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Diploma of Higher Education in Mathematical Sciences - Learning outcomes

Educational aims

This diploma develops the concepts and approach of mathematics, providing a basis for the study of mathematics and the mathematical sciences. You should achieve:

  • understanding of the notion of a mathematical approach
  • ability to use mathematical and statistical software
  • the skills necessary to use mathematics in employment
  • an introduction to some topics in statistics and probability
  • understanding of the basic ideas of at least two of the following three strands:
    (a) pure mathematics (particularly analysis, linear algebra and group theory), and the technique of recognising and constructing valid mathematical proofs
    (b) applied mathematics (particularly mathematical methods including calculus, mathematical modelling, mechanics and numerical methods)
    (c) exploratory data analysis, models for distributions, statistical inference, experimental design, statistical modelling techniques and a range of probabilistic models.

Learning outcomes

Knowledge and understanding

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

  • the need for rigorous mathematical proof, and  ability to use and understand some of the techniques involved
  • at least two of the following three strands:
    (a) the elements of linear algebra, analysis and group theory and understand and use some of the techniques of rigorous mathematical proof
    (b) the basic concepts behind the methods of Newtonian mechanics, differential equations, vector calculus, linear algebra and numerical analysis
    (c) the use and application of a variety of methods for exploring, summarising and presenting data; and a range of methodologies for data analysis.

Cognitive skills

On completion of this diploma, you will have acquired (at a level appropriate to the diploma) ability:

  • in mathematical and statistical manipulation and calculation, using a computer package when appropriate
  • to analyse real world problems in appropriate contexts
  • to select and apply a range of mathematical/statistical tools and techniques, and the ability to create appropriate mathematical or statistical models and draw appropriate inferences
  • to reason with abstract concepts
  • to interpret the results obtained from analysis of mathematical or statistical models
  • in qualitative and quantitative problem-solving skills.

Practical and/or professional skills

On completion of this diploma, you will be able to demonstrate the following skills (appropriate to the level of the diploma):

  • apply mathematical and statistical concepts, principles and methods
  • analyse 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 diploma, you will be able to demonstrate the following key skills:

  • read and/or listen to documents and discussions having mathematical/statistical content, with an appropriate level of understanding
  • communicate information having mathematical or statistical content accurately and effectively, using a format, structure and style that suits the purpose
  • prepare mathematical 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 topic. Preparation of some content may require working collaboratively with others on projects
  • exhibit a high level of numeracy, appropriate to the level of the diploma
  • use information technology with confidence to acquire and present mathematical and statistical knowledge, and to model and solve practical problems.

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 Stage 2 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 online tutorials, 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.