Maths EE ideas library
Maths Extended Essay ideas: number theory
Primes, divisibility, Diophantine equations and the patterns in the integers. Number theory suits an EE because a narrow question can be stated exactly and the results can be proved, not just observed.
Number theory ideas (12)
- Which numbers are sums of two squares?Number theorySolid
- Generating every Pythagorean tripleNumber theoryAccessible
- Solving Pell's equation with continued fractionsNumber theoryAmbitious
- When Fermat's little theorem fools usNumber theorySolid
- Perfect numbers and Mersenne primesNumber theorySolid
- Divisibility tests in any baseNumber theoryAccessible
- Patterns in Collatz stopping timesNumber theorySolid
- Farey sequences and Ford circlesNumber theorySolid
- Counting partitions with generating functionsNumber theoryAmbitious
- How long is the repeating block of 1/n?Number theoryAccessible
- The Chinese remainder theorem and calendar cyclesNumber theoryAccessible
- Best rational approximations to πNumber theorySolid
Frequently asked questions
Is number theory a good area for a maths EE?
It can be, if you narrow it to one question you can answer with mathematics you understand. Make sure there is something to prove or analyse, not just a pattern to admire. A good number-theory EE states a conjecture from examples and then explains why it is true (or finds where it fails).
Can I use one of these research questions as it is?
Use it as a starting point. Change the case, the comparison or the limit until the question is your own, and agree it with your supervisor.
Other areas: Algebra · Analysis & calculus · Geometry · Probability · Statistics · Modelling · Graph theory · Codes & algorithms · Optimisation & games · History of maths