History of mathematics · Maths EE idea · Accessible
The problem of points
A research question to start from
How did Pascal and Fermat solve the problem of dividing stakes in an unfinished game, and how do their methods relate to modern probability?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Two historical methods for one problem, reconstructed and compared.
Mathematics you would need
- Combinatorics
- Expected value
- Recursion
- Binomial probabilities
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Solve the problem with Fermat's enumeration.
- Solve it with Pascal's recursive method.
- Show they agree in general and connect to binomial probabilities.
Scope and difficulty
Accessible. Accessible.
Pitfalls
- Letters summarised without mathematics.
- Only one method.
Where to start reading
Search a library catalogue or a university's open lecture notes for: problem of points Pascal Fermat solution; division of stakes. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).