Groups Of The Order P^M Which Contain Cyclic Subgroups Of Order P^(M-3)
Foundations of Numerical Methods and Data Analysis
This book offers a comprehensive journey into the world of numerical methods, beginning with the essential mathematical preliminaries: calculus, vectors, matrices, and programming concepts before moving into deeper areas such as error analysis, curve fitting, interpolation, and the numerical solution of ordinary and partial differential equations. Advanced chapters extend into systems of equations, finite element methods, and spectral techniques, ensuring that readers not only understand the fundamentals but also gain exposure to methods at the frontier of computational practice. A distinguishing feature of the book is the integration of theory with practice. Each concept is accompanied by carefully chosen examples, figures, and end- of-chapter exercises designed to strengthen understanding and encourage hands-on application. Historical notes and bibliographical references enrich the discussion, situating modern numerical methods in their broader intellectual context. In addition, the book pays special attention to the use of contemporary computational tools such as MATLAB, Python, and other numerical libraries, thereby bridging traditional methods with current software-driven practice. In short, it is both a textbook and a reference, meant to serve readers across different stages of their academic or professional journey. For more details, please visit https: //centralwestpublishing.com
Advanced Analytical and Numerical Methods with their Application to Industrial Problems
This book covers the models of different real-world problems that include the models using ordinary and partial differential equations and dynamical systems, uncertainty quantifications using fuzzy systems, computational methods for differential equations, modern control theory and applications, neural networks and neural computing, computational heat and mass transfer and computational fluid dynamics. It also includes various research problems on developing advanced analytical and numerical methods for solving real-world situations, with its theoretical derivations and engineering and science applications. For more details, please visit https: //centralwestpublishing.com
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.
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.
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.
Statistics for Composite Indicators
This book provides a systematic and integrated approach to construct measures of complex and multidimensional concepts called composite indicators. One of the most pressing needs of scientists and policy makers is to measure phenomena that are important to our lives in society using numbers, to observe their evolution over time, and to analyse the relationships between them in order to understand the complex reality and decide on the right actions to achieve specific goals. Many socio-economic phenomena, as well as ecological, biological and of other sciences, are multidimensional and, to be measured, require the use of statistical-mathematical techniques that facilitate their reading and use for studies and analyses. This book is a guide to the knowledge and application of statistical tools suitable for the construction of "optimal" composite indicators, i.e. indicators that provide the most accurate measure of multidimensional reality. The book is aimed at all those - statisticians, sociologists, economists, and policy makers - who wish to construct composite indicators to measure and evaluate the complex reality that surrounds us.
Unequal
Why the familiar equal sign isn't just a marker of sameness but a gateway into math's--and humanity's--most profound questions Math is famous for its equations: 1 + 1 = 2, a^2 + b^2 = c^2, or y = mx + b. Much of the time it can seem like that's all mathematics is: following steps to show that what's on one side of an equation is the same as what's on the other. In Unequal, Eugenia Cheng shows that's just part of the story, and the boring part to boot. Mathematics isn't only about showing how numbers and symbols are the same. It isn't even just about numbers and symbols at all, but a world of shapes, symmetries, logical ideas, and more. And in that world, the boundary between things being equal and unequal is a gray area, or perhaps a rainbow of beautiful, vibrant, subtly nuanced color. As Unequal shows, once you go over that rainbow, almost everything can be considered equal and unequal at the same time, whether it's shapes (seen from the right perspective, a circle is the same as an ellipse), words (synonyms), or people--even numbers! It all depends on what features we care about. And it's up to us what we do about it. That's because mathematics isn't a series of rules, facts, or answers. It's an invitation to a more powerful way of thinking.
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.
Classical Mechanics
Classical Mechanics is a textbook for undergraduate students majoring in Physics (or Mathematics and Physics). The book introduces the main ideas and concepts of Newtonian, Lagrangian and Hamiltonian mechanics, including the basics of rigid body motion and relativistic dynamics, at an intermediate to advanced level. The physical prerequisites are minimal, with a short primer included in the first chapter. As to the mathematical prerequisites, only a working knowledge of linear algebra, basic multivariate calculus and the rudiments of ordinary differential equations is expected.Features- Numerous exercises and examples- A focus on mathematical rigour that will appeal to Physics students wanting to specialize in theoretical physics, or Mathematics students interested in mathematical physics- Sufficient material to service either a one or two semester course.
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?
Lectures on the Theory of Plane Curves; Delivered to Post-graduate Students in the University of Calcutta
Essays in Classical Number Theory
Offering a comprehensive introduction to number theory, this is the ideal book both for those who want to learn the subject seriously and independently, or for those already working in number theory who want to deepen their expertise. Readers will be treated to a rich experience, developing the key theoretical ideas while explicitly solving arithmetic problems, with the historical background of analytic and algebraic number theory woven throughout. Topics include methods of solving binomial congruences, a clear account of the quantum factorization of integers, and methods of explicitly representing integers by quadratic forms over integers. In the later parts of the book, the author provides a thorough approach towards composition and genera of quadratic forms, as well as the essentials for detecting bounded gaps between prime numbers that occur infinitely often.
A Primer on Semiconvex Functions in General Potential Theories
This book examines the symbiotic interplay between fully nonlinear elliptic partial differential equations and general potential theories of second order. Starting with a self-contained presentation of the classical theory of first and second order differentiability properties of convex functions, it collects a wealth of results on how to treat second order differentiability in a pointwise manner for merely semicontinuous functions. The exposition features an analysis of upper contact jets for semiconvex functions, a proof of the equivalence of two crucial, independently developed lemmas of Jensen (on the viscosity theory of PDEs) and Slodkowski (on pluripotential theory), and a detailed description of the semiconvex approximation of upper semicontinuous functions. The foundations of general potential theories are covered, with a review of monotonicity and duality, and the basic tools in the viscosity theory of generalized subharmonics, culminating in an account of the monotonicity-duality method for proving comparison principles. The final section shows that the notion of semiconvexity extends naturally to manifolds. A complete treatment of important background results, such as Alexandrov's theorem and a Lipschitz version of Sard's lemma, is provided in two appendices. The book is aimed at a wide audience, including professional mathematicians working in fully nonlinear PDEs, as well as master's and doctoral students with an interest in mathematical analysis.
Recent Progress Numeric Analy Nonlinear Dispersive Equation
This book presents an overview of recent advances in the numerical analysis of nonlinear dispersive partial differential equations (PDEs) - including the nonlinear Schr繹dinger equation, the Korteweg-de Vries (KdV) equation, and the nonlinear Klein-Gordon equation. These fundamental models are central to mathematical physics and computational PDE theory, and their analysis, both individually and through asymptotic relationships, has become an active and evolving area of research.Recent progress includes the extension of harmonic analysis tools, such as Strichartz estimates and Bourgain spaces, into discrete settings. These innovations have improved the accuracy and flexibility of numerical methods, especially by relaxing regularity assumptions on initial data, potentials, and nonlinearities. Additionally, enhanced long-time numerical estimates now support simulations over substantially longer time intervals, expanding the practical reach of computational models.The analytical breakthroughs that underpin these developments trace back to the seminal work by Jean Bourgain in the 1990s, which introduced powerful techniques for studying dispersive PDEs. Adapting these continuous tools to discrete frameworks has proven both challenging and rewarding, offering new insights into the interface between numerical computation and theoretical analysis.Aimed at graduate students, researchers, and practitioners in numerical analysis, applied mathematics, and computational physics, this volume provides a clear entry point into cutting-edge research, supported by a rich bibliography for further exploration.
Communicating the Quantum Way
The book consists of scientific essays dedicated to A S Holevo on the occasion of his 80th birthday, written by prominent researchers in theoretical-mathematical physics. It is a snapshot of contemporary research at the frontier of quantum information science, work that builds on Holevo's pioneering contributions during the decades of his distinguished career.While a portion of the book are the 15 articles published in a special issue of IJQI, the book contains additional material such as a summary of Holevo's scientific life, with comments on research directions not covered in the 15 articles, and the list of his publications.
Social Impact of Ai: Research, Diversity and Inclusion Frameworks
The workshop proceedings SIAI 2025 constitutes the refereed proceedings of the fourth International Workshop on Social Impact of AI, SIAI 2025, which was held in Philadelphia, PA, USA, in March 2025. The 8 full papers, 4 short papers, and one poster presented in these proceedings were carefully reviewed and selected from 26 submissions. SIAI-ReDI 2025 centered on the development and assessment of inclusive AI frameworksthat prioritize ethical design, equitable deployment, and cultural context. The workshop'scall for papers invited submissions across a range of urgent topics, including: Algorithmic fairness and transparencyInclusive AI education and workforce strategiesAI in marginalized and underrepresented communitiesIntersectionality, gender, and accessibility in AICross-cultural AI governance and regulationPublic trust, participatory AI, and responsible design
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
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.
Data Clustering with Python
Data clustering, an interdisciplinary field with diverse applications, has gained increasing popularity since its origins in the 1950s. Over the past six decades, researchers from various fields have proposed numerous clustering algorithms. In 2011, I wrote a book on implementing clustering algorithms in C++ using object-oriented programming. While C++ offers efficiency, its steep learning curve makes it less ideal for rapid prototyping. Since then, Python has surged in popularity, becoming the most widely used programming language since 2022. Its simplicity and extensive scientific libraries make it an excellent choice for implementing clustering algorithms.Features: - Introduction to Python programming fundamentals- Overview of key concepts in data clustering- Implementation of popular clustering algorithms in Python- Practical examples of applying clustering algorithms to datasets- Access to associated Python code on GitHubThis book extends my previous work by implementing clustering algorithms in Python. Unlike the object-oriented approach in C++, this book uses a procedural programming style, as Python allows many clustering algorithms to be implemented concisely. The book is divided into two parts: the first introduces Python and key libraries like NumPy, Pandas, and Matplotlib, while the second covers clustering algorithms, including hierarchical and partitional methods. Each chapter includes theoretical explanations, Python implementations, and practical examples, with comparisons to scikit-learn where applicable.This book is ideal for anyone interested in clustering algorithms, with no prior Python experience required. The complete source code is available at: https: //github.com/ganml/dcpython.
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.
Eleven-Digit Regular Sexagesimals and Their Recipricols
This is a print on demand edition of an important, hard-to-find publication. Illustration.
Mathematical Methods for Accident Reconstruction
Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective, Second Edition demonstrates the application of mathematics to modeling accident reconstructions involving a range of moving vehicles, including automobiles, small and large trucks, bicycles, motorcycles, all-terrain vehicles, and construction equipment such as hoists and cranes.The book is anchored on basic principles of physics that may be applied to any of the above-named vehicles or equipment. Topics covered include the foundations of measurement, the various energy methods used in reconstruction, momentum methods, vehicle specifications, failure analysis, geometrical characteristics of highways, and softer scientific issues such as visibility, perception, and reaction. The authors examine the fundamental characteristics of different vehicles, discuss the retrieval of data from crash data recorders, and review low speed impacts with an analysis of staged collisions. Finally, the book details established standards and protocols for accident reconstruction--for use in both investigations and in the courtroom. In addition, this new edition covers non-vehicle related topics like slips and falls analysis, fall protection, as well as engine and mechanical failure as well as federal rules and laws that have been established for the work environment. Many reconstructions of incidents require extensive analysis that may require a variety of methods in order to properly model the incident.Exploring a broad range of accident scenarios, the breadth and depth of the book's coverage makes Mathematical Methods for Accident Reconstruction, Second Edition a critical reference for engineers and scientists who perform vehicular accident reconstructions.
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.
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.
