Why Does Math Work ... If It's Not Real?
According to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless, ' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.
Classification of Musical Objects for Analysis and Composition
This book presents and discusses the fundamental topic of classification of musical objects, such as chords, motifs, and gestures. Their classification deals with the exhibition of isomorphism classes. Our structure types include local and global constructions, the latter being similar to global structures in geometry, such as differentiable manifolds. The discussion extends to the role, which classification plays for the creative construction of musical compositions. Our examples include references to classical compositions, such as Beethoven's sonatas, and some of the author's own compositions of classical and jazz styles. We also discuss software that enables the application of classification to musical creativity. The volume is addressed to an audience that would apply classification to programming and creative musical construction.
Multivariate Calculus
This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students.
Geometry of Continued Fractions
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects.Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics.The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Discrete Mathematics
Discrete Mathematics: A Gateway to the Mathematical Garden is an introduction to finite and discrete mathematics. This book includes all the important and foundational mathematics to support the student learning finite mathematics for the first time: logic, set theory, number theory, proofs, combinatorics, and graph theory. The exposition helps the student-reader learn to think logically and reasonably about mathematical structures. Discussions of cryptology, computer science, machine-readable codes, and operations research are used to give the student a sense of how the mathematics is applied. Throughout the book, examples illustrate the material and provide insight into the mathematical theory. The book is essentially self-contained. There are very few prerequistes aside from some mathematical maturity and familiarity with algebra. Problems to help the student master the concepts are included at the end of each section. Each chapter concludes with a set of supplementary problems and a set of sample test questions. Discrete Mathematics: A Gateway to the Mathematical Garden, Chuck Garner, paperback, color, first edition, 7.44in by 9.68 in, 217 pages, ISBN 978-1-312-71237-9, copyright 2023 Charles R. Garner Jr.
Computational Mathematics and Applied Statistics
Rapid advances in modelling research have created new challenges and opportunities for statisticians. Statistical inference in observational studies and many other emerging fields have motivated statisticians worldwide to develop cutting-edge methods and analytical strategies.The aim of this book is to showcase the applications and methodological research in all fields of computational statistics. This book will provide a forum for computer scientists, mathematicians, and statisticians working in a variety of areas in statistics, including biometrics, econometrics, data analysis, graphics, and simulation.
Stochastic Differential Equations for Science and Engineering
The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises.
Special Functions with Applications to Mathematical Physics
This MDPI booklet lists the articles published in three Special Issues of the journal Mathematics devoted to special functions with applications in mathematical physics in the years 2020-2021.The call for papers considered theories and applications of high transcendental functions, including topics found mainly in the list of keywords: - Mittag-Leffler and related functions, and their applications in mathematical physics;- Wright and related functions and their applications in mathematical physics;- exponential integrals and their extensions with applications in mathematical physics;- generalized hypergeometric functions and their extensions with applicationsHowever, the Special Issues were not limited to the above list, for example, when the content of a paper was clearly related to some high transcendental functions and their applications.Special attention was reserved for distinct functions exhibiting some relevance in the framework of the theories and applications of the fractional calculus and in their visualization through illuminating plots.Both research and survey articles were included in this booklet, according to the content list.
The Volume of Vector Fields on Riemannian Manifolds
This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject's introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs. A wide range of topics is covered, including: a discussion on the conditions for a vector field on a Riemannian manifold to determine a minimal submanifold within its tangent bundle with the Sasaki metric; numerous examples of minimal vector fields (including those of constant length on punctured spheres); athorough analysis of Hopf vector fields on odd-dimensional spheres and their quotients; and a description of volume-minimizing vector fields of constant length on spherical space forms of dimension three. Each chapter concludes with an up-to-date survey which offers supplementary information and provides valuable insights into the material, enhancing the reader's understanding of the subject. Requiring a solid understanding of the fundamental concepts of Riemannian geometry, the book will be useful for researchers and PhD students with an interest in geometric analysis.
Game Theory: A Nontechnical Introduction to the Analysis of Strategy (Fourth Edition)
As with the previous editions, this fourth edition relies on teaching by example and the Karplus Learning Cycle to convey the ideas of game theory in a way that is approachable, intuitive, and interdisciplinary. Noncooperative equilibrium concepts such as Nash equilibrium, mixed strategy equilibria, and subgame perfect equilibrium are systematically introduced in the first half of the book. Bayesian Nash equilibrium is briefly introduced. The subsequent chapters discuss cooperative solutions with and without side payments, rationalizable strategies and correlated equilibria, and applications to elections, social mechanism design, and larger-scale games. New examples include panic buying, supply-chain shifts in the pandemic, and global warming.
Differential Equations for Studies in Computational Electrophysiology
This open access text aims at giving you the simplest possible introduction to differential equations that are used in models of electrophysiology. It covers models at several spatial and temporal scales with associated numerical methods. The text demonstrates that a very limited number of fundamental techniques can be used to define numerical methods for equations ranging from ridiculously simple to extremely complex systems of partial differential equations. Every method is implemented in Matlab and the codes are freely available online. By using these codes, the reader becomes familiar with classical models of electrophysiology, like the cable equation, the monodomain model, and the bidomain model. But modern models that have just started to gain attention in the field of computational electrophysiology are also presented. If you just want to read one book, it should probably not be this one, but if you want a simple introduction to a complex field, it is worth considering the present text.
A Journey Into the World of Exponential Functions
This book illustrates why abstract mathematical entities are needed to represent some aspects of physical reality. It provides an overview of different types of numbers and functions along with their historical background and applications.
Intermittent Convex Integration for the 3D Euler Equations
A new threshold for the existence of weak solutions to the incompressible Euler equations To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.
Numerical Analysis of Ordinary and Delay Differential Equations
This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering.One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.
More (Almost) Impossible Integrals, Sums, and Series
This book, the much-anticipated sequel to (Almost) Impossible, Integrals, Sums, and Series, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author's previous book, these fascinating mathematical problems are shown in new and engaging ways, and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren't afraid of a challenge.
Algebra 1 Through Stories
Unravel the Mysteries of AlgebraStep into a thrilling mathematical escapade with "Algebra 1: The Mystery of the Algebraic Artifact"! This dynamic guide offers a unique spin on mastering Algebra 1 concepts, making it an excellent supplementary resource for students aged 11-13 (8th-9th grade) and a compelling teaching tool for educators.A Novel Approach to LearningNo more wading through old-fashioned, dry textbooks! This book cleverly intertwines vital algebraic ideas into an exciting story that captures students' attention, making learning a captivating and effortless process.Essential Topics UncoveredOur journey uncovers all the key Algebra 1 concepts. The 19 exciting chapters delve into: Equations and ExpressionsInequalitiesLinear FunctionsExponents and PolynomialsQuadratic EquationsSystems of EquationsCompound InequalitiesReinforce and Validate UnderstandingEach chapter includes a comprehensive review and a carefully selected range of practice problems that reinforce understanding and allow the application of newly gained knowledge in various situations. These end-of-chapter exercises empower students to flex their algebraic muscles and gain confidence in their understanding.Ideal For"Algebra 1: The Mystery of the Algebraic Artifact" is a valuable resource for: 8th-9th graders studying Algebra 1, aiming to supplement their learning with an engaging twist.Parents looking for innovative methods to encourage and support their child's math education.Teachers in search of an engaging, narrative-driven technique to illuminate algebra concepts.With "Algebra 1: The Mystery of the Algebraic Artifact", algebra becomes an epic quest filled with adventure and intrigue. Join us as we unlock the wonders of Algebra 1 and make math an exciting mystery to solve!
Computing and Analysing Energy Minimisation Problems in Liquid Crystals: Implementation Using Firedrake
How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects?There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc.This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems.
Temporal Logic: From Philosophy and Proof Theory to Artificial Intelligence and Quantum Computing
Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
The First Hundred Thousand Prime Numbers
A prime number is any integer greater than one which has only itself and one as factors. For example, 5 is prime since it does not have 2, 3, or 4 as a factor. 1 and 5 are the only factors of 5.Prime numbers have been studied since antiquity. Eratosthenes of Cyrene lived about 276 BCE to 194 BCE. He developed a method of finding prime numbers that is still taught today. It is called the Sieve of Eratosthenes.Prime numbers continue to fascinate mathematicians today. Prime numbers are used in number theory, and in cryptography.
Chaos, Complexity, and Nonlinear Economic Theory
What do economic chaos and uncertainties mean in rational or irrational economic theories? How do simple deterministic interactions among a few variables lead to unpredictable complex phenomena? Why is complexity of economies causing so many conflicts and confusions worldwide?This book provides a comprehensive introduction to recent developments of complexity theory in economics. It presents different models based on well-accepted economic mechanisms such as the Solow model, Ramsey model, and Lucas model. It is focused on presenting complex behaviors, such as business cycles, aperiodic motion, bifurcations, catastrophes, chaos, and hidden attractors, in basic economic models with nonlinear behavior. It shows how complex nonlinear phenomena are identified from various economic mechanisms and theories. These models demonstrate that the traditional or dominant economic views on evolution of, for instance, capitalism market, free competition, or Keynesian economics, are not generally valid. Markets are unpredictable and nobody knows with certainty the consequences of policies or other external factors in economic systems with simple interactions.
Guide to Advanced Statistical Analysis in R
Features- Worked examples- Clear programming code, usable by R novices- Without mathematical formulae- structural equation modeling- survival analysis- longitudinal analysis- multivariate analysis- GLM, Poisson regression, multilevel modeling- power analysis, reliability- Further reading recommendations in each chapter- Data sets on the website
Guide to Advanced Statistical Analysis in R
Features- Worked examples- Clear programming code, usable by R novices- Without mathematical formulae- structural equation modeling- survival analysis- longitudinal analysis- multivariate analysis- GLM, Poisson regression, multilevel modeling- power analysis, reliability- Further reading recommendations in each chapter- Data sets on the website
Application-Inspired Linear Algebra
This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, oneof which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors' website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
Statistical Testing with jamovi Sport
FeaturesWorked examples from sportClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Statistical Testing with jamovi Sport
Features Worked examples from sportClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Corruption, Infrastructure Management and Public-Private Partnership
Public-Private Partnerships (PPP or 3Ps) allow the public sector to seek alternative funding and expertise from the private sector during procurement processes. Such partnerships, if executed with due diligence, often benefit the public immensely. Unfortunately, Public-Private Partnerships can be vulnerable to corruption. This book looks at what measures we can put in place to check corruption during procurement and what good governance strategies the public sector can adopt to improve the performance of 3Ps.The book applies mathematical models to analyze 3Ps. It uses game theory to study the interaction and dynamics between the stakeholders and suggests strategies to reduce corruption risks in various 3Ps stages. The authors explain through game theory-based simulation how governments can adopt a evaluating process at the start of each procurement to weed out undesirable private partners and why the government should take a more proactive approach.Using a methodological framework rooted in mathematical models to illustrate how we can combat institutional corruption, this book is a helpful reference for anyone interested in public policymaking and public infrastructure management.
Statistical Testing with jamovi Health
FeaturesWorked examples from health settingsClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Statistical Testing with jamovi Health
FeaturesWorked examples from health settingsClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Applied Functional Analysis
This textbook offers a concise and thorough introduction to the topic of applied functional analysis. Targeted to graduate students of mathematics, it presents standard topics in a self-contained and accessible manner. Featuring approximately 300 problems sets to aid in understanding the content, this text serves as an ideal resource for independent study or as a textbook for classroom use. With its comprehensive coverage and reader-friendly approach, it is equally beneficial for both students and teachers seeking a detailed and in-depth understanding of the subject matter.
Applications of Holomorphic Functions in Geometry
This book expounds on the recent developments in applications of holomorphic functions in the theory of hypercomplex and anti-Hermitian manifolds as well as in the geometry of bundles. It provides detailed information about holomorphic functions in algebras and discusses some of the areas in geometry with applications. The book proves the existence of a one-to-one correspondence between hyper-complex anti-K瓣hler manifolds and anti-Hermitian manifolds with holomorphic metrics, and also a deformed lifting to bundles. Researchers and students of geometry, algebra, topology and physics may find the book useful as a self-study guide.
Chatting with ChatGPT
This past April Ermes engaged ChatGPT in a wide variety of chats, ranging from philosophy to paradoxes to Canadian lit, to name just a few. Artificial intelligence is developing and improving very fast, so that no one should be surprised if a few years down the road one looks back at the ChatGPT responses given in this volume only to be amazed at the primitiveness and inaccuracy of some of the responses. For now, though, what stands out is ChatGPT's impressive ability to comment quickly and succinctly on any one of the given topics.
Near Extensions and Alignment of Data in R^n
Near Extensions and Alignment of Data in Rn Comprehensive resource illustrating the mathematical richness of Whitney Extension Problems, enabling readers to develop new insights, tools, and mathematical techniques Near Extensions and Alignment of Data in Rn demonstrates a range of hitherto unknown connections between current research problems in engineering, mathematics, and data science, exploring the mathematical richness of near Whitney Extension Problems, and presenting a new nexus of applied, pure and computational harmonic analysis, approximation theory, data science, and real algebraic geometry. For example, the book uncovers connections between near Whitney Extension Problems and the problem of alignment of data in Euclidean space, an area of considerable interest in computer vision. Written by a highly qualified author, Near Extensions and Alignment of Data in Rn includes information on: Areas of mathematics and statistics, such as harmonic analysis, functional analysis, and approximation theory, that have driven significant advances in the field Development of algorithms to enable the processing and analysis of huge amounts of data and data sets Why and how the mathematical underpinning of many current data science tools needs to be better developed to be useful New insights, potential tools, and mathematical techniques to solve problems in Whitney extensions, signal processing, shortest paths, clustering, computer vision, optimal transport, manifold learning, minimal energy, and equidistribution Providing comprehensive coverage of several subjects, Near Extensions and Alignment of Data in Rn is an essential resource for mathematicians, applied mathematicians, and engineers working on problems related to data science, signal processing, computer vision, manifold learning, and optimal transport.
Mathfatuated
Mathfatuated includes unique poems representing math topics associated with the lovable subject, making it the perfect gift for the math lover. Creating a poetry book about math can be a unique way of exploring mathematical concepts that may seem boringly challenging to some. Poetry can give a fresh perspective and bring an imaginative approach to learning about math. It can also help people remember mathematical concepts better. Moreover, it can bridge the gap between math and art and appeal to a larger audience. Overall, a poetry book about math can be an appealing and creative way to engage with the subject.
Complex Geometry of Slant Submanifolds
This book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers. The book discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler, locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results on slant submanifolds of para-Hermitian manifolds. This book also includes recent results on slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in general theory of relativity and potential applications in radiation and electromagnetic fields. Various open problems and conjectures on slant surfaces in complex space forms are also included in the book. It presents detailed information on the most recent advances in the area, making it valuable for scientists, educators and graduate students.
Math Mammoth Grade 5 Skills Review Workbook
Some students benefit from spiral review, and that is exactly what Math Mammoth Grade 5 Skills Review Workbook offers! It has been designed to complement the lessons in Math Mammoth Grade 5 complete curriculum, providing spiral review of the concepts in the Grade 5 curriculum.Math Mammoth Grade 5 Skills Review Workbook is divided into chapters, which correspond to the chapters in Math Mammoth Grade 5 curriculum. It is meant to be used during the school year, alongside the main curriculum. Spiral reviewing means that after a particular concept or skill has been studied in the main curriculum, it is then reviewed repeatedly over time in several different worksheets of this book.You can choose exactly when to use the worksheets within the chapter, and how many of them to use. Not all students need all of these worksheets to help them keep their math skills fresh, so please vary the amount of worksheets you assign your student(s) according to their need.Each worksheet is designed to be one page, and includes a variety of exercises in a fun way without becoming too long and tedious.The answer key is available as a separate book.
Math Mammoth Grade 5 Skills Review Workbook Answer Key
Math Mammoth Grade 5 Skills Review Workbook Answer Key contains answers to all the worksheets in Math Mammoth Grade 5 Skills Review Workbook. The workbook itself is available separately. (This is the 2023 edition.)
Statistical Testing with jamovi Criminology
FeaturesWorked examples from CriminologyClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Advanced Topics in Fractional Differential Equations
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers' understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts - Approaches the topic of fractional differential equations while employing fixed point theorems as tools - Presents novel results, which build upon previous literature and many years of research by the authors
Practical solution of selected geometrical problems by the iterative approximation method
Scientific Essay from the year 2023 in the subject Mathematics - Geometry, language: English, abstract: The book presents practical solutions for geometric problems using iterative approximation. But what is a geometric problem, and in particular its solution by iterative approximation? I will not discuss or define the basic principles of Euclidean geometry, nor its origins, which are lost in the darkness of history, nor will I discuss its development. I merely want the reader to find a practical way to solve geometrical problems. At the same time, geometry should not only be considered a technician's, engineer's or scientist's field of work but as a toy that opens the way to an intellectually active mind, at the highest level.
A Textbook of Advanced Engineering Mathematics
Engineering is the practical application of science and technology. Mathematical models of these practical applications are obtained using various governing laws from science and technology. Most of the mathematical models lead to ordinary differential equations, partial differential equations or systems of partial or ordinary differential equations. The solution of these models plays a vital role in the analysis of the effect of parameters on the system. Solving the mathematical problem obtained by one of the many techniques covered in Engineering Mathematics. This book is a unique combination of differential equation theory and its fascinating application to "real-world" problems. The main aims of this book are: Elaborative discussion of the fundamental concepts of the relevant topicExtremely minute details have been addressed with sufficient justifications, and special care has been taken to make the explanation adequate, straightforward, and methodicalA large number of worked-out examples have been provided to aid in swiftly comprehending the subject matter and increasing self-confidence.Solution of engineering problem with detailed calculation.For more details, please visit https: //centralwestpublishing.com
Twisted Isospectrality, Homological Wideness, and Isometry
The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings).The methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do not focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology.The main goal of the book is to present the construction of finitely many "twisted" Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds.The book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and "class field theory" for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. This is an open access book.
Research in Computational Topology 2
This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariantsfor directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.
On the Synthesis of the Distribution amongst the Integers of the Prime Number Counting Function, pi(k), viewed as a Geometric Object
Academic Paper from the year 2023 in the subject Mathematics - Analysis, grade: 2.00, language: English, abstract: A method is devised in which the prime number counting function, pi(k) is viewed as having the properties of a staircase. The terminology appropriate to a staircase is used to describe the parts of the distribution amongst the integers. Strings of limited extent of consecutive numbers which may contain prime numbers are generated from an iterative equation which contains Gauss' prime number counting function. In honour of Gauss we call these strings of numbers, Gauss strings., and they are used in the construction of the staircase. Further, we show that the prime number counting function may be represented in number space by an infinite set of connected trapezia, the individual areas of which are numerically equal to the gap between the primes that are situated on two of the borders of any given trapezium.
Matrix Mathematics
Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.
Chapters from G繹del's Unfinished Book on Foundational Research in Mathematics
A Topology of Mind
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: -The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. - Connection between math cognition and symbolism, annotation and other semiotic processes. - Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. - Whether mathematics is an innate faculty or forged in cultural-historical context- What, if any, structures are shared between mathematics and language
