Symmetry in Electromagnetism
Electromagnetism plays a crucial role in basic and applied physics research. The discovery of electromagnetism as the unifying theory for electricity and magnetism represents a cornerstone in modern physics. Symmetry was crucial to the concept of unification: electromagnetism was soon formulated as a gauge theory in which local phase symmetry explained its mathematical formulation. This early connection between symmetry and electromagnetism shows that a symmetry-based approach to many electromagnetic phenomena is recurrent, even today. Moreover, many recent technological advances are based on the control of electromagnetic radiation in nearly all its spectra and scales, the manipulation of matter-radiation interactions with unprecedented levels of sophistication, or new generations of electromagnetic materials. This is a fertile field for applications and for basic understanding in which symmetry, as in the past, bridges apparently unrelated phenomena―from condensed matter to high-energy physics. In this book, we present modern contributions in which symmetry proves its value as a key tool. From dual-symmetry electrodynamics to applications to sustainable smart buildings, or magnetocardiography, we can find a plentiful crop, full of exciting examples of modern approaches to electromagnetism. In all cases, symmetry sheds light on the theoretical and applied works presented in this book.
International Comparative Studies in Mathematics
This open access book examines the cultural and educational factors that influence how successfully students learn mathematics; focuses on international comparative studies as a means of generating theories and improving students' learning; and discusses four valuable lessons that can be learned from international comparative studies with regard to improving students' learning. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Teaching and Learning Mathematical Modelling
This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term "mathematical model" as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Polynomials
Polynomial and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on polynomial and its applications has been done in mathematics, applied mathematics, and sciences. This book is based on recent results in all areas related to polynomial and its applications. This book provides an overview of the current research in the field of polynomials and its applications. The following papers have been published in this volume: 'A Parametric Kind of the Degenerate Fubini Numbers and Polynomials'; 'On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals'; 'Fractional Supersymmetric Hermite Polynomials'; 'Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation'; 'Iterating the Sum of M繹bius Divisor Function and Euler Totient Function'; 'Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations'; 'Truncated Fubini Polynomials'; 'On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights'; 'Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity'; 'Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials'; 'Some Identities Involving Hermite Kamp矇 de F矇riet Polynomials Arising from Differential Equations and Location of Their Zeros.'
Advances and Novel Approaches in Discrete Optimization
Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled 'Advances and Novel Approaches in Discrete Optimization'. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms.
History of the Theory of Numbers (Volume III) Quadratic and Higher Forms With A Chapter on the Class Number
Unlock the intricate world of number theory as Leonard Eugene Dickson leads you through the labyrinth of quadratic and higher forms. This is mathematics history at its most profound: a sweeping analysis of class number, quadratic forms, and the evolution of advanced mathematical concepts that shaped the early 20th century. Every page pulses with the intellectual energy of a field in transformation. For those captivated by number theory analysis or the scholarly pursuit of historical mathematical theories, this volume is indispensable. History Of The Theory Of Numbers (Volume III) stands as a testament to Dickson's meticulous scholarship and enduring influence. Drawing from the fertile period of mathematical research in the 1920s, Dickson crafts a comprehensive number theory collection that bridges foundational discoveries with the academic rigour that modern mathematicians demand. The chapter on the class number in mathematics illuminates a pivotal theme, making this not only an academic reference for mathematicians but also an essential scholarly mathematics resource for anyone fascinated by the evolution of mathematical thought. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. Works by Leonard Eugene Dickson have long been sought by classic literature collectors and students of mathematical history. Now restored for a new era, this book invites both the curious reader and the seasoned scholar to explore a cultural treasure.
Sobre ?lgebras com Identidades Polinomiais
Neste trabalho apresentamos defini癟繭es e resultados preliminares sobre a teoria das 獺lgebras com identidades polinomiais, que teve in穩cio na d矇cada de 30 do s矇culo XX. Al矇m disso, enunciamos e demonstramos o Teorema de Amitsur-Levitzki em caracter穩stica zero, que afirma que o polin繫mio standard de grau 2n 矇 uma identidade polinomial para ?s 獺lgebras matriciais quadradas de ordem n. Por fim, apresentamos uma condi癟瓊o para que o polin繫mio Pn(x) seja uma identidade polinomial para a 獺lgebra Ma, b(E).
F繹rderung Von Diagnostischen Kompetenzen
In der vorliegenden Studie wurde empirisch nachgewiesen, dass eine gezielte Intervention dazu beitragen kann, die Fehler-Ursachen-Diagnosekompetenz von Mathematik-Lehramtsstudierenden zu f繹rdern. Diese spezifische Diagnosekompetenz ist notwendig, um Sch羹lerfehler und deren Ursachen zu diagnostizieren, denn die abschlie?ende Diagnose bildet die Grundlage f羹r eine Differenzierung im Unterricht sowie diverse F繹rderangebote. Auch in der aktuellen Bildungspolitik erhalten diese Aspekte eine immer st瓣rkere Beachtung aufgrund der zunehmenden Heterogenit瓣t der Sch羹lerschaft.
Probleml繹sen Mit Strategieschl羹sseln
Lernhilfen in Form von Hilfe- oder auch Tippkarten werden als Material zur Differenzierung im Unterricht eingesetzt. Ob diese Lernenden tats瓣chlich helfen, ist bisher unzureichend gekl瓣rt. F羹r die vorliegende Untersuchung dienen sog. Strategieschl羹ssel als Interventionsinstrument. Theoretisch ist zu vermuten, dass die Schl羹ssel den Einsatz von Strategien triggern und die Selbstregulation im Bearbeitungsprozess anregen. Im Kontext des mathematischen Probleml繹sens wird untersucht, auf welche Art und Weise die Strategieschl羹ssel den Problembearbeitungsprozess von Dritt- bis Viertkl瓣sslern beeinflussen. Die quantitativen Analysen ergeben einen statistisch hoch signifikanten Zusammenhang zwischen der Interaktion mit den Strategieschl羹sseln, dem Heurismeneinsatz und dem Wechsel zwischen Episoden im Problembearbeitungsprozess. Die qualitativen Analysen zeigen, dass die Strategieschl羹ssel auf neun verschiedene Weisen genutzt werden, der Einsatz von Heurismen durch sie getriggert wird und dassselbstregulatorische T瓣tigkeiten angeregt werden. Bei der Verwendung der Strategieschl羹ssel werden neun Muster identifiziert.
Semi-Classical Analysis for Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition)
The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schr繹dinger equations in negative order Sobolev spaces.The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.
Computational Intelligence and Optimization Methods for Control Engineering
This volume presents some recent and principal developments related to computational intelligence and optimization methods in control. Theoretical aspects and practical applications of control engineering are covered by 14 self-contained contributions. Additional gems include the discussion of future directions and research perspectives designed to add to the reader's understanding of both the challenges faced in control engineering and the insights into the developing of new techniques. With the knowledge obtained, readers are encouraged to determine the appropriate control method for specific applications.
Hyperbolicity in Delay Equations
This book provides a comprehensive introduction to the study of hyperbolicity in both linear and nonlinear delay equations. This includes a self-contained discussion of the foundations, main results and essential techniques, with emphasis on important parts of the theory that apply to a large class of delay equations. The central theme is always hyperbolicity and only topics that are directly related to it are included. Among these are robustness, admissibility, invariant manifolds, and spectra, which play important roles in life sciences, engineering and control theory, especially in delayed feedback mechanisms.The book is dedicated to researchers as well as graduate students specializing in differential equations and dynamical systems who wish to have an extensive and in-depth view of the hyperbolicity theory of delay equations. It can also be used as a basis for graduate courses on the stability and hyperbolicity of delay equations.
Many Body Quantum Chaos
The field of chaos in many-body quantum systems has a long history, going back to Wigner's simple models for heavy nuclei. Quantum chaos is being investigated in a broad variety of experimental platforms such as heavy nuclei, driven (few-electron) atoms, ultracold quantum gases, and photonic or microwave realizations. Quantum chaos plays a new and important role in many branches of physics, from condensed matter problems of many-body localization, including thermalization studies in closed and open quantum systems, and the question of dynamical stability relevant for quantum information and quantum simulation. This Special Issue and its related book address theories and experiments, methods from classical chaos, semiclassics, and random matrix theory, as well as many-body condensed matter physics. It is dedicated to Prof. Shmuel Fishman, who was one of the major representatives of the field over almost four decades, who passed away in 2019.
Quantum Communication-Celebrating the Silver Jubilee of Teleportation
To celebrate the 25th anniversary of the seminal 1993 quantum teleportation paper, we are pleased to present research works, reviews, and stories about quantum communication, quantum entanglement, and quantum teleportation: * How was quantum teleportation invented? * Which teleportation experiments were performed at the Sapienza University in Rome? * Can we use joint measurements to generate nonclassical correlations? * How is classical sampling related to quantum entanglement? * How is classical communication related to a special quantum ensemble? * How can simplifying a quantum key distribution protocol make it insecure? * Can we teleport a two-qubit quantum state using a nonsymmetric channel? This book includes submissions by some of the most prominent quantum teleportation contributors, including Gilles Brassard, Francesco De Martini, Nicolas Gisin, and William K. Wootters, as well as additional researchers, all presenting their up-to-date insights regarding quantum communication.
Mathematical and Numerical Analysis of Nonlinear Evolution Equations
The topic of this book is the mathematical and numerical analysis of some recent frameworks based on differential equations and their application in the mathematical modeling of complex systems, especially of living matter. First, the recent new mathematical frameworks based on generalized kinetic theory, fractional calculus, inverse theory, Schr繹dinger equation, and Cahn-Hilliard systems are presented and mathematically analyzed. Specifically, the well-posedness of the related Cauchy problems is investigated, stability analysis is also performed (including the possibility to have Hopf bifurcations), and some optimal control problems are presented. Second, this book is concerned with the derivation of specific models within the previous mentioned frameworks and for complex systems in biology, epidemics, and engineering. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of complex systems.
An Introduction to Linear and Nonlinear Scattering Theory
This monograph has two main purposes, first to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable, self-contained introduction to linear and nonlinear scattering theory for those who might wish to begin working in the area. Secondly, to indicate how these various aspects might be applied to problems in mathematical physics and the applied sciences. Of particular interest will be the influence of boundary conditions.
Quantitative Aptitude
For each topic in the book, initially a brief concept has been presented, followed by the solved examples of various types including shortcuts in most of the cases. At the end of each topic, an assessment test has been provided for students in order to assess the knowledge. This content is mainly useful for the students who are preparing for various competitive examinations, campus recruitment training (CRT), MBA entrance tests like GMAT, MAT, CMAT, XAT, etc., along with the M. Tech. entrance examination (GATE). For more details, please visit https: //centralwestpublishing.com
Quantitative Aptitude
For each topic in the book, initially a brief concept has been presented, followed by the solved examples of various types including shortcuts in most of the cases. At the end of each topic, an assessment test has been provided for students in order to assess the knowledge. This content is mainly useful for the students who are preparing for various competitive examinations, campus recruitment training (CRT), MBA entrance tests like GMAT, MAT, CMAT, XAT, etc., along with the M. Tech. entrance examination (GATE). For more details, please visit https: //centralwestpublishing.com
13th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas
In June 2019, the International Symposium on Atomic Structure and Oscillator Strengths for Fusion and Astrophysical Plasma Research (ASOS) held the 13th edition of this series. ASOS originated at the University of Lund, Sweden in 1983, and this was the first time that it was held outside of Europe and the Americas. The meeting participants were a mixed international group from Europe, the Americas and Asia. This book represents a flavor of presentations made by internationally renowned experts, in a variety of fields relevant to the ASOS community. The book contains a special contribution entitled "Charlotte Froese Fischer-Her Work and Her Impact", written and presented by Professor Alan Hibbert of The Queen's University Belfast. The ASOS timing was chosen to overlap with Charlotte's 90th birthday and a significant part of the meeting was a tribute to her work. The meeting ended with a hope to meet all the participants again in Paris in 2022.
Paths
This open access book explores the amazing similarity between paths taken by people and many other things in life, and its impact on the way we live, teach and learn.Offering insights into the new scientific field of paths as part of the science of networks, it entertainingly describes the universal nature of paths in large networked structures. It also shows the amazing similarity in the ways humans and other - even nonliving - things navigate in a complex environment, to allow readers to easily grasp how paths emerge in many walks of life, and how they are navigated.Paths is based on the authors recent research in the area of paths on networks, which points to the possible birth of the new science of "paths" as a natural consequence 'and extension) of the science of "networks."The approach is essentially story-based, supported by scientific findings, interdisciplinary approaches, and at times, even philosophical points of view. It alsoincludes short illustrative anecdotes showing the amazing similarities between real-world paths and discusses their applications in science and everyday life.Paths will appeal to network scientists and to anyone interested in popular science. By helping readers to step away from the "networked" view of many recent popular scientific books and start to think of longer paths instead of individual links, it sheds light on these problems from a genuinely new perspective.--------------------------------------------------------------------------------- The path is the goal. The essence behind this short sentence is known to many people around the world, expressed through the interpretations of some of the greatest thinkers like Lao-Tze and Gandhi. It means that it is the journey that counts, not the destination. When speaking about such subjective and intangible things, philosophy and religion are some of the only approaches that are addressed. In this book, the authors address this conventional wisdom from the perspective of natural science. They explore a sequence of steps that leads the reader closer to the nature of paths and accompany him on the search for "the path to paths".
Beweisen Lernen Schritt F羹r Schritt
Dieses Lehrbuch f羹hrt Studienanf瓣nger und -anf瓣ngerinnen Schritt f羹r Schritt in die Spielregeln des mathematischen Argumentierens und Beweisens ein. Anhand einfacher Beispiele werden zielf羹hrende Gedanken sichtbar gemacht, die zum Verstehen und Verfassen von Beweisen unverzichtbar sind. Logische Regeln und Zwischenschritte werden systematisch erkl瓣rt. Der ?berblick wird erleichtert durch eine Randspalte, die zentrale Hinweise und Zusammenfassungen enth瓣lt. Ein gro?es Spektrum an Aufgaben l瓣dt zum direkten Nachvollziehen und Ausprobieren ein, Hilfestellungen und vollst瓣ndige L繹sungen erleichtern dabei das Selbststudium. Der Umgang mit abstrakten Sachverhalten wird durch Bez羹ge zu Alltagserfahrungen vereinfacht. Das Buch bildet somit eine ideale Grundlage f羹r ein erfolgreiches Studium der Mathematik oder mathematiknaher F瓣cher. Da nur vergleichsweise wenig mathematisches Vorwissen vorausgesetzt wird, ist das Buch auch f羹r interessierte Sch羹lerinnen und Sch羹ler ab der fortgeschrittenen Mittelstufe geeignet.
Selbststudium Im Digitalen Wandel
Selbststudium ist ein wichtiges Element im Zuge der Digitalisierungsbestrebungen an Hochschulen. Das Projekt optes widmet sich dem digitalen, begleiteten Selbststudium im Fach Mathematik. Es bietet mit seinen webbasierten Angeboten die M繹glichkeit, das Selbstlernen in der Studienvorbereitung zu unterst羹tzen, um so die Abbruchquoten in MINT-F瓣chern zu reduzieren. Neben dem Studienvorbereitungsprogramm und Assessment-Tools in der Mathematik im Lernmanagementsystem ILIAS wurden in optes diverse Materialien zur Lernprozessbegleitung entwickelt, inklusive adaptiver Lernempfehlungen, diagnostischer Testverfahren zur Pr羹fung des Wissensstandes (vor und w瓣hrend des Studiums), Selbstreflexionstools und 羹berfachlicher Lernmodule sowie pers繹nliche E-Mentoring- und E-Tutoring-Programme. Der vorliegende Open-Access-Sammelband stellt die wissenschaftlichen Erkenntnisse und praktischen Umsetzungen aus dem Projektkontext von optes dar.
Poems That Solve Puzzles
Algorithms are the hidden methods that computers apply to process information and make decisions. Nowadays, our lives are run by algorithms. They determine what news we see. They influence which products we buy. They suggest our dating partners. They may even be determining the outcome of national elections. They are creating, and destroying, entire industries. Despite mounting concerns, few know what algorithms are, how they work, or who created them. Poems that Solve Puzzles tells the story of algorithms from their ancient origins to the present day and beyond. The book introduces readers to the inventors and inspirational events behind the genesis of the world's most important algorithms. Professor Chris Bleakley recounts tales of ancient lost inscriptions, Victorian steam-driven contraptions, top secret military projects, penniless academics, hippy dreamers, tech billionaires, superhuman artificial intelligences, cryptocurrencies, and quantum computing. Along the way, the book explains, with the aid of clear examples and illustrations, how the most influential algorithms work. Compelling and impactful, Poems that Solve Puzzles tells the story of how algorithms came to revolutionise our world.
Facetten Der Mathematikdidaktik
Die Idee der beiden Gr羹ndungsv瓣ter der Mathematischen Semesterberichte, Heinrich Behnke und Otto Toeplitz, war es, den Zusammenhalt von Universit瓣t und Schule zu st瓣rken. Deshalb informierte die von ihnen gegr羹ndete Zeitschrift die Leserinnen und Leser nicht nur 羹ber neue Entwicklungen in der Mathematik, sondern ber羹cksichtigte auch angrenzende Gebiete wie die Mathematikdidaktik, insbesondere die Stoffdidaktik, und Fragen des Mathematikunterrichts. Einen breiten Raum nahmen zudem Beitr瓣ge zur Lehrerbildung und zum Verh瓣ltnis von Universit瓣t und Schule ein. Die Auswahl von Beitr瓣gen im vorliegenden Band deckt mit mehr als acht Jahrzehnten die gesamte Historie der Semesterberichte ab. Inhaltlich spannt sich der Bogen des vorliegenden Bandes von verschiedenen Standortbestimmungen der Mathematikdidaktik 羹ber Beitr瓣ge aus den Anf瓣ngen der Zeitschrift in den 1930er-Jahren bis etwa 1960 羹ber die sogenannte neue Mathematik der 1960er- und 1970er-Jahre zu den nachfolgenden Versuchen, dem Mathematikunterricht weitere inhaltliche Perspektiven jenseits der neuen Mathematik und angesichts moderner Medien zu er繹ffnen. Den Abschluss bilden mehrere Artikel zu Fragen der Lehrerbildung.
Linear and Quasilinear Complex Equations of Hyperbolic and Mixed Types
This volume deals with first- and second-order complex equations of hyperbolic and mixed types. The authors investigate in detail general boundary value problems for linear and quasilinear complex equations and present some discontinuous boundary value problems for elliptic complex equations. Mixed complex equations are included in the quasilinear case, and the text considers both boundary value conditions in the general oblique derivative case and multiply-connected domains. The authors also use complex analytical methods to investigate various problems. In particular, they introduce hyperbolic numbers and hyperbolic complex functions to handle hyperbolic complex equations.
Introduction to Holomorphic Functions of Several Variables, Volume II
This book introduces the reader to a wide range of topics in the theory of holomorphic functions of several variables, with fairly complete proofs. It reviews the relevant properties of subharmonic functions and discusses the basic properties of plurisubharmonic functions.
The Legacy of Kurt Sch羹tte
This book on proof theory centers around the legacy of Kurt Sch羹tte and its current impact on the subject. Sch羹tte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Sch羹tte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Sch羹tte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts closeto his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Sch羹tte himself that have never been published before.
Basic Insights in Vector Calculus: With a Supplement on Mathematical Understanding
Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.
An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases
This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book's main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, includingboth scalar PDEs and systems of equations.
Wittgenstein's Annotations to Hardy's Course of Pure Mathematics
Examines the annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy's classic textbook, A Course of Pure Mathematics Features images of the annotations Explores Wittgenstein's later philosophy of mathematics as applied to the real numbers
Miscellaneous problems in mathematics
A man can ride a boat in calm water with u ms-1 continuous velocity. A dog can swim in calm water v ms-1 continuous velocity. The man and dog both stay on the same bank of a straight river on points A, B respectively which is flowing with V ms-1 continuous velocity of width a meters. The length of AB is d meters. AB is in the direction of V(Vuv).The man ride the boat across the river such that he can reach the point C which is situated directly opposite to the point A. Show that, the time taken by him to move from A to C is given by a√u2-V2 seconds.
Design of Passive Filters
Passive filters are very much helpful for mitigation of harmonic component and used traditionally. Passive filter are used for the mitigation of harmonic in the electrical society for last 3 decades and a continuous development has been reported in this technique for the better use of filter and convert the filter more useful to achieve the optimum approach to utilization with reduced rating and cost. Passive filters are widely used in industries. However, very perfect and accurate design methods has not been well established for the filter. This seminar report presents a simple design method along with formulas. Here we are going to analyze all the possible configuration of passive filters one by one.
Ancient Measurement
The Sumerians were not the only ones to create remarkably accurate standards of measurement in the Ancient world. Some would travel to the ends of the Earth, some would be with us still today. Roland A. Boucher, a licensed professional engineer, examines incredible achievements of the past in this book that highlights standards of measure from the ancient Sumerians, Egyptians, Minoans, and others. The Sumerians left two wonderful monuments which demonstrate their system of measurement. The Great Pyramid at Giza, which was built to Sumerian standards with an error of only 185 parts per million; and The Parthenon, in Athens, built 2000 years later to the same Sumerian standard. Filled with tables, formulas, and images to promote the understanding of the mathematical concepts involved, this book celebrates the achievements of the Sumerians and other ancient civilizations. Embark on a journey of discovery as the author recreates eight additional standards from the distant past.
Ancient Measurement
The Sumerians were not the only ones to create remarkably accurate standards of measurement in the Ancient world. Some would travel to the ends of the Earth, some would be with us still today. Roland A. Boucher, a licensed professional engineer, examines incredible achievements of the past in this book that highlights standards of measure from the ancient Sumerians, Egyptians, Minoans, and others. The Sumerians left two wonderful monuments which demonstrate their system of measurement. The Great Pyramid at Giza, which was built to Sumerian standards with an error of only 185 parts per million; and The Parthenon, in Athens, built 2000 years later to the same Sumerian standard. Filled with tables, formulas, and images to promote the understanding of the mathematical concepts involved, this book celebrates the achievements of the Sumerians and other ancient civilizations. Embark on a journey of discovery as the author recreates eight additional standards from the distant past.
Gamification and Advanced Technology to Enhance Motivation in Education
This book, entitled "Gamification and Advanced Technology to Enhance Motivation in Education", contains an editorial and a collection of ten research articles that highlight the use of gamification and other advanced technologies as powerful tools for motivation during learning. Motivation is the driving force behind many human activities, especially learning. Motivated students are ready to make a significant mental effort and use deeper and more effective learning strategies. Numerous studies indicate that playing promotes learning, since when fun pervades the learning process, motivation increases and tension is reduced. Therefore, games can be very powerful tools in the improvement of learning processes from three different and complementary perspectives: as tools for teaching content or skills, as an object of the learning project itself and as a philosophy to be taken into account when designing the training process. Each contributions presented in this book falls into one of these categories; that is to say, they all deal with the use of games or related technologies, and they all study how playing enhances motivation in education.
George Spencer Brown’s ”design with the Nor”
George Spencer Brown, a polymath and author of Laws of Form, brought together mathematics, electronics, engineering and philosophy to form an unlikely bond. This book investigates Design with NOR, the title of the yet unpublished 1961 typescript by Spencer Brown. The typescript formed through the author's experiences as technical engineer and developer of a new form of switching algebra for Mullard Equipment Ltd., a British manufacturer of electronic components, and is published here for the first time. Related essays contextualise the typescript drawing on a variety backgrounds from mathematics and engineering to philosophy and sociology, and thus invite readers to a reverse-engineering of both the form and its laws.
Mathematical exercises for home work Second Series
Step into the world of early 20th century mathematics, where rigour meets curiosity and every exercise sharpens the mind. Mathematical Exercises For Home Work Second Series by A.T. Richardson stands as a testament to timeless educational craftsmanship. Designed as a supplementary learning material, this classic math textbook offers a rich collection of mathematical problems-each carefully chosen to foster math skills development and encourage independent problem-solving techniques. Blending arithmetic and algebra practice with the methodical clarity that defines Richardson's work, this educational workbook series is ideal for students seeking to master foundational concepts or for anyone with a passion for vintage educational resources. Whether used as a home study math guide or as an engaging challenge for the classroom, the problems within reflect a thoughtful approach to building confidence and competence in mathematics. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. A.T. Richardson books are prized by those who appreciate the enduring value of classic instruction, and this volume remains a cultural treasure for both casual learners and collectors of historic mathematical problem collections.
Mathematical Logic And Combinatorics
The Present Book ' Mathematical Logic and Combinatorics' teaches students the mathematical foundations of computer science, including logic, Boolean algebra, basic graph theory, coding and helps them understand mathematical reasoning for reading, comprehension and construction of mathematical arguments. The aim of this book is to provide a concise introduction to some significant topics covered in the subject discrete mathematics. This book will also serve as a handbook for the teachers in class room teaching as it contains many solved examples.
Recurrent Sequences
This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics.For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.
Modelling Puzzles in First Order Logic
Keeping students involved and actively learning is challenging. Instructors in computer science are aware of the cognitive value of modelling puzzles and often use logical puzzles as an efficient pedagogical instrument to engage students and develop problem-solving skills. This unique book is a comprehensive resource that offers teachers and students fun activities to teach and learn logic. It provides new, complete, and running formalisation in Propositional and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference puzzles. Solving puzzles with theorem provers can be an effective cognitive incentive to motivate students to learn logic. They will find a ready-to-use format which illustrates how to model each puzzle, provides running implementations, and explains each solution. This concise and easy-to-follow textbook is a much-needed support tool for students willing to explore beyond the introductory level of learning logic and lecturers looking for examples to heighten student engagement in their computer science courses.
The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages, ' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity, ' discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel.Examining the nineteenth and earlytwentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincar矇, Brouwer, and Weyl.Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry.No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Exact Traveling Wave Solutions Of Some Nonlinear Models
Nonlinear waves and its comprehensible formation have been described in modern theories through the variety of field dispersion, dissipation, diffusion, reaction and convection in many non-linear wave fields such as mathematics, physics, biology, chemistry, mechanics, meteorology, engineering, optical fibers, fluid mechanics, gas dynamics, elasticity, relativity, chemical reactions, ecology, optical fiber, solid state physics, bio-mechanics, plasma physics, solid-state physics, optical fibers, biophysics and so on. These are forceful prevalence of NLEEs. To visualize the nonlinear dynamics, research on the solitary wave solutions of NLEEs is very popular. So, we consider the complex Generalized Schrodinger-Boussinesq (CGSB) equations, (3+1) Dimensional KP equation, Burger Huxley Equation, Modified BBM and FitzHugh-Nagumo equation with the help of MSE and EMSE methods. We obtain some traveling wave solution in terms of exponential, hyperbolic function solutions and trigonometric function solutions etc. The nature of the obtained traveling wave solution of the models are plotted. Finally, we give some concluding remarks at the end of our work.
Dynamic Analysis of An Elastic Beam
In this research work, the dynamic analysis of an elastic beam subjected to distributed moving loads is investigated. The finite Fourier sine transform method of analytical approximation solution is used, varying magnitude distributed moving load is been considered.From the analysis it is observed that, as the axial force (N) increase, the deflection of elastic thin beam under the action of distributed moving load decreases.
B-Spline Finite Element Method
Computational Simulation of Physical Problem is one of the encouraging field now a days. Keeping in view this in mind the present work is focus on numerical solution of some physical problems. The B-Spline Finite Element Method is adopted for the solution for the physical problem. The aim of the book to introduce the advance level method in simplest way. The numerical simulation is also presented in each chapter along with exact solution of the problems.
Equations of multi-Rees algebras
Describing defining equations of Rees algebra is a central problem in commutative algebra. More generally, given a family of ideals, one would like to describe the equations of the multi-Rees algebra of these ideals. Indeed, the multi-Rees algebra in question is simply the Rees algebra of the module. There is little work on the defining equations of the multi-Rees algebra compared to the ordinary Rees algebra. Another motivation for investigating the multi-Rees algebra is an illustration of the theory of Rees algebra of modules. In this work first, we describe defining equations of multi-Rees algebras of powers of an ideal of linear type. In the second part we describe defining equations of multi-Rees algebras of a family of ideals, where these ideals are generated by subsets of a regular sequence.
One to Ten Look Again
One to Ten Look Again is a short book for children to explore counting and reading. It's never too early to begin showing our children images and words to get them started on their path to learning. This is a book that can be looked at and read over and over again. Each time your child might find something new to count that they didn't see before, or they may make a new connection with numbers and words that makes better sense to them. Children will learn how to count from 1 to 10. They will learn how to recognize numerals and how they are related to their sets. The number is spelled out for the child to begin making connections between the written numbers name and the numeral. Patterns show how arranged items can be recognized as sets that the number represents. Toddlers, preschool, home-school and young learners can start their counting journey with this illustrated counting book from One to Ten.In addition to counting, children will also see many connections to numbers that are part of life. Patterns are used to help with number count recognition. Numerals and the spelled word for the number helps establish cognitive connections between numbers and letters. Other shapes and patterns help to nurture a base for remembering. The imagery is designed to inspire creativity and to make learning fun. For those who want to help their children begin counting, this is an easy starter book.Keep counting and don't forget to count along. Every child needs positive reinforcement to establish these early learning skills. These are experiences that will be with you and your child for a lifetime.
Vector Measures, Integration and Integral Representation Theory
The aim of this work is intended to present a unified, mostly self-contained, survey of the theory of integral representation of bounded operators in topological spaces. It is written for the graduate students who are familiar with abstract measure and integration, and also with the main topics of Banach spaces and topological vector spaces. A lot of work has been done on various extensions of this theorem and it is still the object of many investigations. The objective of this work is a presentation of some prominent generalizations of Riesz Theorem, frequently used in the literature. Each representation theorem considered here has its own integration process which goes through duality of function spaces. We will essentially be concerned by the following settings: In the first part, we consider Banach spaces X, Y, and form the Banach space C(S, X) of all continuous functions from the compact space S into X, equipped with the uniform norm. In the second part, the objective is to go beyond the Banach space setting, to X a topological vector space context
