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# BA/BSc (Honours) Mathematics and Statistics - Learning Outcomes

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## Educational aims

This degree introduces you to mathematical and statistical concepts and thinking, and helps you to develop a mathematical approach. By the end of the degree you will be:

• familiar with the key ideas of probability and statistics (particularly basic distributions and inference, linear and generalised linear models, time series, multivariate statistics, Bayesian statistics applied probability including Markov processes), and have an ability to apply their main tools to a range of applications
• familiar with the essential ideas of pure mathematics (particularly analysis, linear algebra and group theory), and the ability to recognise a rigorous mathematical proof
• able to apply the main tools of applied mathematics (particularly Newtonian mechanics, differential equations, vector calculus, numerical methods and linear algebra)
• able to model real world situations and to use mathematics and statistics to help develop solutions to practical problems
• able to follow complex mathematical and statistical arguments and to develop brief arguments of your own
• experienced in of the study of mathematics and statistics in some breadth and depth
• able to understand some of the more advanced ideas within mathematics and statistics
• capable of working with abstract concepts
• able to communicate mathematical and statistical ideas, arguments and conclusions effectively
• equipped with the skills necessary to use mathematics and statistics in employment, or to progress to further study of mathematics and/or statistics
• able to use modern mathematical and statistical computer software packages.

## Learning outcomes

The learning outcomes of this degree are described in four areas (although there is considerable overlap between the last two).

### Knowledge and understanding

On completion of this degree, you will have knowledge and understanding of:

• a range of simple and more advanced methods for analysing statistical data (including data from medical applications, time series data and multivariate data), working with probability models and carrying out statistical inference (including in particular methods for linear and generalised linear models, and Bayesian methods)
• one or both of the elements of linear algebra, analysis and group theory and/or the concepts behind the methods of Newtonian mechanics, differential equations, multi-variable functions, vector calculus, linear algebra, numerical analysis and mathematical modelling.

The degree programme is flexible, offering you a considerable choice of mathematical topics at Level 3. You will further develop your mathematical knowledge and understanding in the topics you choose to study. Currently the following topics are available:

• pure mathematics: number theory, combinatorics, geometry, topology, mathematical logic, further group theory and analysis
• applied mathematics: advanced calculus, fluid mechanics, advanced numerical analysis, methods for partial differential equations, variational principles.

The topics may change from time to time, and if they do they will be replaced by others at a similar level and providing similar learning outcomes.

### Cognitive skills

On completion of this degree, you will have acquired

• the ability to carry out mathematical and statistical manipulation and calculation, using a computer package when appropriate
• the ability to assemble relevant information for mathematical or statistical arguments and proofs, and/or judgment in selecting and applying a wide range of mathematical tools and techniques
• the ability to construct appropriate mathematical and statistical arguments of your own
• the ability to create appropriate mathematical and statistical models and draw justifiable inferences
• the ability to reason with abstract concepts
• qualitative and quantitative problem-solving skills.

### Practical and/or professional skills

On completion of this degree, you will be able to demonstrate the following skills

#### Application

Apply mathematical and statistical concepts, principles and methods.

#### Problem solving

Analyse and evaluate problems (both theoretical and practical) and plan strategies for their solution.

#### Information technology

Use information technology with confidence to acquire and present mathematical and statistical knowledge and data, to model and solve practical problems and to develop mathematical and statistical insight.

#### Independence

Be an independent learner, able to acquire further knowledge with little guidance or support.

### Key skills

On completion of the degree, you will be able to demonstrate the following key skills:

Communication

• Read and/or listen to documents and discussions that have mathematical or statistical content, with an appropriate level of understanding.
• Communicate information having mathematical or statistical content, accurately and effectively in written form, using a structure and style that suits the purpose.

Application of number

• Exhibit a high level of numeracy, appropriate to a graduate in Mathematics and Statistics.

Information technology

• Use information technology with confidence to acquire and present mathematical and statistical knowledge, to model and solve practical problems and to develop mathematical insight.

Learning how to learn

• Be an independent learner, able to acquire further knowledge with little guidance or support.

## Teaching, learning and assessment methods

Knowledge, understanding and application skills, as well as cognitive (thinking) skills, are acquired through distance-learning materials that include specially written module texts, guides to study, assignments and (where relevant) projects, and specimen examination papers; through a range of multimedia material (including computer software on some modules); and through tutor feedback on your assignments.

You will work independently with the distance-learning materials, but are encouraged (particularly at Level 1) to form self-help groups with other students, communicating face-to-face, by telephone, by email or by computer conferencing. Students will generally be supported by optional tutorials and day schools, which you are strongly advised to attend whenever possible.

Written tutor feedback on assignments provides you with individual tuition and guidance. Modules at higher levels build on the foundations developed in recommended modules at lower levels.

Using mathematics (MST121) has an examination, as do most modules at Levels 2 and 3. Generally, these permit you to bring and use the module handbook. This reduces the need for memorisation and allows you to concentrate on your ability to apply concepts and techniques and express them clearly and coherently. For each individual module, you must pass both the continuous assessment and the examination (or end-of-module assessment) in order to obtain a pass. At Level 2 and above your pass will be graded, and the grades will contribute to the determination of the class of Honours degree that you are awarded.

Skills of applying mathematics and statistics are taught and assessed throughout the programme. Problem solving as described above is assessed, particularly in the Statistics part of the programme (and the Applied Mathematics modules if you choose them).

The use of information technology is developed in the modules Using mathematics (MST121), Exploring mathematics (MS221), Mathematical methods and models (MST209), Mathematical methods and models (MST210), Analysing data (M248), Practical modern statistics (M249), Linear statistical modelling (M346), Optimization (M373) and Graphs, networks and design (MT365). All of these modules, with the exception of MT365, also assess this skill.

Communication skills are developed and assessed throughout the programme as you work on assignments and receive feedback from your tutor.

Independence: the university experience, including distance learning using OU study materials, should develop your ability as a strong independent learner.

Application of number is crucial for all higher-level mathematical and statistical skills. It is explicitly taught and assessed in Discovering mathematics (MU123). The other modules in the programme assume that you already have this skill to an extent appropriate to the module level. On completion of the degree you will certainly have acquired a high level of numeracy.

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