Quantum Field Theory, Quantum Geometry, and Quantum Algebras [PDF]
arXiv, 2017 We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
arxiv
Set-Theoretic Completeness for Epistemic and Conditional Logic
, 1999 The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of formulas in the ...
Halpern, Joseph Y.
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A computational introduction to number theory and algebra
, 2005 This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience.
V. Shoup
semanticscholar +1 more source
Towards Visual Type Theory as a Mathematical Tool and Mathematical User Interface [PDF]
arXiv, 2016 A visual type theory is a cognitive tool that has much in common with language, and may be regarded as an exceptional form of spatial text adjunct. A mathematical visual type theory, called NPM, has been under development that can be viewed as an early-stage project in mathematical knowledge management and mathematical user interface development.
arxiv
On a Final Theory of Mathematics and Physics [PDF]
arXiv, 2015 Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is mounting evidence this ultimate theory of physics will also be a unified theory of mathematics.
arxiv
, 2001 M. Nair
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Gauge field theories: various mathematical approaches [PDF]
arXiv, 2014 This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories.
arxiv
Chern--Simons Terms as an Example of the Relations Between Mathematics and Physics [PDF]
Relations between Mathematics and Physics (IHES publications 1998), 1998 The inevitability of Chern--Simons terms in constructing a variety of physical models, and the mathematical advances they in turn generate, illustrates the unexpected but profound interactions between the two disciplines.
arxiv
Problem-solving and selected topics in number theory: in the spirit of the mathematical Olympiads [PDF]
, 2011 Michael Th. Rassias
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