IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
https://www.youtube.com/watch?v=mhlc7peGlGg A brief summary of the Monty Hall problem. There are 3 doors. Behind 2 doors are goats and behind 1 door is a car. You choose a door at random. The host then opens another door to reveal a goat. Should you stick with your original choice or swap to the other unopened door?... Continue Reading →
Maths Games and Markov Chains This post carries on from the previous one on Markov chains - be sure to read that first if this is a new topic. The image above is of the Russian mathematician Andrey Markov [public domain picture from here] who was the first mathematician to work in this field (in... Continue Reading →
Life on the Beach with Markov Chains Markov chains are exceptionally useful tools for calculating probabilities - and are used in fields such as economics, biology, gambling, computing (such as Google's search algorithm), marketing and many more. They can be used when we have the probability of a future event dependent on a current event.... Continue Reading →
The Barnsley Fern: Mathematical Art This pattern of a fern pictured above was generated by a simple iterative program designed by mathematician Michael Barnsely. I downloaded the Python code from the excellent Tutorialspoint and then modified it slightly to run on repl.it. What we are seeing is the result of 40,000 individual points - each plotted... Continue Reading →
Martingale II and Currency Trading We can use computer coding to explore game strategies and also to help understand the underlying probability distribution functions. Let's start with a simple game where we toss a coin 4 times, stake 1 counter each toss and always call heads. This would give us a binomial distribution with... Continue Reading →
https://www.youtube.com/watch?v=Ry3B9hJbBfk The Martingale system The Martingale system was first used in France in 1700s gambling halls and remains used today in some trading strategies. I'll look at some of the mathematical ideas behind this and why it has remained popular over several centuries despite having a long term expected return of zero. The scenario You... Continue Reading →