Book Reviews

Book Reviews

The Riemann Hypothesis and the Distribution of Prime Numbers

“In the book, The Riemann Hypothesis and the Distribution of Prime Numbers, Dr. Arwashan provides a clear and concise account of all the undergraduate-level mathematical topics relevant to an understanding of the Riemann Hypothesis, with careful attention to issues that commonly cause confusion — the multiple values of a logarithm in the complex plane, for example. This is a valuable addition to the literature on the Hypothesis.” – John Derbyshire, writer, critic, commentator, columnist, and magazine journalist

Perturbation Methods in Matrix Analysis and Control

“The sensitivity of a given mathematical object (or of the corresponding computational problem) is among its most important properties. It shows how the solution of the problem varies under the perturbations of small changes in the data. This property is subject of the so called Perturbation Theory which is widely used in Science and Engineering. In the separate scientific disciplines various perturbation theories have been developed which differ in the problems solved and mathematical methods used, for instance in the Celestial Mechanics, Theory of Nonlinear Oscillations and Control Theory. All these theories are based on the idea to investigate a system whose behavior deviates slightly from the behavior of a simple ideal system for which the full solution of the problem under consideration is known. Perturbation Theory for Linear Operators, which is relevant to the given case, was created by the physicists Strutt and Lord Rayleigh [17] and Schrödinger [16] and the modern perturbation theory for linear operators is developed by Kato [7]…In this book, the authors present new, original results in perturbation linear algebra and control, based on the Method of Splitting Operators and Lyapunov Majorant Functions. Combined with the Schauder or Banach fixed point principles, this method allows to obtain rigorous non-local perturbation bounds for a set of important objects in matrix analysis and control theory. Thus, the perturbation problems in these important fields are investigated in a uniform way, which presents a significant contribution to perturbation theory. As a direction of further work, I would recommend to extend the results obtained to the case of component-wise perturbation analysis in order to find perturbation bounds for the individual super-diagonal elements of the Schur form and for the angles between the perturbed and unperturbed invariant subspaces of the matrix. This will allow to develop full perturbation theory in this important form and go deeper into the properties of the corresponding problems…READ MORE
Reviewed by Ivan Popchev for the Bulgarian Academy of Sciences, Cybernetics and Information Technologies, Volume 20, No 4, Sofia, 2020

Science and Mathematics Education for 21st Century Citizens: Challenges and Ways Forward

“Laurinda Leite, Elizabeth Oldham, Ana S. Afonso, Floriano Viseu, Luĩs Dourado, and Maria Helena Martinho’s edited collection Science and Mathematics Education for 21st Century Citizens: Challenges and Ways Forward strives to offer ways forward to developing human capital by advancing science and math knowledge. This is for the few who will innovate and contribute fundamentally to the betterment of human life. This is for the general populations who can align behind science for improved human health and a healthier and more sustainable environment. This collection was inspired during the 2019 Association for Teacher Education in Europe Winter Conference. A short year later, this collection offers educational programs for teachers, research, new pedagogical models and methods, and ways to build the capabilities of people and infrastructures for new generations…This book introduces programs (global, national, and local) that may help move humanity forward to meeting the challenges of the near-future, which is fast approaching. Humanity will need people with solid science rigor in all dimensions; they will need people who are creative, collaborative, conscientious and woke… READ MORE
Shalin Hai-Jew for C2C Digital Magazine (Spring/Summer 2021)
Instructional Designer
Kansas State University

This book could not have been published at a more opportune time. Given the pandemic of 2020 and the constant barrage of statistics and mixed messages from politicians who tell us they have been ‘guided by the science’; this collection of 19 wide-ranging, excellent chapters offers the kind of critical analysis that the public now crave. It truly is a book for citizens of our newly-changed 21st century.”
Jerry Wellington
University of Sheffield, UK

“This stimulating book guides the reader through a wide range of important problem areas such as innovative approaches to teaching science and mathematics, inclusive schools, interdisciplinary approaches with technology, the STEM agenda or new ways of students´ assessment.”
António Cachapuz
Aveiro University, Portugal

This book is very exciting and breathtaking for science and mathematics educators because it covers all the new developments of the 21st century together. Especially taking into account teachers’ emotions in the teaching has brought a new sense to science teaching books. Innovative strategies for science teaching has excited me and I think it will be very helpful for educators.”
Neslihan Ültay
Giresun University, Turkey

“Multiple pathways are examined to address a wide range of pressing challenges that impinge specifically on Science and Mathematics Education. These challenges for 21st century education are comprehensively addressed throughout this book. Authors have identified and provide approaches, offering innovative and inclusive strategies that respond to the needs of a rapidly changing world.”
Christine Redman
University of Melbourne, Australia

This book may lead teachers to develop new strategies for teaching mathematics and science and learners to become scientific thinkers, which is one of the most important challenges for the future.”
Davide Parmigiani, University of Genoa, Italy;
President of the Association for Teacher Education in Europe

This book presents a lively and exciting collection of research and practice for science and mathematics educators at all levels! I found it fascinating, particularly the passion of many of the authors coming through in the chapters. Inclusion of primary science and mathematics is another delight, omitted in many similar texts. I learned a lot, and thoroughly enjoyed reading this book!”
Colette Murphy
Trinity College Dublin, the University of Dublin, Ireland

Understanding the Schrödinger Equation: Some [Non]Linear Perspectives

“The book contains various approaches to the Schrödinger equation (SE) as a fundamental equation of quantum mechanics. In Chapter 1, a new pedagogical paradigm is proposed which allows one to understand quantum mechanics as an extension of probability theory; its purpose is providing alternative methods to understand the Schrödinger equation. Chapter 2 is devoted to the derivation of SE from the classical Hamiltonian by some procedure of second quantization. In Chapters 3–5, the authors consider the nonlinear SE with many applications: from nonlinear waves in deep water to formation of a cosmogonical body, surface gravity waves, superconductivity and nonlinear optics. The goal of Chapter 6 is to establish the connection of Schrödinger, Madelung and Gross-Pitaevskii equations. Chapter 7, “Paradigm of infinite dimensional phase space,” describes the deep connection between SE and the infinite chain of equations for distribution functions of high-order kinematical values (Vlasov chain). The authors formulate the principles which allow one to combine and treat in unified form the physics of classical, statistical and quantum mechanical phenomena. And in final Chapter 8 it is shown that SE can be mathematically derived from Hamilton’s equation if one uses the metaplectic representation of canonical transformations. All that makes the book interesting for a wide community of physicists.” – E.E. Perepelkin, B.I. Sadovnikov (Lomonosov Moscow State University, Department of Quantum Statistics and Field Theory, Moscow, Russia), and N.G. Inozemtseva (Moscow Technical University of Communications and Informatics, Department of Physics, Moscow, Russia)

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An Introduction to Capstone in Applied Analysis: A Fundamental Guide for Students and Instructors

“This is an excellent reference for anyone interested in applied analysis, especially for students and teachers working on Science, Technology, Engineering and Mathematics (STEM) capstone projects. It is an easy to read textbook that will help build mathematical foundations needed for capstone projects with plethora of examples in wide range of applications.” – Sudhir Shrestha, Ph.D., Department of Engineering Science, Sonoma State University, Rohnert Park, California

“A surge in undergraduate and capstone research has been noticed in the past several years. This is due to the great explosion in the advancement of technology. The traditional class courses taken are not enough anymore. This book aims to facilitate students and instructors working in capstone and undergraduate research projects. The book is written well, carefully designed for undergraduate students in mathematics and applied sciences. We see that we are looking at a very analytic and easy to read map in the exciting area of capstone projects, written by an experienced mathematician. It is certainly a must-read book. We strongly and enthusiastically recommend it for usage in classroom or as a study guide for capstone projects.” – Ioannis K. Argyros, Ph.D., Professor, Department of Mathematical Sciences, Cameron University, Lawton, Oklahoma

For more information about this book, please click here.

Mathematical Modeling of Real World Problems: Interdisciplinary Studies in Applied Mathematics

“The book is a compilation of a number of scientific papers providing a view on how mathematics can be applied to model some real world problems. In depth analyses and discussions are given by researchers applying wavelet to environmental problems, to water management and in medical sciences. The book can be recommended as a reference ‘handbook’ for those working in applications of data processes and in engineering applications.” – Honorary Professor Donald Gabriels, Ghent University, Belgium with the UNESCO Chair on Eremology

“The proposed book looks very interesting and covers a variety of subjects like environment, water management and medicine. Such interdisciplinary topics could prove to be useful to many researchers working in these fields.” – Professor Dr. Pammy Manchanda, Guru Nanak Dev University, India

“This book serves as an up-front review of mathematical modeling of real world problems and interdisciplinary studies in applied mathematics that not only scientists, engineers, planners, social scientists but also everyone can read and understand the real world problems. The content ranges from environmental problems to medicine and their interaction to mathematical implementation. Thank all contributors who ensure such extended and comprehensive study.” – Professor Dr. Hasan Saygin, Istanbul Aydin University, Turkey

“This book covers a broad spectrum of applying mathematical tools to solve problems in the real world, mainly in the environmental and medical sciences. I am very interested in chapters about the application of wavelet to the time series analysis and the use of numerical models to the meteorological and environmental studies. I believe that this book will be a valuable reference for those who work on or are interested in data processing and data mining researches.” – Professor Dr. Lin Wang, Chinese Academy of Sciences, China

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An Essential Guide to Fuzzy Systems

“The book is original and interesting. The authors prove to be mastering the subject of fuzzy information processing and intelligent algorithms. Apart from the fuzzy sets theory it is also related to the following research areas: computational thinking systems, intelligent computing, recent trends of machine learning and Artificial Intelligence techniques.” READ MORE…Professor Abdel-Badeeh M. Salem, Professor of Computer Science, Founder & Head of Artificial Intelligence and Knowledge Engineering Research Labs, Faculty of Computer and Information Sciences, Ain Shams University, Abbasia, Cairo, Egypt

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Hyperbolic Equations and General Relativity

“This is an excellent book that can be used to introduce the reader to the theory of hyperbolic equations and to the mathematical theory of gravitational waves and Einstein equations. Several basic concepts such as wavelike propagation, fundamental solution, Riemann kernel and its existence, world function and its role in the fundamental solution, characteristic conoid, are well presented. The reader is then offered the opportunity to learn in detail how Choquet-Bruhat proved existence and uniqueness of the solution of vacuum Einstein equations with non-analytic Cauchy data. Last, an introduction to some important aspects of high-speed black hole collisions, a masterpiece work of D’Eath and Payne, is presented. The appendices on Sobolev spaces and Kasner spacetime are also very useful, as well as the suggested literature at the end. The author should be congratulated for having written a book of high pedagogical value for future generations of research workers in general relativity.” – Giampiero Esposito, INFN Sezione di Napoli, Naples, Italy

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Understanding Banach Spaces

“Banach spaces as well as their specializations such as Hilbert or Euclidean spaces to mention a few are of great interest in Pure as well as Applied Mathematics. In particular Dr. González is connecting Banach spaces to applications using iterative methods. Researchers and practitioners consider Banach spaces general enough for studying operator equations, since problems from diverse disciplines can be reduced to locating a zero of a Banach space valued operator. These zeros are needed in closed form but this is achieved in rare situations. That is why he has presented a plethora of alternative iterate methods generating a sequence approximating a zero under certain initial conditions about a zero (local convergence) or about in an initial point (semilocal convergence). These methods converge with linear, quadratic or higher order of convergence and under weak conditions. Researchers and practitioners will find this book very useful as a source book, utilize its methods and also use it as a classroom text for a senior undergraduate or graduate course. It is certainly an excellent must read book.” – Ioannis K. Argyros, Cameron University, Department of Mathematics, Lawton, Oklahoma, USA

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New Trends in Fractional Programming

“The author in his six chapters of this book presents a very well thought of study of, in particular smooth and unified generalized programming problems. See for example Problem (P). Numerous study cases are presented involving convexity and non-convexity, specializations of which reduce to earlier results by the author or others. The material is very elegantly presented. It is highly recommended to researchers and practitioners who will find it very readable and useful for their research. Parts of this book can also be used in seminars for graduate students as well as senior undergraduate students with interests in this area of research. The bibliography is very informed and updated which makes the book also a great reference source.” – Professor Dr. Ioannis K. Argyros, Cameron University, Department of, Mathematical Sciences, Lawton, OK, USA

For more information about this book, please click here.