Elementary Mathematics

do basic arithmetic

125 + 375

do exact arithmetic with fractions

1/4 * (4 - 1/2)

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

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

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

compute eigenvalues and eigenvectors of a matrix

eigenvalues {{4,1},{2,-1}}

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

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

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

Advanced Mathematics

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

e^z

do vector analysis computations

div (x^3 y, y^3 z, z^3 x)

compute properties of a knot

8_1 knot

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