term 1Module No. Title Lecturer

11.3YA1 Complex Analysis M. Levitin11.3YB1 Applied Math. Methods B.J.Schroers11.3YC1 Intro. Numerical J.C. Eilbeck11.3YD1 Number Theory D.E.R.Clark11.3YQ1 Intro. Applied Maths. A.A. Lacey

Year 3 Honours Terms 2 & 3Module No. Title Lecturer

11.3YE2 & 3YK3 Algebra and Analysis 1&2 P.R. Turner11.3YF2 & 3YL3 Mathematical Techniques 1&2 K.J. Brown11.3YG2 & 3YM3 Numerical Analysis 1&2 G.J. Lord11.3YH2 & 3YN3 Discrete Mathematics 1&2 A.R. Prince11.3YJ2 & 3YP3 Applied Mathematics 1&2 A.A. Lacey


Honours DegreesIn general, students on joint degrees take 3 mathematics and one other module each term and those on the B.Sc. in Mathematics Degree take 4 mathematics modules from those which have been listed above. In term 1 the modules in Complex Analysis and Applied Maths Methods are compulsory as are the modules in Algebra and Analysis 1&2 and Mathematical Techniques 1&2 in terms 2 and 3. Ordinary DegreesIndividual module choices vary with the degree you have decided to follow, but the mathematics courses are chosen from those listed above. In general, students take three mathematics modules in term 1, and at least two in terms 2 and 3. Students doing a joint degree have one module per term specified in that subject.

The remaining module slots (recall that you study four per term) give you a chance to broaden your knowledge by studying any course for which you have the entry qualification. These include any of the options available to first and second year students, IT and communications skills courses and history of science. Discuss this choice with the Third Year Director of Studies.

Past experience suggests that the Algebra and Analysis 1&2 and the Applied Mathematics 1&2 modules are the most demanding of the year 3 courses and so students registered for Ordinary Degrees should think carefully before registering for these modules.

8.3Third Year Module SummariesA brief outline for each of these mathematics modules is given below; a detailed syllabus for each module together with information about textbooks you may wish to read or buy will be handed out at the start of the term in which the module is given.

TERM 1

Complex Analysis. Analytic functions, Cauchy Theorem and integral formula, Taylor series, contour integration and the calculus of residues.

Applied Mathematics Methods. Ordinary differential equations with series and Laplace transform solutions, boundary value problems.

Introductory Numerical Analysis. Introduction to MATLAB, numerical solution of equations, numerical integration, errors and computer arithmetic.

Number Theory. Congruences, modular arithmetic, quadratic residues, prime numbers.

Introductory Applied Mathematics. Asymptotic methods for solving algebraic equations, approximate evaluations of integrals and solutions of differential equations, introductory modelling. TERMS 2 and 3

Algebra and Analysis 1 & 2. Analysis : metric spaces, convergence, continuity, compactness, completeness, contraction mapping theorem. Algebra: Rings, integral domains, fields, ideals, unique factorisation domains, Euclidean domains.

Mathematical Techniques 1 & 2. Fourier series, partial differential equations, systems of ordinary differential equations, phase planes.


Numerical Analysis 1 & 2. Numerical linear algebra, advanced numerical integration, interpolation. Practical examples using MATLAB.

Discrete Mathematics 1 & 2. Counting arguments, distribution problems, graph theory.

Applied Mathematics 1 & 2. Modelling, derivation of partial differential equations, elementary fluid dynamics, special methods of solution of PDE and fluids problems.

8.4Assessment and Exams· The third year mathematics courses are examined at the end of term 1 (2 hour exam) and

term 3 (3 hour exam). The term 3 exams cover material taught in terms 2 and 3.

· The final mark for each course includes 15% from work done during the course (20% in the case of Numerical Analysis modules).

· Students are eligible for an Ordinary Core/Joint degree if they pass 32 or more modules out of 36. (recall that there are 12 modules per year) and have attended at least 3 modules outwith the mathematics department in year 3.

· Students who reach the end of third year without 32 module passes out of 36 can resit modules to gain enough passes to obtain an Ordinary degree.

· Students registered for an Honours degree may choose to leave with an Ordinary degree at the end of third year if they have passed sufficiently many modules.

· We review progress of honours degree students after the 1st term exams in third year, and may advise some students to change to the ordinary degree course then. However, failing a module in December does not necessarily mean that you cannot get an Honours degree.

· For honours maths students, all third level modules taken count towards their final degree assessment. (See Section 9.4 for more details.)

· You will be allowed to proceed to the final year of the Honours course if 1. You obtain passes in all year 3 modules and satisfy the prerequisites for all the

modules you will study in year 4. 2. At least 9 of these passes are at ‘D’ or better.3. Your overall average mark is sufficiently good.

· If, at the end of the year you have not passed the required number of modules, please see the Third Year Director of Studies for advice.

9 FOURTH YEAR COURSE INFORMATION 20

9Fourth Year Course Information

9.1General Information about Fourth YearDirector of Studies: Dr D.B. Duncan, Room 2.09

In fourth year we offer a choice from 10 half-year courses: Pure Mathematics 1 and 2, Partial Differential Equations, Optimization, Numerical Analysis 3 and 4, and Special Topics 1, 2 , 4 and 5. Each half-course runs over the full 10 weeks of term 1 or term 2. Students on the degree of BSc in Mathematics also do a supervised project over terms 2 and 3.

With the exception of the project, or in some degrees where a level 3 module or a module from another department is taken in term 3, the third term is left free for revision in preparation for the examinations at the end of term. The module system plays little part in our final year, but, for administrative reasons, each half-course is regarded as a module, and you should register for the appropriate number of ‘revision’ modules in term 3.

9.2Fourth Year Courses

Year 4 Honours Mathematics Half-coursesModule No. Title Lecturer

11.4ZA1 Pure Mathematics 1 (Topology) J. Howie11.4ZB1 Partial Differential Equations J. Kristensen11.4ZC1 Numerical Analysis 3 (Numerical Solution of ODEs) D.B. Duncan11.4ZE1 Special Topics 1 (Functional Analysis) M.A. Youngson11.4ZR1 Special Topics 4 (Mathematical Biology) A.R. White11.4ZF2 Pure Mathematics 2 (Fields and Codes) N.D. Gilbert11.4ZG2 Optimization J. Kristensen11.4ZH2 Numerical Analysis 4 (Numerical Solution of PDEs) C.J. Boulter11.4ZK2 Special Topics 2 (Differential Geometry) B.P. Rynne11.4ZS2 Special Topics 5 (Fractals and Chaos) S. Kuksin

Year 4 Honours Mathematics Revision Modules (Term 3)Module No. Title Revision for

11.4ZL3 Pure Mathematics 3 11.4ZA1/ZF211.4ZM3 PDEs and Optimization 3 11.4ZB1/ZG211.4ZN3 Numerical Analysis 5 11.4ZC1/ZH211.4ZQ3 Special Topics 3 11.4ZE1/ZK211.4ZT3 Special Topics 6 11.4ZR1/ZS2

Course 11.411 (B.Sc. Mathematics)Take four from the above list in term 1, three in term 2, and a project (11.4PA2/11.4PB3). Projects will be allocated during term 1, under the overall supervision of Dr D.B. Duncan. In addition, you should register for three third term revision modules appropriate to your other choices.


Course 11.491 (B.Sc. Mathematics with a European Language)An appropriate combination of level 3 and level 4 modules. A maximum of two 3-module streams at level 3 is permitted.

Course 11.4B1 ( B.Sc. Mathematics with Finance )A stream of three finance modules together with mathematics modules chosen from level 4 modules and the year 3 modules 11.3YD1/YH2/YN3 Number Theory/Discrete Mathematics (see section 8).

All other B.Sc. degrees in Mathematics with an External SubjectThree of the above half-courses in term 1, three in term 2, three revision modules in term 3, and one approved course (or stream of three modules) in the external subject.

9.3ExaminationsEach half-course will have a 2-hour examination paper in June. The paper will contain four questions, of which the candidate is expected to answer three. Each linked pair of half-courses will have a synoptic 3-hour examination in June consisting of the union of the two single module papers (8 questions in all). Candidates will be expected to answer 5 questions with a maximum of 3 from either part. The module code for the synoptic examination will be that of the appropriate third term revision module. All three examinations will start simultaneously.

Thus, for example, a candidate taking both Special Topics 4 and Special Topics 5 will sit a 3-hour examination called 11.4ZT3 Special Topics 6, while a candidate taking only one of these will sit a 2 hour examination called 11.4ZR1 Special Topics 4 or 11.4ZS2 Special Topics 5.

9.4Classification of Honours Degrees· With the exception of students on the degrees of Mathematics with a European Language

and Mathematics with Finance, the Honours degree assessment is based on examinations held in both the third and fourth years, weighted 60% on the fourth year results and 40% on the third year. The formula is

final mark = (2T+3F)/5 where T and F are the average marks for the third and fourth level

courses. All half-courses taken in fourth year have equal weight, and the project has the same weight as a half-course.

· For Mathematics with Finance, the algorithm is slightly different. The level 1 Economics modules that you take in third year are not qualifying modules, ie they do not count towards your degree classification. The level 3 modules in Number Theory and in Discrete Mathematics that you take in fourth year do count towards your degree classification, but are weighted as third year modules rather than fourth year modules. Thus the formula is

final mark = (8T+9F)/17 where T and F are the average marks over the twelve level 3 modules and the 9 level 4 modules respectively.

· The assessment for the degree of mathematics with a European Language is based entirely on courses taken in the fourth year, together with an oral examination in your European Language, which is taken in October of year 4. The modules taken in fourth year are equally weighted, irrespective of whether they are level 3 or level 4. The oral


examination counts 20% towards the final degree classification. Thus the formula isfinal mark = (O+4F)/5

where O is the oral examination mark and F is the average mark over all modules taken in your final year.

· Assessment is carried out by a board of examiners made up of the Head of Department, external examiners covering Pure Maths, Applied Maths and Numerical Analysis, and the lecturers who taught the courses. The external examiners ensure that degrees awarded are of comparable standard to those given by other universities. The examiners also make sure that a reasonable standard applies to the individual examinations and may occasionally normalise results to achieve this outcome. The table below shows the average marks per paper used by the examiners as a starting point in the degree classification process.

Average Mark Degree Classification³ 70 160-69 2.150-59 2.240-49 3

below 40 Ordinary

· There is no quota system on the number of degrees of different classes awarded. It is not impossible (although highly unlikely) for everyone to get a 1st class degree, and similarly for everyone to get an Ordinary degree.

10 STAFF AND HOW TO CONTACT THEM 23

10Staff and How to Contact Them

Mathematics DepartmentName Room e-mail :

Z=ma.hw.ac.ukProf C E Beevers 2.06 C.E.Beevers@Z

Dr C J Boulter G.06 C.J.Boulter@ZProf K J Brown 3.13 K.J.Brown@Z

Prof J Carr 1.06 J.Carr@ZDr D E R Clark 2.05 D.E.R.Clark@ZDr D B Duncan 2.09 D.B.Duncan@ZProf J C Eilbeck 1.08 J.C.Eilbeck@Z Dr N D Gilbert G.07 N.D.Gilbert@ZDr R N Hills 3.05 R.N.Hills@ZProf J Howie 3.02 J.Howie@Z

Prof D A Johnston G.01 D.A.Johnston@ZDr J Kristensen ME106 J.Kristensen@Z Prof S B Kuksin 2.02 S.B.Kuksin@ZProf A A Lacey 3.03 A.A.Lacey@Z

Dr M Levitin 3.04 M.Levitin@ZDr G J Lord ME107 G.J.Lord@Z

Dr S J Malham 3.10 S.J.Malham@ZDr G R McGuire 2.04 G.R.Mcguire@ZDr L E Nicholas 2.03 L.E.Nicholas@Z

Mrs C Noble G.04 C.Noble@Z Dr K J Painter PC2 K.J.Painter@ZDr A R Prince 2.07 A.R.Prince@Z

Dr H U Rahman 2.08 H.U.Rahman@ZDr B P Rynne 1.01 B.P.Rynne@Z

Dr B J Schroers 3.19B B.J.Schroers@ZProf J A Sherratt 1.09 J.A.Sherratt@Z

Dr R J Szabo 3.19B R.J.Szabo@ZDr P Turner 1.03 P.R.Turner@Z

Dr R A Weston 1.04 R.A. Weston@ZDr A R White G.03 A.R.White@Z

Mr D G Wilkinson HNDr M A Youngson 1.05 M.A.Youngson@Z

Actuarial Mathematicsand Statistics Department

Name RoomDr F Avram ME108Dr S Basu 3.17

Dr A Cairns 3.08Dr T Chan G.05

Dr I D Currie 1.07Dr S Foss

Mr D Forfar G.02Prof G Gibson 3.07Mr R J Gray 2.11Dr J Hansen G.10

Mr A A Korabinski 2.10Prof A S Macdonald 1.10Prof J J McCutcheon 3.09

Prof D Mollison 3.17Mr D Sales HN

Prof H R Waters 1.02Dr A Wiese 3.10

Mr M Willder G.08Dr S Zachary 3.06

ME refers to Mechanical Engineering BuildingHN refers to Hugh Nisbet BuildingPC refers to PortacabinsAll other room numbers refer to the Mathematics Building.

Photographs of staff are displayed at the main stairway on the first floor.

e-mail: An easy way to contact most mathematics staff is by e-mail.

Telephone & Fax: All staff, 0131-451-3221 (0131-451-3249 fax).

Post: Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS.

In Person: Staff can be contacted through their offices or the Departmental Office.

10 STAFF AND HOW TO CONTACT THEM 24

WWW: A great deal of information about the Department of Mathematics, its staff and postgraduate students can be found on the web at http://www.ma.hw.ac.uk/maths.html

11 COURSE STRUCTURES FOR ALL MATHEMATICS COURSES 25

11Course Structures For All Mathematics Courses

11.1B.Sc. in Mathematics (Honours) / General Mathematics (Ordinary)

YEAR 1 (Honours 11.111, Ordinary 11.112)

Students should choose three optional modules from appendix A. These modules should be chosen from the same group e.g. Moral and Social Philosophy (32.1MS1, 32.1MT2, 32.1MU3). It may be possible to switch options at the end of the first or second term but the choice then is likely to be restricted.

TERM 1 TERM 2 TERM 311.1MA1 - ALGEBRA 1sets, functions, complex numbers,recurrence relations

11.1MC2 - ALGEBRA 2linear systems, matrices,determinants, vectors

11.1ME3 - ALGEBRA 3proof by induction,algebraic structures

11.1MB1 - CALCULUS 1limits, differential calculus,applications

11.1MD2 - CALCULUS 2integration,1st order ODE’s,applications

11.1MF3 - MATH. MODELLING2nd order ODE’s, modelling,introductory mechanics

17.1YA1 - STATISTICS 1elementary probability, discrete random variables

17.1YB2 - STATISTICS 2data analysis, IT, use of statistical analysis packages

17.1YC3 - STATISTICS 3statistical inference, hypothesis testing, introduction to MAPLE

OPTION (see appendix A) OPTION (see appendix A) OPTION (see appendix A)


Students taking the ordinary degree choose two or more modules from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 311.2MG1 - ADV. CALCULUScalculus for functions of several variables

11.2MK2 - REAL ANALYSIS 1limits, convergence of sequences,continuity of functions

11.2MN3 - REAL ANALYSIS 2applications of analysis to calculus

11.2MH1 - LINEAR ALGEBRAsystems of equations, vector spaces, eigenvalues/vectors

11.2ML2 - C.A.Madvanced use of MAPLE as a computer tool

11.2MP3 - ABSTRACT ALGEBRAabstract algebraic structures,elementary group theory

11.2MJ1 - MATH. METHODSvector analysis and geometry,surface and volume integrals

11.2MM2 - PTCLE. DYNAMICSNewton’s laws, vectorial methods

11.2MQ3 - RIGID BODY DYN.S

conservation laws and their consequences

OPTION (see appendix A) 17.2SD2 - STATISTICS 4expectations, variance, etc.weak law of large numbers

17.2XB3 - STATISTICS FOR THE ENVIRONMENT* statistical inference, analysis of environmental studies OR17.2SE3 - STATISTICS 5*statistical inference, confidence intervals and statistical testing

(*) course 17.2SE3 is a prerequisite for later statistics courses



Honours degree students must choose the analysis and methods modules plus any two of the other three listed below in each term.Ordinary degree students choose two or more modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options given in appendix A.

TERM 1 TERMS 2 & 311.3YA1 - COMPLEX ANALYSISanalytic functions, Cauchy theorem,Taylor series, contour integration

11.3YE2 & 3YK3 - ALGEBRA AND ANALYSIS 1 & 2metric spaces, convergence, continuity, compactness, etc.rings, integral domains, fields, ideals

11.3YB1 - APPLIED MATH. METHODSsolving ODE’s by series/Laplace transforms

11.3YF2 & 3YL3 - MATHEMATICAL TECHNIQUES 1 & 2Fourier series, PDE’s, systems of ODE’s, phase planes

11.3YC1 - INTRO. NUMERICALnumerical integration, errors

11.3YG2 & 3YM3 - NUMERICAL ANALYSIS 1 & 2numerical linear algebra, advanced numerical integration

11.3YD1 - NUMBER THEORYcongruences, prime numbers

11.3YH2 & 3YN3 - DISCRETE MATHEMATICS 1 & 2counting arguments, distribution problems, graph theory

11.3YQ1 - INTRO. APPLIED MATHSasymptotic methods for solving equations,approximate evaluation of integrals

11.3YJ2 & 3YP3 - APPLIED MATHEMATICS 1 & 2modelling, derivation of PDE’s, elementary fluid dynamics,special methods of solution of PDE and fluid problems

YEAR 4 (Honours 11.411)

Students choose any four modules from term 1 and any three from term 2 plus a project.

TERM 1 TERM 2 TERM 311.4ZA1 - PURE MATHEMATICS 1topology

11.4ZF2 - PURE MATHEMATICS 2fields and codes

REVISION

11.4ZB1 - PARTIAL DIFF. EQUATIONS 11.4ZG2 - OPTIMIZATION REVISION11.4ZC1 - NUMERICAL ANALYSIS 3numerical solution of ODE’s

11.4ZH2 - NUMERICAL ANALYSIS 4numerical solution of PDE’s

REVISION

11.4ZD1 - APPLIED MATHEMATICS 3 11.4ZJ2 - APPLIED MATHEMATICS 4 REVISION11.4ZE1 - SPECIAL TOPICS 1functional analysis

11.4ZK2 - SPECIAL TOPICS 2differential geometry

REVISION

11.4ZR1 - SPECIAL TOPICS 4mathematical biology

11.4ZS2 - SPECIAL TOPICS 5fractals and chaos

REVISION


11.2B.Sc. in Mathematics (Hons.) / General Mathematics (Ord.) with Physics

Course Director : Dr H.U. Rahman, Room 2.08


TERM 1 TERM 2 TERM 313.1SA1 - PHYSICS FOR SCIENTISTS + ENGINEERS 1kinematics, dynamics, vibrations, modern physics, nuclear physics

13.1SB2 - PHYSICS FOR SCIENTISTS + ENGINEERS 2electric and magnetic fields

13.1SC3 - PHYSICS FOR SCIENTISTS + ENGINEERS 3circuits and semiconductor devices

11.1MA1 - ALGEBRA 1sets, functions, complex numbers,recurrence relations










Students taking the ordinary degree choose the physics module plus at least two others from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 313.2AA1 - OPTICS / ELECTROMAGNETISM electro- and magneto-statics, Maxwell’s equations, superposition, interference and diffraction

13.2CA2 - DYNAMICS / ATOMIC PHYSICSharmonic motion, normal modes of motion, 2D dynamics, black body radiation, wave mechanics

13.2FC3 - ENVIRONMENTAL PHYSICSatmospheric physics, energy studies, remote sensing

11.2MG1 - ADV. CALCULUScalculus for functions of several variables












Honours degree students must choose the physics options 13.3MQ1, 13.3MT2 and 13.3NP3. They must further choose the analysis and methods modules plus one other maths module listed below in each term.Ordinary degree students choose a physics module plus at least two further modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A.

TERM 1 TERMS 2 & 313.3MQ1 - QUANTUM THEORY OR13.3QC1 - QUANTUM CONCEPTS

Term 2 : 13.3MT2 QUANTUM THERMODYNAMICS OR 13.3CM2 COMPUTER MODELLINGTerm 3 : 13.3NP3 - NUCLEAR PHYSICS

11.3YA1 - COMPLEX ANALYSISanalytic functions, Cauchy theorem,Taylor series, contour integration











Students should choose the physics module plus any other three listed below in each term.

TERM 1 TERM 2 TERM 313.4AA1 - SOLID STATE PHYSICS / MODERN OPTICS

13.4AJ2 - THEORETICAL PHYSICS REVISION

11.4ZA1 - PURE MATHEMATICS 1topology


REVISION



REVISION



REVISION



REVISION


11.3B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Economics

Course Director : Dr A.R. Prince, Room 2.07


TERM 1 TERM 2 TERM 332.1OA1 - MICROECONOMICS 1resource allocation, supply and demand, cost theory

32.1OB2- MACROECONOMICS 1national income accounting, aggregate demand and supply, multiplier theory

32.1OC3 - INTERNATIONAL ECONOMICSeconomic benefits of international trade, functions of foreign exchange markets











Ordinary degree students choose the economics module plus at least two others from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 332.2AB1 - INTERMEDIATE MICROECONOMICS 1demand theory, theory of market structures, mathematical techniques in economics

32.2AC2 - INTERMEDIATE MICROECONOMICS 2alternative welfare criteria, market failure, mathematics for microeconomic analysis

32.2AD3 - LABOUR ECONOMICSoperation of contemporary labour markets








17.2SD2 - STATISTICS 4expectations, variance, etc.weak law of large numbers

17.2XB3 - STATISTICS FOR THE ENVIRONMENT* statistical inference, analysis of environmental studies OR17.2SE3 - STATISTICS 5*statistical inference, confidence intervals and statistical testing

(*) course 17.2SE3 is a prerequisite for later statistics courses



Honours degree students choose the economics, analysis and methods modules plus one other listed below in each term.Ordinary degree students choose the economics module plus at least two further modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A in consultation with the 3rd year director of studies.

TERM 1 TERMS 2 & 332.3AE1 - INDUSTRIAL ORGANISATION

32.3AF2 & 3AG3 - PUBLIC ECONOMICS (Term 2) AND INTERNATIONAL TRADE (Term 3)












Students choose the economics module plus any other three listed below in each term.

TERM 1 TERM 2 TERM 332.4AH1 – ADVANCED MICROECONOMICS 1

32.4AJ2 - ADVANCED MICROECONOMICS 2

REVISION



REVISION



REVISION



REVISION



REVISION


11.4B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Education

Course Director : Prof K.J. Brown, Room 3.13


TERM 1 TERM 2 TERM 300.1EL1 - EDUCATION 1Life in classrooms, gender, ethnicity, culture and class

00.1EM2 - EDUCATION 2Pupils, teachers ,schools, basic characteristics of British Secondary Education, changing role of teacher

00.1EN3 - EDUCATION 3National Curriculum, children with learning difficulties, the teacher and the law, health education











Students taking the ordinary degree choose the education module plus at least two others from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 3OPTION (see appendix A) 00.2EM2 & 00.2EN3 - EDUCATION 4 &5

Developing basic classroom skills for teaching mathematics, considering general issues on how to become a good teacher













Honours degree students choose the education, analysis and methods modules plus one other listed below in each term.Ordinary degree students choose the education module plus at least two further modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A in consultation with the 3rd year director of studies.

TERM 1 TERMS 2 & 300.3EM1 - EDUCATION 6Classroom management and skills

00.3EN2 & 3EO3 - EDUCATION 7 & 8Pupil support, problem solving in the teaching of mathematics












Students should choose the education project plus any other three listed below in each term.

TERM 1 TERM 2 TERM 300.4EM1 & 00.4EN2 & 00.4EO3 EDUCATION 9,10 &11Education project11.4ZA1 - PURE MATHEMATICS 1topology


REVISION



REVISION



REVISION



REVISION

NOTE : In order to obtain a teaching certificate enabling students to teach in Scotland and England they must spend a further term undergoing a period of teaching practice under the

auspices of Stirling University.


11.5B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Applied Mechanics

Course Director : Dr D.E.R. Clark, Room 2.05


TERM 1 TERM 2 TERM 323.1EA1 – MECHANICAL ENGINEERING SCIENCE 1

23.1EB2 – MECHANICAL ENGINEERING SCIENCE 2

23.1EC3 – MECHANICAL ENGINEERING SCIENCE 3











TERM 1 TERM 2 TERM 323.2EI1 - MECHANICAL ENGINEERING SCIENCE 4A

23.2EJ2 - MECHANICAL ENGINEERING SCIENCE 4B

23.2EL3 - MECHANICAL ENGINEERING SCIENCE 5B


23.2EK2 - MECHANICAL ENGINEERING SCIENCE 5A











Honours degree students choose the engineering, analysis and methods modules in term 1 plus one other module listed below. In terms 2 & 3 students choose the engineering and methods modules plus any other two from the list below.Ordinary degree students choose the engineering module plus at least two further modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A in consultation with the 3rd year director of studies.

TERM 1 TERMS 2 & 323.3EH1 - MECHANICAL ENGINEERING SCIENCE 8

23.3TA2 & 3FA3 - THERMODYNAMICS 1 AND FLUID DYNAMICS 1












Students choose an engineering module plus any other three listed below in each term.

TERM 1 TERM 2 TERM 323.4TB1 - THERMODYNAMICS 2 OR23.4FB1 - FLUID MECHANICS 2

23.4TC2 - THERMODYNAMICS 3 OR23.4FC2 - FLUID DYNAMICS 3

REVISION



REVISION



REVISION



REVISION



REVISION


11.6B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Computer Science

Course Director : Dr D.B. Duncan, Room 2.09


TERM 1 TERM 2 TERM 312.1XA1 - INTRODUCTION TO PROGRAMMING 1

12.1XB2 - INTRODUCTION TO PROGRAMMING 1

12.1XF3 - INTRODUCTION TO SOFTWARE ENGINEERING 1











Students taking the ordinary degree choose the computer science module plus at least two others from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 312.2AA1 -DATA STRUCTURES AND ALGORITHMS

12.2AB2 -DATA STRUCTURES AND ALGORITHMS 2

12.2HD3 - SOFTWARE ENGINEERING 2








11.2MM2 - PTCLE. DYNAMICSNewton’s laws, vectorial methodsOR 17.2SD2 - STATISTICS 4expectations, variance, etc.


conservation laws and consequencesOR 17.2XB3 - STATISTICS FOR THE ENVIRONMENTstatistical inference, analysis of environmental studies



Honours degree students choose the computing, analysis and methods modules plus one other from list below in each term.Ordinary degree students choose the computer science module plus at least two further modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A in consultation with the 3rd year director of studies.

TERM 1 TERMS 2 & 312.3PD1 - PROGRAMMING 3 12.3AF2 & 3AE3 - DATABASE SYSTEMS + COMPUTER

GRAPHICS AND C.A.D (exams at end of each term)11.3YA1 - COMPLEX ANALYSISanalytic functions, Cauchy theorem,Taylor series, contour integration











Students choose the computer science module plus any other three from the list below in each term.

TERM 1 TERM 2 TERM 312.4AU1 - GRAPHICS, ROBOTICS AND VISION 1

12.4AV2 - GRAPHICS, ROBOTICS AND VISION 2

12.4WM3PROJECT



REVISION



REVISION



REVISION



REVISION


11.7B.Sc. in Mathematics (Honours) with a European Language

Course Director : Dr M.A. Youngson, Room 1.05


For students studying French the language options will be 34.2FX1, 34.2FY2 and 34.2FZ3. For students studying German the language options will be 34.1GI1, 34.1GJ2 and 34.1GK3. For students studying Spanish the language options will be 34.1SI1, 34.1SJ2 and 34.1SK3.

TERM 1 TERM 2 TERM 3LANGUAGE(see above)

LANGUAGE(see above)

LANGUAGE(see above)











For students studying French the language options will be 34.3FX1, 34.3FY2 and 34.3FZ3. For students studying German the language options will be 34.2GI1, 34.2GJ2 and 34.2GK3. For students studying Spanish the language options will be 34.2SI1, 34.2SJ2 and 34.2SK3.

TERM 1 TERM 2 TERM 3LANGUAGE(see above)

LANGUAGE(see above)

LANGUAGE(see above)













Students must attain a satisfactory standard in an approved course of study in mathematics in a university whose working language is French, German or Spanish.


Students choose four modules in each term from the list below plus Year 3 modules from the mathematics degree (see earlier). A maximum of two 3-module streams at level 3 is permitted.

TERM 1 TERM 2 TERM 311.4ZA1 - PURE MATHEMATICS 1topology


REVISION

11.4ZB1 - PARTIAL DIFF. EQUATIONS 11.4ZG2 - OPTIMIZATION REVISION11.4ZE1 - SPECIAL TOPICS 1functional analysis


REVISION



REVISION


11.8B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Statistics

Course Director : Dr M. Levitin, Room 3.04

YEAR 1 (Honours 11.1A1, Ordinary 11.1A2)

Students should choose three optional modules from appendix A. These modules should be chosen from the same group e.g. Moral and Social Philosophy (32.1MS1, 32.1MT2, 32.1MU3). It may be possible to switch options at the end of the first or second term but the choice then is likely to be restricted.

TERM 1 TERM 2 TERM 317.1YA1 - STATISTICS 1elementary probability, discrete random variables









OPTION (see appendix A) OPTION (see appendix A) OPTION (see appendix A)


Students taking the ordinary degree choose the statistics module plus at least two others from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 3OPTION (see appendix A) 17.2SD2 - STATISTICS 4

expectations, variance, etc.weak law of large numbers

17.2SE3 - STATISTICS 5statistical inference, confidence intervals and statistical testing













Honours degree students choose the data analysis, methods and analysis modules plus one other listed below in each term.Ordinary degree students choose the data analysis module plus at least two further modules from the list below in each term. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A in consultation with the 3rd year director of studies.

TERM 1 TERMS 2 & 317.3SF1 - DATA ANALYSIS 1 17.3SJ2 & 3SM3 - DATA ANALYSIS 2 & 311.3YA1 - COMPLEX ANALYSISanalytic functions, Cauchy theorem,Taylor series, contour integration










YEAR 4 (Honours 11.4A1)

Students choose the statistics module plus any other three listed below in each term.

TERM 1 TERM 2 TERM 317.3SG1 - STATISTICAL INFERENCE 17.3SK2 - STOCHASTIC PROCESSES

(continues in term 3)17.3SN3



REVISION



REVISION



REVISION



REVISION


11.9B.Sc. in Mathematics (Hons.) / General Maths (Ord.) with Finance

Course Director : Dr C.J. Boulter, Room G.06

YEAR 1 (Honours 11.1B1, Ordinary 11.1B2)

TERM 1 TERM 2 TERM 333.1OA1 - FINANCIAL ACCOUNTINGfinancial reporting, basic accounting transactions, balance sheets

33.1OB2 - MANAGEMENT ACCOUNTINGcost and decisions, budgeting

33.1OC3 - INTRODUCTION TO FINANCEinvestment appraisal, financial markets and institutions, introduction to taxation











Students taking the ordinary degree choose the finance module plus at least two others from the list below in each of terms 2 & 3. The remaining slots (if any), to make a total of four modules in each term, are chosen from among the options in appendix A plus ‘approved options’ selected in consultation with the 2nd year director of studies.

TERM 1 TERM 2 TERM 333.2PT1 - INVESTMENT AND PORTFOLIO THEORYutility theory, modern portfolio theory, stock market indices, technical analysis of shares

33.2CF2 - CORPORATE FINANCEmanagement objectives, capital structure decisions, dividend policy

33.2RC3 - STRUCTURE AND REGULATION OF CAPITAL MARKETSregulation, flotation, trading mechanisms and privitisations








17.2SD2 - STATISTICS 4expectations, variance, etc.weak law of large numbers

17.2XB3 - STATISTICS FOR THE ENVIRONMENT statistical inference, analysis of environmental studies



Honours degree students must choose the finance, economics, analysis and methods modules in each term.Ordinary degree students must choose the finance, economics and methods modules plus any one other module listed below in each term.

TERM 1 TERMS 2 & 333.3II1 - INTERNATIONAL FINANCIAL INVESTMENT

33.3FD2 - FINANCIAL DERIVATIVES

33.3IM3 - INTERNATIONAL FINANCIAL MARKETS

32.1OA1 - MICROECONOMICS 1 32.1OB2 - MACROECONOMICS 1,

32.1OC3 - INTERNATIONAL ECONOMICS









YEAR 4 (Honours 11.4B1)

Students must choose the finance module plus any other three listed below in each term.

TERM 1 TERM 2 TERM 333.4SY1 - SECURITY ANALYSIS AND DERIVATIVE APPLICATIONS

33.4SX2 – SECURITIES MARKETS

33.4SZ3 - SECURITY TOPICS AND ISSUES (private study)


11.4ZF2 -PURE MATHEMATICS 2fields and codes

REVISION

11.4ZB1 - PARTIAL DIFF. EQUATIONS

11.4ZG2 - OPTIMIZATION REVISION

11.4ZE1 - SPECIAL TOPICS 1functional analysis


REVISION



REVISION


11.3YH2 - DISCRETE MATHS 1counting arguments, distribution problems, graph theory

11.3YN3 - DISCRETE MATHS 2

12 APPENDIX A : OTHER COURSE OPTIONS 43

12Appendix A : Other course options

YEAR 1

TERM 1 TERM 2 TERM 3COMPUTER SCIENCE 1 12.1XA1 12.1XB2 12.1XF3PHYSICS 13.1SA1 13.1SB2 13.1SC3CHEMISTRY 1 14.1GQ1 14.1GR2 14.1GS3CHEMISTRY 2* 14.1EQ1 14.1RE2 14.1SE3 MANAGEMENT 31.1MA1 31.1MB2 31.1MC3MORAL AND SOCIAL PHILOSOPHY 32.1MS1 32.1MT2 32.1MU3ECONOMICS 32.1OA1 32.1OB2 32.1OC3ACCOUNTANCY 33.1OA1 33.1OB2 33.1OC3FRENCH 1** 34.1FX1 34.1FX2 34.1FX3FRENCH 2* 34.2FX1 34.2FX2 34.2FX3GERMAN 1 34.1GX1 34.1GX2 34.1GX3GERMAN 2* 34.2GX1 34.2GX2 34.2GX3SPANISH 1 34.1SX1 34.1SX2 34.1SX3SPANISH 2* 34.2SX1 34.2SX2 34.2SX3ARABIC 1 34.1AX1 34.1AX2 34.1AX3RUSSIAN 34.1RX1 34.1RX2 34.1RX3(*) Students should already hold a pass in the subject at Higher grade or equivalent.(**) Students should already hold a pass in the subject at Standard grade or equivalent.

YEARS 2 & 3 Students may choose options from the table (above but may encounter timetable difficulties) plus the following modules

COMPUTER SCIENCE* 12.2AA1PHYSICS* 13.2AA1ECONOMICS* 32.2AB1ACCOUNTANCY* 33.2PT1FRENCH* 34.3FX1(*) Students should hold a pass in the corresponding level 1 module stream.

YEAR 3

The following modules are available for year 3 students on Ordinary Degrees

IT FUNDAMENTALS 12.1XC1 12.1XD2 12.1XE3BIOLOGY 15.1AL1 15.1BL2 15.1CL3STUDY SKILLS etc 30.1CS1 30.1CP2 30.1PS3HISTORY OF SCIENCE 10.3PP1 10.3CC2 10.3BB3

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