BA/BSc (Honours) Mathematics - Learning Outcomes
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This degree introduces you to mathematical concepts and thinking, and helps you to develop a mathematical approach. Our aims are that 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: number theory, mathematical logic, combinatorics, geometry, topology
- 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
- ability to model real-world situations and to use mathematics to help develop solutions to practical problems
- ability to follow complex mathematical arguments and to develop mathematical arguments of your own
- experience of study of mathematics in some breadth and depth
- understanding of some of the more advanced ideas within mathematics
- development of your capability for working with abstract concepts
- ability to communicate mathematical ideas, proofs and conclusions effectively
- ability to work with others on mathematical modelling problems and their validation
- skills necessary to use mathematics in employment, or to progress to further study of mathematics
- ability to use a modern mathematical computer software package in pursuance of the above aims.
You will also have the opportunity to develop knowledge of, and the ability to apply, some important concepts and techniques of Statistics.
Learning outcomes
The learning outcomes of this degree (of which there is considerable overlap between the last two) are described in four areas:
Knowledge and understanding
On completion of this degree, you will:
- know and understand the elements of linear algebra, analysis and group theory
- know and understand 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 degree programme is flexible, offering you also 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.
There is the possibility of limited study in related areas, according to your interests: physics and/or statistics up to Level 3, or the history of mathematics at Level 2.
Depending on your Level 3 study, you will be able to apply your knowledge and understanding to practical problems or to further advancing your understanding of mathematics. (For example, after completion of this degree you may wish to consider going on to the Mathematics MSc programme.)
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:
- ability in mathematical manipulation and calculation, using a computer package when appropriate
- ability to assemble relevant information for mathematical arguments and proofs
- ability to understand and assess mathematical proofs and construct appropriate mathematical proofs of your own
- ability to reason with abstract concepts
- judgement in selecting and applying a wide range of mathematical tools and techniques
- 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 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 knowledge, to model and solve practical problems and to develop mathematical insight
Communication: communicate relevant information accurately and effectively, using a form, structure and style that suit the purpose (including written and face-to-face presentation)
Collaboration: work collaboratively with others on projects requiring mathematical knowledge and input
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 having mathematical content, with an appropriate level of understanding
- communicate information having mathematical content accurately and effectively, using a form, structure and style that suits the purpose (including face-to-face presentation)
- work collaboratively with others on projects requiring mathematical knowledge and input.
Application of number
- exhibit a high level of numeracy, appropriate to a Mathematics graduate.
Information technology
- use information technology with confidence to acquire and present mathematical 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 feedback from tutors 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 online forums. 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 pre-requisite modules at lower levels.
Level 1 modules have no examination. (The module Using mathematics (MST121) had an examination up to and including its February 2004 presentation.) Most modules at Levels 2 and 3 do have a final examination. Generally, these permit you to bring and use the module handbook, thus reducing the need for memorisation and concentrating 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.
Application
Skills are taught and assessed throughout the programme. Problem solving as described above is assessed, particularly in the Applied Mathematics part of the programme (and the Statistics modules if you choose them).
Information technology
The use of computing and IT is developed in the modules Using mathematics (MST121), Exploring mathematics (MS221), Mathematical methods and models (MST209), Mathematical modelling (MSXR209), Optimization (M373) and Graphs, networks and design (MT365). All of these modules, with the exception of MT365, also assess this skill. (Some MT365 assignments allow, but do not require, you to use software packages in your assignments.)
Communication
Communication skills are developed and assessed throughout the programme as you work on assignments and receive feedback from your tutor.
Communication skills in a face-to-face context, as well as collaboration skills, are developed by the compulsory module Mathematical modelling (MSXR209), which involves a residential week including assessed group work.
Independence
The university experience, including distance learning using OU study materials, should develop your ability as a strong independent learner.
The acquisition of the skills of communication, information technology and independence (or learning how to learn) have been covered above.
Application of number is crucial for all higher-level mathematical skills. It is explicitly taught and assessed in the Openings module Starting with maths (Y162) and (at a higher level) 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.