25 Unique Math IA Ideas
Need help with IB Exam preparation or Internal Assessment? Struggling with understanding concepts?
Sign up for our Trial IB Lesson Now!
What is an internal assessment?
It is a project that every IB student has to complete to achieve the diploma. The process is aided by your course teacher (or your tutor) to create an in-depth mathematical exploration. The work is in the majority completed on your own, therefore it makes room for creativity, expression of your personal interests and creating fascinating connections between seemingly disconnected subjects. As the topic has to be decided upon by you, many students find it challenging or even intimidating to come up with just the right idea for their IA. We have therefore created a list with original ideas that could inspire your next mathematical exploration!
Characteristics of a good Math IA
The goal of the exploration is to show your ability to use the knowledge acquired during classes in practice. It does not need to be innovative or groundbreaking, so you don’t have to worry about needing to come up with new areas of mathematics. You are asked to create a research question, which by using appropriate mathematical formulas and calculations can be answered. You don’t have to limit yourself to just one area of maths. Creating an exploration that ties together areas such as trigonometry and calculus will make it more interesting, as well as help you see just how closely related all fields are to each other.
As you will spend many days working on the IA, you should choose a subject that personally interests you. An exploration written on an easier topic but showing clear understanding and passion will always be perceived better than a complicated one, which does not resonate with you in any way.
25 original Math IA ideas
Koch Snowflake and other fractals
The most interesting feature of the snowflake is its finite area, yet an infinite perimeter! You can find general equations describing these two features for different iterations, and explore how they are connected to arithmetic and geometric sequences.
Cryptography and Caesar’s Cipher
This topic allows you to explore the mathematics and logic behind message encryption and decryption. If you are a fan of cybersecurity, you will definitely enjoy learning how Caesar Cipher works and how to apply and use it efficiently.
Zipf’s law
Ever wondered how frequent certain words are in English, or whether this correlation exists in other languages? This law will help you learn about and explore speech and writing patterns, with the use of statistics and probabilities.
Linear and non-linear regression
What’s the best age to be at the prime of one’s athletic abilities? What LEGO set has the best price to amount of pieces ratio? By finding correlation coefficients and defining functions describing such relationships you can find answers to these and many more questions!
Modelling and optimizing everyday objects
Do you need to paint an object that has an original shape and don’t know what volume of paint to buy? Through the use of calculus, you could find functions describing the contours of the object, which will allow for finding its area and volume.
Euler’s identity
Complex numbers may not be as complex as they seem! This beautiful identity can be explored through the use of the Taylor series, the polar form of complex numbers, polynomial interpretations and many more. A true treat for fans of pure mathematics.
Fourier series
This is a way of representing a seemingly patternless wave as a combination of the sine and cosine functions. If your personal interests involve music, learning about sound waves through the use of the Fourier series will help you understand the mathematics behind it.
Population growth and decline
In the post-Covid world, we now have a better understanding of how viral infections can spread. What if there was a mathematical expression that could help us predict the potential growth or decline of such viruses? Exponential and logistic functions are the best solution for the exploration of such models.
Benford’s law
In times where information transfer occurs within fractions of a second, the amount of fake news and skewed statistics is on a steady rise. Is there a way to successfully identify fake data? Benford’s law does exactly that, proving that there is a pattern in the way people fake their data.
Markov chain
When writing emails, Gmail’s suggested next words often correctly predict what you were meaning to say. But how exactly does that work? Markov chain is the answer you are looking for. You can explore this model, which predicts the likelihood of certain events occurring based on the outcome of the most recent event.
Coastline paradox
A real-life application of fractals! If the Koch snowflake seemed too theoretical and detached from reality, this is a great example of its use in practice. Have you ever thought about how exact the lengths of country borders are? This paradox will resolve your doubts and explain the mathematics behind coastlines.
Palindrome numbers
You have definitely heard of palindromes such as kayak or level, but what about 123 321? These numbers share interesting properties regarding their divisibility, for example, by 3 and 11. You can also take a look at general formulas to check whether a number is a palindrome.
Basel problem and series
Thanks to Euler, since 1735 we have had a solution to one of the greatest problems in number theory. The Basel problem deals with the exact series value of reciprocals of squares of positive integers. If limits and series sparked your interest in class, the exploration of Euler’s solution can be a great exercise for your mathematical skills.
Riemann sphere
A great example of non-Euclidean geometry, which is the basis for our understanding of the universe. You can think of Riemann’s sphere as the Argand (complex) plane wrapped to form a sphere. Another great topic for fans of pure mathematics would involve an in-depth analysis of complex numbers and their applications.
Modelling projectile motion
For any physics fans, this can be the perfect topic for you! In classes, you have encountered questions about a ball thrown into the air at a certain angle, yet were told to ignore air friction. Your IA could explore what would happen if that friction became no longer negligible, and how that can affect the equations describing the motion of the projectile.
Monte Carlo simulations
This is a model used to model the probability of different events, which are easily affected by random variables. Examples of its application are the prediction of the probability of a client running out of money during their retirement plan, and estimating the value of 𝜋.
Modelling radioactive decay
Ever wondered how scientists predicted the radioactive decay that occurred due to the Chernobyl or Three Mile Island accidents? Through the use of an exponential function and its derivative, you can find the amount of radioactive materials remaining after a certain period and the atom’s decay rate.
Wason selection task
This topic can allow you to take a look at human psychology and predictability from a mathematical perspective. It is a logical puzzle that shows just how easily one can fall into a logical fallacy. Your IA could be based on finding probabilities for certain outcomes and whether the results follow a particular distribution.
Graph theory in telephone numbers
Phone numbers form a sequence of integers that explains how a certain number of people can be connected by person-to-person calls. You could dive deeper into this topic by making use of recursive formulas, permutations and natural exponential functions.
Logarithmic scales and their applications
Ever wondered why the Richter scale experiences a large difference between a 5 and a 6, or why the noise-level scale is in decibels? An exploration of logarithmic scales could show why we need them in the first place - an easy way to represent data spanning across a wide range of values.
Differential equations in real life
How many math exercises can you solve before your coffee cools down? Using derivatives and related rates can help you find the answer to these questions. Take a look at heat equations and have fun with calculus!
The Monty Hall problem
If probabilities involving tree diagrams are in your lane, this problem is the perfect one for you. It is an interesting, counter-intuitive puzzle that puts Bayes’ theorem (conditional probability) into practice. There are many variations of the Monty Hall problem, so there’s always room for new analyses.
Patterns in Alhambra tiles
The geometrical structure of Alhambra tiles involves many intricate and precise mathematical shapes such as stars, squares, ovals, circles, and many more. An example exploration could take one of the tiles and deconstruct its structure into smaller and more basic geometrical shapes.
Chaos theory in weather predictions
In the morning the forecast predicted sun but you ended the day completely drenched in rain? Chaos theory will help you explore just how (un)predictable weather can be, as well as create space to find your own weather forecast. This topic is perfect for fans of statistics and probability distributions.
Knot theory and topology
This topic is heavy on pure mathematics yet very rewarding. It also makes for great tricks to confuse your friends. Knot theory is the study of three-dimensional closed curves and their potential deformations without needing to cut one part through another. If you ever need to untangle a cable, this theory can be put into direct practice!
Still unsure?
We understand that it is not easy to choose a subject that you’d like to pursue for your exploration. Do not worry, our tutors are ready to help! We can help you with finding a suitable research question, general structuring and resolving any additional issues you may encounter while writing your IA. Simply sign up here for the Think Smart Tutoring services to set up your introductory lesson and connect you with the best suitable tutor for your needs.
