Proof by induction is a really useful way of proving results about the natural numbers. If you haven't met this powerful technique before, this module will introduce you to the idea and method of induction. If you're already familiar, check out some of the problems and STEP questions that can be answered in this way!
article
An introduction to mathematical induction
This article gives an introduction to mathematical induction, a powerful method of mathematical proof.
article
Some induction examples
Some statements which can be proved using induction, and some example proofs.
problem
Dirisibly yours
Age
16 to 18
Challenge level
Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) +
17^(2n+1) is divisible by 33 for every non negative integer n.
problem
Tens
Age
16 to 18
Challenge level
When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?
page
Prepare for university - pure mathematics
Helpful preparation for those intending to study a course involving pure mathematics at university.
page
Prepare for university - applied mathematics
Helpful preparation for university for those intending to study a
course involving applied mathematics at university.
page
NRICH and Olympiads
A useful entry point into the NRICH site for those students interested in Mathematical Olympiad problems or the Maths Challenges.