Miscellaneous Mathematical Texts and Snippets
by
Klaus Pommerening
Sets and Mappings
Finding the Period of a Periodic Sequence
(for example by Floyd's algorithm)
Number Theory
The Euclidean Algorithm
A Remark on Subset Sums
A Remark on Subsemigroups
(Dickson's lemma)
The Indecomposable Solutions of Linear Diophantine Equations
The Indecomposable Solutions of Linear Congruences
Groups
The Number of Orbits of Finite Group Actions
Permutations and Rejewski's Theorem
Fields and Polynomials
Quadratic Equations in Finite Fields of Characteristic 2
Polynomial Functions
(interpolation from an algebraic view)
Fourier Analysis of Boolean Maps
Algebraic Geometry and Invariant Theory
Hilbert's Nullstellensatz over the complex numbers
(a very short proof)
Gordan's Finiteness Theorem
(Hilbert's proof – slightly modernized)
Lie Theory and Algebraic Groups
Richardson's Finiteness Theorem
The Morozov-Jacobson Theorem
(on 3-dimensional simple Lie subalgebras)
Analysis
Stirling's Formula
(with tight bounds)
Complex Analysis
Extension of Conformal Maps to the Boundary
Probability
Uniformly Distributed Random Variables in Groups
(another view at the One Time Pad)