Elementary Math

Do basic arithmetic:

125 + 375

Do exact arithmetic with fractions:

1/4 * (4 - 1/2)

Algebra

Solve an equation:

x^3 - 4x^2 + 6x - 24 = 0

Factor a polynomial:

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48

Simplify an expression:

1/(1+sqrt(2))

Calculus & Analysis

Compute an integral:

integrate sin x dx from x=0 to pi

Calculate a derivative:

derivative of x^4 sin x

Solve an ordinary differential equation:

y'' + y = 0

Geometry

Compute properties of a geometric figure:

annulus, inner radius=2, outer radius=5

Plot a conic section and identify its type:

2x^2 - 3xy + 4y^2 + 6x - 3y - 4 = 0

Compute properties of a polyhedron:

dodecahedron

Differential Equations

Solve a linear ordinary differential equation:

Specify initial values:

y'' + y = 0, y(0)=2, y'(0)=1

Solve a nonlinear equation:

f'(t) = f(t)^2 + 1

Plotting & Graphics

Plot a function:

plot x^3 - 6x^2 + 4x + 12

Plot a region satisfying multiple inequalities:

plot x^2+y^2<1 and y>x

Numbers

Compute a decimal approximation to a specified number of digits:

pi to 1000 digits

Convert a decimal number to another base:

219 to binary

Trigonometry

Compute values of trigonometric functions:

sin(pi/5)

Solve a trigonometric equation:

sin x + cos x = 1

Linear Algebra

Compute properties of a vector:

vector <3, -4>

Calculate properties of a matrix:

{{6, -7}, {0, 3}}

Determine whether a set of vectors is linearly independent:

Are (2, -1) and (4, 2) linearly independent?

Number Theory

Compute a prime factorization:

factor 70560

Solve a Diophantine equation:

solve 3x+4y=5 over the integers

Discrete Mathematics

Compute a possible formula and continuation for a sequence:

5, 14, 23, 32, 41, ...

Analyze a graph specified by adjacency rules:

1->2, 2->3, 3->1, 3->4, 4->1

Solve a recurrence:

f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2

Complex Analysis

Compute properties of a function of a complex variable (use the variable ,<i>z</i>,):

e^z

Compute the residue of a function at a point:

residue of 1/(z^2+4)^2 at z=2i

Applied Mathematics

Minimize or maximize a function:

maximize x(1-x)e^x

Numerically integrate functions that cannot be integrated symbolically:

integrate sin(cos x) from x=0 to 1

Logic & Set Theory

Compute a truth table:

P && (Q || R)

Generate a Venn diagram:

(complement S) intersect (A union B)

Mathematical Functions

Do computations with special functions:

d/dx Si(x)^2

Do computations with number theoretic functions:

phi(110)

Find representations for a function:

gamma(x) integral representation

Mathematical Definitions

Find information about a math concept:

tangram

Get a brief definition:

basic definition of prime number

Famous Math Problems

Get information about a mathematical conjecture:

Riemann Hypothesis

Get historical information about a theorem:

Fermat's little theorem

Continued Fractions

Find the continued fraction representation of a number:

continued fraction pi

Find definitions of continued fraction terminology:

what is a regular continued fraction

Find continued fraction papers by author:

continued fraction papers by Stern

Statistics

Calculate basic descriptive statistics for a data set:

{25, 35, 10, 17, 29, 14, 21, 31}

Find the sample size needed to estimate a binomial parameter:

sample size for binomial parameter

Probability

Compute the probability of a union of events:

probability of the union of three events

Compute coin‐toss probabilities:

32 coin tosses