Mathematics develops ways to work with numbers, structure, reasoning and problems. Its areas include pure, applied and computational mathematics, with applications across several fields.
Foundations and progression
Related study considers a progression from fundamental concepts to more advanced mathematical work. That sequence is an important part of evaluating a study plan: the preparation expected at each stage should be clear, as should the relationship between introductory material and later topics.
Pure, applied and computational interests
Pure mathematics, applied mathematics and computational mathematics are the broad interests. The Applied Mathematics guide offers related reading on numerical methods, models and the assumptions connecting mathematics with an application.
Study connects applied mathematics with economics, engineering and biology. In considering such an application, it is useful to distinguish the mathematical question from the assumptions about the situation being represented.
Research and practical problem solving
Research, industry projects and practical mathematical problems recur. These themes emphasize the connection between enquiry and the use of mathematical reasoning. A project needs a defined problem and an explanation of how its mathematical work relates to that problem.
A prospective student can ask to see the actual project requirements and assessment approach.
Resources and academic exchange
Mathematical literature, computing resources and discussion support different aspects of learning. Reading can develop an argument or introduce a method, while computational work can explore an example or model. Discussion offers an opportunity to explain reasoning, consider a different approach and test whether the steps in an argument are clear. The Computer Science guide provides related context for algorithms, computational tools and the reasoning behind their use.
Professional interests and further study
Finance, technology, data science and academic work are among the professional interests. The Statistics guide adds a related perspective on data, probability and the interpretation of analytical results.
Planning further study
For a particular course, request the current curriculum, entry requirements, award details and assessment arrangements. Confirm practical supervision, facilities, placements and any professional recognition directly for the intended programme.
Questions about this subject
What makes a mathematical project clear?
A clear project states the problem, the assumptions and the mathematical reasoning used. It explains how the result relates to the question and what the analysis does not establish.
Can a worked example replace understanding a mathematical argument?
Examples and applications can make an abstract idea easier to examine, but a worked example is not a replacement for understanding the reasoning behind a result.
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The MIT Single Variable Calculus course connects differentiation and integration with examples and applications. This archived external course provides an example of how mathematical topics can be organised for study.
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