Projective geometry: 

square.mws
How to find a central perspective mapping a generic 4-gon to a square.

Quadrics:

lineare algebra.mws
Short demonstration of linear algebra computations with Maple.

kern und bild.mws
Kernel and image of a homomorphism.

basiswechsel.mws
Change of bases for homomorphisms.

inverse.mws
Computing the inverse.

normalform.mws
Classification of homomorphisms.

gauss.mws
Gauß algorithm, elementary transformations, basis of kernel, basis of image, lineare systems of equations, linear independence, bases, basis of sum of subspaces, basis of intersection of subspaces, subfamilies of system of generators forming a basis.

normalformen.mws
Normal forms of endomorphisms via built in Maple functions (characteristic polynomial, eigenspaces, Jordan normal form).
diagonalisierung.mws

rank.mws
Rank of a random matrix over a finite field.

jordan.mws
Implementing the Jordan normal form algorithm.

General Maple:

maple.mws
Short introduction to Maple.

3Dplots.mws
Plots and 3D-plots.

Proofs by induction:

shortestpaths.mws
All shortest paths in a rectangular lattice; with plot.

hanoi.mws
The towers of Hanoi; with plot.

Algebra and Number Theory:

rsa.mws
RSA public-key cryptography.

fermat pseudoprimzahlen.mws
Fermat pseudoprimes.

interpolation.mws
Lagrange interpolation via Chinese remainder theorem.

Fpk.mws
Finite fields: Irreducible polynomials, representation of finite fields, computing in finite fields, primitive roots, primitive elements, subfields.

grad4.mws
Solutions of an equation of degree 4.

galois.mws
Computing galois groups with theorem of Dedekind and theorem of Chebotarev.
galois examples.mws
Examples computing Galois groups.

semidirektes Produkt.txt (GAP)
Semidirect product in GAP.

Diskriminante.txt (Macaulay2)
Representation of the discriminant in the elementary symmetric functions.

divrest.mws
Division with remainder and Euclidian algorithm in the Euclidian rings ZZ[sqrt(n)], n=-1,-2,2,3.

euklid.mws
Euclidian algorithm in ZZ

gruppen.mws
Orbit, stabilizer, elements of a group, generators of stabilizer, group order.

wuerfelgruppe.mws
Symmetry group of a cube, permutations, orthogonal matrices, conjugacy classes.

icosaeder.mws
The five inscribed octahedra in an icosahedron inducing the isomorphism of the symmetry group of rotations of the icosahedron to A5.

twisted cubic.mws
The twisted cubic.

conic intersections.mws
Intersections of conics.

bezier spline.mws
Bezier splines.

Calculus: 

stetigkeit.mws
Continuity.

diffbarkeit.mws
Differentiability, difference quotient, continuous differentiability.

rational.mws
cos.mws
wurzel.mws
The graph of a function.

integration.mws
Riemann integral, numeric integration.

taylor.mws
Taylor series.

glmkonv.mws
Examples of sequences of function which do not converge uniformly, discontinuity of limit function, uniform convergence and integration, uniform convergence and differentiation, power series expansion of ln(1+x) and arctan(x), radius of convergence, Abel's limit theorem.

Multivariate calculus:

mtaylor.mws
Multivariate Taylor series.

extrema.mws
extrema_mit_nebenbedingungen.mws
Extremal values.

lokalaufloesen.mws

kegel_steiner.mws
Moment of inertia tensor of a cone, Steiner's theorem.

durchschnittzylinder.mws
The volume of the intersection of two orthogonal cylinders.

kegelhalbkugelzylinder.mws
Cone, half sphere and cylinder with same volume.

kugelkoordinaten.mws
Spherical coordinates.

torus.mws
Volume and inertia tensor of a torus.

Statistics:

ausgleichsgerade.mws
Regression line.

konfidenzintervall.mws
Confidence interval.

dichte.mws
Piecewise linear approximation of the density of a random variable.

Plane and space curves:

logspirale.mws
Logarithmic spiral.

kruemmung.mws
Curvature of space curve.

spacecurve.mws
Torsion of a curve.