Format: Hardback, 200 pages
Pub. Date: 04-Jul-2024
ISBN-13: 9789811291982
The Wonders of Science reveals that the physical world is a far more complex and amazing world than it appears to be, so wondrous that it almost defies comprehension. Brilliant scientists have devoted their lives to uncovering these secrets. However, everyone should be able to share the joy of learning about these wonders. No detailed knowledge of science is required to understand these new discoveries, which include quantum theory, relativity theory, string theory, chaos theory, black holes, dark matter, dark energy, the multidimensional universe, quarks, and much more. These many topics are here described in a clear and accessible presentation that can be enjoyed by everyone.Even the greatest scientists sometimes make mistakes. Included in the book are some of the blunders made by leading scientists, including Nobel Prize winners.
Introduction
The Wonders of Physics:
The Submicroscopic Universe
Dark Matter and Dark Energy
Quantum Theory: The Future Does Not Exist
Quantum Theory: Knowledge Does Not Exist Without a Measurement
Black Holes
Gravity: Theories of Newton and Einstein
Quantum Gravity, String Theory and the Ten-Dimensional Universe
Chaos Theory: Predicting the Weather and the Butterfly Effect
The Solar System: Geocentric versus Heliocentric
Mathematics in the Service of Science
The Fine-Tuned Universe: Why Does the Sun Shine?
The Wonders of Evolution:
Evolution: Denial
Evolution: Religion
Challenges to Evolution
Gradualism versus the Fossil Record
Mass Extinctions: "Bad Genes or Bad Luck?"
Darwin's Theory of Evolution: Pro and Con
Darwin's Theory of Evolution: Confusion
Evolution of Human Beings
Are Contemporary Human Beings Continuing to Evolve?
Are Contemporary Human Beings Unique Creatures? The Neolithic Revolution
Blunders of Great Scientists:
Isaac Newton
Albert Einstein
Charles Darwin
Lord Kelvin
Lev Landau
Robert Boyle
Enrico Fermi
Alan Turing
Marie Curie
Niels Bohr
Ernest Rutherford
Henry Fairfield Osborn
Marcellin Boule
Sir Grafton Eliot Smith
Epilogue
Index of Names
Subject Index
Format: Hardback, 234 pages
Series: Essential Textbooks in Mathematics
Pub. Date: 04-Jul-2024
ISBN-13: 9781800615717
Paperback
ISBN-13:9781800615861
Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters.The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort to solve. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiads level, but solutions are provided in all cases.The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.
Format: Hardback, 1200 pages
Pub. Date: 30-Jul-2024
ISBN-13: 9789811289361
Logic is a foundational mathematical discipline for Computer Science. This unique compendium provides the main ideas and techniques originating from logic. It is divided into two volumes propositional logic and predicate logic. The volume presents some of the most important concepts starting with a variety of logic formalisms Hilbert/Frege systems, tableaux, sequents, and natural deduction in both propositional and first-order logic, as well as transformations between these formalisms. Topics like circuit design, resolution, cutting planes, Hintikka sets, paramodulation, and program verification, which do not appear frequently in logic books are discussed in detail.The useful reference text has close to 800 exercises and supplements to deepen understanding of the subject. It emphasizes proofs and overcomes technical difficulties by providing detailed arguments. Computer scientists and mathematicians will benefit from this volume.
Preliminaries
Propositional Logic?Syntax and Semantics
Propositional Logic?Formal Systems
First-Order Logic?Syntax and Semantics
First-Order Logic?Formal Systems
Program Verification
Bibliography
Format: Hardback, 560 pages
Pub. Date: 14-Jul-2024
ISBN-13: 9789811286445
The Numerical Jordan Form is the first book dedicated to exploring the algorithmic and computational methods for determining the Jordan form of a matrix, as well as addressing the numerical difficulties in finding it. Unlike the 'pure' Jordan form, the numerical Jordan form preserves its structure under small perturbations of the matrix elements so that its determination presents a well-posed computational problem. If this structure is well conditioned, it can be determined reliably in the presence of uncertainties and rounding errors.This book addresses the form's application in solving some important problems such as the estimation of eigenvalue sensitivity and computing the matrix exponential. Special attention is paid to the Jordan-Schur form of a matrix which, the author suggests, is not exploited sufficiently in the area of matrix computations. Since the mathematical objects under consideration can be sensitive to changes in the elements of the given matrix, the book also investigates the perturbation analysis of eigenvalues and invariant subspaces. This study is supplemented by a collection over 100 M-files suitable for MATLAB in order to implement the state-of-the art algorithms presented in the book for reducing a square matrix into the numerical Jordan form.Researchers in the fields of numerical analysis and matrix computations and any scientists who utilise matrices in their work will find this book a useful resource, and it is also a suitable reference book for graduate and advance undergraduate courses in this subject area.
Preface
List of Algorithms
Notation
Numerical Matrix Computations
The Eigenvalue Problem
The Eigenvalue Sensitivity Problem
Numerical Solution of the Eigenvalue Problem
Geometry of Jordan Forms
Reduction into Jordan?Schur Form
Reduction into Weyr and Jordan Form
Case Study 1. Eigenvalue Sensitivity Analysis
Case Study 2. Computing the Matrix Exponential
Appendix: Review of Linear Algebra and Matrix Analysis
Bibliography
Index
Format: Hardback, 200 pages
Pub. Date: 06-Oct-2024
ISBN-13: 9781800615885
The existence of transcendental numbers was first proved in 1844, by Joseph Liouville. Advances were made by Charles Hermite, proving the transcendence of the number e, and Ferdinand von Lindemann, proving the transcendence of the number . The consequence of these discoveries was the negative solution of the problem of squaring the circle, which has stood for many years. In the 20th century, the theory of transcendental numbers developed further, with general methods of investigating the arithmetic nature of various classes of numbers. One of these methods is the Siegel-Shidlovskii method, previously used for the so-called E- and G-functions.Polyadic Transcendental Number Theory outlines the extension of the Siegel-Shidlovskii method to a new class of F-series (also called Euler-type series). Analogues of Shidlovskii's famous theorems on E-functions are obtained. Arithmetic properties of infinite-dimensional vectors are studied, and therefore elements of direct products of rings of integer p-adic numbers are considered. Hermite-Pade approximations are used to investigate the values of hypergeometric series with algebraic irrational parameters. Moreover, the book describes how to use Hermite-Pade approximations to obtain results on the values of hypergeometric series with certain transcendental (polyadic Liouville) parameters. Based on quite recent results, this book contains indications of promising areas in a new field of research. The methods described allow readers to obtain many new results.
Introduction
Polyadic Numbers
F-series
Generalization of Siegel?Shidlovskii's Method for F-series
Euler's Factorial Series and Direct Generalizations
Arithmetic Properties of Polyadic Series with Periodic Coefficients
Hypergeometric F-series
Arithmetic Properties of Generalized Hypergeometric Series with Algebraic Irrational Coefficients
Arithmetic Properties of Generalized Hypergeometric Series with Transcendental Polyadic Parameters
Transcendence of p-adic Values of Generalized Hypergeometric Series with Transcendental Polyadic Parameters
Format: Hardback, 400 pages
Series: Series On Analysis, Applications And Computation 13
Pub. Date: 30-Jul-2024
ISBN-13: 9789811290275
The book is devoted to rigorous mathematical results on discrete nonlinear Schrodinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations emerge as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there is necessary material from the spectral theory of discrete Schrodinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.
Preliminaries
Time Dependent Discrete Nonlinear Schrodinger Equation
Critical Point Theorems
Stationary Discrete Nonlinear Schrodinger Equation with Unbounded Potentials
Stationary Discrete Nonlinear Schrodinger Equation with Periodic Potentials
Stationary Discrete Nonlinear Schrodinger Equation with Nonlocal Nonlinearity
Constrained Minimization and Excitation Thresholds
Format: Hardback, 300 pages
Pub. Date: 28-Mar-2024
ISBN-13: 9789811277870
This book provides an updated discussion of fixed point theory using the framework of p-vector spaces, a core component of nonlinear analysis in mathematics. The book covers three main topics: 1) the 'best approximation approach' for classes of semiclosed 1-set contractive set-valued mappings in both p-vector spaces (including locally p-convex spaces); 2) the general principle of Leray-Schauder alternatives; and 3) various forms of fixed point theorems for non-self mappings.Specifically, the book focuses on the development of general fixed point theory for both single and set-valued mappings. It provides affirmative answers to the Schauder conjecture under the general setting of p-vector spaces (including topological vector spaces as a special class), and locally p-convex spaces. The book establishes best approximation results for upper semi-continuous and 1-set contractive set-valued mappings, which are used as tools to establish new fixed point theorems for non-self set-valued mappings with either inward or outward set conditions under various situations. These results improve or unify corresponding results in the existing literature for nonlinear analysis, and allow for the establishment of the fundamental general theory for the development of fixed point theorems in topological vector spaces since Schauder's conjecture was raised in 1930.This new book is a staple textbook for undergraduate and postgraduate students, a reference book for researchers in the field of fixed point theory in nonlinear functional analysis, and is easily accessible to general readers in mathematics and related disciplines.
Introduction
p-vector Spaces
KKM Principle
Fixed Point Theorem in locally p-convex Spaces
Fixed Point Theorem in p-vector Spaces
Best Approximation Theorems in p-vector Spaces
Fixed Point Theorem for non-self Mappings in p-vector Spaces
Principle of Nonlinear Alternatives in p-vector Spaces
Illustration and Remarks
References
Index