900 topic ideas – page 4 of 36.

Turn “Optimal Nim strategy using binary representation” 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.

Turn “Electrolysis of water: electrode mass change versus applied voltage” 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.

Develop “The coupon collector problem for trading cards” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches.

Turn “Which teapot material retains heat longest: cast iron, glass or porcelain?” 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.

Turn “Decomposing tides with harmonic 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.

Turn “Rainwater: precipitation amount, temperature and electrical conductivity” 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.

Turn “Skin-surface temperature recovery after a safe cold-water exposure” 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.

Turn “Heat distribution around skateboard or longboard axles after riding” 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.

Turn “Modelling population growth: logistic versus exponential 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.

Turn “Newton's law of cooling: modelling with differential equations” 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.

Turn “The birthday paradox: simulation versus theoretical probability” 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.

Turn “Predator-prey dynamics: the Lotka-Volterra equations” 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.

Turn “The Seven Bridges of Königsberg and graph theory” 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.

Turn “Mortgage repayment: how much can an extra payment save?” 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.

Turn “Boolean algebra and logic gates: De Morgan's laws” 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.

Turn “Analysing sorting algorithms: running time and comparisons” 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.

Turn “Optimising how to pack a suitcase or backpack” 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.

Turn “The mathematics of auction systems: English versus Dutch auctions” 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.

Turn “Shortest route versus fastest route under time-dependent traffic” 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.

Turn “Heart-rate variability analysed with statistical methods” 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.

Turn “Staff scheduling with integer linear optimisation” 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.

Turn “Modelling seasonal water levels in local lakes” 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.

Turn “Epidemic thresholds in networks with different degree distributions” 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.

Turn “Modelling force distribution while climbing on different wall angles” 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.

Turn “Error correction with Hamming codes under simulated channel noise” 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.