# Mathematics Summer School

Guided only by their feelings for symmetry and simplicity, creative mathematicians are inspired by the art of mathematics rather than by any prospect of its ultimate usefulness. And yet, we live in a world in which mathematical ideas find application in almost every branch of human knowledge. Since ancient times, the puzzles, problems and challenges that arise from mathematical thought have shaped the way in which we interpret both the physical and the spiritual. In a rapidly changing technological world, mathematics remains as critical as ever to our scientific, philosophical and mechanical endeavours.

The Mathematics Summer School is an opportunity for A-level students to spend five days exploring some of the most exciting and challenging ideas in contemporary mathematics.  As a general structure, students will develop a theoretical understanding of a particular branch of mathematics in the morning session, before exploring the practical applications of these ideas in the afternoon. Topics will include:

• Linear Algebra: vector spaces, linear independence, matrix mechanics, eigenvectors, Leslie matrices, Google PageRank algorithms and encryption.
• Differential Equations: Linear and non-linear differential equations, first and second order differential equations, population growth, financial markets, radioactivity and quantum mechanics.
• Series: convergence, divergence, comparison tests, harmonic series, Taylor series, estimating pi and the Riemann-zeta function.
• Calculus: limits, differential calculus, integral calculus, formal definitions, the fundamental theorem of calculus, applications.
• Proofs and Algorithms: proof by induction, proof by contradiction, graph theory, randomised algorithms and recursive algorithms.
• Set Theory: natural numbers, integers, rational numbers, irrational numbers, real numbers, algebraic numbers, transcendental numbers, counting infinities, cardinality, power sets, Cantor’s diagonalization argument, paradoxes.
• Cryptography: substitution ciphers, public key cryptography, RSA algorithm, modular arithmetic, code-breaking.

Classes are small, typically containing twelve to fifteen students, all of whom should have a passion for mathematics, a curiosity to build on their existing knowledge and be keen to embrace and exchange new ideas. An expert Tutor will lead each session in a seminar format, but learning will be largely student-led wherever practical. Classes will focus on discussion and on problem questions and exercises, creating a comfortable environment for students to share ideas amongst their peers and to progress from their existing knowledge toward more challenging material.

Feedback from previous students

‘If you love Mathematics and are thinking of taking the subject beyond A-level do not hesitate to attend this course. I came away from this week with crazy enthusiasm for maths as well helpful guidelines and knowledge to support my career in the subject. I made some great new friends and met inspirational maths-minded people who I will never forget!’

‘You won’t regret it! If you love the subject, you’ll love the entire week. It gives an unparalleled taster into university mathematics and allows you to explore some absolutely fascinating concepts – some of which will be almost entirely alien to you! The teachers were excellent and the friendly atmosphere ensures that everyone has a great time. I wish I could go again.’

‘The Mathematics Summer School is a great introduction to maths at university. During the five days, I was presented with a variety of new topics in mathematics which had not been covered in the A level course. I would highly recommend attending the Debate Chamber Summer School, as it gives you a great opportunity to look at other areas of maths.’

‘This is a great event as it gives you lots of exposure to university style teaching and ideas, really testing your knowledge and dedication to your subject. The tutors guide you through it, pushing you to your full potential but in a fun and engaging manner. This course is definitely worth taking part in.’

Bursaries

Debate Chamber is committed to ensuring that financial circumstances do not prevent any student from attending our events. Students can apply for bursaries covering up to 100% of the course fee through our website.

How can my students attend?

The Mathematics Summer School will be held at University of London venues in Bloomsbury, Central London, and is open to students aged 15 – 18 who have completed a minimum of AS-Level Mathematics (or the equivalent in another qualification structure) at the time of the course.

The summer school will take place on 17th – 21st July (and repeated 7th – 11th August and 21st August – 25th August) 2017.

You can find full details of schedules, dates, costs, student reviews and tutors at http://debatechamber.com/project/mathematics-summer-school/.

To book a place please visit http://debatechamber.com/project/mathematics-summer-school/, call us on 0845 519 4827, or email info@debatechamber.com. Places will be allocated on a first come first served basis.