Maths EE ideas library
Maths Extended Essay ideas: discrete mathematics and graph theory
Graphs, networks, combinatorics and counting. Many questions here can be explored with small cases by hand and then proved in general.
Discrete mathematics and graph theory ideas (10)
- Why five colours are enoughGraph theoryAmbitious
- Routes that use every street onceGraph theoryAccessible
- Ramsey numbers: order in any partyGraph theorySolid
- The Catalan numbers everywhereGraph theorySolid
- Derangements and the hat-check problemGraph theoryAccessible
- Colouring graphs to build timetablesGraph theorySolid
- Why greedy works for spanning treesGraph theoryAccessible
- How good is a quick tour?Graph theoryAmbitious
- Stable matchingsGraph theorySolid
- Surprising results from the pigeonhole principleGraph theoryAccessible
Frequently asked questions
Is discrete mathematics and graph 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. Start from small cases you can check by hand, find the pattern, then prove it. Keep a record of the cases: it is evidence for your reflection too.
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: Number theory · Algebra · Analysis & calculus · Geometry · Probability · Statistics · Modelling · Codes & algorithms · Optimisation & games · History of maths