Projective geometry:
|
square.mws How
to find a central perspective mapping a generic 4-gon
to a square.
|
|
Quadrics:
|
normalform.mws Implementation
of the normal form algorithm for a quadric as a procedure.
Gives the output of the intermediate steps. The following
file does the individual steps for an example: normalform
schrittweise.mws
|
|
Linear algebra: |
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.
|
gramschmidt.mws Maple
worksheet doing Gram-Schmidt orthonormalization with
some polynomial examples with various scalar products,
projection on subspaces. |
Fourierapproximation Fourier
approximation of functions, uses Gram-Schmidt. |
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.
|
general maple.mws intro.mws Some
general Maple syntax and examples. |
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:
|
probedivision.mws Factorization
of integers via trial division. |
eratosthenes.mws The sieve
of Erathostenes. |
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.
|