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IB Mathematics · Complete topic list
900 topic ideas – page 8 of 36.
Topics 176 to 200 with explanations, methods, course and equipment guidance.
Mathematics and applications
Compare 900 ideas clearly.
The list mixes calculus, statistics, modelling, geometry, number theory, computer science, sport, environmental topics and other areas. Each entry includes a short explanation and visible methods such as differential calculus, integral calculus, statistics or regression.
Planning guidance, not official topic approvalThe IA, EE, AA, Math AI, SL and HL classifications are editorial guidance. The current subject guide, assessment session, mathematical depth, focus and school approval remain decisive.
1
Select an idea. Titles and areas are starting points, not finished research questions.
2
Check A and C. These codes give an initial indication of assessment type, course and level.
3
Read P, M and S. They show possible independent direction, tools, and safety or data-protection needs.
| No. | Topic idea | A | C | P | M | S |
|---|---|---|---|---|---|---|
| 176 | Algebra & number theoryPascal's triangle: patterns, binomial coefficients and combinatorics Turn “Pascal's triangle: patterns, binomial coefficients and combinatorics” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 1 | 0 | 0 |
| 177 | Analysis & calculusConvergence of series: the harmonic series, Basel problem and geometric series Turn “Convergence of series: the harmonic series, Basel problem and geometric series” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 10 | 0 | 0 |
| 178 | Statistics & probabilityThe Monty Hall problem: simulation versus theory Turn “The Monty Hall problem: simulation versus theory” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
1 | 7 | 17 | 13 | 0 |
| 179 | Mathematical modellingLogistic growth in social-media followers and viral trends Turn “Logistic growth in social-media followers and viral trends” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
1 | 9 | 1 | 0 | 1 |
| 180 | Geometry & topologyPlatonic solids: Euler's formula and why there are exactly five Turn “Platonic solids: Euler's formula and why there are exactly five” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 2 | 20 | 0 |
| 181 | Financial mathematicsSaving strategies: lump-sum investment versus regular deposits Turn “Saving strategies: lump-sum investment versus regular deposits” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 4 | 1511 | 0 | 0 |
| 182 | Logic, set theory & proofArrow's impossibility theorem and voting systems Develop “Arrow's impossibility theorem and voting systems” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches. |
2 | 2 | 10 | 0 | 0 |
| 183 | Discrete mathematics & computer scienceModelling networks with adjacency matrices Turn “Modelling networks with adjacency matrices” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 111 | 13 | 0 |
| 184 | Applied & interdisciplinary mathematicsModelling an optimal running pace Turn “Modelling an optimal running pace” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 1311 | 13 | 0 |
| 185 | Game theory & decision-makingOptimal positioning in penalty kicks using mixed strategies Turn “Optimal positioning in penalty kicks using mixed strategies” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 8 | 1311 | 7 | 0 |
| 186 | Transport & mobility mathematicsReliability of train headways using coefficients of variation and outliers Turn “Reliability of train headways using coefficients of variation and outliers” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 6 | 16912 | 613 | 0 |
| 187 | Biomathematics & medicineMathematical analysis of mosquito-population spread Turn “Mathematical analysis of mosquito-population spread” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 6 | 12 | 0 |
| 188 | Operations research & logisticsLocation optimisation for public defibrillators under response-time constraints Turn “Location optimisation for public defibrillators under response-time constraints” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 691112 | 813 | 0 |
| 189 | Environmental mathematics & sustainabilityCalculating optimal home insulation using heat conduction Turn “Calculating optimal home insulation using heat conduction” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 1211 | 313 | 0 |
| 190 | Networks & social systemsSmall-world properties of a regional transport network Turn “Small-world properties of a regional transport network” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 697 | 13 | 0 |
| 191 | Sports biomechanics & movementOptimising launch angles in archery Turn “Optimising launch angles in archery” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 1311 | 1 | 1 |
| 192 | Information & coding theoryMutual information between weather variables and forecast accuracy Turn “Mutual information between weather variables and forecast accuracy” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
2 | 8 | 91112 | 13 | 0 |
| 193 | Data science & introductory algorithmsCalculating text similarity with introductory vector models Turn “Calculating text similarity with introductory vector models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 1712 | 13 | 0 |
| 194 | Robotics, control & sensingSensor fusion for accelerometer and gyroscope data Turn “Sensor fusion for accelerometer and gyroscope data” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 8 | 271112 | 71320 | 1 |
| 195 | Chaos & dynamical systemsCalculating Lyapunov exponents for simple functions Turn “Calculating Lyapunov exponents for simple functions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 710 | 13 | 0 |
| 196 | Image processing & computer graphicsColour segmentation using k-means clustering Turn “Colour segmentation using k-means clustering” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 9 | 2711 | 713 | 0 |
| 197 | Music, acoustics & wavesCalculating string lengths for alternative tuning systems Turn “Calculating string lengths for alternative tuning systems” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 18 | 91314 | 3 |
| 198 | Language & text mathematicsUncertainty in sentiment scores from different lexicons Turn “Uncertainty in sentiment scores from different lexicons” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 6 | 7912 | 13 | 0 |
| 199 | Art, design & architectureCalculating optimal stage lighting through angle analysis Turn “Calculating optimal stage lighting through angle analysis” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 1811 | 11013 | 0 |
| 200 | Education & learning analyticsOptimising test-item order under fatigue Turn “Optimising test-item order under fatigue” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 8 | 471112 | 1314 | 3 |
No topic ideas match this combination.
Code legend
What A, C, P, M and S mean.
The table stays narrow on a phone by replacing long descriptions with numeric codes. Entries may contain several P and M codes.
AAssessment type
- 1
- Internal Assessment (IA)
- 2
- Mathematics Extended Essay (EE)
- 3
- Potentially suitable for an IA or EE, depending on focus and mathematical depth
CCourse and level
- 1
- Mathematics AA SL
- 2
- Mathematics AA HL
- 3
- Mathematics AA at SL or HL
- 4
- Mathematics AI SL
- 5
- Mathematics AI HL
- 6
- Mathematics AI at SL or HL
- 7
- Mathematics AA or AI at SL
- 8
- Mathematics AA or AI at HL
- 9
- Mathematics AA or AI at SL or HL
PWays to demonstrate independent direction and personal engagement
- 1
- Own data, measurements, observations or experiment
- 2
- Own photographs, drawings, constructions or models
- 3
- Own sport, video, GPS or tracker context
- 4
- Own school or class survey or observation
- 5
- Own everyday, household, consumer or financial data
- 6
- Local context: environment, buildings, traffic, climate or nature
- 7
- Own programming, simulation or algorithm
- 8
- Personal interest: music, art, games, design or another hobby
- 9
- Public data selected, prepared and analysed independently
- 10
- Own conjecture, proof idea, generalisation or theoretical comparison
- 11
- Own modelling decision, construction, optimisation or adaptation
- 12
- Critical comparison of assumptions, errors, limitations or ethical issues
MMeasuring instruments, tools or data access
- 0
- No specialist physical instrument; a calculator, CAS, spreadsheet or open data may be sufficient
- 1
- Ruler, tape measure, calliper or protractor
- 2
- Balance or precision scale
- 3
- Contact thermometer or temperature data logger
- 4
- Infrared thermometer or thermal camera
- 5
- Multimeter or another electrical measuring instrument
- 6
- Stopwatch or timer
- 7
- Camera or smartphone for photographic and video analysis
- 8
- GPS device or fitness tracker
- 9
- Microphone, sound-level meter or audio-analysis software
- 10
- Light meter, light sensor or solar sensor
- 11
- Conductivity, pH or salinity meter
- 12
- Weather instruments, such as an anemometer or rain gauge
- 13
- Computer, spreadsheet, CAS, GeoGebra, Desmos or Python
- 14
- Survey form, data sheet or observation record
- 15
- Force sensor or spring balance
- 16
- Laboratory glassware, measuring cylinder or pipette
- 17
- Telescope, binoculars or a suitable camera
- 18
- Humidity or material-moisture sensor
- 19
- Non-invasive physiology sensor, such as heart-rate or reaction-time measurement
- 20
- Physical model, 3D printer or material samples
- 21
- Specialist school laboratory equipment
SSafety and data protection
- 0
- Likely to be low risk within normal school practice
- 1
- Supervision recommended, for example for heat, electricity, sport or traffic observation
- 2
- Carry out only in a school laboratory or with qualified supervision
- 3
- Sensitive personal or health data: consent, anonymisation and preferably secondary data; no medical self-intervention
From heading to investigation
A topic becomes workable only through independent decisions.
The table is designed to speed up the first step. The actual research question emerges through focus, mathematical choice and critical checking.
Select the mathematics
Decide which models, proofs, statistical procedures or optimisation steps can genuinely answer the question.
Plan independent direction
Use your own data, comparisons, modelling choices, extensions or proof ideas rather than reproducing a standard procedure.
Reflect on limitations
Examine assumptions, sources of error, data quality, model limitations, safety and possible improvements.
Personal engagement and independent direction
A personal connection is more than one sentence in the introduction.
The P codes indicate possible ways to shape an investigation independently. Independent thinking becomes visible through justified decisions, appropriate data selection, personal model variants, meaningful comparisons and critical reflection. A code does not guarantee a particular mark.
Review the IA requirementsFrequently asked questions
Use the topic list correctly.
Are the titles finished research questions?
No. They name a possible direction. A question for assessed work must be focused more narrowly, matched to the course and level, and connected to a clear mathematical method.
What does A = 3 mean?
The broad direction could be developed as an IA or Mathematics EE, depending on focus and depth. An EE will normally require a substantially deeper mathematical argument and an appropriate research scope.
Is C an official IB classification?
No. C is editorial guidance for Mathematics AA or Math AI and SL or HL. Final suitability depends on the specific research question and the current requirements.
Do I need to own the listed instruments?
No. M indicates typical or possible tools. Many topics can use open data, a spreadsheet, CAS, GeoGebra, Desmos or Python. Adapt the topic to resources that are genuinely available.
How should topics involving health or personal data be handled?
Prefer anonymised or publicly available secondary data. Original data collection needs consent, data protection, school approval and a low-risk method. Diagnosis, medication changes and invasive self-experimentation do not belong in a Mathematics project.
The complete list is also machine-readable.
The same 900 entries are available as plain text and bilingual JSON for search, accessibility and AI systems.
Authoritative foundations
Check the current curriculum version before starting.
The catalogue complements the PreLearning explanations. Current official IB documents and the school's instructions remain authoritative.