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.

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

#### Do basic arithmetic:

#### Do exact arithmetic with fractions:

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 geometric figure:

#### Plot a conic section and identify its type:

#### Compute properties of a polyhedron:

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

#### Compute a decimal approximation to a specified number of digits:

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

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

#### Compute a prime factorization:

#### Solve a Diophantine equation:

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

#### Minimize or maximize a function:

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

Make queries about various definitions and descriptions in mathematics.

#### Find information about a math concept:

#### Get a brief definition:

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

#### Calculate basic descriptive statistics for a data set:

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

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

#### Solve an equation:

#### Factor a polynomial:

#### Simplify an expression:

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

#### Solve a linear ordinary differential equation:

#### Specify initial values:

#### Solve a nonlinear equation:

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

#### Compute values of trigonometric functions:

#### Solve a trigonometric equation:

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

#### Compute a possible formula and continuation for a sequence:

#### Analyze a graph specified by adjacency rules:

#### Solve a recurrence:

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

#### Compute a truth table:

#### Generate a Venn diagram:

Gather information about famous problems, conjectures, theorems and paradoxes. Learn about them and their formulators.

#### Get information about a mathematical conjecture:

#### Get historical information about a theorem:

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

#### Compute the probability of a union of events:

#### Compute coin‐toss probabilities:

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

#### Compute an integral:

#### Calculate a derivative:

#### Solve an ordinary differential equation:

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

#### Plot a function:

#### Plot a region satisfying multiple inequalities:

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

#### Compute properties of a vector:

#### Calculate properties of a matrix:

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

Analyze functions and expressions containing imaginary numbers or complex variables.

#### Compute properties of a function of a complex variable (use the variable z):

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

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

#### Do computations with special functions:

#### Do computations with number theoretic functions:

#### Find representations for a function:

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

#### Find the continued fraction representation of a number:

#### Find definitions of continued fraction terminology:

#### Find continued fraction papers by author:

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