Choosing your Math Extended Essay (EE) topic can feel daunting—but it’s also one of the most rewarding parts of the IB Diploma Programme. You’ll spend up to 4,000 words exploring a question you genuinely care about, showcasing your mathematical thinking, research skills, and independence.
This guide will help you:
– Understand what the Math EE is
– Choose a strong, focused topic
– Structure your essay effectively
– Avoid common pitfalls
– Get inspired with unique research questions across key math areas
What is the Math EE?
| Feature | Details |
| Length | Up to 4,000 words (excluding equations, tables, diagrams, and appendices) |
| Structure | Abstract (optional), Introduction, Main Body, Conclusion, References |
| Assessment | Externally marked out of 34 points, graded A–E |
| Focus | Research-based, with emphasis on mathematical reasoning and modeling |
| Subject Choice | Any IB subject, but choosing a Higher Level (HL) subject is recommended |
| Academic Integrity | All sources must be cited to avoid plagiarism |
According to the official IB Math EE guide, students are expected to either extend their knowledge beyond the DP syllabus or apply known techniques to model real-world or abstract problems.
How to Choose a Winning Math EE Topic
– Align with Your Strengths
– Narrow the Scope
– Ensure Feasibility
– Aim for Mathematical Depth
– Stay Curious
Unique IB Math EE Research Questions by Topic Area
Pure Mathematics
- To what extent can continued fractions be used to approximate irrational numbers like π and e, and how do their convergence rates compare?
- How can group theory be applied to solving symmetric puzzles like the Rubik’s Cube? A study of permutation groups and move optimality.
- What role does modular arithmetic play in modern cryptography? A focused study on congruences in RSA key generation.
- How can the Fibonacci sequence and related recurrences be derived and generalized using linear algebra and eigenvalues?
- To what extent is Fermat’s Little Theorem effective for primality testing compared with probabilistic tests like Miller–Rabin?
- How do different notions of infinity manifest across ℕ, ℤ, ℚ, ℝ, and transfinite cardinals, and what are the implications for countability?
- What are the combinatorial and algebraic structures underlying magic squares and Latin squares?
Statistics and Probability
- Is there a measurable statistical correlation between ocean temperature anomalies and the frequency of specific natural disasters? A time-series approach.
- How effective is the Elo rating system in predicting chess outcomes compared with Glicko or TrueSkill?
- What is the probability of winning under different lottery formats, and how do expected value and variance inform rational play?
Calculus and Mathematical Modelling
- How can differential equations model the spread of pandemics, and how do SIR variants (SEIR, SIRS) change prediction accuracy?
- To what extent can calculus-based optimization be used to design rollercoaster elements that balance safety (g-limits) and thrill (jerk/curvature)?
- Can logistic and predator–prey models predict the population growth of an endangered species under conservation constraints?
- How are matrices and partial derivatives used in training neural networks?
Mathematical Finance
- How can the Black–Scholes model be used to price European call options, and where does it break down in real markets?
- What is the mathematical advantage of dollar-cost averaging versus lump-sum investing under various return distributions?
- How does compound interest outperform simple interest over long horizons? Sensitivity analysis across rate and time.
Game Theory and Decision Making
- How can Nash equilibrium be applied to analyze bidding strategies in first-price vs. second-price auctions?
- What is the optimal strategy in simplified poker variants using probability and expected value?
- How does the Prisoner’s Dilemma model real-world business decisions, and how do repeated games change outcomes?
Geometry and Topology
- What role does topology play in understanding the Möbius strip and Klein bottle, and how do orientation and boundary influence properties?
- How can fractal geometry model natural phenomena like coastlines? An investigation of fractal dimension and scaling.
- How do minimal surfaces relate to soap films, Plateau’s problem, and optimization?
How to Structure Your Math EE
1. Abstract (Optional, ~300 words)
- Summarize the research question, method, and main conclusions.
- Write this last.
2. Introduction
- State your research question clearly and narrowly.
- Explain why it’s significant—in math and, if relevant, in the real world.
- Outline the scope and what you will and won’t cover.
- Briefly preview your approach (proof, model, simulation, comparative analysis).
3. Main Body
- a) Mathematical Foundations
- Define key terms, theorems, and notation you will use.
- Provide only the background needed for your analysis; cite original sources (textbooks, papers).
- b) Methodology
- Describe your approach: derivations, proof strategy, model design, simulations, or statistical tests.
- Include diagrams, graphs, tables, or code outputs (with explanations).
- If using software (Python, GeoGebra, Excel, R), explain parameters and justify choices.
- c) Analysis and Discussion
- Present results clearly, step-by-step.
- Interpret findings: accuracy, limitations, sensitivity, potential sources of error.
- Compare alternative methods or models where appropriate.
4. Conclusion
- Answer the research question directly.
- Reflect on the significance and limitations of your work.
- Suggest realistic avenues for further research.
5. References/Bibliography
- Use a consistent citation style (APA, MLA, Chicago).
- Include textbooks, academic articles, reputable websites, and any interviews.
- For software or datasets, cite versions and access dates.
Tips for Writing a Successful Math EE
| Tip | Why It Matters |
| Start early | Gives you time to explore, refine, and iterate. |
| Focus on original thinking | Apply known mathematics in a novel context, compare methods, or extend a classroom idea. |
| Use graphs and visuals | Well-labeled graphs, tables, and diagrams make mathematical arguments clearer. |
| Consult your supervisor | Regular check-ins keep you aligned with the rubric and help you set realistic scope and milestones. |
| Avoid plagiarism | Paraphrase thoughtfully, credit ideas, and cite all sources. Use a reference manager if possible. |
| Manage complexity | Build your argument from simple to complex. Clearly state assumptions and keep notation consistent. |
| Validate your results | For proofs: ensure each step logically follows and state theorems used. For models: test sensitivity to parameters and compare with empirical data where possible. For statistics: justify tests used, check conditions (e.g., independence, normality), and report uncertainty. |
Summary: Strong vs. Weak Math EE Topics
| Strong Topics | Weak Topics |
| Involve higher-level or extended math ideas | Rely on basic or descriptive math |
| Have a narrow, focused research question | Are too broad or vague |
| Show originality and personal engagement | Lack depth or personal insight |
| Use multiple credible sources | Depend on a single or unreliable source |
| Apply or extend known math | Merely summarize textbook content |
Learning the All Round Way
Craft a focused IB Economics Extended Essay by selecting a well-defined research question and applying relevant economic theory to a specific, real-world context. If you find yourself needing more guidance, we invite you to connect with us at All Round Education Academy. Our dedicated team is here to support you in achieving your academic goals. For more information, please contact us at tuition@allround-edu.com or +852 6348 8744.