![]() The Risk of Insurance: An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse.The Tragedy of the Commons: Our population of fish is dwindling, but how much do we need to reduce our production by in order to ensure the fish can replenish faster than we kill?.Modelling the Spread of a Virus: How long would it take for us all to be wiped out if a deadly influenza spreads throughout the population?.Mathematical Card Tricks: Look at the probabilities at play in the famous 3 card monte scam.The Stable Marriage Problem: Is there a matching algorithm that ensures each person in society ends up with their one true love? What is the next best alternative if this is not viable?.The Wobbly Table: Many tables are wobbly because of uneven ground, but is there a way to orient the tables to make sure they are always stable?.Stacking Balls: Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively?.Cracking a Password: How long would it take to be able to correctly guess a password? How much safer does a password get by adding symbols or numbers?.The Toast problem: If there is a room of some number of people, how many toasts are necessary for everyone to have toasted with everyone?.Rock Paper Scissors: If I played and won with rock already, should I make sure to change what I play this time? Or is it better to switch?.Monopoly: Is there a strategy that dominates all others? Which properties should I be most excited to land on?.Tic Tac Toe: What is the optimal strategy in this legendary game? Will my probability of winning drastically increase by some move that I can make?.The Prisoner’s Dilemma: Use game theory in order to deduce the optimal strategy in this famous situation.Linear regressions: Run linear regressions using OLS to predict and estimate the effect of one variable on another.Gini coefficient: Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality?.Football statistics #2: How does a manager sacking affect results?.Football statistics: Does spending a lot of cash during the transfer window translate to more points the following year? Or is there a better predictor of a team’s success like wages, historic performance, or player valuation?.Flow of traffic: How does mathematics feed into our traffic jams that we endure every morning?.Optimizing volumes: Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint.Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon?.Harmonic series: Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes.Birthday paradox: Why is it that in a room of people probability dictates that people are very likely to share a birthday?.Sum of all positive integers is -1/12? Explore this fascinating physics phenomenon through the world of sequences and series.The Chinese Remainder Theorem: An insight into the mathematics of number theory. ![]() Monty Hall problem: How does Bayesian probability work in this real-life example, and can you add a layer of complexity to it?.Pythagorean triples: Can you find patterns in what numbers form a pythagorean triple?.Pascal’s triangle: Discovering patterns within this famous array of numbers.Even though many of these topics led to high scores for some of our graduates in the past, it is important that you listen to the advice of your subject teacher before choosing any topic! NOTE: These topics are purely meant as inspiration and are not to be chosen blindly. Once you have chosen your topic, you may want to check out our other posts on how to structure and format your Maths IAor how to write your IA. To make matters worse, on top of just doing the dreaded maths exam, we’re also expected to write a Maths IA exploration into a topic of our choice! Where do you even begin such a task? How do you even choose a topic? To make things easier, we have plenty of free Maths resources!Firstly though, we’ve compiled 50 common Maths IA topics that may spark some creative juices and set you on your way to conquering one of the hardest assignments of the diploma! IB Maths is a struggle for most people going through their diploma.
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