Geometry deals with sets of points in a plane or in space. In its most elementary form geometry is concerned with such metrical problems as determining the areas and diameters of two-dimensional figures and the surface areas and volumes of solids. The study of plane curves, angles, polygons, and lines is called plane geometry . The study of curves in three-dimensional space such as spheres, cones, cylinders, and polyhedra is called solid geometry . Analysis and Calculus Analysis is concerned with abstract objects such as sets of numbers, sets of geometric points, or sets of functions that map numbers into numbers or points into points and with the processes, called limit processes , that depend on a measure of closeness between numbers, points, or functions.
Analysis uses the concept of a limit .
Calculus Calculus is concerned with concepts such as the rate of change of one variable quantity with respect to another, the slope of a curve at a prescribed point, the computation of the maximum and minimum values of functions, and the calculation of the area bounded by curves. Evolved from algebra, arithmetic, and geometry, it is the basis of that part of mathematics called analysis. Analytical topics depend on the concepts of calculus, such as differential equations, vector analysis, real analysis, and complex analysis . Differential calculus involves derivatives and deals with such topics as maxima and minima and rates of change of functions. Calculus can be applied to many problems involving the notion of extreme amounts, such as the fastest, the most, the slowest, or the least.