Focus the object
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
IB Mathematics · Complete topic list
900 topic ideas – page 3 of 36.
Topics 51 to 75 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 |
|---|---|---|---|---|---|---|
| 51 | Environmental mathematics & sustainabilityOptimising waste separation with probability models Turn “Optimising waste separation with probability models” 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 | 6 | 1611 | 13 | 3 |
| 52 | Networks & social systemsCommunity detection in a network of music artists Turn “Community detection in a network of music artists” 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 | 897 | 13 | 0 |
| 53 | Sports biomechanics & movementMathematical analysis of rotation in figure skating using angular momentum Turn “Mathematical analysis of rotation in figure skating using angular momentum” 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 | 2 | 13 | 715 | 0 |
| 54 | Information & coding theoryArithmetic coding compared with Huffman coding Turn “Arithmetic coding compared with Huffman coding” 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 | 71012 | 13 | 0 |
| 55 | Data science & introductory algorithmsA basic Fourier-based classification of music genres Turn “A basic Fourier-based classification of music genres” 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 | 2 | 178 | 913 | 0 |
| 56 | Robotics, control & sensingUsing a Kalman filter to smooth a noisy distance sensor Turn “Using a Kalman filter to smooth a noisy distance sensor” 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 | 132021 | 1 |
| 57 | Chaos & dynamical systemsModelling the double pendulum and its unpredictability Turn “Modelling the double pendulum and its unpredictability” 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 | 2 | 1711 | 13 | 0 |
| 58 | Image processing & computer graphicsPerspective correction of a photograph using a homography Turn “Perspective correction of a photograph using a homography” 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 | 2710 | 713 | 0 |
| 59 | Music, acoustics & wavesOvertone series in different musical instruments Turn “Overtone series in different musical instruments” 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 | 913 | 0 |
| 60 | Language & text mathematicsModelling letter sequences with Markov chains Turn “Modelling letter sequences with Markov chains” 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 | 7810 | 13 | 0 |
| 61 | Art, design & architectureCalculating perspective in painting using one-point perspective Turn “Calculating perspective in painting using one-point perspective” 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 | 12 | 1713 | 0 |
| 62 | Education & learning analyticsSimplified item response theory for estimating item difficulty Turn “Simplified item response theory for estimating item difficulty” 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 | 471012 | 1314 | 3 |
| 63 | Astronomy & spaceflightModelling tidal forces and their mathematical periodicity Turn “Modelling tidal forces and their mathematical periodicity” 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 | 1611 | 613 | 0 |
| 64 | Economic models & marketsLorenz curves and decomposition of the Gini coefficient Turn “Lorenz curves and decomposition of the Gini coefficient” 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 | 91012 | 13 | 0 |
| 65 | Psychology & cognitionModelling the Ebbinghaus forgetting curve with exponential decay Turn “Modelling the Ebbinghaus forgetting curve with exponential decay” 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 | 1411 | 13 | 3 |
| 66 | Time series & forecastingSeasonal decomposition of bicycle-rental data Turn “Seasonal decomposition of bicycle-rental data” 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 | 6 | 6911 | 13 | 0 |
| 67 | Probability & riskModelling smoking risk with life-expectancy data Turn “Modelling smoking risk with life-expectancy data” 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 | 6 | 12 | 0 | 3 |
| 68 | Geospatial & cartographic mathematicsComparing great-circle and rhumb-line routes for long journeys Turn “Comparing great-circle and rhumb-line routes for long journeys” 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 | 6910 | 813 | 0 |
| 69 | Culinary mathematicsModelling coffee brewing through extraction rates and temperature Turn “Modelling coffee brewing through extraction rates and temperature” 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 | 1511 | 31316 | 0 |
| 70 | Engineering design & optimisationOptimising a beam cross-section under bending Turn “Optimising a beam cross-section under bending” 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 | 21011 | 1320 | 0 |
| 71 | ThermodynamicsInsulating performance of cup materials: time taken to approach room temperature Turn “Insulating performance of cup materials: time taken to approach room temperature” 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 | 112 | 3416 | 0 |
| 72 | Epidemiology & public healthEstimating the effective reproduction number from a public case series Turn “Estimating the effective reproduction number from a public case series” 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 |
| 73 | Material propertiesDetermining the density of different woods from mass and volume Turn “Determining the density of different woods from mass and volume” 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 | 3 | 1 | 211314 | 3 |
| 74 | Sports analytics & tacticsEntropy of serve placement in tennis Turn “Entropy of serve placement in tennis” 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 | 13812 | 713 | 0 |
| 75 | ElectricitySolar-cell power at different light angles and distances Turn “Solar-cell power at different light angles and distances” 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 | 111 | 511013 | 1 |
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.