The Art of Finding Hidden Risks
This text gives a comprehensive, largely self-contained treatment of multivariate heavy tail analysis. Emphasizing regular variation of measures means theory can be presented systematically and without regard to dimension. Tools are developed that allow a flexible definition of "extreme" in higher dimensions and permit different heavy tails to coexist on the same state space leading to "hidden regular variation" and "steroidal regular variation". This emphasizes when estimating risks, it is important to choose the appropriate heavy tail. Theoretical foundations lead naturally to statistical techniques; examples are drawn from risk estimation, finance, climatology and network analysis. Treatments target a broad audience in insurance, finance, data analysis, network science and probability modeling. The prerequisites are modest knowledge of analysis and familiarity with the definition of a measure; regular variation of functions is reviewed but is not a focal point.
Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953). It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition.The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks. The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory).
Harmonic Numbers and Open problems in Series
Problems involving harmonic numbers are so strange in solution way and those approaches or results are attracting the attention of students interested in mathematics as well as mathematicians and engineers, as there are many areas of application. In scientific and technological calculations that occur in various fields of mathematics and engineering, computational problems associated with various mathematical constants are often encountered, some of which are important tools for solving scientific and technological problems. There have been many open problems that have not been addressed before, due to the high level of scientific theory and the high performance of computer-based computing tools. Nevertheless, the world of mathematics still has a lot of problems to be discovered, so new and diverse methods are needed to solve these problems. This book contains open problems and challenging problems presented in several mathematical reference books and add their new generalizations written by us.
The Daring Invention of Logarithm Tables
In the early 17th century, both Jost B羹rgi and John Napier dared to invent a logarithm table whose construction required tens of thousands of computing steps. These tables reduced computing effort for multiplication and division by an order of magnitude. Indeed, their invention launched a computing revolution that continues to this day. The book, which is the color edition of the original black and white edition published in 2020, tells the story of B羹rgi's and Napier's work, and how Henry Briggs built on Napier's idea, creating a table of logarithms that was easier to use. John Napier and Henry Briggs described their methods in detail; distribution of their results was widespread. In contrast, Jost B羹rgi did not leave detailed records of his work. Just a few copies of his table and terse handwritten instructions for its use have survived. To fill this gap, the book reconstructs B羹rgi's thinking leading up to his table. The reader looks over his shoulder, so to speak, and learns how B羹rgi came upon the idea, how he decided on the specific format of the table, and how his instructions should be interpreted. And so the reader experiences the magic of the invention of logarithms. The final chapters examine the question "Who invented logarithms?". For centuries, few people were aware of B羹rgi's work; John Napier was considered to be the sole inventor. This changed at the middle of the 19th century when Jost B羹rgi's work became more widely known. Since then there has been extensive debate whether B羹rgi should be considered an independent co-inventor. Careful parsing of the history of logarithm going back to Archimedes of antiquity then reveals that, without doubt, John Napier and Jost B羹rgi are independent co-inventors of logarithms.
Elements of Stochastic Modelling (Third Edition)
This is a thoroughly revised and expanded third edition of a successful university textbook that provides a broad introduction to key areas of stochastic modelling. The previous edition was developed from lecture notes for two one-semester courses for third-year science and actuarial students at the University of Melbourne.This book reviews the basics of probability theory and presents topics on Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. It also features elements of stochastic calculus and introductory mathematical finance. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling.To make the text covering a lot of material more appealing and accessible to the reader, instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. It is in this aspect that the present, third edition differs from the second one: the included background material and argument sketches have been extended, made more graphical and informative. The whole text was reviewed and streamlined wherever possible to make the book more attractive and useful for readers. Where appropriate, the book includes references to more specialised texts on respective topics that contain both complete proofs and more advanced material.
Elements of Stochastic Modelling
This is a thoroughly revised and expanded third edition of a successful university textbook that provides a broad introduction to key areas of stochastic modelling. The previous edition was developed from lecture notes for two one-semester courses for third-year science and actuarial students at the University of Melbourne.This book reviews the basics of probability theory and presents topics on Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. It also features elements of stochastic calculus and introductory mathematical finance. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling.To make the text covering a lot of material more appealing and accessible to the reader, instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. It is in this aspect that the present, third edition differs from the second one: the included background material and argument sketches have been extended, made more graphical and informative. The whole text was reviewed and streamlined wherever possible to make the book more attractive and useful for readers. Where appropriate, the book includes references to more specialised texts on respective topics that contain both complete proofs and more advanced material.
Krasner Hyperring Theory
The theory of algebraic hyperstructures, in particular the theory of Krasner hyperrings, has seen a spectacular development in the last 20 years, which is why a book dedicated to the study of these is so vital. Krasner hyperrings are a generalization of hyperfields, introduced by Krasner in order to study complete valued fields. A Krasner hyperring (R, +, .) is an algebraic structure, where (R, +) is a canonical hypergroup, (R, .) is a semigroup having zero as a bilaterally absorbing element and the multiplication is distributive with respect to the hyperoperation +.Krasner Hyperring Theory presents an elaborate study on hyperstructures, particularly Krasner hyperrings, across 10 chapters with extensive examples. It contains the results of the authors, but also of other researchers in the field, focusing especially on recent research. This book is especially addressed to doctoral students or researchers in the field, as well as to all those interested in this interesting part of algebra, with applications in other fields.
Primes and Particles
Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature.
Notes on Tug-Of-War Games and the P-Laplace Equation
This book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems. Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful.
Supportive Foundation for High School Mathematics
This book is written to help students acquire a solid foundation in high school mathematics and enable them to develop problem-solving skills. Considerable effort has been devoted to ensure that the text is understandable and covers areas where learners have common difficulty. Numerous carefully selected examples are provided with detailed solutions to illustrate the mathematical concepts and enhance students understanding of the subject matter. The book has five chapters: (1) Relations and graphs of equations; (2) Functions with emphasis on linear, quadratic, and polynomial functions; (3) Exponential and logarithmic functions; (4) Topics of geometry that are basic to high school; (5) Trigonometric functions, trigonometric equations, and applications involving triangles.Undoubtedly, students who work through this manuscript will find that the book presents a comprehensive foundation to successfully understand high school mathematics. The other book of the author, namely, "Supportive Foundation for Basic Algebra" provides a comprehensive approach to the fundamental concepts and techniques of algebra and offers a useful supplementary background for enhanced mathematical competence.
Diophantine M-Tuples and Elliptic Curves
This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators. The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting Mordell-Weil groups, including curves of record rank with agiven torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems. This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.
Lagrangian Floer Theory and Its Deformations
A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces. At the beginning of the 1990s, a similar structure was introduced by Fukaya in his categorification of Floer homology in symplectic topology. This structure plays a fundamental role in the celebrated homological mirror symmetry proposal by Kontsevich and in more recent developments of symplectic topology.A detailed construction of A-infinity algebra structure attached to a closed Lagrangian submanifold is given in Fukaya, Oh, Ohta, and Ono's two-volume monograph Lagrangian Intersection Floer Theory (AMS-IP series 46 I & II), using the theory of Kuranishi structures-a theory that has been regarded as being not easily accessible to researchers in general. The present lecture note is provided by one of the main contributors to the Lagrangian Floer theory and is intended to provide a quick, reader-friendly explanation of the geometric part of the construction. Discussion of the Kuranishi structures is minimized, with more focus on the calculations and applications emphasizing the relevant homological algebra in the filtered context.The book starts with a quick explanation of Stasheff polytopes and their two realizations-one by the rooted metric ribbon trees and the other by the genus-zero moduli space of open Riemann surfaces-and an explanation of the A-infinity structure on the motivating example of the based loop space. It then provides a description of the moduli space of genus-zero bordered stable maps and continues with the construction of the (curved) A-infinity structure and its canonical models. Included in the explanation are the (Landau-Ginzburg) potential functions associated with compact Lagrangian submanifolds constructed by Fukaya, Oh, Ohta, and Ono. The book explains calculations of potential functions for toric fibers in detail and reviews several explicit calculations in the literature of potential functions with bulk as well as their applications to problems in symplectic topology via the critical point theory thereof. In the Appendix, the book also provides rapid summaries of various background materials such as the stable map topology, Kuranishi structures, and orbifold Lagrangian Floer theory.
Data and Process Visualisation for Graphic Communication
This book guides the reader through the process of graphic communication with a particular focus on representing data and processes. It considers a variety of common graphic communication scenarios among those that arise most frequently in practical applications. The book is organized in two parts: representing data (Part I) and representing processes (Part II). The first part deals with the graphical representation of data. It starts with an introductory chapter on the types of variables, then guides the reader through the most common data visualization scenarios - i.e.: representing magnitudes, proportions, one variable as a function of the other, groups, relations, bivariate, trivariate and geospatial data. The second part covers various tools for the visual representation of processes; these include timelines, flow-charts, Gantt charts and PERT diagrams. In addition, the book also features four appendices which cover cross-chapter topics: mathematics and statistics review, Matplotlib primer, color representation and usage, and representation of geospatial data. Aimed at junior and senior undergraduate students in various technical, scientific, and economic fields, this book is also a valuable aid for researchers and practitioners in data science, marketing, entertainment, media and other fields.
Calculus for Beginners
Foundations of Calculus: A Beginner's Comprehensive GuideCalculus for Beginners stands out as a pioneering educational tool, designed to demystify the complexities of calculus for novices. This book is crafted to cater to the needs of beginners, providing a clear and thorough foundation in calculus concepts, principles, and applications. Its unique structure and comprehensive coverage make it an indispensable resource for anyone looking to grasp the fundamentals of calculus.Empowering Learners with a Multifaceted ApproachCentral to this guide is its multifaceted approach to teaching calculus, which addresses the subject's inherent complexity and variations through a meticulously designed curriculum. Each chapter unfolds logically, guiding learners from basic principles to more intricate concepts. This pedagogical strategy is augmented by a wealth of resources aimed at reinforcing understanding and facilitating practical application.Highlights of the Book: Interactive Learning Experience: For each topic covered, the book includes a QR code and a dedicated link to an accompanying online course. This feature provides learners with instant access to detailed lessons, examples, exercises, video lessons, and worksheets, creating a rich, interactive learning environment.Comprehensive Curriculum: The book covers all fundamental aspects of calculus, including limits, derivatives, integrals, and differential equations, ensuring a solid foundation in each area. The content is presented in a clear, understandable language, making complex concepts accessible to beginners.Practical Application and Examples: Real-world applications and examples are woven throughout the text, illustrating how calculus principles are applied in various fields. This approach not only enhances comprehension but also demonstrates the relevance of calculus in solving practical problems.Enhanced Learning Tools: Each section is supplemented with exercises and worksheets, allowing learners to practice and apply what they have learned. Video lessons offer visual explanations of complex topics, catering to different learning styles.Accessible Solutions: A complete set of solutions for all exercises and questions is provided, enabling learners to check their work and understand the rationale behind each answer. This feedback mechanism is crucial for self-assessment and improvement. Calculus for Beginners is more than just a textbook; it is a comprehensive learning system that integrates traditional teaching methods with innovative digital resources. By offering a blend of written content, interactive online components, and practical exercises, this book ensures that learners not only understand calculus concepts but also know how to apply them in real-world contexts. Whether you are a student, a professional seeking to refresh your knowledge, or a curious mind venturing into the world of calculus for the first time, this guide offers the tools and guidance necessary to master calculus with confidence and ease. Ideal for self-study and classroom usage!
The Logic of Partitions
This book is an introduction to the logic of partitions on a set as well as the (quantum) logic of partitions (direct-sum decompositions or DSDs) on a vector space. Partitions of a set are categorically dual to subsets of a set. Thus the logic of partitions is, in that sense, the dual to the Boolean logic of subsets (usually presented as the special case of propositional logic).Since partitions can be seen as the inverse image partitions of random variables or numerical attributes, partition logic is the logic of random variables or numerical attributes (abstracted from the actual values). On the lattice of partitions of an arbitrary unstructured set, there is a rich algebraic structure of dual operations of implication and co-implication - resembling a non-distributive version of Heyting and co-Heyting algebras.
Four Famous Numbers
WE DELVE DEEP INTO THE SCIENCE AND INTER-RELATIONSHIPS OF FOUR FAMOUS MATHEMATICAL CONSTANTS: EULER'S NUMBER, e, THE LUDOLPHINE CONSTANT, ( pi ), PYTHAGORAS' CONSTANT AND THE RATIO OF PHIDIAS ( phi ). ALONG THE WAY WE ASSESS THE USEFULNESS OF DIVERSE METHODS OF COMPUTING THESE NUMBERS, TECHNIQUES DATING FROM THE BRONZE AGE TO THE TWENTY-FIRST CENTURY. FROM THE EARLIEST DAYS OF VISIBLE LIFE TO OUR OWN TIMES, TINY ANIMALS HAVE PLOWED AND BURROWED THE DEEP SEA FLOOR IN SYSTEMATIC, GEOMETRICAL PATHS. THEY OFTEN SEEMED TO HAVE CONFORMED TO THE MATHEMATICS OF OUR FAMOUS NUMBERS! CAN THIS REALLY BE TRUE? WE CONSIDER THE EVIDENCE. THIS SECOND EDITION, CORRECTED AND EXTENDED, IS PROFUSELY ILLUSTRATED AND HAS ORIGINAL RESEARCH, ALGEBRAIC DERIVATIONS, FULL ACADEMIC REFERENCES, AND A COMPREHENSIVE INDEX. "FOUR FAMOUS NUMBERS" WILL APPEAL TO ENTHUSIASTS, UNDERGRADUATES AND TEACHERS IN HIGHER EDUCATION.
Nonlinear Control Systems with Recent Advances and Applications
In the rapidly evolving landscape of nonlinear control systems, this reprint stands as a beacon of knowledge, showcasing the remarkable progress made over the last few decades. With a focus on design methodologies and their applications, this text employs various mathematical tools to address the myriad challenges inherent in nonlinearly controlled systems.This reprint extends its reach beyond traditional boundaries, presenting applications of nonlinear control across diverse fields such as energy, health care, robotics, biology, and big data research. As technology continues to advance, nonlinear control emerges as a critical player in shaping the future of theory and technology adoption across these domains.Despite the wealth of the existing literature, synthesizing control strategies for a broader class of nonlinear systems, especially those integrated with emerging technologies in communication and computation, remains a formidable task. This reprint addresses this gap, providing a cutting-edge collection of articles that push the boundaries of both theoretical background and practical applications. With its emphasis on novel developments and the broader class of applications, this reprint opens doors to new possibilities, making it a must-read for anyone seeking to navigate the intricate challenges of nonlinear control systems in the 21st century.
Industrial Engineering and Industrial Management
This CCIS post conference volume constitutes the proceedings of the 5th International Conference, IEIM 2024, in Nice, France, in January 2024. The 18 full papers together with 3 short papers in this volume were carefully reviewed and selected from 71 submissions. The were organized in 5 tracks as follows: five topics of IEIM were classified as follows: "Data Analysis and Demand Calculation in Industrial Production", "Process Optimization and Intelligence in Green Manufacturing Systems", "Lean Manufacturing and Process Optimization", "Enterprise Digital Transformation and Business Management" and "Modern Logistics Information Systems and Distribution Services".
Symplectic and Contact Geometry
This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics. Organized into four chapters, this work serves as a stepping stone for readers to delve into the subject, providing a succinct and motivating foundation. The content covers definitions, symplectic linear algebra, symplectic and contact manifolds, Hamiltonian systems, and more. Prerequisite knowledge includes differential geometry, manifolds, algebraic topology, de Rham cohomology, and the basics of Lie groups. Quick reviews are included where necessary, and examples and constructions are provided to foster understanding. Ideal for advanced undergraduate students and graduate students, this volume can also serve as a valuable resource for independent researchers seeking a quick yet solid understanding of symplectic and contact geometry.
Mathematical Logic
Presents an introduction to of formal mathematical logic and set theoryPresents simple yet nontrivial results in modern model theoryProvides introductory remarks to all results, including a historical background
Comparative Perspectives on Inquiry-Based Science Education
The core practice of professional scientists is inquiry, often referred to as research. If educators are to prepare students for a role in the professional scientific and technological community, exposing them to inquiry-based learning is essential. Despite this, inquiry-based teaching and learning (IBTL) remains relatively rare, possibly due to barriers that teachers face in deploying it or to a lack of belief in the teaching community that inquiry-based learning is effective. Comparative Perspectives on Inquiry-Based Science Education examines stories and experiences from members of an international science education project that delivered learning resources based around guided inquiry for students to a wide range of schools in 12 different countries in order to identify key themes that can provide useful insights for student learning, teacher support, and policy formulation at the continental level. The book provides case studies across these 12 different settings that enable readers to compare and contrast both practice and policy issues with their own contexts while accessing a cutting-edge model of professional development. It is designed for educators, instructional designers, administrators, principals, researchers, policymakers, practitioners, and students seeking current and relevant research on international education and education strategies for science courses.
Strategic Applications of Measurement Technologies and Instrumentation
Measurement techniques form the basis of scientific, engineering, and industrial innovations. The methods and instruments of measurement for different fields are constantly improving, and it's necessary to address not only their significance but also the challenges and issues associated with them. Strategic Applications of Measurement Technologies and Instrumentation is a collection of innovative research on the methods and applications of measurement techniques in medical and scientific discoveries, as well as modern industrial applications. The book is divided into two sections with the first focusing on the significance of measurement strategies in physics and biomedical applications and the second examining measurement strategies in industrial applications. Highlighting a range of topics including material assessment, measurement strategies, and nanoscale materials, this book is ideally designed for engineers, academicians, researchers, scientists, software developers, graduate students, and industry professionals.
Algebra and Trigonometry
In this book the author covers topics in mathematics from basic algebra through trigonometry, providing definitions, properties, theorems, terminology, notation, formulas, and examples. The author has also reserved space within the book for the student to work exercises alongside the examples provided. Thus it functions as both a textbook and a workbook. It is especially well-suited to students who: wish to learn algebra or trigonometry without the aid of a teacher;are currently enrolled in a course in algebra or trigonometry at an educational institution but do not want to attend lectures or watch videos online; orhave studied algebra or trigonometry in the past but would like to review the subjects.This book does not include an ample set of additional algebraic exercises at the end of each section and may serve a student best when used in conjunction with a separate source of sets of exercises, such as Exercises in Algebra and Trigonometry by the same author. When combined with Exercises in Algebra and Trigonometry, this book will serve instructors and students well in any course in algebra or trigonometry, including those: conducted online;where the classroom is "flipped" and students complete exercises in advance of a lecture from the instructor;where not all students progress at the same pace;where the student learns independently or at home.
The P-Adic Simpson Correspondence and Hodge-Tate Local Systems
This book delves into the p-adic Simpson correspondence, its construction, and development. Offering fresh and innovative perspectives on this important topic in algebraic geometry, the text serves a dual purpose: it describes an important tool in p-adic Hodge theory, which has recently attracted significant interest, and also provides a comprehensive resource for researchers. Unique among the books in the existing literature in this field, it combines theoretical advances, novel constructions, and connections to Hodge-Tate local systems.This exposition builds upon the foundation laid by Faltings, the collaborative efforts of the two authors with T. Tsuji, and contributions from other researchers. Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence, whose construction has been taken up in several different ways. Following the approach they initiated with T. Tsuji, the authors develop new features of the p-adic Simpson correspondence, inspired by their construction of the relative Hodge-Tate spectral sequence. First, they address the connection to Hodge-Tate local systems. Then they establish the functoriality of the p-adic Simpson correspondence by proper direct image. Along the way, they expand the scope of their original construction. The book targets a specialist audience interested in the intricate world of p-adic Hodge theory and its applications, algebraic geometry and related areas. Graduate students can use it as a reference or for in-depth study. Mathematicians exploring connections between complex and p-adic geometry will also find it valuable.
Differential Equations
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
Elementary Linear Algebra with Applications
This text offers a unique balance of theory and a variety of standard and new applications along with solved technology-aided problems. The book includes the fundamental mathematical theory, as well as a wide range of applications, numerical methods, projects, and technology-assisted problems and solutions in Maple, Mathematica, and MATLAB. Some of the applications are new, some are unique, and some are discussed in an essay. There is a variety of exercises which include True/False questions, questions that require proofs, and questions that require computations. The goal is to provide the student with is a solid foundation of the mathematical theory and an appreciation of some of the important real-life applications. Emphasis is given on geometry, matrix transformations, orthogonality, and least-squares. Designed for maximum flexibility, it is written for a one-semester/two semester course at the sophomore or junior level for students of mathematics or science.
Asymptotic Issues for Some Partial Differential Equations (Second Edition)
The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Fractional Partial Differential Equations
This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier-Stokes equations, fractional Rayleigh-Stokes equations, fractional Fokker-Planck equations, and fractional Schr繹dinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts.The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications.
Determinantal Ideals of Square Linear Matrices
This book explores determinantal ideals of square matrices from the perspective of commutative algebra, with a particular emphasis on linear matrices. Its content has been extensively tested in several lectures given on various occasions, typically to audiences composed of commutative algebraists, algebraic geometers, and singularity theorists.Traditionally, texts on this topic showcase determinantal rings as the main actors, emphasizing their properties as algebras. This book follows a different path, exploring the role of the ideal theory of minors in various situations-highlighting the use of Fitting ideals, for example. Topics include an introduction to the subject, explaining matrices and their ideals of minors, as well as classical and recent bounds for codimension. This is followed by examples of algebraic varieties defined by such ideals. The book also explores properties of matrices that impact their ideals of minors, such as the 1-generic property, explicitly presenting a criterion by Eisenbud. Additionally, the authors address the problem of the degeneration of generic matrices and their ideals of minors, along with applications to the dual varieties of some of the ideals.Primarily intended for graduate students and scholars in the areas of commutative algebra, algebraic geometry, and singularity theory, the book can also be used in advanced seminars and as a source of aid. It is suitable for beginner graduate students who have completed a first course in commutative algebra.
From Computational Logic to Computational Biology
Alfredo Ferro's impact on information technology has traversed diverse domains, encompassing Computational Logic, Data Mining, Bioinformatics, and Complex Systems. After first studying Mathematics at the University of Catania, he received a Ph.D. in Computer Science from NYU in 1981, working under the supervision of Jacob Theodor (Jack) Schwartz. He returned to the University of Catania where he established the Computer Science undergraduate program, served as the coordinator of the Ph.D. program in Computer Science, cofounded the Ph.D. program in Biology, Human Genetics, and Bioinformatics, and retired as a full professor in 2021.Alfredo's academic career as a computer scientist is characterized by two distinct research phases: Computational Logic until approximately 1995, followed by a notable focus on Data Mining and Bioinformatics. The contributions in this volume reflect the quality and the scope of his personal and collaborative successes.He also taught andinspired many excellent scientists. A pioneering initiative was to establish summer schools for Ph.D. students in 1989, leading to the so-called Lipari School, now the J.T. Schwartz International School for Scientific Research, where Alfredo continues to serve as director. This prestigious series includes schools focused on Computer Science, Complex Systems, and Computational Biology, featuring world-class scientists as lecturers and mentors.
A Course in Combinatorics and Graphs
This compact textbook consists of lecture notes given as a fourth-year undergraduate course of the mathematics degree at the Universitat Polit癡cnica de Catalunya, including topics in enumerative combinatorics, finite geometry, and graph theory. This text covers a single-semester course and is aimed at advanced undergraduates and masters-level students. Each chapter is intended to be covered in 6-8 hours of classes, which includes time to solve the exercises. The text is also ideally suited for independent study. Some hints are given to help solve the exercises and if the exercise has a numerical solution, then this is given. The material covered allows the reader with a rudimentary knowledge of discrete mathematics to acquire an advanced level on all aspects of combinatorics, from enumeration, through finite geometries to graph theory. The intended audience of this book assumes a mathematical background of third-year students in mathematics, allowing for a swifter useof mathematical tools in analysis, algebra, and other topics, as these tools are routinely incorporated in contemporary combinatorics. Some chapters take on more modern approaches such as Chapters 1, 2, and 9. The authors have also taken particular care in looking for clear concise proofs of well-known results matching the mathematical maturity of the intended audience.
Sacred Geometry
Uncover the Hidden Wisdom of Sacred Geometry: Your Gateway to Divine Alignment and TransformationIn a world where challenges often appear insurmountable, where climate change serves as an urgent reminder of a deeper crisis, there exists a beacon of hope-a profound wisdom concealed within the timeless realm of Sacred Geometry.Sacred Geometry: The Universal Language of Divine Alignment beckons both newcomers and seasoned seekers on a vivid voyage into the heart of reality's concealed enigmas. This book is your key to unlocking the secrets vital for our survival and spiritual evolution.Embark on a journey where you will: 1. Unveil Universal Wisdom: Shift your energy and awareness by immersing yourself in the profound truths concealed within the very fabric of time and space, governed by the geometric dance of the Sun, Moon, and Earth.2. Explore Your Inner Architecture: Acquire fresh insights into the intricate structure of your existence and discover how divine alignment holds the power to transform life's challenges into opportunities for growth.3. Ascend to Higher Dimensions: Sacred geometry serves as the ancient key that unlocks gateways to elevated realms of understanding and consciousness.4. Tools for Inner Peace: Learn the art of constructing and utilizing sacred geometry tools to attain emotional equilibrium, conquer stress, and craft a life of abundance and well-being.5. Blueprint for Survival: Delve deep within the recesses of your heart center to open a portal to the wisdom of your soul. Transcend the illusion of separation and unlock your true potential to not merely survive but thrive.With over four decades of dedicated expertise, Gail and Gregory Hoag have pioneered groundbreaking technologies that have transformed the lives of tens of thousands across the globe with their teaching and tools. They have harnessed the power of divine archetypes to amplify higher dimensional energies and elevate the human experience, catalyzing personal and spiritual growth towards the path of higher consciousness, well-being, and profound connection.
Student Solutions Manual for Non Linear Dynamics and Chaos
This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the third edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.
Discrete Choice Analysis with R
This book is designed as a gentle introduction to the fascinating field of choice modeling and its practical implementation using the R language. Discrete choice analysis is a family of methods useful to study individual decision-making. With strong theoretical foundations in consumer behavior, discrete choice models are used in the analysis of health policy, transportation systems, marketing, economics, public policy, political science, urban planning, and criminology, to mention just a few fields of application. The book does not assume prior knowledge of discrete choice analysis or R, but instead strives to introduce both in an intuitive way, starting from simple concepts and progressing to more sophisticated ideas. Loaded with a wealth of examples and code, the book covers the fundamentals of data and analysis in a progressive way. Readers begin with simple data operations and the underlying theory of choice analysis and conclude by working with sophisticated models including latent class logit models, mixed logit models, and ordinal logit models with taste heterogeneity. Data visualization is emphasized to explore both the input data as well as the results of models. This book should be of interest to graduate students, faculty, and researchers conducting empirical work using individual level choice data who are approaching the field of discrete choice analysis for the first time. In addition, it should interest more advanced modelers wishing to learn about the potential of R for discrete choice analysis. By embedding the treatment of choice modeling within the R ecosystem, readers benefit from learning about the larger R family of packages for data exploration, analysis, and visualization.
Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations
Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. This book provides these real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems.
Engaging Young Students in Mathematics through Competitions - World Perspectives and Practices
Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.
Methods of Geometry in the Theory of Partial Differential Equations
Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.
Local Mathematics for Local Physics
The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.
Sharpening Everyday Mental/Thinking Skills Through Mathematics Problem Solving and Beyond
Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.
Sharpening Everyday Mental/Thinking Skills Through Mathematics Problem Solving and Beyond
Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.
Mathematics for Fisheries Economics
The institute (ICAR-CIFE) has continuously adopted itself to meet the current needs, methodological challenges, and quality enhancement in fisheries education with the advances in information technology. The increasing application of mathematics to various branches/courses of economics in the past decade has made it necessary for economists to have an elementary knowledge of mathematics. To this end, an attempt has been made to bring out a practical manual on mathematics for catering to needs of fisheries students, most of whom having a non-mathematical background during their tertiary education. This book has been structured to solve problems on a wide range of topics such as matrix, determinants, limit & continuity, differentiation, integration, partial differentiation, etc. It is hoped that the book brought out will serve as a useful source of knowledge to the students and also will help them in solving various types of mathematical problems.
Modeling with Stochastic Programming
This is an updated version of what is still the only text to address basic questions about how to model uncertainty in mathematical programming, including how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This second edition has important extensions regarding how to represent random phenomena in the models (also called scenario generation) as well as a new chapter on multi-stage models. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental modeling issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research and head of Center for Shipping and Logistics at NHH Norwegian School of Economics, Bergen, Norway.
A Full Axiomatic Development of High School Geometry
This textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content of high school geometry. It begins with a set of points, a measure of distance between pairs of points and ten simple axioms. From there the notions of length, area and angle measure, along with congruence and similarity, are carefully defined and their properties proven as theorems. It concludes with a proof of the consistency of the axioms used and a full description of their models. It is provided in guided inquiry (inquiry-based) format with the intention that students will be active learners, proving the theorems and presenting their proofs to their class with the instructor as a mentor and a guide.The book is written for graduate and advanced undergraduate students interested in teaching secondary school mathematics, for pure math majors interested in learning about the foundations of geometry, for faculty preparing future secondary school teachers and as a reference for any professional mathematician. It is written with the hope of anchoring K-12 geometry in solid modern mathematics, thereby fortifying the teaching of secondary and tertiary geometry with a deep understanding of the subject.
Recent Trends and Future Challenges in Learning from Data
This book collects together selected peer-reviewed contributions presented at the European Conference on Data Analysis, ECDA 2022, held in Naples, Italy, September 14-16, 2022. Highlighting the role of statistics in discovering novel and interesting patterns in the era of big data, it follows the motto of the conference: "Avoiding drowning in the data: recent trends and future challenges in learning from data". The central focus is on multidisciplinary approaches to data analysis, classification, and the interface between computer science, data mining and statistics. Both methodological and applied topics are covered. The former includes supervised and unsupervised techniques with particular emphasis on advances in regression and clustering analysis and constructing composite indicators. The applications are mainly in risk analysis, biology, and education. The volume is organized into four main macro themes: methodological contributions in the social sciences and education, multivariate analysis methods for big data, innovative contributions for applications inspired by biology, and strategies for analyzing complex data in finance.
Fundamentals of Real and Complex Analysis
The primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science.Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter's unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy's theorem through the integral formula and residue theorem are presented.
Rank 2 Amalgams and Fusion Systems
This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups. It demonstrates a broad range of techniques from local group theory and fusion systems, several of which can be applied in more general settings. Addressing research problems that have not been treated in the past, it is the first text to explicitly use the amalgam method in this context. Fusion systems offer an enticing way to unify various p-local methods employed in group theory, representation theory and homotopy theory; but as abstract constructions they are still somewhat mysterious. This book paves the way to a broad and systematic study of these categories by applying the amalgam method, thus modernizing a methodology widely used to understand the local structure of finite groups. With this comes an introduction to several vital techniques in local group theory, a generous survey of the structure and modular representation theory of some important families of finite groups, and a demonstration of the value of combinatorial methods in finite group theory and fusion systems. Primarily aimed at researchers active in fusion systems and group amalgams, the book will also be of interest to anyone working with finite groups and their modular representations, group actions on trees, or classifying spaces. The inclusion of preliminary chapters outlining the theoretical prerequisites make it ideal for a short lecture course or as a reading group text for early career researchers and graduate students.
