UCL Mathematical & Physical Sciences


Year 12 Maths Summer School - Logic and Proof

Join UCL’s Mathematics department for a free 5 day summer school for current year 12 students from 15-19 July. This is a chance to experience academic content first hand.

Taking part in the summer school is completely free

 *food and travel to and from the summer school are all included.

Experience life as a UCL student by taking part in general university sessions where you will learn about student finance and its repayments, how to write and structure the best personal statement, find out about UCL and what it can offer you. 

Maths Summer school

Sign up to the Summer School

As well as the above you will also take part in the academic content to help you decide if Maths 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 induction, by contradiction, by contraposition, existence proofs, disprove by counterexample
  • Identifying logical errors in proofs


Entry Requirements

Grades - A*A*C *learn more about contextual offersSubjects - 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.GCSEs - English Language and Mathematics at grade C or 5.

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 Elise Polley