Evidence for Dark Numbers
This book contains several arguments for the existence of dark numbers, i.e., numbers which cannot be manipulated as individuals but only collectively. Their existence depends on the premise of actual infinity. Whether actually infinite sets exist is unknown and cannot be proven; it can only be assumed as an axiom. But if actually infinite sets exist then dark elements are unavoidable. This concept helps to explain many paradoxes of set theory like Zeno's paradox or the paradox of the binary tree or the completely scattered space of the real axis.
Compound Poisson Distributions
This book presents a comprehensive overview of compound Poisson distributions. All of the distributions listed in this book were derived, or invented, by the original authors as ""new"" statistical distributions, to fit a dataset(s) of experimental data. The properties of each newly proposed distribution were derived ab initio, sometimes with much effort by the original authors. Hence the title and motivation for this book: the primary focus here is the compound Poisson distributions themselves. We show that they are all exemplars of a common underlying formalism. General formulas (this includes both exact results and recurrences) are presented which apply to all compound Poisson distributions. In individual chapters, we apply that underlying formalism to selected compound Poisson distributions. We also derive new formulas not published in the literature. Having said the above, this book also presents a new technique for parameter estimation for a set of widely used compound Poisson distributions. The new technique is applied to several published experimental datasets, i.e. real data, not simulations. It yields equal or better fits to the data than those obtained by the original authors (in some cases, significantly better). Numerous graphs are plotted, to demonstrate the good/better fits obtained by the new technique. Hence this book contains not only pure theory, but also visually demonstrates the merits of the new formalism for fitting experimental data.
The Hidden Poetry & Music of Mathematics for Teaching Professionals
When poetry and music are interlinked with mathematics to provide phenomenal strategies to teaching mathematics. This would invite a plethora of thinking beyond classical frames to exceptional intelligent practice for teaching mathematics, including thinking outside classical frames to innovatively and creatively teach mathematics. This book is an open invite to all teaching professionals of mathematics.
The Pattern of Change
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
The Pattern of Change
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
Banach Algebras and Harmonic Analysis
The book includes recent articles on various topics studied recently in Banach algebras and abstract harmonic analysis. On the Banach algebra side, the reader will find idempotents and socle of a Banach algebra; closed subspaces of a Banach space, including the classical sequence spaces, which are realized as the kernel of a bounded operator; the connection between the stable rank one and Dedekind-finite property of the algebra of operators on a Banach space; spectral synthesis properties in convolution Sobolev algebras on the real line. The harmonic analysis side includes a generalization of the famous Beurling theorem; groups with few finite-dimensional unitary representations; relations between ideals of the Figa-Talamanca Herz algebra of a locally compact group and ideals of Figa-Talamanca Herz algebra of its closed subgroup; the tame functionals on Banach algebras and in harmonic analysis; and cancellation, factorization, and isometries in algebras on a locally compact group. The book also includes four surveys written by leaders in the area of full sheaf cohomology theory for noncommutative C - algebras; one-parameter semigroups of bounded operators on a Banach space which are weakly continuous in the sense of Arveson.
Master CUNY Math
CUNY(R) Math Mastery: Complete Tutorials & Practice Workbook with 300+ QuestionsYou have arrived!Here is everything you need to pass this tough test!We have helped thousands of students and we can help you! Over 200 CUNY(R) math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! CUNY(R) Math Practice Questions and Tutorials for: Numerical SkillsScientific NotationExponents and Radicals Square RootFractions, Decimals and Percent Algebra World problems with ratio and proportion One and two variable equations quadratic using different methods Translate real world problems into quadratic equa-tions and solve Advanced Algebra Trigonometry Logarithms Sequences Simple Geometry Slope of a line Linear equations from a graph Perimeter, circumference and volume Pythagorean theorem Geometric transformations CUNY(R) is a registered trademark of the City University of New York, who are not involved in the production of, and do not endorse this product.Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Partial Differential Equations
Partial Differential Equations: Foundations and Applications offers a clear, precise, and conceptually rich introduction to one of the most fundamental areas of mathematics. Far beyond abstract formalism, partial differential equations form the language through which the laws of nature are expressed, governing phenomena in physics, engineering, and the life sciences - from heat diffusion and wave propagation to fluid motion, electromagnetism, and quantum systems.This volume is designed for undergraduate and postgraduate students in mathematics, physics, and engineering, as well as for motivated self-learners and researchers seeking a unified and reliable reference. It balances mathematical depth with conceptual clarity, integrating theory and application so that abstract methods emerge from physical motivations.This book includes: Fundamental definitions, classification, and formation of partial differential equations First-order partial differential equations: method of characteristics, Lagrange's method, Charpit's method, and applications such as transport equations and Burgers' equation Second-order partial differential equations: classification into hyperbolic, parabolic, and elliptic types, canonical forms, and associated physical models Separation of variables and Sturm-Liouville theory, with orthogonal functions and eigenfunction expansions Fourier series and Fourier transforms, convergence theorems, Parseval's identity, and applications to the heat and wave equations The heat, wave, and Laplace equations in one or more dimensions, steady-state and time-dependent solutions, and coordinate-based techniques Laplace transform methods for problems on semi-infinite domains, impulsive sources, and delta function initial conditions Each chapter is structured to develop both analytical techniques and physical insight, supported by solved examples, graded exercises, and pedagogical explanations. Special attention is given to connecting mathematical derivations with their physical interpretations, ensuring the reader gains not only procedural skill but also a comprehensive insight of the underlying principles of the subject.
College Placement Math Workbook
College Placement Math Mastery: Complete Tutorials & Practice Workbook with 200+ QuestionsYou have arrived!Here is everything you need to pass this tough test!We have helped thousands of students and we can help you!Over 200 College math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies!College Math Practice Questions and Tutorials for: Basic MathScientific NotationExponents and Radicals Square RootFractions, Decimals and PercentMeans, Median and ModesAlgebra Solve real world problems with ratio and proportion Solve one and two variable equations Identify and solve quadratic equations given values or graphs Solve quadratic using different methods Translate real world problems into quadratic equa-tions and solve Basic Geometry Slope of a line Identify linear equations from a graph Calculate perimeter, circumference and volume Solve problems using the Pythagorean theorem Determine geometric transformations You also receive: Math Multiple Choice Strategy- How to Study for a Math Test- How to make a study plan- How to Take a TestHeard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book.Remember though, it only a few percentage points divide the PASS from the FAIL students!
An Invitation to Real Analysis
Adopting a student-cantered approach, this book anticipates and addresses the common challenges that students face when learning abstract concepts like limits, continuity, and inequalities. The text introduces these concepts gradually, giving students a clear pathway to understanding the mathematical tools that underpin much of modern science and technology. In addition to its focus on accessibility, the book maintains a strong emphasis on mathematical rigor. It provides precise, careful definitions and explanations while avoiding common teaching pitfalls, ensuring that students gain a deep understanding of core concepts. Blending algebraic and geometric perspectives to help students see the full picture. The theoretical results presented in the book are consistently applied to practical problems. By providing a clear and supportive introduction to real analysis, the book equips students with the tools they need to confidently engage with both theoretical mathematics and its wide array of practical applications.Features- Student-Friendly Approach making abstract concepts relatable and engaging.- Balanced Focus combining algebraic and geometric perspectives.- Comprehensive Coverage: Covers a full range of topics, from real numbers and sequences to metric spaces and approximation theorems, while carefully building upon foundational concepts in a logical progression.- Emphasis on Clarity: Provides precise explanations of key mathematical definitions and theorems, avoiding common pitfalls in traditional teaching. - Perfect for a One-Semester Course: Tailored for a first course in real analysis.- Problems, exercises and solutions.
Model Theory, Computer Science, and Graph Polynomials
This festschrift honors Johann A. Makowsky on the occasion of his 75th birthday. Gathering 24 research articles authored by scientific companions, friends, and colleagues, it covers a broad variety of areas to which Johann A. Makowsky made significant contributions himself. These include several areas of mathematical logic and its relevance for Computer Science including Graph polynomials, Algorithms for graph invariants, Algorithms and descriptive complexity theory, complexity of real and algebraic computations, Mathematical logic, Model theory, Design and theory of databases, Logic in computer science and AI and Logic programming. The volume is enriched with 4 biographical essays, and two contributions by the celebrant himself.
Eleven-Digit Regular Sexagesimals and Their Recipricols
This is a print on demand edition of an important, hard-to-find publication. Illustration.
The Mathematicians' Library
Discover the story of mathematics like never before with The Mathematicians' Library, an extraordinary collection that chronicles the evolution of mathematical thought and its profound impact on the world. This expertly curated anthology brings together the most influential works and authors from across history, showcasing the journey of mathematical discovery from ancient tablets to contemporary volumes.The Mathematicians' Library takes you through the pages of history, featuring groundbreaking works like Euclid's Elements, Fibonacci's Liber Abaci, Hilbert's Foundations of Geometry, and Mandelbrot's The Fractal Geometry of Nature. Each book offers a unique glimpse into how mathematics has shaped human civilization, guiding everything from transportation and commerce to art, science, and beyond.Mathematics is the invisible force that governs our daily lives, influencing everything from the weather forecasts we trust to the technology we depend on. It has been a cornerstone of human progress, evolving through centuries of research, discovery, and collaboration across cultures. This book reveals that legacy by presenting works that have changed the way we understand our world, from ancient knowledge inscribed on clay tablets, the contributions of Babylonian, Greek, Roman, Chinese, Islamic, and Maya scholars, The Mathematicians' Library offers unparalleled access to the greatest minds in mathematics--Plato, Pythagoras, Euclid, Hypatia, Galileo, Einstein, and more.The Mathematicians' Library is more than just a collection; it's a journey through the intellectual milestones that have defined our understanding of the world. Whether you're a scholar, a history enthusiast, or simply curious about the forces that shape our lives, this collection will captivate and inspire. Unlock the secrets of mathematics and discover the brilliance behind the numbers that rule our world. Table of contents: IntroductionThe Origins of MathematicsPrehistoricThe Global Evolution of Mathematics (Babylon, Egypt, Greece, Rome, China, India, Islam, Maya, Medieval Europe)The Scientific RevolutionModern MathematicsThe FutureBibliographyIndex
Freedom in Mathematics
This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and C矇dric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. C矇dric Villani's popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.
Compact Closed 2-Categories
While the Cobordism Hypothesis provides a translation between topological and categorical structures, the subject of fusion categories arising from representations of finite groups has shown the need for a robust theory of duality in monoidal 2-categories. This book intertwines 3-dimensional category theory with enriched and symmetric monoidal 2-categories to present a comprehensive foundation for duals in dimension two. This framework is presented using wire diagrams, a typographical tool that combines the geometric appeal of ordinary string diagrams with the clarity of standard commutative diagrams in category theory. Chapters on enriched 2-categories, closed 2-categories, and compact closed 2-categories build the theory from the ground up and in full detail. Shorter appendices on technical topics from higher category theory such as icons, strictification theorems, and computads provide readers with concise explanations of key results, as well as references for researchers interested in more depth. The book concludes with a chapter of examples from algebra and topology, including a detailed construction for the example of cobordisms.
Exact Methods for Nonlinear Pdes
Exact Methods for Nonlinear PDEs describes effective analytical methods for finding exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations and also demonstrates the practical applications of these methods. It covers the methods of generalized separation of variables, methods of functional separation of variables, the classical method of symmetry reductions, the direct method of symmetry reductions, the method of weak symmetry reductions, and the method of differential constraints. The book presents several simple methods for finding exact solutions to nonlinear partial differential equations (PDEs). These methods do not require specialized knowledge and aim to minimize intermediate calculations. For the first time, it discusses the application of nonrigorous, intuitive reasoning in deriving exact solutions to nonlinear PDEs.Each section provides numerous examples, problems, and exercises to help readers develop practical skills in applying the methods. The material is illustrated with equations of mass and heat transfer, hydrodynamics, wave theory, nonlinear optics, and other nonlinear equations of mathematical physics. The key points that distinguish this book from others in the field include: - it presents many methods in a simpler and more visual format; - it describes a number of simple methods for constructing exact solutions to nonlinear PDEs and delay PDEs;- it emphasizes and details the practical use of non-rigorous reasoning to derive exact solutions for nonlinear PDEs. The book is intended for a diverse audience, including researchers, university professors, engineers, postgraduates, and students specializing in applied mathematics, theoretical physics, and engineering sciences.
Asclepius of Tralles
This is a print on demand edition of an important, hard-to-find publication.
The Fundamentals of Fractional Calculus
Fractional calculus is one of the most important divisions of theoretical and applied mathematics. This new book presents a wide variety of interesting technologies and practices used in fractional calculus, providing detailed insight into recent developments and the latest research in the field of science, engineering, etc., using fractional calculus.The result of the teaching experiences of the editors and authors to engineering and science students, the volume discusses fractional calculus via generalized functions and integral transforms of pathway type; Laplace transformation of fractional integrals and derivatives; estimating the order of derivation in a fractional differential equation; a new class of integro-differential equations with non-singular differential operators; various uses of the Caputo approach; a gingerbread-man discrete system; etc. The various applications of fractional calculus are shown with examples such as for creating and/or solving epidemic models, alcoholism models, model for divorce dynamics, and more.Giving a rigorous and thorough analysis of various aspects of fractional calculus, this volume helps scientific readers as well as researchers working in the area of fractional calculus to establish the key steps followed in the research methodology and concept development.
Error Functions - Approximations and Implementations with modern FORTRAN. Volume I
