APPLIED MATHEMATICS
PRECISION, PROOF AND FORMAL REASONING
Can a single equation capture centuries of philosophical debate about justice? Can game theory predict when rational people will betray one another? Can probability theory tell us when to trust our intuitions and when to override them?
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Mathematics is not merely calculation. It is a language for expressing ideas with precision, a method for detecting hidden assumptions, and a tool for reasoning about problems that ordinary language handles only imprecisely.
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Over seven days in Cambridge, you will learn mathematical techniques that philosophers use to construct rigorous arguments, economists use to model strategic behaviour, and political scientists use to analyse institutions and collective choice.
WHAT IS APPLIED MATHEMATICS?
Applied mathematics provides the formal tools for reasoning about strategic interaction, uncertainty, and collective choice.
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Our curriculum covers game theory (including – but by no means limited to – Nash equilibrium, sequential games, and mechanism design), decision theory under uncertainty, probability and statistics, propositional and predicate logic, and mathematical modelling of both markets and voting systems.
LOGIC VERSUS PERSUASION
The philosopher who claims "utility should be distributed equally" must eventually confront the mathematician's question: "what do you mean by utility, and what do you mean by equally?"
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After a week in Cambridge, you will possess both greater technical understanding of mathematical reasoning and an enhanced appreciation for when formal thinking clarifies problems and when it obscures them. You will understand not only how to construct proofs, but why they matter more than persuasive language.
FACULTY
You will learn from mathematicians, philosophers, and economists associated with the University of Cambridge, and other leading British universities. Our world-renowned faculty will help you to appreciate both the power and the limitations of mathematical approaches when tackling social, political, and economic questions.
IS THIS RIGHT FOR ME?
This programme suits students aged 15-19 who want to strengthen their quantitative reasoning skills. You need not have studied mathematics at an advanced level, though comfort with algebra and familiarity with basic calculus will be helpful.
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The programme is particularly appropriate for students applying to study PPE, mathematics, economics, philosophy, or related subjects at university. It equally suits students interested in other disciplines who recognise the value of formal reasoning and want to develop their capacity for it.
WHAT WILL I GET
FROM THIS EXPERIENCE?
You will develop the capacity to think with mathematical precision about questions of justice, equality, and rationality. This proves valuable regardless of your eventual field of study. Mathematics forces you to make assumptions explicit, to reason step-by-step, and to distinguish between what you can prove and what you merely suspect.
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Beyond specific techniques, you will explore how mathematical models enable rigorous reasoning about phenomena that ordinary language handles only imprecisely.
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After a week in Cambridge, you will approach arguments differently. You will notice when people conflate correlation with causation, when they assert claims that cannot be proven, and when informal reasoning masks questionable assumptions. These habits of mind extend far beyond mathematics itself.
CAMBRIDGE
Cambridge has been home to mathematical thought for centuries: from Newton's calculus, to Ramsey's decision theory, to contemporary scholarship in game theory and mechanism design. The university's tradition of applying mathematical rigour to substantive problems makes it an appropriate setting for this programme.
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The city itself combines medieval architecture with vigorous intellectual life. Its colleges, libraries, and academic culture create an environment conducive to serious study. You will have opportunities to explore both the university and the town during your free time.
HOUSING
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Accommodation is in single rooms with shared bathroom facilities. Male and female students will stay in different buildings. Students will also be living with people of the same age.
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Meals are served in the college dining hall (breakfast, lunch, afternoon tea and dinner).
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Free WiFi.​
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ARRIVAL & DEPARTURE
Arrival ​
The check-in time is between 10 am and 11.30 am. We advise you to arrive early to give you enough time to check in, be shown to your room and receive your course timetable. A welcome talk is scheduled for 12 o'clock midday. Parents and guardians are welcome to attend.
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If you would like to be met by a driver at the airport on the check in day, we are offering a shuttle service from Heathrow airport at an extra charge. If you plan to take the shuttle please book a flight that arrives no later than 8.30am.
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It is your responsibility to determine whether you need a visa and, if so, what kind of visa you need and how you should apply for it. Every overseas student must have a valid passport to enter the United Kingdom. You can find all the information about UK visas here. For attending a short course in the UK, the Standard Visitor Visa is the one you would need. We can provide individual support on request for those who will need a visa.
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We advise you to purchase travel insurance.
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Departure
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On the departure day, check out is by 9am.
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We will be running a shuttle to Heathrow airport at an extra cost. If you plan to take the shuttle please book a flight that departs no earlier than 12 midday.
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Our staff will be available to help you on the departure day so you don't miss your flight!
