Students participate in a series of lecture courses from mathematicians in a number of branches of mathematics at a relatively advanced level.

The main course which runs each year for the entire two weeks is Number Theory. Students will explore modulo arithmetic, primes, Diophantine equations, rings and fields and much, much more.

Other courses which run for only one week vary from year to year and include:

- Projective geometry – students learn how parallel lines can meet at infinity, how a circle can cast a parabolic shadow and more
- Topology – mobius bands, klein bottles, why is a coffee cup like a doughnut and how to think about and analyse different surfaces
- Knot theory – which knots are equivalent to which other knots and how do we decide?
- Chaos theory – which rules produce the most predictable sequences and what sorts of rules generate pseudo-random sequences
- Cryptography – from basic substitution cyphers to number-theoretic codes
- Languages and Automata – how do computers process strings and decide waht is an acceptable word in a given language

Students attend a one hour lecture for each course each day. They also attend tutorials under the guidance of a range of staff: postgraduate students, mathematics teachers and academic mathematicians. They are also given time each evening to work on problems associated with each course.

By the end of the two weeks, most students are amazed at how much they have accomplished and post-school surveys indicate that the NMSS has succeeded in raising their intellectual horizons. Almost everyone returns home with a considerably enhanced view of their own potential.