Schlagwort-Archive: mathematics

Chen: Networks and graphs

Zitat

Veröffentlicht am von

“Networks, or graphs (a collection of nodes with edges connecting them), have long been studied in a prolific branch of mathematics known as “graph theory” and are often used by scientists to model the structure of many complex systems, ranging from technological systems and biological systems to social systems and economic systems. Human beings are surrounded by a variety of different types of networks.” (p. 1) #Chen #Network #graph #mathematics #structure #system

Chen, Wei, Explosive Percolation in Random Networks. Berlin/Heidelberg: Springer 2014. 63 S.

Newman: Networks

Zitat

Veröffentlicht am von

“The study of networks, in the form of mathematical graph theory, is one of the fundamental pillars of discrete mathematics.” (p. 2) #Newman #networks #GraphTheory #mathematics

Newman, Mark E. J., The Structure and Function of Complex Networks, in: SIAM Review 45 (2003), 167–256.

Mandelbrot: Mathematics

Zitat

Veröffentlicht am von

„A contribution to mathematics and/or science does not consist of a picture, but rather of a picture combined with a description. Without words and formulas, a picture can, at best, be praised for artistic quality. Without an interest in pictures and other aspects of ‚reality,‘ pictures can play no role whatsoever.“ (p. 26) #Mandelbrot #mathematics #picture

Mandelbrot, Benoît B., Fractals and Chaos. The Mandelbrot Set and Beyond. New York: Springer 2004, ISBN 978-1-4419-1897-0.

Bourbaki: A Mathematical Theory

Zitat

Veröffentlicht am von

„A mathematical theory (or simply a theory) contains rules which allow us to assert that certain assemblies of signs are terms or relations of the theory, and other rules which allow us to assert that certain assemblies are theorems of the theory.“ (p. 16) #Bourbaki #theory #relation #theorem

Bourbaki, Nicolas, Elements of Mathematics: Theory of Sets. Berlin, Heidelberg, New York: Springer 2004.

Bourbaki: Mathematics and Truth

Zitat

Veröffentlicht am von

„Mathematicians have always been convinced that what they prove is ‚true‘. It is clear that such a conviction can be only of a sentimental or metaphysical order, and cannot be justified, or even ascribed a meaning which is not tautological, within the domain of mathematics. The history of the concept of truth in mathematics therefore belongs to the history of philosophy and not of mathematics; but the evolution of this concept has had an undeniable influence on the development of mathematics, and for this reason we cannot pass over it in silence.“ (p. 306f.) #Bourbaki #mathematics #truth

Bourbaki, Nicolas, Elements of Mathematics: Theory of Sets. Berlin, Heidelberg, New York: Springer 2004.