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This is the British International School Phuket’s IB maths exploration (IA) page.This list is for SL and HL students – if you are doing a Maths Studies IA then go to this page instead.I have supplemented these with some more possible areas for investigation.With a bit of ingenuity you can enrich even quite simple topics to bring in a range of mathematical skills.5) Diophantine equations: These are polynomials which have integer solutions.

26) Fermat’s little theorem: If p is a prime number then a^p – a is a multiple of p.

Algebra and number 1) Modular arithmetic – This technique is used throughout Number Theory.

For example, Mod 3 means the remainder when dividing by 3.

How all our digital communications are kept safe through the properties of primes. A post which looks at the maths behind this particularly troublesome series. How strange things happen when we start to manipulate divergent series.

33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur.

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