Examples for

# Mathematics

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge. Get help with math homework, solve specific math problems or find information on mathematical subjects and topics.

Elementary Math

Do basic arithmetic. Work with fractions, percentages and similar fundamentals. Solve place value and word problems.

#### Do exact arithmetic with fractions:

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Geometry

Compute the properties of geometric objects of various kinds in 2, 3 or higher dimensions. Explore and apply ideas from many subfields of geometry.

#### Compute properties of a polyhedron:

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Numbers

Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases.

#### Convert a decimal number to another base:

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Number Theory

Analyze integers; subsets of the integers, including the prime numbers; and related ideas.

#### Solve a Diophantine equation:

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Applied Mathematics

Perform numerical analysis and optimization of systems and objects, including packing and covering of objects and control systems.

#### Numerically integrate functions that cannot be integrated symbolically:

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Mathematical Definitions

Make queries about various definitions and descriptions in mathematics.

#### Get a brief definition:

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Statistics

Compute properties of datasets, perform statistical inference or model data. Work with probability distributions and random variables.

#### Find the sample size needed to estimate a binomial parameter:

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Algebra

Find roots of and expand, factor or simplify mathematical expressions—everything from polynomials to fields and groups.

#### Simplify an expression:

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Differential Equations

Solve differential equations of any order. Examine solutions and plots of the solution families. Specify initial conditions to find exact solutions.

#### Solve a nonlinear equation:

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Trigonometry

Perform trigonometric calculations and explore properties of trigonometric functions and identities.

#### Solve a trigonometric equation:

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Discrete Mathematics

Explore sequences and recurrences, solve common problems in combinatorics and compute properties of graphs and lattices.

#### Solve a recurrence:

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Logic & Set Theory

Evaluate Boolean logic expressions and expressions involving sets and set operators. Solve Boolean equations. Compute truth tables. Generate Venn diagrams.

#### Generate a Venn diagram:

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Famous Math Problems

#### Get historical information about a theorem:

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Probability

Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.

#### Compute coin‐toss probabilities:

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Calculus & Analysis

Compute integrals, derivatives and limits as well as analyze sums, products and series.

#### Solve an ordinary differential equation:

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Plotting & Graphics

Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots.

#### Plot a region satisfying multiple inequalities:

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Linear Algebra

Explore and compute properties of vectors, matrices and vector spaces.

#### Determine whether a set of vectors is linearly independent:

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Complex Analysis

Analyze functions and expressions containing imaginary numbers or complex variables.

#### Compute the residue of a function at a point:

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Mathematical Functions

Examine the properties of mathematical functions, such as continuity, surjectivity and parity. Utilize notable special functions or number theoretic functions.

#### Find representations for a function:

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Continued Fractions

Compute; learn about algorithms, definitions and theorems involving; or find properties of continued fractions.

#### Find continued fraction papers by author:

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Common Core Math

Get information about math Common Core Standards for kindergarten through eighth grade.

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