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

Do basic arithmetic:

Do exact arithmetic with fractions:

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:

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:

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

Solve an equation:

Factor a polynomial:

Compute eigenvalues and eigenvectors of a matrix:

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

Compute an integral:

Calculate a derivative:

Solve an ordinary differential equation:

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:

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

Compute a prime factorization:

Solve a Diophantine 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:

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:

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:

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:

Explore topics in higher level mathematics including analysis, topology and more.

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

Do vector analysis computations:

Compute properties of a knot:

Make queries about various definitions and descriptions in mathematics.

Find information about a math concept:

Get a brief definition:

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

Find the continued fraction representation of a number:

Find definitions of continued fraction terminology:

Find continued fraction papers by author:

Compute properties of data sets, 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:

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: