The Internal Assessment (IA) in IB Math is a unique opportunity to explore a mathematical topic of your choice in depth. A successful IA not only demonstrates your understanding and application of mathematical concepts but also showcases your creativity and curiosity. Here are some inspiring examples of successful IB Math IA topics and tips on how to choose your own.

### Example 1: The Mathematics of Music

**Topic:** Exploring the relationship between mathematics and music through the analysis of musical scales, frequencies, and patterns.

**Why It’s Successful:**

**Interdisciplinary Appeal:**Combines mathematics with a field of personal interest (music), making it engaging.**Variety of Concepts:**Covers a range of mathematical areas such as geometry (waveforms), algebra (frequency ratios), and even calculus (harmonic analysis).**Practical Applications:**Demonstrates how mathematical principles can explain and enhance understanding of musical theory and practice.

**Possible Exploration:**

- Investigate the frequencies of different musical notes and their mathematical ratios.
- Analyze the patterns in different musical scales using modular arithmetic.
- Model sound waves using trigonometric functions.

### Example 2: The Geometry of Origami

**Topic:** Analyzing the geometric principles behind origami and how mathematical concepts can be applied to create complex designs.

**Why It’s Successful:**

**Visual and Tactile:**Provides a hands-on approach to learning geometry.**Wide Range of Applications:**Discusses real-world applications such as in engineering and design.**Innovative:**Shows creativity in applying mathematics to art and design.

**Possible Exploration:**

- Examine the geometric transformations involved in creating specific origami models.
- Use graph theory to analyze the crease patterns and their properties.
- Investigate the mathematical principles that allow origami to be used in practical applications like space structures and medical devices.

### Example 3: Predicting Stock Market Trends

**Topic:** Using statistical methods and mathematical models to predict stock market trends.

**Why It’s Successful:**

**Real-World Relevance:**Applies mathematics to a relevant and practical problem.**Advanced Techniques:**Involves the use of complex mathematical concepts such as statistics, probability, and calculus.**Data-Driven:**Utilizes real-world data, making the analysis more rigorous and applicable.

**Possible Exploration:**

- Apply statistical methods such as moving averages or linear regression to historical stock data.
- Use probability models to predict future trends and assess risks.
- Explore the use of calculus in modeling stock price changes over time.

### Example 4: The Mathematics of Epidemics

**Topic:** Modeling the spread of infectious diseases using mathematical models.

**Why It’s Successful:**

**Timely and Relevant:**Especially relevant in light of recent global events.**Complex Problem-Solving:**Involves differential equations, statistics, and probability.**Impactful:**Shows how mathematics can be used to address critical real-world issues.

**Possible Exploration:**

- Develop and analyze SIR (Susceptible, Infected, Recovered) models.
- Use differential equations to model the rate of spread and recovery.
- Apply statistical methods to real-world data to validate the models.

### Example 5: Game Theory and Strategy Optimization

**Topic:** Analyzing strategies in games using game theory.

**Why It’s Successful:**

**Engaging:**Relates to popular games and strategies, making it interesting.**Theoretical and Practical:**Combines theoretical concepts with practical applications.**Broad Scope:**Can be applied to a variety of games, from board games to sports.

**Possible Exploration:**

- Use matrix algebra to analyze payoffs in different game scenarios.
- Apply probability theory to assess optimal strategies.
- Investigate Nash equilibria in competitive games.

### Tips for Choosing Your Own IA Topic

**Interest and Passion:**Choose a topic that genuinely interests you. This will make the research process enjoyable and the final product more compelling.**Scope and Depth:**Ensure your topic is specific enough to allow for in-depth analysis but broad enough to find sufficient data and resources.**Mathematical Rigor:**Select a topic that allows you to demonstrate a range of mathematical skills and concepts.**Real-World Applications:**Topics with practical applications often make for more engaging and relevant IAs.**Feasibility:**Consider the availability of data and resources, as well as the time you have to complete your IA.

Choosing a successful IB Math IA topic involves finding a balance between personal interest, mathematical rigor, and real-world relevance. The examples provided showcase a range of possibilities, from music and art to finance and epidemiology. Use these examples as inspiration to find a topic that excites you and allows you to explore the fascinating world of mathematics.