17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics)

<p>The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.</p>

Crafts, Hobbies & Home

Křížek, Michal

Luca, Florian

Somer, Lawrence

Gardening & Landscape Design

Springer

<p>Mathematical modeling plays an essential role in science and engineering. Costly and time consuming experiments (if they can be done at all) are replaced by computational analysis. In industry, commercial codes are widely used. They are flexible and can be adjusted for solving specific problems of interest. Solving large problems with tens or hundreds of thousands unknowns becomes routine. The aim of analysis is to predict the behavior of the engineering and physical reality usually within the constraints of cost and time. Today, human cost and time are more important than computer cost. This trend will continue in the future. Agreement between computational results and reality is related to two factors, namely mathematical formulation of the problems and the accuracy of the numerical solution. The accuracy has to be understood in the context of the aim of the analysis. A small error in an inappropriate norm does not necessarily mean that the computed results are usable for practical purposes.</p>

Mathematical and Numerical Modelling in Electrical Engineering Theory and Applications (Mathematical Modelling: Theory and Applications, 1)

Science & Math

Neittaanmäki, Pekka

Mathematics

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Simplicial Partitions with Applications to the Finite Element Method (Springer Monographs in Mathematics)

<p><div> <div> <div> <div>This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields.</div> <div><br /></div> <div>These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions.&nbsp;</div> <div><br /></div> <div>It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.&nbsp;</div> </div> <div><br /></div> </div> </div></p>

Brandts, Jan

Korotov, Sergey

Chemistry

<p><div> <div> <div> <div>This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields.</div> <div><br /></div> <div>These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions.&nbsp;</div> <div><br /></div> <div>It is aimed at a general mathematical audience who is assumed to be familiar with only a fewbasic results from linear algebra, geometry, and mathematical and numerical analysis.&nbsp;</div> </div> <div><br /></div> </div> </div></p>

<p>About the Author\nMichal Křížek is professor and head of the Numerical Analysis Department of the Institute of Mathematics of the Czech Academy of Sciences. For many years he was Editor-in-chief of the Czech journal Advances of Mathematics, Physics and Astronomy, and the journal Applications of Mathematics. He is a member of the Czech Learned Society and is the author of ten monographs. His research interests include number theory, numerical analysis, the finite element method for solving partial differential equations, mathematical physics, linear algebra, and mathematical and functional analysis.<br />
Lawrence Somer is a professor emeritus at the Catholic University of America in Washington, D.C. He is a member of the Editorial board of the journal Fibonacci Quarterly. His research interests are in number theory, combinatorics, graph theory, group theory, algebra and geometry.\nAlena Šolcová is an associate professor at the Faculty of Information Technology of the Czech Technical University in Prague. She has been the President of the Union of Czech Mathematicians and Physicists since 2018 and is a member of the Editorial board of the Czechoslovak Journal for Physics. She is an active member of the Czech Mathematical Society and the Czech Society for Cybernetics and Informatics (expert group for logic, probability and reasoning). Her research interests include mathematical logic, number theory, some numerical methods and the history of mathematics, informatics and astronomy. Asteroid No. 58 622 was named “Alenašolcová” in her honor by the International Astronomical Union.\nThis book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.</p>

From Great Discoveries in Number Theory to Applications

Šolcová, Alena

<p><p>This book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof.</p> <p>Some nonstandard topics are also covered, including violation of the causality principle in Newtonian mechanics, a critical mathematical and numerical analysis of Mercury's perihelion shift, inapplicability of Einstein's equations to the classical two-body problem due to computational complexity, non-uniqueness of the notion of universe, the topology of the universe, various descriptions of a hypersphere, regular tessellations of hyperbolic spaces, local Hubble expansion of the universe, neglected gravitational redshift in the detection of gravitational waves, and the possible distribution of mass inside a black hole.</p> <p>The book also dispels some myths appearing in the theory of relativity and in contemporary cosmology. For example, although the hidden assumption that Einstein's equations provide a good description of the evolution of the whole universe is considered to be obvious, it is just a null hypothesis which has not been verified by any experiment, and has only been postulated by excessive extrapolations of many orders of magnitude.</p></p>

Mathematical Aspects of Paradoxes in Cosmology: Can Mathematics Explain the Contemporary Cosmological Crisis?

Astronomy & Space Science

<p>The main aim of this book is twofold. Firstly, it shows engineers why it is useful to deal with, for example, Hilbert spaces, imbedding theorems, weak convergence, monotone operators, compact sets, when solving real-life technical problems. Secondly, mathematicians will see the importance and necessity of dealing with material anisotropy, inhomogeneity, nonlinearity and complicated geometrical configurations of electrical devices, which are not encountered when solving academic examples with the Laplace operator on square or ball domains. <br> Mathematical and numerical analysis of several important technical problems arising in electrical engineering are offered, such as computation of magnetic and electric field, nonlinear heat conduction and heat radiation, semiconductor equations, Maxwell equations and optimal shape design of electrical devices. <br> The reader is assumed to be familiar with linear algebra, real analysis and basic numerical methods. <br> Audience: This volume will be of interest to mathematicians and engineers whose work involves numerical analysis, partial differential equations, mathematical modelling and industrial mathematics, or functional analysis.</p>

Mathematical and Numerical Modelling in Electrical Engineering Theory and Applications: Theory And Applications) (Mathematical Modelling: Theory and Applications)

See the best price to sell, buy, or rent books by Křížek, Michal. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Křížek, Michal

See the best price to sell, buy, or rent books by Křížek, Michal. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics)

Mathematical and Numerical Modelling in Electrical Engineering Theory and Applications (Mathematical Modelling: Theory and Applications, 1)

17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics)

Simplicial Partitions with Applications to the Finite Element Method (Springer Monographs in Mathematics)

Simplicial Partitions with Applications to the Finite Element Method (Springer Monographs in Mathematics)

From Great Discoveries in Number Theory to Applications

Mathematical Aspects of Paradoxes in Cosmology: Can Mathematics Explain the Contemporary Cosmological Crisis?

Mathematical and Numerical Modelling in Electrical Engineering Theory and Applications: Theory And Applications) (Mathematical Modelling: Theory and Applications)