Mathematics

Die Mathematik ist die Königin der Wissenschaften und die Zahlentheorie ist die Königin der Mathematik.

— Johann Carl Friedrich Gauß

This page contains a few links to external sites or PDF documents. Please use the navigation bar on the left side or the search function to find the other tutorials.

Algebra

• Group Operations

Dynamical Systems

• Entropie und Ergodizität (Einführung) — G. Bellot (2014)
• Das -Lemma — G. Bellot (2007)

Euclidean Geometry

• The Centroid of Convex Polygons
• Of Planes and Triangles

General

• A Mathematician’s Lament — P. Lockhart
• Why everyone should know number theory — K. Minhyong
• Zweitkorrektur — F. Lemmermeyer

Music

• And Then, There Was Sound

Number Theory

Algebraic Number Theory

• Introduction to p-adic numbers — G. Bellot (2015)

Computational Algebraic Number Theory

• hn++ (wip) - algebraic number theory library, written in C++, with a focus on algorithms for lattices over imaginary quadratic number fields - based on the work of A. Schiemann and B. Hemkemeier.
• MagmaNeighbours - modified version of Boris Hemkemeier’s Two-Neighbours algorithm, implemented in MAGMA.

Information and Coding Theory

• The Berlekamp-Massey Algorithm

Lattices

• New Extremal Lattice in — M. Jürgens, G. Bellot (2015)

Physics

Basics

• Units of Measurement

Kinematics

• Galileo vs. Newton
• Newton’s Laws of Motion
• One-Dimensional Kinematics
• Two-Dimensional Kinematics
• Basic Projectile Kinematics
• The Evil Head of Friction
• Basic Ad Hoc Collision Response

Topology

Differential Topology

• Der Zerlegungssatz von Jordan-Brouwer — G. Bellot (2005)

Quadratic Forms

Introduction to Bilinear and Quadratic Forms

• Bilinear Forms over Rings
• Bilinear Forms over Free Modules
• Orthogonal Decompositions
• Introduction to Quadratic Forms