Finite Math:
* Focus: Deals with mathematical concepts that don't require calculus. It's primarily concerned with techniques and applications useful in business, social sciences, and other fields that don't need the depth of calculus.
* Topics: Typically includes:
* Logic and Sets: Basic set theory, logic statements, Venn diagrams.
* Counting and Probability: Permutations, combinations, probability distributions (often limited to discrete distributions).
* Matrices and Linear Programming: Solving systems of linear equations, linear programming problems (optimization).
* Game Theory (sometimes): Strategies in competitive situations.
* Finance (sometimes): Simple and compound interest, annuities.
* Calculus Requirement: No calculus is required or included.
* Goal: To provide students with mathematical tools for practical applications in fields outside of the physical sciences and engineering.
Precalculus:
* Focus: Prepares students for the study of calculus. It bridges the gap between algebra and calculus by introducing concepts essential for understanding calculus.
* Topics: Typically includes:
* Advanced Algebra: Review and extension of algebra topics, including functions, equations, and inequalities.
* Trigonometry: Trigonometric functions, identities, graphs, and applications.
* Analytic Geometry: Equations of lines and conic sections (circles, parabolas, ellipses, hyperbolas).
* Exponential and Logarithmic Functions: Their properties, graphs, and equations.
* Sequences and Series (sometimes): Arithmetic and geometric sequences and series.
* Calculus Requirement: This course is a direct prerequisite for calculus. Many concepts are foundational to understanding derivatives and integrals.
* Goal: To build a solid mathematical foundation for success in calculus.
In short:
Choose finite math if you need practical math skills for business, social sciences, or other non-calculus-dependent fields. Choose precalculus if you plan to study calculus and related fields like engineering, physics, or advanced mathematics. They are very different courses aimed at different student populations and future goals.