Mathematics with German MMath

Core modules:

Introduction to Probability and Statistics

The module provides an introduction to the fields of probability and statistics, which form the basis of much of applicable mathematics and operations research. The theory behind probability and statistics will be introduced, along with examples occurring in diverse areas. Some of the computational statistical work may make use of the statistics package R.

20 credits

Mathematics Core 1

The module explores topics in mathematics which will be used throughout many degree programmes. The module will consider techniques for solving equations, special functions, calculus (differentiation and integration), differential equations, Taylor series, complex numbers and finite and infinite series.

20 credits

Mathematics Core II

The module continues the study of core mathematical topics begun in MS4F1015, which will be used throughout many degree programmes. The module will discuss 2-dimensional co-ordinate geometry, discussing the theory of matrices geometrically and algebraically, and will define and evaluate derivatives and integrals for functions which depend on more than one variable, with an emphasis on functions of two variables.

20 credits

Numbers and Groups

The module provides an introduction to more specialised Pure Mathematics. The first half of the module will consider techniques of proof, and these will be demonstrated within the study of properties of integers and real numbers. The second semester will study symmetries of objects, and develop a theory of symmetries which leads to the more abstract study of groups.

20 credits

German Advanced 1

Assuming a good A level in the language or equivalent, this unit aims to provide an initial preparation for a prolonged professional, academic or recreational stay in a country where the language is spoken and introduces the full range of linguistic and cultural skills required to engage in authentic and spontaneous interaction with native speakers (CEF level B2-). Based on 33 hours of small group (15-20) interactive seminars and tutorials predominantly delivered in the foreign language, the unit also comprises 67 hours of monitored private study. https://www.sheffield.ac.uk/mltc/lfa/courses/german/stage_3a

10 credits

German Advanced 2

Assuming successful completion of the Advanced 1 unit or equivalent, this unit aims to consolidate an initial preparation for a prolonged professional, academic or recreational stay in a country where the language is spoken and introduces the full range of linguistic and cultural skills required to engage in authentic and spontaneous interaction with native speakers (CEF level B2). Based on 36 hours of small group (15-20) interactive seminars and tutorials predominantly delivered in the foreign language, the unit also comprises 64 hours of monitored private study. https://www.sheffield.ac.uk/mltc/lfa/courses/german/stage_3b

10 credits

You'll then take one of these two groups of modules, as determined by the Modern Languages Teaching Centre.

German-English Tandem Advanced 1

This unit aims to enable students to develop their spoken proficiency and intercultural awareness in relation to the language they are studying through weekly meetings with a native-speaker partner and to acquire independent language learning skills through regular supervision from a language tutor and the completion of a personal planning and reflexive diary. Partners will reciprocally support each other in achieving their own pre-agreed goals, alternatively acting as learner and teacher, taking responsibility for their own learning and providing constructive opportunities for language practice and feedback to their partner. https://www.sheffield.ac.uk/mltc/lfa/courses/german/tandem

10 credits

German Project Advanced 2

This unit aims to enable students at an 'Advanced' level of competence in the language to work semi-independently, exploring critically a specialised topic normally related to their main field of study, in order to acquire subject-specific terminology and basic discursive skills in the language, as well as develop sound research skills. Through weekly tutorials, students will be guided and suppported in their completion of a written portfolio (1,500 words) and their preparation of an oral presentation summarizing their research and demonstrating their acquisition of relevant academic and linguistic skills. https://www.sheffield.ac.uk/mltc/lfa/courses/german/project_advanced

10 credits

Or:

German Project Advanced 1

This unit aims to enable students at an 'Advanced' level of competence in the language to work semi-independently, exploring critically a specialised topic normally related to their main field of study, in order to acquire subject-specific terminology and basic discursive skills in the language, as well as develop sound research skills. Through weekly tutorials, students will be guided and suppported in their completion of a written portfolio (1,500 words) and their preparation of an oral presentation summarizing their research and demonstrating their acquisition of relevant academic and linguistic skills.  https://www.sheffield.ac.uk/mltc/lfa/courses/german/project_advanced

10 credits

German-English Tandem Advanced 2

This unit aims to enable students to develop their spoken proficiency and intercultural awareness in relation to the language they are studying through weekly meetings with a native-speaker partner and to acquire independent language learning skills through regular supervision from a language tutor and the completion of a personal planning and reflexive diary. Partners will reciprocally support each other in achieving their own pre-agreed goals, alternatively acting as learner and teacher, taking responsibility for their own learning and providing constructive opportunities for language practice and feedback to their partner. https://www.sheffield.ac.uk/mltc/lfa/courses/german/tandem

10 credits

Core modules:

Advanced Calculus and Linear Algebra

Advanced Calculus and Linear Algebra are basic to most further work in pure and applied mathematics and to much of statistics. This course provides the basic tools and techniques and includes sufficient theory to enable the methods to be used in situations not covered in the course.
The material in this course is essential for further study in mathematics and statistics.

20 credits

Analysis

This course is a foundation for the rigorous study of continuity, differentiation and integration of functions of one real variable. As well as providing the theoretical underpinnings of calculus, we develop applications of the theory and examples that show why the rigour is needed, even if we are focused on applications.

The material in this course is vital to further studies in metric spaces, measure theory, parts of probability theory, and functional analysis.

20 credits

Statistical Inference and Modelling

This unit develops methods for analysing data, and provides a foundation for further study of probability and statistics at Level 3. It introduces some standard distributions beyond those met in MAS113, and proceeds with study of continuous multivariate distributions, with particular emphasis on the multivariate normal distribution. Transformations of univariate and multivariate continuous distributions are studied, with the derivation of sampling distributions of important summary statistics as applications. The concepts of likelihood and maximum likelihood estimation are developed. Data analysis is studied within the framework of linear models. There will be substantial use of the software package R.

20 credits

German Higher Advanced 1

Assuming a one-year post-A-level study of the language or equivalent, this module aims to provide a full linguistic and cultural preparation for learners wishing to undertake an extended professional, academic or recreational stay in a country where the language is spoken and to expand the range of linguistic and cultural skills required to operate effectively in most situations encountered when engaging with native speakers (CEF level B2+). Based on 33 hours of small group (15-20) interactive seminars almost exclusively delivered in the foreign language, the unit also comprises 67 hours of monitored private study. https://www.sheffield.ac.uk/mltc/lfa/courses/german/stage_4a

10 credits

German Higher Advanced 2

Assuming successful completion of the Higher Advanced 1 unit or equivalent, this module aims to consolidate the full linguistic and cultural preparation of learners wishing to undertake an extended professional, academic or recreational stay in a country where the language is spoken and to consolidate the full range of linguistic and cultural skills required to operate effectively in most situations encountered when engaging with native speakers (CEF level C1). Based on 36 hours of small group (15-20) interactive seminars almost exclusively delivered in the foreign language, the unit also comprises 64 hours of monitored private study. https://www.sheffield.ac.uk/mltc/lfa/courses/german/stage_4b

10 credits

German Placement Preparation

The aim of this unit is to provide linguistic, cultural and practical preparation to students about to undertake an extended work placement or study exchange abroad. Students will research their destination (region, institution, etc.) and learn how to carry out a broad range of practical and study-related tasks using the language, including securing a residence or work permit, travelling throughout the country, arranging accommodation, registering for a course of study, opening a bank account, registering with and consulting a doctor, translating forms and other documents, taking lecture and seminar notes, writing letters, reports and/or essays, etc. https://www.sheffield.ac.uk/mltc/lfa/courses/german/placement_preparation

10 credits

Optional modules:

Algebra

This unit continues the study of abstract algebra begun in MAS114, going further with the study of groups, and introducing the concepts of a ring, which generalises the properties of the integers, and a vector space, which generalises the techniques introduced in linear algebra to many more examples.

As well as demonstrating the interest and power of abstraction, this course is vital to further studies in most of pure mathematics, including algebraic geometry and topology, functional analysis and Galois theory.

20 credits

Mathematics and Statistics in Action

This module will demonstrate, in a series of case studies, the use of applied mathematics, probability and statistics in solving a variety of real-world problems. The module will illustrate the process of mathematical and statistical modelling, whereby real-world questions are translated to mathematical and/or statistical questions. Students will see how techniques learned earlier in their degree, as well as simple computer programming, can be used to explore these problems. There will be a mix of individual and group projects, and some projects will involve the use of R or Python, but MAS115 is not a prerequisite.

10 credits

Probability Modelling

The course introduces a number of general models for processes where the state of a system is fluctuating randomly over time. Examples might be the length of a queue, the size of a reproducing population, or the quantity of water in a reservoir. The aim is to familiarize students with an important area of probability modelling.

10 credits

You'll then take one of these two groups of modules, as determined by the Modern Languages Teaching Centre.

German-English Tandem Higher Advanced 1

Students will be required to work in collaboration with a native-speaker with whom they will communicate in the target language. At the start of the module, students will exercise responsibility for the organisation of their own learning, establish and maintain contact with their partners, negotiate and set objectives; and seek and offer the correction of language errors. They should give proof of effective time-management, sequence sessions logically to demonstrate management of learning and demonstrate use of reviewing and evaluating procedures. They will be required to sign a learning contract and to keep a learner diary, in which they will record progress made, plan their next steps and reflect on their work during the semester. Their progress will be monitored in advisory and counselling sessions with MLT Centre Tutors. https://www.sheffield.ac.uk/mltc/lfa/courses/german/tandem

10 credits

German Project Higher Advanced 2

The aims are to enable students to work independently and collaboratively in German, to foster the acquisition of subject-specific terminology and discourse in German; to encourage interaction with native speakers of German, by e-mail or face-to-face. Students will be expected to investigate an agreed topic closely related to their main course of study. This will entail devising a project proposal and plan, gathering information from a range of written and spoken sources (normally including German native-speakers), and synthesising this to form the basis of a formal written report and a structured oral presentation. On completion, students should be able to: collaborate successfully with native-speakers of German: use international e-mail links to do so where appropriate; analyse information, distinguishing fact from opinion and main ideas from supporting detail; and present findings in speech and writing using formal register and - where appropriate - subject-specific language. https://www.sheffield.ac.uk/mltc/lfa/courses/german/project_higher_advanced

10 credits

Or:

German Project Higher Advanced 1

The aims are to enable students to work independently and collaboratively in German, to foster the acquisition of subject-specific terminology and discourse in German; to encourage interaction with native speakers of German, by e-mail or face-to-face. Students will be expected to investigate an agreed topic closely related to their main course of study. This will entail devising a project proposal and plan, gathering information from a range of written and spoken sources (normally including German native-speakers), and synthesising this to form the basis of a formal written report and a structured oral presentation. On completion, students should be able to: collaborate successfully with native-speakers of German: use international e-mail links to do so where appropriate; analyse information, distinguishing fact from opinion and main ideas from supporting detail; and present findings in speech and writing using formal register and - where appropriate - subject-specific language.  https://www.sheffield.ac.uk/mltc/lfa/courses/german/project_higher_advanced

10 credits

German-English Tandem Higher Advanced 2

Students will be required to work in collaboration with a native speaker with whom they will communicate in the target language. At the start of the module, students will exercise responsibility for the organisation of their own learning, establish and maintain contact with their partners, negotiate and set objectives; and seek and offer the correction of language errors. They should give proof of effective time-management, sequence sessions logically to demonstrate management of learning and demonstrate use of reviewing and evaluating procedures. They will be required to sign a learning contract and to keep a learner diary, in which they will record progress made plan their next steps and reflect on their work during the semester. Their progress will be monitored in advisory and counselling sessions with MLT Centre tutors.  https://www.sheffield.ac.uk/mltc/lfa/courses/german/tandem

10 credits

Core modules:

Study Abroad

contact convenor for more infortmation

100 credits

German Year Abroad 1

This unit aims to enable students to heighten their awareness of cultural and linguistic aspects of the country where they are studying, encouraging their social integration and fostering their independent and/or collaborative study in the foreign language. Students will complete a diary in which they will record and reflect upon their linguistic and cultural integration progress over a period of at least 10 weeks. They will also contribute to a blog intended to share language learning advice and practical tips about living in the region and country with other students currently abroad or preparing for a year abroad. https://www.sheffield.ac.uk/mltc/lfa/courses/german/year_abroad

10 credits

German Year Abroad 2

This unit aims to enable students to heighten their awareness of cultural and linguistic aspects of the country where they are studying, encouraging their social integration and fostering their independent and/or collaborative study in the foreign language. Students will complete a diary in which they will record and reflect upon their linguistic and cultural integration progress over a period of at least 10 weeks. They will also contribute to a blog intended to share language learning advice and practical tips about living in the region and country with other students currently abroad or preparing for a year abroad. https://www.sheffield.ac.uk/mltc/lfa/courses/german/year_abroad

10 credits

Core modules:

German Proficient 1

Assuming a solid, two year post-A-level study of the language and, ideally, a prolonged stay in a country where the language is spoken, this unit aims to provide the linguistic and cultural skills required to operate as a near-native speaker in the target country, whether for professional, academic or recreational purposes, and to develop strategies and techniques to become a fully autonomous, life-long learner of the language and culture (CEF level C1+). Based on 33 hours of small group (15-20) interactive seminars almost exclusively delivered in the foreign language, the unit also comprises 67 hours of monitored private study. https://www.sheffield.ac.uk/mltc/lfa/courses/german/stage_5a

10 credits

German Proficient 2

Assuming successful completion of the Proficient 1 unit or equivalent, this unit aims to perfect the linguistic and cultural skills required to operate as a near-native speaker in the target country, whether for professional, academic or recreational purposes, and to consolidate the strategies and techniques to become a fully autonomous, life-long learner of the language and culture (CEF level C2). Based on 36 hours of small group (15-20) interactive seminars almost exclusively delivered in the foreign language, the unit also comprises 64 hours of monitored private study. https://www.sheffield.ac.uk/mltc/lfa/courses/german/stage_5b

10 credits

Optional modules:

Undergraduate Ambassadors Scheme in Mathematics

This module provides an opportunity for Level Three students to gain first hand experience of mathematics education through a mentoring scheme with mathematics teachers in local schools. Typically, each student will work with one class for half a day every week for 11 weeks. The classes will vary from key stage 2 to sixth form. Students will be given a range of responsibilities from classroom assistant to the organisation and teaching of self-originated special projects. Only a limited number of places are available and students will be selected on the basis of their commitment and suitability for working in schools.

20 credits

Operations Research

Mathematical Programming is the title given to a collection of optimisation algorithms that deal with constrained optimisation problems. Here the problems considered will all involve constraints which are linear, and for which the objective function to be maximised or minimised is also linear. These problems are not continuously differentiable; special algorithms have to be developed. The module considers not only the solution of such problems but also the important area of post-optimality analysis; i.e. given the solution can one answer questions about the effect of small changes in the parameters of the problem (such as values of the cost coefficients)?

10 credits

Topics in Number Theory

In this module we study intergers, primes and equations. Topics covered include linear and quadratic congruences, Fermat Little Theorem and Euler's Theorem, the RSA cryptosystem, Quadratic Reciprocity, perfect numbers, continued fractions and others.

10 credits

Metric Spaces

This unit explores ideas of convergence of iterative processes in the more general framework of metric spaces. A metric space is a set with a distance function which is governed by just three simple rules, from which the entire analysis follows. The course follows on from MAS207 `Continuity and Integration', and adapts some of the ideas from that course to the more general setting. The course ends with the Contraction Mapping Theorem, which guarantees the convergence of quite general processes; there are applications to many other areas of mathematics, such as to the solubility of differential equations.

10 credits

Complex Analysis

It is natural to use complex numbers in algebra, since these are the numbers we need to provide the roots of all polynomials. In fact, it is equally natural to use complex numbers in analysis, and this course introduces the study of complex-valued functions of a complex variable. Complex analysis is a central area of mathematics. It is both widely applicable and very beautiful, with a strong geometrical flavour. This course will consider some of the key theorems in the subject, weaving together complex derivatives and complex line integrals. There will be a strong emphasis on applications. Anyone taking the course will be expected to know the statements of the theorems and be able to use them correctly to solve problems.

10 credits

Generalised Linear Models

This module introduces the theory and application of generalised linear models. These models can be used to investigate the relationship between some quantity of interest, the “dependent variable”, and one or more “explanatory” variables; how the dependent variable changes as the explanatory variables change. The term “generalised” refers to the fact that these models can be used for a wide range of different types of dependent variable ,continuous, discrete, categorical, ordinal etc. The application of these models is demonstrated using the programming language R.

15 credits

Machine Learning

Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of “Big Data”, statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.

15 credits

Medical Statistics

This module introduces an important application of statistics: medical research, specifically, the design and analysis of clinical trials. For any new drug to be approved by a regulator (such as the Medicines and Healthcare products Regulatory Agency in the UK) for use on patients, the effectiveness of the drug has to be demonstrated in a clinical trial. This module explains how clinical trials are designed and how statistical methods are used to analyse the results, with a particular focus on ‘survival’ or ‘time-to-event’ analysis.

15 credits

Sampling Theory and Design of Experiments

Whereas most statistics modules are concerned with the analysis of data, this module is focussed on the collection of data. In particular, this module considers how to collect data efficiently: how to ensure the quantities of interest can be estimated sufficiently accurately, using the smallest possible sample size. Three settings are considered: sample surveys (for example when conducting an opinion poll), physical experiments, as may be used in industry, and experiments involving predictions from computer models, where there is uncertainty in the computer model prediction.

15 credits

Combinatorics

Combinatorics is the mathematics of selections and combinations. For example, given a collection of sets, when is it possible to choose a different element from each of them? That simple question leads to Hall's Theorem, a far-reaching result with applications to counting and pairing problems throughout mathematics.

10 credits

Differential Geometry

What is differential geometry? In short, it is the study of geometric objects using calculus. In this introductory course, the geometric objects of our concern are curves and surfaces. Besides calculating such familiar quantities as lengths, angles and areas, much of our focus is on how to measure the 'curvature' of a geometric object. The story is relatively simple for curves, but naturally becomes more involved for surfaces - and more interesting too.

10 credits

Fields

A field is set where the familiar operations of arithmetic are possible. It is common, particularly in the study of equations, that a field may need to be extended. This module will study the idea of field extension and the various problems that may arise as a result. Particular use is made of this to answer some of the classical problems of Greek geometry, to ask whether certain geometrical constructions such as angle trisection or squaring the circle are possible.

10 credits

Financial Mathematics

The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.

10 credits

Graph Theory

.A graph is a simple mathematical structure consisting of a collection of points, some pairs of which are joined by lines. Their basic nature means that they can be used to illustrate a wide range of situations. The aim of this course is to investigate the mathematics of these structures and to use them in a wide range of applications.

10 credits

Measure and Probability

The module will give students an additional opportunity to develop skills in modern analysis as well as providing a rigorous foundation for probability theory. In particular it would form a companion course to MAS436 (Functional Analysis) and MAS452 (Stochastic Processes and Finance), the latter of which is fundamentally dependent on measure theoretic ideas.

10 credits

History of Mathematics

The course aims to introduce the student to the history of mathematics. The topics discussed are Egyptian and Babylonian mathematics, early Greek mathematics, Renaissance mathematics, and the early history of the calculus.

10 credits

Knots and Surfaces

The course studies knots, links and surfaces in an elementary way. The key mathematical idea is that of an algebraic invariant: the Jones polynomial for knots, and the Euler characteristic for surfaces. These invariants will be used to classify surfaces, and to give a practical way to place a surface in the classification. Various connections with other sciences will be described.

10 credits

Codes and Cryptography

The word `code' is used in two different ways. The ISBN code of a book is designed in such a way that simple errors in recording it will not produce the ISBN of a different book. This is an example of an `error-correcting code' (more accurately, an error-detecting code). On the other hand, we speak of codes which encrypt information - a topic of vital importance to the transmission of sensitive financial information across the internet. These two ideas, here labelled `Codes' and `Cryptography', each depend on elegant pure mathematical ideas: codes on linear algebra and cryptography on number theory. This course explores these topics, including the real-life applications and the mathematics behind them.

10 credits

Groups and Symmetry

Groups arise naturally as collections of symmetries. Examples considered include symmetry groups of Platonic solids. Groups can also act as symmetries of other groups. These actions can be used to prove the Sylow theorems, which give important information about the subgroups of a given finite group, leading to a classification of groups of small order.

10 credits

Game Theory

The module will give students the opportunity to apply previously acquired mathematical skills to the study of Game Theory and to some of the applications in Economics.

10 credits

Practical and Applied Statistics

The overall aim of the course is to give students practice in the various stages of dealing with a real problem: objective definition, preliminary examination of data, modelling, analysis, computation, interpretation and communication of results. It could be said that while other courses teach how to do statistics, this teaches how to be a statistician. There will be a series of projects and other exercises directed towards this aim. Projects will be assessed, but other exercises will not.

20 credits

Bayesian Statistics

This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference and is becoming the approach of choice in many fields of applied statistics. This course will cover both the foundations of Bayesian statistics, including subjective probability, inference, and modern computational tools for practical inference problems, specifically Markov Chain Monte Carlo methods and Gibbs sampling. Applied Bayesian methods will be demonstrated in a series of case studies using the software package R.

10 credits

Applied Probability

The unit will link probability modelling to Statistics. It will explore a range of models that can be constructed for random phenomena that vary in time or space - the evolution of an animal population, for example, or the number of cancer cases in different regions of the country. It will illustrate how models are built and how they might be applied: how likelihood functions for a model may be derived and used to fit the model to data, and how the result may be used to assess model adequacy. Models examined will build on those studied in MAS275

10 credits

Time Series

Time series are observations made in time, for which the time aspect is potentially important for understanding and use. The course aims to give an introduction to modern methods of time series analysis and forecasting as applied in economics, engineering and the natural, medical and social sciences. The emphasis will be on practical techniques for data analysis, though appropriate stochastic models for time series will be introduced as necessary to give a firm basis for practical modelling. Appropriate computer packages will be used to implement the methods.

10 credits

Mathematical Biology

This module provides an introduction to the mathematical modelling of the dynamics of biological populations. The emphasis will be on deterministic models based on systems of differential equations that encode population birth and death rates. Examples will be drawn from a range of different dynamic biological populations, from the species level down to the dynamics of molecular populations within cells. Central to the module will be the dynamic consequences of feedback interactions within the populations. In cases where explicit solutions are not readily obtainable, techniques that give a qualitative picture of the model dynamics (including numerical simulation) will be used.

10 credits

You'll then take one of these two groups of modules, as determined by the Modern Languages Teaching Centre.

German Project Proficient 1

This unit aims to enable students at a 'Proficient' level of competence in the language to engage critically and independently with a highly specialised topic normally closely related to their main field of study in order to acquire expert use of subject-specific terminology and discourse and to consolidate advanced research skills in relation to the language and field of study. Working under regular supervision, students will complete a written portfolio (2,500 - 3,000 words) and prepare a structured oral presentation summarizing authoritatively their research for a specialist audience and demonstrating their acquisition of relevant academic and linguistic skills. https://www.sheffield.ac.uk/mltc/lfa/courses/german/project_proficient

10 credits

German-English Tandem Proficient 2

Students will be required to work in collaboration with a native-speaker with whom they will communicate in the target language. At the start of the module, students will exercise responsibility for the organisation of their own learning, establish and maintain contact with their partners, negotiate and set objectives; and seek and offer the correction of language errors. They should give proof of effective time-management, sequence sessions logically to demonstrate management of learning and demonstrate use of reviewing and evaluating procedures. They will be required to sign a learning contract and to keep a learner diary in the target language in which they will record progress made, plan their next steps and reflect on their work during the semester. Their progress will be monitored in advisory and conselling sessions with MLT Centre Tutors. https://www.sheffield.ac.uk/mltc/lfa/courses/german/tandem

10 credits

Or:

German-English Tandem Proficient 1

Students will be required to work in collaboration with a native-speaker with whom they will communicate in the target language. At the start of the module, students will exercise responsibility for the organisation of their own learning, establish and maintain contact with their partners, negotiate and set objectives; and seek and offer the correction of language errors. They should give proof of effective time-management, sequence sessions logically to demonstrate management of learning and demonstrate use of reviewing and evaluating procedures. They will be required to sign a learning contract and to keep a learner diary in the target language in which they will record progress made, plan their next steps and reflect on their work during the semester. Their progress will be monitored in advisory and counselling sessions with MLT Centre Tutors. https://www.sheffield.ac.uk/mltc/lfa/courses/german/tandem

10 credits

German Project Proficient 2

This unit aims to enable students at a 'Proficient' level of competence in the language to engage critically and independently with a highly specialised topic normally closely related to their main field of study in order to acquire expert use of subject-specific terminology and discourse and to consolidate advanced research skills in relation to the language and field of study. Working under regular supervision, students will complete a written portfolio (2,500 - 3,000 words) and prepare a structured oral presentation summarizing authoritatively their research for a specialist audience and demonstrating their acquisition of relevant academic and linguistic skills. https://www.sheffield.ac.uk/mltc/lfa/courses/german/project_proficient

10 credits