Mathematics

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

--- Johann Carl Friedrich Gauß

Lattices and Genera

• Extremal lattices in $II_{20}(5^{+10})$ --- M. Jürgens, 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.

Mathematics for Games

• The Centroid of Convex Polygons
• Of Planes and Triangles

Arithmetic Theory of Quadratic Forms

Introduction to Bilinear and Quadratic Forms

• Bilinear Forms over Rings
• Bilinear Forms over Free Modules
• Orthogonal Decompositions
• Introduction to Quadratic Forms
• Primitive Modules
• Hyperbolic Forms
• A Theorem of Witt

Mathematical Physics

• Galileo versus Newton

Algebraic Number Theory

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

Dynamical Systems

• Entropie und Ergodizität (Einführung) --- G. Bellot (2014)
• Das $\lambda$-Lemma --- G. Bellot (2007)

Differential Topology

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

Information and Coding Theory

• Linear-Feedback Shift Registers

General

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