Year 12 Maths Summer School - Logic and Proof

Taking part in the summer school is completely free*

 *food will be provided and UCL will fund travel to and from its campus for eligible students, in accordance with the university’s travel policy.

Experience life as a UCL student by taking part in university sessions where you will learn about student finance and repayments, get information on how to write and structure your personal statement, and find out about student life at UCL. 

Apply for a place on the Summer School

As well as the above you will also take part in academic sessions to help you decide if Mathematics at UCL is right for you. At the heart of mathematics, we have reasoning and rigour but the ability to convey ideas and write convincing arguments goes beyond mathematics. This course covers the fundamentals of logic and standard mathematical proofs. It naturally builds from interpreting and creating logical statements, to thinking critically and identifying errors in deductions, leading to being able to construct mathematically sound proofs. You can find a short list of topics below: 

• Logical operators and truth tables (“or”, “and”, “not”)
• Statements with “if”, “only if” and “if and only if”   
• Converses and contrapositives
• Necessary and sufficient conditions
• Universal and existential quantifiers (“for all”, “there exists”)
• Proofs: by deduction, by contradiction, by contraposition, existence proofs, disprove by counterexample
• Identifying logical errors in proofs
   

This summer school will be particularly helpful for students considering applying to university courses that require the TMUA admissions test.

Deadline for applications is 2 June 2026 please note you will not receive a response until after this date. 
 

Mathematics:

Entry Requirements

Grades - A*A*C learn more about contextual offers
Subjects - A*A* in Mathematics and Further Mathematics, or A*AC with A*A in Mathematics and Further Mathematics, in any order, and a 2 in any STEP Paper or a Distinction in the Mathematics AEA. Biology, Chemistry, Computer Science, Economics, English Language, English Literature, Physics and Statistics preferred.
GCSE - English Language and Mathematics at grade C or 4.

Additional criteria -

This programme does not accept resits. A resit is a second or subsequent attempt to improve a qualification outcome, for which you already hold an award. For further information on what UCL considers a resit, please see UCAS explained. 

Participants for this programme will be selected using the shortlisting criteria found on the Who we work with webpage to prioritise young people from the least represented groups at UCL.

Sign up & get in contact!

To submit an application please complete this sign-up form with all of your details. You will need a parent or guardian present with you while you complete the form. If you have any questions regarding the summer school, please contact MAPS-WP@ucl.ac.uk. 

Summer School 

Code of Behaviour

Any questions?

If you have any questions regarding the summer school, please contact MAPS-WP@ucl.ac.uk.