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# BSc (Honours) Mathematics - Learning outcomes

## Educational aims

This degree introduces you to mathematical concepts and thinking, and helps you to develop a mathematical approach, with the option to engage with some elements of statistics. You should achieve

- familiarity with the essential ideas of pure mathematics (particularly analysis, linear algebra and group theory), with the opportunity also to become acquainted with some of the following: number theory, combinatorics, metric spaces, rings, fields and groups, complex analysis
- ability to apply the main tools of applied mathematics (particularly Newtonian mechanics, differential equations, vector calculus, numerical methods and linear algebra), with the opportunity also to meet some of: advanced calculus, fluid mechanics, advanced numerical analysis, deterministic and stochastic dynamics
- an opportunity to become acquainted with some of the following: data analysis, applications of probability, linear statistical modelling, mathematical statistics
- ability to model real-world situations and to use mathematics and/or statistics to help develop solutions to practical problems
- ability to follow complex mathematical and/or statistical arguments and to develop mathematical and/or statistical arguments of your own
- experience of study of mathematics and/or statistics in some breadth and depth
- understanding of some of the more advanced ideas within mathematics and/or statistics
- development of your capability for working with abstract concepts
- ability to communicate mathematical and/or statistical ideas and conclusions, and mathematical proofs effectively
- ability to work on mathematical and/or statistical modelling problems and their validation
- skills necessary to use mathematics and/or statistics in employment, or to progress to further study of mathematics and/or statistics
- ability to use a modern mathematical and/or statistical computer software package in pursuance of the above aims.

## Learning outcomes

### Knowledge and understanding

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

- elements of linear algebra, analysis and group theory, the concepts behind the methods of Newtonian mechanics, differential equations, vector calculus, linear algebra and numerical analysis, and be able to model real-world situations using these concepts.
- the basic elements of data analysis and statistical methods, and optionally more advanced topics in statistics
- a selection (depending on what you study at earlier stages of the qualification) of advanced topics including

(a) pure mathematics: number theory, combinatorics, metric spaces, further group theory, complex analysis, rings and fields

(b) applied mathematics: advanced calculus, fluid mechanics, advanced numerical analysis, partial differential equations, deterministic and stochastic dynamics

(c) statistics: applied probability, linear statistical modelling, mathematical statistics, the ability to model real-world situations using these methods.

### Cognitive skills

On completion of this degree, you will have acquired ability

- in mathematical and statistical manipulation and calculation, using a computer package when appropriate
- to assemble relevant information for mathematical and statistical arguments and proofs
- to understand and assess mathematical proofs and construct appropriate mathematical proofs of your own
- to reason with abstract concepts
- to make judgements in selecting and applying a wide range of mathematical and/or statistical tools and techniques
- in 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:

- apply mathematical and statistical concepts, principles and methods
- analyse and evaluate problems (both theoretical and practical) and plan strategies for their solution
- be an independent learner, able to acquire further knowledge with little guidance or support.

### Key skills

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

- read and/or listen to documents and discussions having mathematical and/or statistical content, with an appropriate level of understanding
- communicate information having mathematical and/or statistical content accurately and effectively, using a format, structure and style that suits the purpose
- prepare mathematical and/or statistical content for a range of purposes, which may include writing for both specialist and non-specialist audiences; writing reports on mathematical or statistical experiments or models; producing and/or delivering a presentation on a mathematical or statistical. Preparation of some content may require working collaboratively with others on projects
- exhibit a high level of numeracy, appropriate to a graduate in mathematics
- use information technology with confidence to acquire and present mathematical and statistical knowledge, to model and solve practical problems and to develop mathematical insight.

## 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 with practice exercises, guides to study and mathematical handbooks, comprehensive websites and a range of multimedia material (including computer software). Modules at higher levels build on the foundations developed in pre-requisite modules at lower levels.

You will work independently with the distance-learning materials, while being supported by a tutor. You will be offered the opportunity to attend face-to-face or online tutorials and day schools, which you are strongly advised to attend. You are also encouraged to interact with other students, for example via moderated online forums.

Written tutor feedback on assignments provides you with individual tuition and guidance. Your learning is further assessed through examinations and projects. Generally, you are permitted to bring the module handbook into examinations, thus reducing the need for memorisation, and concentrating on your ability to apply concepts and techniques and express them clearly and coherently. Your module results will be determined by your performance on both the assignments and the examination/project. For each module the final result will be based on a combination of the examination (or end-of-module assessment) score and the score obtained on (or engagement with) the continuous assessment. In some cases there is a threshold on individual components.