Set Theory And Its Applications In Physics And Computing
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Set Theory And Its Applications In Physics And Computing
Why learn set theory? This book provides the answer — it is interesting, and also useful! Taking a new approach and looking from a fresh perspective, the discussion flows in a friendly and transparent way, supplemented with a lot of examples and figures. This makes the theory easily comprehensible: the proofs get vivid and visual, enveloped with interesting applications for students in (applied) math, physics, and engineering. Given the theory and the applications, the book could serve as a textbook in four (undergraduate) math courses: Introduction to set theory and its application; Chaos theory and stability — a geometrical point of view; Functional analysis — Han-Banach theory; and Cryptography with quantum computing. It teaches set theory from the basics, including the axiom of choice, the well ordering theorem, and Zorn's lemma. Furthermore, it uses Cantor's set to introduce chaos theory from a geometrical point of view. Moreover, it introduces the binomial formula (and other related formulas), and uses them in quantum statistical mechanics. And finally, it uses Zorn's lemma in functional analysis, general relativity, and quantum mechanics. There are also practical applications in cryptography, error correction, quantum computing and programming.
Group Theory and Its Applications
Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger's and Dirac's for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.
Neutrosophic Theory and Its Applications, Vol. I
Author: Florentin Smarandache
language: en
Publisher: Infinite Study
Release Date: 2014-12-01
This volume contains 45 papers, written by the author alone or in collaboration with the following co-authors: Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri Kroumov, Pabitra Kumar Maji, Maikel Leyva-Vazquez, Feng Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel, Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar Sunderraman, Luige Vladareanu, Magdalena Vladila, Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing Zhang.