---
title: "Finite Mathematics"
language: "en"
type: "Guide"
summary: "Finite mathematics refers to a collection of topics that are typically studied by students of business management, social sciences and the life sciences at the undergraduate level. The topics include elementary algebra, matrix computation, optimization, financial mathematics, probability and Markov chains. The Wolfram Language has a unique combination of powerful and friendly tools for mastering this subject in an enjoyable way, using graphical visualization, symbolic and numerical computation, data analysis, etc."
sections: 
  - 
    title: "Elementary Algebra"
    link: "null"
  - 
    title: "Linear Systems"
    link: "null"
  - 
    title: "Matrix Computation"
    link: "null"
  - 
    title: "Optimization"
    link: "null"
  - 
    title: "Financial Mathematics"
    link: "null"
  - 
    title: "Set Operations"
    link: "null"
  - 
    title: "Probability"
    link: "null"
  - 
    title: "Markov Chains"
    link: "null"
keywords: 
- business
- management
- social sciences
- algebra
- matrices
- finance
- sets
- probability
- Markov chains
- precalculus
- optimization
canonical_url: "https://reference.wolfram.com/language/guide/FiniteMathematics.html"
source: "Wolfram Language Documentation"
related_guides: 
  - 
    title: "Equation Solving"
    link: "https://reference.wolfram.com/language/guide/EquationSolving.en.md"
  - 
    title: "Linear Systems"
    link: "https://reference.wolfram.com/language/guide/LinearSystems.en.md"
  - 
    title: "Matrices & Linear Algebra"
    link: "https://reference.wolfram.com/language/guide/MatricesAndLinearAlgebra.en.md"
  - 
    title: "Optimization"
    link: "https://reference.wolfram.com/language/guide/Optimization.en.md"
  - 
    title: "Financial Mathematics"
    link: "https://reference.wolfram.com/language/guide/Finance.en.md"
  - 
    title: "Operations on Sets"
    link: "https://reference.wolfram.com/language/guide/OperationsOnSets.en.md"
  - 
    title: "Probability & Statistics"
    link: "https://reference.wolfram.com/language/guide/ProbabilityAndStatistics.en.md"
  - 
    title: "Finite Markov Processes"
    link: "https://reference.wolfram.com/language/guide/MarkovProcesses.en.md"
related_functions: 
  - 
    title: "Annuity"
    link: "https://reference.wolfram.com/language/ref/Annuity.en.md"
  - 
    title: "Cashflow"
    link: "https://reference.wolfram.com/language/ref/Cashflow.en.md"
  - 
    title: "Det"
    link: "https://reference.wolfram.com/language/ref/Det.en.md"
  - 
    title: "DiscreteMarkovProcess"
    link: "https://reference.wolfram.com/language/ref/DiscreteMarkovProcess.en.md"
  - 
    title: "Dot"
    link: "https://reference.wolfram.com/language/ref/Dot.en.md"
  - 
    title: "Expectation"
    link: "https://reference.wolfram.com/language/ref/Expectation.en.md"
  - 
    title: "FirstPassageTimeDistribution"
    link: "https://reference.wolfram.com/language/ref/FirstPassageTimeDistribution.en.md"
  - 
    title: "Intersection"
    link: "https://reference.wolfram.com/language/ref/Intersection.en.md"
  - 
    title: "Inverse"
    link: "https://reference.wolfram.com/language/ref/Inverse.en.md"
  - 
    title: "LinearModelFit"
    link: "https://reference.wolfram.com/language/ref/LinearModelFit.en.md"
  - 
    title: "LinearOptimization"
    link: "https://reference.wolfram.com/language/ref/LinearOptimization.en.md"
  - 
    title: "LinearSolve"
    link: "https://reference.wolfram.com/language/ref/LinearSolve.en.md"
  - 
    title: "MarkovProcessProperties"
    link: "https://reference.wolfram.com/language/ref/MarkovProcessProperties.en.md"
  - 
    title: "Maximize"
    link: "https://reference.wolfram.com/language/ref/Maximize.en.md"
  - 
    title: "Minimize"
    link: "https://reference.wolfram.com/language/ref/Minimize.en.md"
  - 
    title: "Probability"
    link: "https://reference.wolfram.com/language/ref/Probability.en.md"
  - 
    title: "Reduce"
    link: "https://reference.wolfram.com/language/ref/Reduce.en.md"
  - 
    title: "RowReduce"
    link: "https://reference.wolfram.com/language/ref/RowReduce.en.md"
  - 
    title: "Simplify"
    link: "https://reference.wolfram.com/language/ref/Simplify.en.md"
  - 
    title: "Solve"
    link: "https://reference.wolfram.com/language/ref/Solve.en.md"
  - 
    title: "Subsets"
    link: "https://reference.wolfram.com/language/ref/Subsets.en.md"
  - 
    title: "TimeValue"
    link: "https://reference.wolfram.com/language/ref/TimeValue.en.md"
  - 
    title: "Union"
    link: "https://reference.wolfram.com/language/ref/Union.en.md"
  - 
    title: "Variance"
    link: "https://reference.wolfram.com/language/ref/Variance.en.md"
---
# Finite Mathematics

Finite mathematics refers to a collection of topics that are typically studied by students of business management, social sciences and the life sciences at the undergraduate level. The topics include elementary algebra, matrix computation, optimization, financial mathematics, probability and Markov chains.
The Wolfram Language has a unique combination of powerful and friendly tools for mastering this subject in an enjoyable way, using graphical visualization, symbolic and numerical computation, data analysis, etc.

---

### Elementary Algebra

[`Solve`](https://reference.wolfram.com/language/ref/Solve.en.md) — exact solutions to equations and systems

[`Simplify`](https://reference.wolfram.com/language/ref/Simplify.en.md) — simplify an expression

[`Reduce`](https://reference.wolfram.com/language/ref/Reduce.en.md) — reduce equations and inequalities

### Linear Systems

[`LinearSolve`](https://reference.wolfram.com/language/ref/LinearSolve.en.md) — solve linear systems in matrix form

[`RowReduce`](https://reference.wolfram.com/language/ref/RowReduce.en.md) — generate a row echelon form

[`LinearModelFit`](https://reference.wolfram.com/language/ref/LinearModelFit.en.md) — construct a linear regression model from data

### Matrix Computation

[`Dot`](https://reference.wolfram.com/language/ref/Dot.en.md) — dot products of vectors and matrices

[`Inverse`](https://reference.wolfram.com/language/ref/Inverse.en.md) — inverse of a matrix

[`Det`](https://reference.wolfram.com/language/ref/Det.en.md) — determinant of a matrix

### Optimization

[`LinearOptimization`](https://reference.wolfram.com/language/ref/LinearOptimization.en.md) — linear programming in matrix form

[`Minimize`](https://reference.wolfram.com/language/ref/Minimize.en.md), [`Maximize`](https://reference.wolfram.com/language/ref/Maximize.en.md) — symbolic global optimization

### Financial Mathematics

[`Annuity`](https://reference.wolfram.com/language/ref/Annuity.en.md) — regular premium or pension payments

[`Cashflow`](https://reference.wolfram.com/language/ref/Cashflow.en.md) — cash flow of premiums

[`TimeValue`](https://reference.wolfram.com/language/ref/TimeValue.en.md) — time value of money computations

### Set Operations

[`Subsets`](https://reference.wolfram.com/language/ref/Subsets.en.md) — find all possible subsets of a set (the powerset)

[`Union`](https://reference.wolfram.com/language/ref/Union.en.md) — union of sets

[`Intersection`](https://reference.wolfram.com/language/ref/Intersection.en.md) — intersection of sets

### Probability

[`Probability`](https://reference.wolfram.com/language/ref/Probability.en.md) — probability of an event

[`Expectation`](https://reference.wolfram.com/language/ref/Expectation.en.md) — expected value of an expression

[`Variance`](https://reference.wolfram.com/language/ref/Variance.en.md) — variance of a probability distribution

### Markov Chains

[`DiscreteMarkovProcess`](https://reference.wolfram.com/language/ref/DiscreteMarkovProcess.en.md) — represents a finite-state, discrete-time Markov process

[`MarkovProcessProperties`](https://reference.wolfram.com/language/ref/MarkovProcessProperties.en.md) — structural, transient and limiting properties

[`FirstPassageTimeDistribution`](https://reference.wolfram.com/language/ref/FirstPassageTimeDistribution.en.md) — distribution of times for hitting a set of states

## Related Guides

* [Equation Solving](https://reference.wolfram.com/language/guide/EquationSolving.en.md)
* [Linear Systems](https://reference.wolfram.com/language/guide/LinearSystems.en.md)
* [Matrices & Linear Algebra](https://reference.wolfram.com/language/guide/MatricesAndLinearAlgebra.en.md)
* [`Optimization`](https://reference.wolfram.com/language/guide/Optimization.en.md)
* [Financial Mathematics](https://reference.wolfram.com/language/guide/Finance.en.md)
* [Operations on Sets](https://reference.wolfram.com/language/guide/OperationsOnSets.en.md)
* [Probability & Statistics](https://reference.wolfram.com/language/guide/ProbabilityAndStatistics.en.md)
* [Finite Markov Processes](https://reference.wolfram.com/language/guide/MarkovProcesses.en.md)