Programme Specification
A statement of the knowledge, understanding and skills that underpin a
taught programme of study leading to an award from
The University of Sheffield
This programme specification covers the curriculum in Mathematics and Statistics for the following dual
honours degree programmes and should be read in conjunction with the relevant programme specification for
the second subject.
1. Programme Titles
2. Programme Codes
3. JACS Codes
Mathematics with Study in Europe
MASU10 / MASU11
G100
Mathematics with Spanish Language
MASU12
G100
Mathematics with French Language
MASU13
G100
Mathematics with German Language
MASU14
G100
4
Level of Study
Undergraduate
5a
Final Qualification
Bachelor of Science with Honours (BSc Hons) (MASU11)
Master of Mathematics with Honours (MMath Hons) (MASU10,
MASU12, MASU13, MASU14)
5b
Position in the QAA Framework for
Higher Education Qualifications
Honours (BSc), Masters (MMath)
6a
Intermediate Qualification(s)
BSc (MMath)
6b
Position in the QAA Framework for
Higher Education Qualifications
Honours
7
Teaching Institution (if not Sheffield)
Not applicable
8
Faculty
Science
9
Home Department
School of Mathematics and Statistics
10
Other Department(s) involved in
teaching the programme
Modern Languages Teaching Centre (MLTC)
11
Mode(s) of Attendance
Full-time
12
Duration of the Programme
4 years
13
Accrediting Professional or Statutory
Body
Not applicable
14
Date of production/revision
January 2008, updated January 2009, March 2012, February
2014, March 2016.
Dual Degrees
The University of Sheffield defines a dual degree as the independent study of two parallel subjects. Dual
degrees offer students the flexibility to choose a programme of study that reflects their interests and gives the
opportunity to develop detailed knowledge and key skills in two major subjects. Whilst the two subjects may be
taught independently, they will complement, inform and illuminate one another. Where there are two programme
specifications for dual degrees, one for each half of the programme, and students should refer to both
documents for a full description of the whole programme. Where there are clear links between the two subjects,
details will be included in Sections 15 and 20 of the programme specifications. However, there are some single
programme specifications for dual degree combinations where there is a substantial degree of integration
between the two subjects.
98959747 – ver16-17
1
15. Background to the programme and subject area
Mathematics involves the study of intangible objects (such as numbers, functions, equations and spaces) which
necessarily arise in our attempts to describe and analyse the world about us. It is a fascinating subject of great
beauty and power. Its abstraction and universality lie behind its huge range of applications, to physical and
biological sciences, engineering, finance, economics, secure internet transactions, reliable data transmission,
medical imaging and pharmaceutical trials, to name a few. Mathematicians were responsible for the invention of
modern computers, which in turn have had a great impact on mathematics and its applications.
Teaching in the School of Mathematics and Statistics (SoMaS) is in the three areas of Pure Mathematics,
Applied Mathematics, and Probability and Statistics. Pure mathematics is a subject rich in patterns and one in
which the development of a theory may begin with identification of behaviour common to various simple
situations and proceed, through precise analysis, to the point where rigorous general results are obtained.
Solutions of particular problems may involve standard analytical techniques, for example from calculus, or the
application of an abstract general theory to a particular concrete example. In applied mathematics and in
probability and statistics, a common approach to practical problems, from a wide variety of contexts, is first to
model or interpret them mathematically and then apply mathematical or statistical methods to find a solution. In
all three subjects it is vital that work should be presented in a clear, precise and logical way so that it can be
understood by others. For these reasons, graduates from programmes involving mathematics are highly
regarded, by a wide range of employers, for their analytical, problem-solving and communication skills as much
as for their knowledge of mathematics.
These programmes offer the opportunity to spend the third year studying mathematics at a University in another
European country. Several universities offer such opportunities but the Sheffield programme is distinctive for the
amount and quality of the language teaching provided by the Modern Languages Teaching Centre. We believe
that this is reflected in the quality of the graduates from the programmes. The list of partner institutions is
extensive but the most common destinations are in France, Germany and Spain. In their first two years,
students normally spend a third of their time on language studies and the rest on mathematics. The primary
factor in determining whether a student takes the BSc or the MMath is their Level Two examination result but a
student who qualifies for MMath has a choice between the specialist MMath programme, including a substantial
project, and the broader BSc programme, augmenting the courses taken abroad. On all programmes the third
year is spent in Europe. On MASU12, MASU13 and MASU14, students are required to spend one third of their
fourth year studying their chosen language and this component of the programme carries Foreign Languages at
Work accreditation (FLAW). On MASU10 and MASU11, students at Level 4 may concentrate entirely on
mathematics or may take up to 20 credits of language modules.
The single honours programmes in Sheffield have a common SoMaS core, of 40 credits at Level 1 and 20 at
Level 2, together with substantial components from each of the three areas, with a wide choice of modules at
each of Levels 3 and 4. Students on these programmes normally take 40 language credits at Level 1 though, on
MASU10 and MASU11, this may be reduced if the student has a strong background in language. Students
study two of the three Mathematical disciplines. Of these Pure Mathematics and Probability & Statistics are
easiest to accommodate, with 20 credits of each at Level 1, whereas Applied Mathematics will only be available
to students with a strong background in either language or mechanics.
Some SoMaS modules concentrate on applicability while others are more theoretical. Some deal with
contemporary developments, such as error-correcting codes, signal processing and financial mathematics, and
others treat long-established topics of continuing importance. Several, such as the module on History of
Mathematics and the module on Galois theory, put the subject in its historical perspective. All are informed by
the research interests and scholarship of the staff.
Staff in all three areas have international reputations in research, with 89% of research activities being rated as
world leading or internationally excellent in the 2014 Research Excellence Framework exercise. Many modules
are taught by leading experts in the area in which the module is based. In Pure Mathematics there are particular
research strengths in topology, algebra and algebraic geometry, number theory and differential geometry, and
there are modules available in all these areas. The main strengths within Probability and Statistics are in
Bayesian statistics, statistical modelling and applied statistics, and probability and, again, all these are
prominent in the undergraduate curriculum. Several members of the School belong to the Sheffield Centre for
Bayesian Statistics in Health Economics. Applied Mathematics research is strong not only in traditional areas of
the subject, such as fluid mechanics, but in interdisciplinary areas such as solar physics, particle astrophysics,
environmental dynamics and mathematical biology. The School was instrumental, with other departments in the
University, in setting up the Sheffield-based NERC Earth Observation Centre of Excellence for Terrestrial
Carbon Dynamics.
Further information is available from the school web site: http://www.shef.ac.uk/maths
98959747 – ver16-17
2
16. Programme aims
Through its programmes, the School of Mathematics and Statistics aims:
to provide Mathematics degree programmes with internal choice to accommodate the diversity of students’
interests and abilities;
to provide an intellectual environment conducive to learning;
to prepare students for careers which use their mathematical and/or statistical training;
to provide teaching which is informed and inspired by the research and scholarship of the staff;
to provide students with assessments of their achievements over a range of mathematical and statistical skills,
and to identify and support academic excellence.
In its single honours programmes with Study in Europe and in its dual programmes with French Language,
German Language or Spanish Language, it aims:
to provide a degree programme in which students may choose either to specialise in one mathematical
discipline (Pure Mathematics, Applied Mathematics, Probability and Statistics) or to choose a more balanced
programme incorporating two of these disciplines;
to offer students the opportunity to study mathematics and statistics in another European country.
In its MMath programmes, it aims:
to prepare students for progression to a research degree in one of the three mathematical disciplines or for
careers in which the use of mathematics is central.
The MMath with language programmes ( MASU12, MASU13, MASU14) also aim:
to provide language instruction beyond that needed to study mathematics and statistics abroad, giving students
the opportunity to acquire all-round fluency in the language.
17. Programme learning outcomes
Knowledge and understanding: a graduate should:
K1
have acquired a working knowledge and understanding of the methods of linear mathematics;
K2
have acquired a working knowledge and understanding of the methods of advanced calculus;
K3
have acquired a broad knowledge and understanding of at least two of Pure Mathematics, Applied
Mathematics and Probability & Statistics;
K4
have acquired a working knowledge and understanding of specialist mathematical or statistical topics;
K5
have acquired a working knowledge of their chosen language.
Knowledge-based skills: a graduate should:
SK1
be able to apply core concepts and principles in well-defined contexts;
SK2
show judgement in the selection and application of mathematical tools and techniques;
SK3
demonstrate skill in comprehending problems and abstracting the essentials of problems;
SK4
be able to formulate problems mathematically;
SK5
be able to obtain solutions of mathematical problems by appropriate methods;
SK6
have experienced first-hand, through a substantial period of study of mathematics at a European
University outside the UK, the life, language and culture of a different European country;
SK7
be able to converse with native speakers of their chosen language;
SK8
be able to interpret mathematical text written in their chosen language.
In addition those graduates whose programmes have included a substantial component of Pure Mathematics
should:
SK9
understand the need for proof and logical precision;
SK10
have developed an understanding of various methods of proof.
98959747 – ver16-17
3
Skills and other attributes: a graduate should:
S1
have skill in calculation and manipulation;
S2
understand logical arguments, identifying the assumptions and conclusions made;
S3
be able to develop and evaluate logical arguments;
S4
be able to present arguments and conclusions effectively and accurately;
S5
demonstrate the ability to work with relatively little guidance;
S6
have developed the skills to acquire further mathematical or statistical knowledge;
S7
have developed the skills to model and analyse physical or practical problems;
S8
appreciate the development of a general theory and its application to specific instances;
S9
have acquired skills in the use of computer algebra packages.
In addition, MMath graduates should:
K6
have enhanced and extended their specialist knowledge in at least one of the three disciplines Pure
Mathematics, Applied Mathematics, Probability & Statistics;
S10
have enhanced and extended the necessary mathematical skills to consider careers as practising
mathematicians or statisticians;
S11
have shown the ability to complete an extended individual study of a mathematical or statistical topic
and to present an account of the topic.
In addition, graduates on the MMath programmes with named languages (MASU12, MASU13, MASU14)
should:
K5+
have acquired a near-native level of proficiency in their chosen language;
SK7+
demonstrate a near-native command of their chosen language in both professional and social contexts;
S4+
be able to present arguments and conclusions effectively and accurately, both in English and their
chosen language;
S12
have acquired a profound cultural understanding of the country where they have studied.
+ indicates an enhancement of a previously listed learning outcome.
18. Teaching, learning and assessment
Development of the programme learning outcomes is promoted through the following teaching and
learning methods:
Lectures
A 10-credit lecture SoMaS module (or half-module) at Level 1 or 2 generally comprises 22 lectures supported by
a weekly or fortnightly problems class. At levels 3 and 4, a typical 10-credit module has around 20 lectures. The
lecturing methods used vary. Effective use is made of IT facilities, for example through computer
demonstrations using data projectors. Students also learn mathematical techniques and theories through seeing
problems being solved and results proved in lectures. Theory is developed and presented in a clear and logical
way and is enhanced by the use of illustrative examples. In many modules, supporting written material is
circulated. Some Level 3 modules include an element of project work for which guidance is provided in lectures.
Learning outcomes supported by lectures:
K
1-4,6
SK
1-5, 9-10
S
1-4, 6-8, 10
Problems classes
At Levels 1 and 2, lecture groups are divided into smaller groups for problems classes lasting fifty minutes.
Ample opportunity is provided for students to obtain individual help. Coursework, usually in the form of sets of
problems, is regularly set and marked and feedback is given. This is usually administered through the problems
classes. For a 20-credit ``core’’ module at Level 1, students meet fortnightly in small groups with their personal
tutor, and may be required to present their solutions and participate in group discussions. Setting of coursework
continues into Levels 3 and 4, together with the associated feedback, but, due to the expected increasing
maturity of students and in support of learning outcome S5, the formal mechanism provided by problems
classes is replaced by informal contact with the module lecturer.
98959747 – ver16-17
4
Learning outcomes supported by problems classes:
K
SK
1-4,6
1-5, 9-10
S
1-8
Project work
At Level 4 all MMath students are required to take 40 credits of project modules with a view to achieving
learning outcome S11. They are given training in presentational skills, including the use of mathematical
typesetting packages, and individual guidance in one-to-one sessions with a nominated supervisor.
Learning outcomes supported by project work:
K
3,4,6, (1,2)*
SK
(1-5,9,10)*
S
11, (1-10)*
* dependent on the nature of the individual project
Computing and Practical Sessions
At Level 1 students taking Probability and Statistics are provided with training on the software package R. This
training contributes to SK2, SK5, S1 and S9.
Learning outcomes supported by computing and practical sessions:
SK
2,5
S
1,9
Language Teaching
Language skills are taught using seminars supplemented by more informal group and pair work. Students may
enrol to use the MLT Centre’s up-to-date Self-Access Centre, comprising a 27 position Computer-Aided
Language Learning (CALL) laboratory, an Audio Visual room, with access to European television channels, and
an extensive library of print material, audio and video cassettes.
Learning outcomes supported by language teaching:
K
5, 5+
SK
6-8, 7+
S
4+, 12
Opportunities to demonstrate achievement of the programme learning outcomes are provided through
the following assessment methods:
Most SoMaS modules are assessed by formal examinations, augmented in some cases by a component of
assessed coursework; several modules now include an element of the latter. The most common format involves
the regular setting of assignments, each consisting of a number of problems based on material recently covered
in lectures. Some of the Level 3/4 modules include a project and/or poster presentation. Examinations are
normally of 1.5, 2 or 2.5 hours’ duration. Where a module is assessed by both examinations and coursework,
the latter contributes between 10% and 30% of the final mark.
All assessment by examination or coursework contributes to demonstrating the achievement of K1-4,6, SK15,9,10 and S1. However as students progress through the programmes, less explicit guidance on selection of
techniques is given and more is expected in terms of formulation of problems and in solving problems requiring
several techniques or ideas. The learning outcomes S2-8 feature in some assessment at Level 1, but again
more is expected later in the programmes, as the students mature mathematically. For example, as students
progress through the programmes, the Pure Mathematics examinations, typically, require more in the way of
rigorous proof. Aspects of S9, the use of computer packages, are assessed in the appropriate modules. The
learning outcomes K1 and K2 are assessed not only in the core Level 2 modules but also in various approved
modules.
Each student is required to submit a report on the year abroad to their Erasmus/Socrates tutor. This should
include a record of courses taken, examination papers, a sample of coursework, their assessment record and,
with SK6 in mind, a discussion of their experiences as a student abroad. The tutor recommends a mark for the
year abroad to the Director of Teaching and the agreed mark is presented to external examiners and the final
SoMaS Examination Board. If, due to practice at the host university, there is insufficient information available on
the assessment of the student’s work in the year abroad, the tutor may recommend that the year abroad mark
should be replaced by a weighted average of the student’s marks in Years 2 and 4. The year abroad mark
accounts for 100, 110, or 120 credits and is augmented by the grades awarded on any MLTC Year Abroad
modules taken in the third year. Learning outcomes K5, 5+, SK7, 7+, S4+ and S12 are assessed through the
language modules by methods including tests, records of independent study and for MLTC Year Abroad
modules at Level 3, a year abroad diary, a project and a presentation in the target language on return to the UK.
There is no direct assessment of SK8 though in many cases it will feature in assessment by the host university.
The additional learning outcome, S10, for the M programmes MASU10, MASU12, MASU13 and MASU14, is
assessed in Level 4 examinations while S11 is assessed through a submitted project report, examined by at
98959747 – ver16-17
5
least two members of staff and subject to moderation.
Learning outcomes assessed by mathematics examinations:
K
SK
1-4,6
S
1-5, 9-10
1-8, 10
Learning outcomes assessed by mathematics coursework:
K
SK
1-4,6
S
1-5, 9-10
1-9
Learning outcomes assessed by mathematics project work (MMath):
K
SK
4,6
S
1-5, (9,10)*
2, 4, 5, 6,10,11, (1,3,7,8,9)*
*dependent on the nature of the individual project
Learning outcomes assessed by report on year abroad:
K
all
SK
1-6, 8-10
S
1-9
Learning outcomes assessed by MLTC modules:
K
5, 5+
SK
7,7+
S
4+, 12
19. Reference points
The learning outcomes have been developed to reflect the following points of reference:
Subject Benchmark Statements
http://www.qaa.ac.uk/AssuringStandardsAndQuality/subject-guidance/Pages/Subject-benchmarkstatements.aspx
University Strategic Plan
http://www.sheffield.ac.uk/strategicplan
Learning and Teaching Strategy (2011-16)
http://www.shef.ac.uk/lets/staff/lts
The QAA Mathematics, Statistics and Operational Research benchmark document at:
http://www.qaa.ac.uk/en/Publications/Documents/SBS-Mathematics-15.pdf
The European Mathematical Society Mathematics Tuning Group report “Towards a common framework for
Mathematics degrees in Europe” at www.maths.soton.ac.uk/EMIS/newsletter/newsletter45.pdf pages 26-28.
The University of Sheffield Students’ Charter at http://www.shef.ac.uk/ssid/ourcommitment/charter/.
The University’s coat of arms, containing the inscriptions Disce Doce (Learn and Teach) and Rerum
Cognoscere Causas (To Discover the Causes of Things; from Virgil's Georgics II, 490), at
http://www.sheffield.ac.uk/about/arms
The research interests and scholarship of the staff.
20. Programme structure and regulations
The teaching year is divided into two semesters each of fifteen weeks, the final three weeks of each being
devoted to examinations. The programmes are fully modular, being delivered mainly in 10-credit modules,
taught and examined during a single semester, and in 20 credit modules, often examined at the end of the year.
Each year of study represents 120 credits.
The two Study in Europe programmes differ mainly in the fourth year when BSc students take modules at Level
3 whereas MMath students take modules at Level 4. On the three dual programmes, MASU12, MASU13 and
MASU14, students must take forty credits in the appropriate language whereas on MASU10 or MASU11 they
may take twenty such credits. The differences in the regulations at Levels 1 and 2 are that MASU12, MASU13
and MASU14 have a named set of four ten credit language modules, and that on MASU10 or MASU11 Applied
Mathematics can be taken. On all five programmes the third year is spent at the European University.
At Level 1 students take two core 20-credit modules. The material in these modules comprises mathematical
methods. The choice of topics is influenced by the potential for application. Depending on their background in
language and mechanics, students take a further 40 credits of Mathematics consisting of two of the following: 20
credits of Pure Mathematics (PM), 20 credits of Applied Mathematics (AM), 20 credits of Probability & Statistics
(PS). In addition, they take 40 credits in their target language. At Level 2, students usually take 20 SoMaS core
credits, a further 60 mathematics credits, and 40 credits of language. The third year is spent at the European
98959747 – ver16-17
6
host university and should include a component of language, provided either by the host or by the Modern
Language Teaching Centre’s Study Abroad modules. The SoMaS modules offered at Level 4 are in specialist
topics and there are no lecture-based core modules. At Level 4, MMath students must take 40 credits of projectbased modules of which 10 credits are core, and 40 further credits of mathematics. The Level 3 and Level 4
SoMaS modules are consistent with the guidelines in the Council for the Mathematical Sciences briefing
document and the European Mathematical Society document cited at 19.
Students on the Study in Europe programmes are normally registered for the MMath programme. At the end of
their second year, these students choose between the BSc programme and the MMath programme, the
essential difference being the level of courses in the final year. Students averaging less than 59.5% on the
mathematics modulesin their Level 1 or Level 2 assessment are required to transfer to the BSc. Students on
MASU12, MASU13 or MASU14 who fail to achieve an average of 59.5% or above at Level 1 or Level 2 will also
be required to transfer to the corresponding one of the BSc programmes MASU**, MASU** or MASU**, or to the
BSc programme MASU11. It is possible for a student who is qualified for the MMath to transfer to the BSc. For
example, a student whose host university has a less significant provision than Sheffield in one of the three
disciplines could choose between a broad BSc programme including that discipline or a more specialised
MMath programme. Students averaging less than 55% on the language modules at Level 1 or Level 2 will be
required to transfer to the MMath or BSc Mathematics programme. Masters graduates do not also obtain a BSc
but an MMath candidate failing to achieve II(ii) standard or higher may be awarded a BSc.
Classification of the final degree is subject to the University of Sheffield General Regulations. Level 1 serves as
a qualifying year and does not contribute to degree classification. The weighting for Level 2, the year abroad
and Level 4 on the MMath is 1:1:2; for the BSc it is 1:0:2, but students are required to pass their year abroad.
Detailed information about the structure of programmes, regulations concerning assessment and progression
and descriptions of individual modules are published in the University Calendar available on-line at
http://www.shef.ac.uk/calendar/
21. Student development over the course of study
Mathematics is essentially a linear subject with key skills and core knowledge taught at Level 1 or Level 2 often
required at subsequent levels.
Level 1 consolidates key technical skills for use throughout the programmes. Ideas of proof and abstraction,
illustrated by concrete examples, are introduced in the Pure Mathematics modules and applications are
developed in Applied Mathematics and Probability & Statistics.
Level 2 introduces more advanced technical methods, in particular those of linear mathematics and advanced
calculus. The Pure Mathematics modules put some topics introduced at Level 1 on a sounder theoretical basis
than before or treats them at a more sophisticated level of abstraction. There is further development of theory
and applications in Applied Mathematics, including differential equations, and Probability & Statistics, including
modelling.
Modules at Level 3 and Level 4 offer a range of specialist options consistent with the principles outlined in
reference points (1), (3) and (4). Some of these build on knowledge acquired in earlier years and others, though
requiring skills already acquired and the corresponding degree of mathematical maturity, introduce topics that
are essentially developed from scratch. Several of those offered at Level 4 have Level 3 prerequisites and the
selection of such modules by an MMath student is monitored to ensure that the student has acquired
appropriate background knowledge during their year abroad.
22. Criteria for admission to the programme
Detailed information regarding admission to the programme is available at http://www.shef.ac.uk/prospective/
98959747 – ver16-17
7
23. Additional information
A list of possible host universities for the year abroad may be viewed at http://www.shef.ac.uk/ieu/.
SoMaS has an active Staff-Student Forum and there is a lively Student Maths Society.
Personal Tutorials
Each of the three SoMaS subject areas has an Erasmus/Socrates tutor and every student on these programmes
is assigned to one of these tutors who oversees the choice of courses in the year abroad and on return to
Sheffield. The tutor also maintains contact with the student throughout the year abroad.
The School of Mathematics and Statistics runs a personal tutorial system conforming to the guidelines in the
University’s Students’ Charter. All students are allocated a personal tutor, who may also be the Erasmus tutor,
at the outset of their University career. It is hoped that the association will remain during the whole of each
student’s course. However, a system is in place to allow a student to transfer to another tutor if they wish.
Personal tutors provide personal support and academic guidance, acting as a point of contact and gateway for
University support services, such as Careers and the Counselling Service. Students are expected to see their
tutor at scheduled sessions, the frequency of which is highest at Level 1, and may contact their tutor at other
times.
Many other staff members also have particular responsibility for student support. In particular, the Senior Tutor
is responsible for all day-to-day issues for individual students, although the Erasmus co-ordinator will often deal
with these for students on MASU10, MASU11, MASU12, MASU13 and MASU14.
The web page for SoMaS is at http://www.shef.ac.uk/maths
This specification represents a concise statement about the main features of the programme and should be
considered alongside other sources of information provided by the teaching department(s) and the University. In
addition to programme specific information, further information about studying at The University of Sheffield can
be accessed via our Student Services web site at www.shef.ac.uk/ssid/
98959747 – ver16-17
8