Mathematics with French Language
Mathematics with German Language
2 / Programme Code / MASU18
MASU19
MASU20
3 / JACS Code / G100
4 / Level of Study / Undergraduate
5a / Final Qualification / Bachelor of Science with Honours (BSc Hons)
5b / QAA FHEQ Level / 6
6a / Intermediate Qualification(s) / BSc Mathematics (MASU01)
6b / QAA FHEQ Level / 6
7 / Teaching Institution (if not Sheffield) / Not applicable
8 / Faculty / Science
9 / Department / School of Mathematics and Statistics
10 / Other Departments 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 / February 2014, March 2016
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. In their first two years, students 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.
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 take 40 language credits at Level 1. Students study Pure Mathematics and Probability & Statistics, with 20 credits of each at Level 1.
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
16. Programme aims
Through its programmes, the School of Mathematics and Statistics aims:1. to provide Mathematics degree programmes with internal choice to accommodate the diversity of students’ interests and abilities;
2. to provide an intellectual environment conducive to learning;
3. to prepare students for careers which use their mathematical and/or statistical training;
4. to provide teaching which is informed and inspired by the research and scholarship of the staff;
5. 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 dual programmes with French Language, German Language or Spanish Language, it aims:
6. to provide a degree programme in which students may choose either to specialise in one mathematical discipline (Pure Mathematics or Probability and Statistics) or to choose a more balanced programme incorporating both of these disciplines;
7. to offer students the opportunity to study mathematics and statistics in another European country.
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 Pure 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;
SK9 / understand the need for proof and logical precision;
SK10 / have developed an understanding of various methods of proof.
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.
18. Teaching, learning and assessment
Development of the 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 / SK / 1-5, 9-10 / S / 1-4, 6-8
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.
Learning outcomes supported by problems classes:
K / 1-4 / SK / 1-5, 9-10 / S / 1-8
Computing and Practical Sessions
At Level 1 all students 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 / SK / 6-8
Opportunities to demonstrate achievement of the 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, SK1-5,9, 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 to the Director of Teaching whether the year abroad is passed or failed, and the final decision is made by the external examiners and the final SoMaS Examination Board. Learning outcomes K5 and SK7 are assessed through the language modules by methods including tests and records of independent study. There is no direct assessment of SK8 though in many cases it will feature in assessment by the host university.
Learning outcomes assessed by mathematics examinations:
K / 1-4 / SK / 1-5, 9-10 / S / 1-8
Learning outcomes assessed by mathematics coursework:
K / 1-4 / SK / 1-5, 9-10 / S / 1-9
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 / SK / 7
19. Reference points
Subject Benchmark Statements
http://www.qaa.ac.uk/AssuringStandardsAndQuality/subject-guidance/Pages/Subject-benchmark-statements.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