Acknowledgement
Abstract
Kurzfassung
Contents
Motivation
1 Introduction
 Organization
I  Common Ground
2 The Value of Abstraction
 2.1 Abstractions and the World
 2.2 Implementations
 2.3 Obstacles
 2.4 Guidance
3 Machines for Computations
 3.1 Paradigms
 3.2 Mathematics and Algorithms
 3.3 Example of Generic Programming
II  Theory
4 Mathematical Tools
 4.1 Bare Basics
 4.2 Algebraic Structures
 4.3 Mappings
 4.4 Topology
 4.5 Fibers
 4.6 Di?erential Geometry
 4.7 Integration
 4.8 Distances
 4.9 Integral Equations
 4.10 Probability
5 Dynamics
 5.1 Newton’s Mechanics and World
 5.2 Lagrangian Formalism
 5.3 Hamiltonian Formalism
 5.4 Statistical Description – Boltzmann’s Equation
 5.5 Macroscopic Quantities
 5.6 Boltzmann’s Equation in Integral Form
 5.7 The Quantum World
III  Methods
6 Components
 6.1 Sets
 6.2 Data Types
 6.3 Topology
 6.4 Fibers
 6.5 Geometric Structures
 6.6 Integration
7 Dynamics in Action
 7.1 Equilibrium and Macroscopic Quantities
 7.2 Tracing Phase Space – Components from Theory
 7.3 Among Quanta
 7.4 Bordering Two Worlds Again
8 Outlook
A Resolvent for Integral Equations
B Random Number Generation
C Richardson Extrapolation
Bibliography
Philipp Schwaha