What theory involves the study of continuous change and motion?

The study of continuous change and motion is fundamentally encompassed by calculus. This branch of mathematics introduces concepts such as limits, derivatives, and integrals, which are essential for analyzing functions that describe changing quantities.

Calculus allows mathematicians and scientists to model and understand real-world phenomena that evolve smoothly over time or distance. For instance, when determining the rate at which an object moves, we use derivatives to find instantaneous rates of change. Integrals, on the other hand, help in calculating areas under curves or accumulated quantities over an interval, reflecting the cumulative effect of continuous change.

The other subjects—algebra, geometry, and statistics—focus on different mathematical principles. Algebra deals primarily with the manipulation of symbols and solving equations, geometry focuses on the properties and relations of points, lines, surfaces, and shapes, and statistics involves the analysis and interpretation of numerical data. None of these areas inherently encapsulate the concept of continuous change and motion in the way calculus does.