Mathematical Structures of Joseon mathematician Hong JeongHa

Mathematical Structures of Space-time * Mathematical Structures of Space-time

At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general relativity, and the conditions for their existence are discussed. The causality conditions are studied through an analysis of strong causality, stable causality ...

Mathematical Structures of Complexity

This article discusses a variety of mathematically-inspired approaches to the study of complexity and their application to the study and understanding of complex systems. These approaches have their origin in the study of limitative results in logic, mathematical linguistics, and the theory of computation, based upon the work of Godel, Turing, Chomsky, and Kolmogorov, among many others. The top...

Jonathan Borwein: Experimental Mathematician

Jonathan M. Borwein unexpectedly died on 2 August 2016, in London, Ontario, Canada, where he had been visiting on leave from home institution, the University of Newcastle, Australia. Since his death, the present author and Nelson H. F. Beebe of the University of Utah have been collecting Borwein’s many published papers, books, reports and talks, as well as a number of articles written by others...

Structures in Mathematical Theories

Packaging Mathematical Structures

This paper proposes generic design patterns to define and combine algebraic structures, using dependent records, coercions and type inference, inside the Coq system. This alternative to telescopes in particular allows multiple inheritance, maximal sharing of notations and theories, and automated structure inference. Our methodology is robust enough to support a hierarchy comprising a broad vari...