Mathematics

Another largish article

Elementary Mathematics
do basic arithmetic
 * 125 + 375

do exact arithmetic with fractions
 * 1/4 * (4 - 1/2)

Numbers
compute a decimal approximation of a specified number of digits
 * pi to 1000 digits

convert a decimal number to another base
 * 219 to binary

Algebra
find the sqaure root


 * square root of 54


 * square root of 1/3


 * square root of 145.12
 * sqrt(421)

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}}

Sum

 * sum[l*2,{l,3,6}]
 * Sum[ sum[k+l,{l,1,3}] ,{k, 1, 4}]

Plotting & Graphics
plot a function
 * plot x^3 - 6x^2 + 4x + 12

plot a region satisfying multiple inequalities
 * plot x^2+y^2 x

plot within a defined set of coordinates
 * Plot[sin[x^2], {x, 0, 3}]

plot a vector field -- defaults to {y,-x} with button to change input values
 * vector plot

Calculus & Analysis
calculate a derivative
 * derivative of x^4 sin x

compute an integral
 * integrate sin x dx from x=0 to pi

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 do the ackermann function
 * gamma(x) integral representation
 * ackermann (m,n)

Advanced Mathematics
compute properties of a function of a complex variable (use the variable z)
 * e^z

do vector analysis computations
 * div (x^3 y, y^3 z, z^3 x)

compute properties of a knot
 * 8_1 knot

External Link

 * Much more maths