Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”), often shortened to maths or math, is the study of topics such as quantity (numbers), structure, space, and change.
Pre-Calculus is a step a after Algebra 2 and was created as a stepping stone between Algebra 2 and Calculus. Topics taught are Linear Optimization, Partial Factor Decomposition, and Trigonometric functions just to name a few.
Algebra 2 is the class after Geometry and is thought of as the beginning to more abstract Mathmatical thinking. The law of Sines and Cosines, Inverse Functions, and Graphing of rational functions are some topics taught.
Geometry is a type of Math that incorporates Algebra and the relation of figures. Its often used in professions such as architecture and engineering. It includes topics like formulas for finding volumes, areas, etc. for polygonal prisms.
Algebra is the foundation of all Math. It teaches important topics and ideas like linear equations, data visualization, and graph/data manipulation.