Math HL IA examples

I'm doing my Math HL IA soon but I'm not sure what topic to pick. Can anyone share some examples or ideas for a Math HL IA that will help me get started?

Certainly! It's important to choose a topic that you're genuinely interested in and passionate about, as this will make the process more enjoyable and your final product more compelling. Here are a few Math HL IA topics to get you started:

1. Cryptography: Dive into the world of secret codes and encryption techniques. You could explore historical methods like the Caesar cipher, Vigenère cipher, or Enigma machine, or examine modern encryption algorithms used in computer science, such as RSA and AES.

2. Fractals: Investigate the beauty and complexity of fractals, such as the Mandelbrot set and the Julia set. You can examine their properties, expand upon their mathematical definitions, and even attempt to create your own by iterating functions.

3. Game Theory: Explore the mathematics behind decision-making and strategy in competitive situations. Analyze well-known games like the Prisoner's Dilemma, Nash Equilibrium, or apply game theory to real-world situations like economics, social sciences, or even biology.

4. Graph Theory: Study the mathematics behind networks and their properties. You can delve into various graph algorithms, such as Djikstra's shortest path, or focus on more specific applications like social network analysis or routing problems.

5. Probability Theory: Investigate the laws of chance and their applications. You could simulate various probability distributions, delve into Bayesian probability, or model real-world scenarios like predicting election results or analyzing casino games.

6. Euler's Formula and Polyhedra: Examine the fascinating relationship between the vertices, edges, and faces of polyhedra, as described by Euler's formula. This can lead to the investigation of various polyhedra properties, creating 3D models, or even exploring Platonic solids.

7. Optimization Problems: Use calculus and linear programming to solve real-world problems involving optimization, such as minimizing cost, maximizing profit, or devising the most efficient transportation routes.

These examples should provide a starting point for your Math HL IA. Remember, it's crucial to select a topic that you're excited about and motivated to explore on a deeper level. Don't hesitate to put your own spin on these ideas or combine aspects of different topics to create a unique project that showcases your intellectual curiosity and mathematical skillset. Good luck!