![The Elements of Euclid for the Use of Schools and Colleges [microform]](https://cdn.kingstone.com.tw/english/images/product/9409/9781013899409m.webp "The Elements of Euclid for the Use of Schools and Colleges [microform]")
How to talk about Mathematics. Wie man 羹ber Mathematik spricht.
In this booklet, you find the language of describing and explaining mathematical concepts, symbols, and procedures in English and German. This booklet is intended to assist people who have to learn, to teach or to apply mathematics while using English or German as a foreign language. In diesem B羹chlein findet man die Sprache der Beschreibung und Erkl瓣rung mathematischer Begriffe, Symbole und Prozeduren. Dieses B羹chlein soll Leute unterst羹tzen, die Mathematik lernen, anwenden oder lehren m羹ssen, w瓣hrend sie Englisch oder Deutsch als Fremdsprache nutzen.
Varia Mesopotamica
The central theme of the 21 essays collected here and written between 1989 and 2019 is Ancient Mesopotamian Mathematics - its techniques and concepts, but also its historical dynamics and its influence on later Greek and Arabic (and thus to later European) mathematical reasoning. In addition, the first essay deals with historical dynamics in the field of language and argues that the Sumerian as a language originated from a creole language of the slaves of the late fourth millennium and only thereafter developed into the elaborate Sumerian language attested in the late 3rd Millennium BCE.
BustaBit
BustaBit: History, Strategies, and Mathematics of the Original Crash Game By Lennart Lopin Unlock the Secrets Behind the Game That Changed Crypto Gambling Forever. In BustaBit, Lennart Lopin pulls back the curtain on the first and most iconic Bitcoin crash game - the phenomenon that fused cryptocurrency, game theory, and human psychology into one electrifying experience. From its wild beginnings in Bitcoin's early days to its survival through a decade of volatility, Bustabit is a living experiment in risk, randomness, and raw decision-making. This book is the ultimate Bustabit bible: - The origin story of how crash gambling was born - The hidden mathematics driving every multiplier - Winning strategies and losing mindsets exposed - The psychology of gamblers, traders, and adrenaline-seekers - The rise of automation, bots, and the API underground - Hard lessons from real legends who won - and lost - fortunes If you love Bitcoin, gaming, statistics, trading, behavioral economics, or just crave a brutally honest exploration of what happens when money meets math meets human nature, this is the book you can't afford to miss. Learn what the house doesn't tell you. Play smarter. Understand deeper. Whether you're a seasoned crypto gambler, a curious trader, or a student of human behavior under pressure - BustaBit will change how you see risk, forever. Ready to outthink the crash? Start your journey today.
Mathematics
This book tells the stories of some of the great quests of mathematics, such as the centuries-long pursuit for the proof of Fermat's Last Theorem. These quests are searches for difficult-to-discover universal truths, pursued with passion not only by mathematicians and scientists, but by kings, emperors and even Jean-Luc Picard, the captain of Star Trek's Starship Enterprise. Some of their exploits are adventures as fascinating as any historical or current-day drama. The truths they have discovered help us understand not only mathematics, but also the Universe - and sometimes, ourselves.In addition to well-known quests such as Fermat's Last Theorem and the Goldbach Conjecture, some of the chapters describe more recent pursuits such as the Traveling Salesman Problem and the Multi-armed Bandit Problem. While some of the quests have been completed, others are still ongoing, and one (the Six Squares Problem) can be understood - and maybe even solved - by a five-year-old child.
Mathematics
This book tells the stories of some of the great quests of mathematics, such as the centuries-long pursuit for the proof of Fermat's Last Theorem. These quests are searches for difficult-to-discover universal truths, pursued with passion not only by mathematicians and scientists, but by kings, emperors and even Jean-Luc Picard, the captain of Star Trek's Starship Enterprise. Some of their exploits are adventures as fascinating as any historical or current-day drama. The truths they have discovered help us understand not only mathematics, but also the Universe - and sometimes, ourselves.In addition to well-known quests such as Fermat's Last Theorem and the Goldbach Conjecture, some of the chapters describe more recent pursuits such as the Traveling Salesman Problem and the Multi-armed Bandit Problem. While some of the quests have been completed, others are still ongoing, and one (the Six Squares Problem) can be understood - and maybe even solved - by a five-year-old child.
Time Series
Time series analysis is one of several branches of statistics whose practical importance has increased with the availability of powerful computational tools. Methodology that was originally developed for specialized applications, for example in finance or geophysics, is now widely available within general statistical packages. The second edition of Time Series: A Biostatistical Introduction is an introductory account of time series analysis, written from the perspective of applied statisticians whose interests lie primarily in the biomedical and health sciences. This edition has a stronger focus on substantive applications, in which each statistical analysis is directed at a specific research question. Separate chapters cover simple descriptive methods of analysis, including time-plots, smoothing, the correlogram and the periodogram; theory of stationary random processes; discrete-time models for single series; continuous-time models for single series; generalized linear models for time series of counts; models for replicated series; spectral analysis, and bivariate time series. The book is unique in its focus on biomedical and health science applications, which has been strengthened in this second edition. Nevertheless, the methods described are more widely applicable. It should be useful to teachers and students on masters-level degree courses in statistics, biostatistics and epidemiology, and to biomedical and health scientists with a knowledge of statistical methods at undergraduate level. Throughout, examples based on real datasets show a close interplay between statistical method and substantive science. This book will also describe the implementation of the methods in the R computing environment and provide access to R code and datasets.
Decision Making Optimization Models for Business Partnerships
Efficiency and productivity improvement are imperative for businesses to remain competitive in an increasingly dynamic marketplace. While business organizations have the potential to thrive independently, collaborating with others fosters a collective strength that can lead to greater innovation, expanded reach, and shared success.Decision making optimization models for business partnerships are essential, as businesses seldom have all the resources they need, and thus, they require alliances and partnerships with others to enable them to meet their goals. Decision Making Optimization Models for Business Partnerships extends non-parametric data envelopment analysis (DEA) and parametric econometrics approaches to better understand how economic efficiency and market competitiveness are achieved for different types of partnerships and strategic alliances.Features Global contributions for a wide range of professionals and academics Invaluable resources for businesses, analysts, and academics interested in DEA, optimization, and operations research more widely Introduces readers to novel approaches, models, and decision making techniques on performance evaluation and business partnerships via the medium of parametric and nonparametric optimization.
An Introduction to String Diagrams for Computer Scientists
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
Ideal Theory of Commutative Rings and Monoids
This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Pr羹fer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.
An Introduction to String Diagrams for Computer Scientists
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
Your First Calculus Journey
Your First Calculus Journey is a beginner-friendly guide that breaks down the fundamental concepts of calculus into simple, relatable explanations. Designed for those who are new to the concepts of calculus, this book aims to make complex mathematical ideas easy to grasp by using real-world examples and step-by-step explanations. Readers will explore essential topics such as functions, graphs, limits, derivatives, and integral. From understanding how a bike's speed relates to derivatives to visualizing integrals as filling a swimming pool, each chapter builds a strong foundation for deeper mathematical concepts. With clear explanations, coherent examples, and engaging visuals, Your First Calculus Journey is the perfect starting point for anyone to grasp the calculus concepts. Whether you're preparing for an upcoming class or simply curious about how calculus shapes the world, this book will guide you every step of the way.
Your First Calculus Journey
Your First Calculus Journey is a beginner-friendly guide that breaks down the fundamental concepts of calculus into simple, relatable explanations. Designed for those who are new to the concepts of calculus, this book aims to make complex mathematical ideas easy to grasp by using real-world examples and step-by-step explanations. Readers will explore essential topics such as functions, graphs, limits, derivatives, and integral. From understanding how a bike's speed relates to derivatives to visualizing integrals as filling a swimming pool, each chapter builds a strong foundation for deeper mathematical concepts. With clear explanations, coherent examples, and engaging visuals, Your First Calculus Journey is the perfect starting point for anyone to grasp the calculus concepts. Whether you're preparing for an upcoming class or simply curious about how calculus shapes the world, this book will guide you every step of the way.
Generalized Quantum Calculus with Applications
Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula. Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.
Time Series: A Biostatistical Introduction
Time series analysis is one of several branches of statistics whose practical importance has increased with the availability of powerful computational tools. Methodology that was originally developed for specialized applications, for example in finance or geophysics, is now widely available within general statistical packages. The second edition of Time Series: A Biostatistical Introduction is an introductory account of time series analysis, written from the perspective of applied statisticians whose interests lie primarily in the biomedical and health sciences. This edition has a stronger focus on substantive applications, in which each statistical analysis is directed at a specific research question. Separate chapters cover simple descriptive methods of analysis, including time-plots, smoothing, the correlogram and the periodogram; theory of stationary random processes; discrete-time models for single series; continuous-time models for single series; generalized linear models for time series of counts; models for replicated series; spectral analysis, and bivariate time series. The book is unique in its focus on biomedical and health science applications, which has been strengthened in this second edition. Nevertheless, the methods described are more widely applicable. It should be useful to teachers and students on masters-level degree courses in statistics, biostatistics and epidemiology, and to biomedical and health scientists with a knowledge of statistical methods at undergraduate level. Throughout, examples based on real datasets show a close interplay between statistical method and substantive science. This book will also describe the implementation of the methods in the R computing environment and provide access to R code and datasets.
A Course in Game Theory
Game theory is a fascinating subject. We all know many entertaining games, such as chess, poker, tic-tac-toe, bridge, baseball, computer games - the list is quite varied and almost endless. In addition, there is a vast area of economic games, discussed in Myerson (1991) and Kreps (1990), and the related political games [Ordeshook (1986), Shubik (1982), and Taylor (1995)]. The competition between firms, the conflict between management and labor, the fight to get bills through congress, the power of the judiciary, war and peace negotiations between countries, and so on, all provide examples of games in action. There are also psychological games played on a personal level, where the weapons are words, and the payoffs are good or bad feelings [Berne (1964)]. There are biological games, the competition between species, where natural selection can be modeled as a game played between genes [Smith (1982)]. There is a connection between game theory and the mathematical areas of logic and computer science. One may view theoretical statistics as a two-person game in which nature takes the role of one of the players, as in Blackwell and Girshick (1954) and Ferguson (1968).Games are characterized by a number of players or decision makers who interact, possibly threaten each other and form coalitions, take actions under uncertain conditions, and finally receive some benefit or reward or possibly some punishment or monetary loss. In this text, we present various mathematical models of games and study the phenomena that arise. In some cases, we will be able to suggest what courses of action should be taken by the players. In others, we hope simply to be able to understand what is happening in order to make better predictions about the future.
Mathematics for Data Science and Artificial Intelligence
This book provides a comprehensive foundation in the mathematical tools essential for modern data science and machine learning. It blends core subjects such as linear algebra, calculus, probability, statistics, optimization, and numerical methods with real-world applications. Readers explore matrix operations, eigenvalues, and dimensionality reduction techniques like PCA and t-SNE. Optimization is covered through gradient-based methods and regularization strategies. Probability theory, Bayes' theorem, and statistical inference form the basis for modeling uncertainty. Information theory concepts like entropy, cross-entropy, and KL divergence are applied to learning and feature selection. Efficient computational methods are introduced using Python/Numpy implementations. Advanced topics include graph theory for network analysis and stochastic models such as Markov chains and ARIMA for time series forecasting. This book bridges theory and practice, offering step-by-step problem-solving, coding exercises, and a deep understanding of the mathematical backbone driving AI and data science.
Polygraphs: From Rewriting to Higher Categories
This is the first book to revisit the theory of rewriting in the context of strict higher categories, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. Illustrated with algorithmic computations on algebraic structures, the only prerequisite in this section is basic category theory. The theory is introduced step-by-step, with detailed proofs. The second half introduces and studies the general notion of n-polygraph, before addressing the homotopy theory of these polygraphs. It constructs the folk model structure on the category on strict higher categories and exhibits polygraphs as cofibrant objects. This allows the formulation of higher-dimensional generalizations of the coherence results developed in the first half. Graduate students and researchers in mathematics and computer science will find this work invaluable.
Geocomputation with R
Geocomputation with R is for people who want to analyze, visualize, and model geographic data with open source software. The second edition features numerous updates, including the adoption of the high-performance terra package for all raster data processing.
Elements Of Arithmetic
Unlock the timeless wisdom of numbers with "Elements of Arithmetic" by Augustus De Morgan, a masterpiece that has been out of print for decades and is now beautifully restored by Alpha Editions. This isn't just a reprint; it's a collector's item and a cultural treasure, meticulously revived for today's and future generations. Dive into the mind of one of history's greatest mathematical thinkers as De Morgan unravels the mysteries of arithmetic with clarity and elegance. This classic work offers a unique blend of rigorous logic and engaging narrative, making complex concepts accessible to all. Whether you're a casual reader or a devoted collector of classic literature, this edition promises to enrich your understanding and appreciation of mathematics. Experience the joy of discovery as you explore the foundational principles that have shaped modern arithmetic. With its timeless insights and enduring value, "Elements of Arithmetic" is more than a book it's a journey into the heart of mathematical beauty. Don't miss the chance to own this exquisite piece of literary history, lovingly restored for you to cherish and enjoy.
Essentials of Nonlinearity Bifurcation and Chaos Theory
"Essentials of Nonlinearity, Bifurcation, and Chaos Theory" provides a concise yet comprehensive overview of these fundamental concepts in dynamical systems theory. This book introduces readers to the principles of nonlinear dynamics, bifurcation theory, and chaos theory, exploring their applications across various scientific disciplines. Through clear explanations and illustrative examples, readers gain insight into the behavior of nonlinear systems, including their stability, bifurcation points, and chaotic dynamics. Whether you're a student, researcher, or practitioner in fields such as physics, engineering, biology, or economics, this book serves as an essential guide to understanding the intriguing phenomena of nonlinearity, bifurcation, and chaos and their implications for modeling and analysis in complex systems.
Introduction to Modern Algebra
It covers a range of topics related to the study of algebra, from the basics of set theory to advanced topics such as Galois Theory and representation theory. The book begins with an overview of modern algebra and its importance in various fields of mathematics and also covers the history and development of ring theory, including its applications in algebraic geometry and number theory.The book covers the basics of set theory, including the axioms of set theory and cardinality and introduces module theory, which is a generalization of vector spaces, and its applications in various fields of mathematics.The book discusses the applications of commutative algebra in algebraic geometry and algebraic number theory and also includes a discussion of current research topics in group theory.The book covers the history and development of Galois Theory and discusses the importance of representation theory in various fields of mathematics, including physics and geometry.It is suitable for undergraduate and graduate students as well as researchers in mathematics and related fields.
Modern Trigonometry
"Modern Trigonometry" provides a comprehensive overview of trigonometric principles, techniques, and applications in contemporary mathematics and scientific inquiry. Through collaboration with experts, this book covers topics such as trigonometric functions, identities, equations, vectors, complex numbers, Fourier analysis, and applications in fields such as physics, engineering, computer graphics, and signal processing. With theoretical foundations and practical applications, readers gain a thorough understanding of modern trigonometry. Bridging theory and application, this book empowers readers to appreciate the beauty and utility of trigonometric concepts in the modern age.
Introduction to Finite Elements in Engineering
"Introduction to Finite Elements in Engineering" provides a comprehensive introduction to the fundamentals of finite element analysis and its application in engineering problem-solving. Through collaboration with experts, this book covers topics such as mathematical foundations, element formulations, numerical techniques, software tools, and practical applications in structural, thermal, and fluid analysis. With theoretical explanations and practical examples, readers gain insights into understanding and applying FEA concepts in engineering practice. Bridging theory and application, this book empowers readers to leverage the power of computational simulation to innovate and advance engineering design and analysis.
Fundamentals of Coordinate Geometry
Coordinate geometry is the study of geometric figures by plotting them in the coordinate axes.The content of the book is sequentially presented in the book for easy and comprehensive learning.This book forms a strong basis for students, teachers, researchers, and person engaged in the field of mathematics.
Handbook of Algebra and Algebraic Topology
Covering all aspects of Elementary Algebra, it will surely serve as the complete elementary textbook for studying different concepts.The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples.The content of the book is sequentially presented in the book for easy and comprehensive learning.This book forms a strong basis for students and teachers engaged in the field of mathematics especially algebra and algebraic topology.
Fractional Order PID and ADR Controls
This book explores the design and analysis of fractional-order and active disturbance rejection control, examining both the theoretical foundations and their practical applications.It covers fractional-order proportional-integral-derivative (PID) control, fractional-order active disturbance rejection (ADR) control, and the combined fractional-order PID-ADR control. The book begins with an analysis of the three-parameter fractional-order PID controller, demonstrating its application to the permanent magnet synchronous motor (PMSM) speed servo system, due to its comprehensive inclusion of proportional, integral, and differential elements. It then delves into active disturbance rejection control and periodic disturbance compensation, comparing the performance of each controller based on various parameters. This comparison enables readers to critically evaluate the advantages and limitations of each approach before implementation. Offering a thorough guide to fractional-order and active disturbance rejection control, the book also includes numerical methods for assessing and developing these systems.The book will be of particular interest to professionals working with numerical methods, fractional-order systems and control, PID controller, active disturbance rejection, control design, and production and is especially relevant to those in mechanical, industrial, and electrical engineering.
Beyond Signals - Exploring Revolutionary Fourier Transform Applications
Fourier Transform is a fundamental mathematical framework that has revolutionized numerous scientific and technological domains. Beyond Signals - Exploring Revolutionary Fourier Transform Applications presents an in-depth analysis of its profound influence on modern research and industry. This volume explores advanced applications in signal processing, spectroscopy, quantum mechanics, biomedical imaging, nanomaterials, and renewable energy, illustrating how Fourier techniques enable precise data interpretation and system optimization. The book integrates theoretical foundations with practical implementations, offering insights into its role in material characterization, sensor technology, and computational modeling. Authored by distinguished experts, including Dr. Muhammad Bilal Tahir-recognized for his contributions to nanomaterials, optoelectronics, and applied physics-this work is a comprehensive resource for researchers, engineers, and scholars. By bridging classical theories with emerging advancements, Beyond Signals - Exploring Revolutionary Fourier Transform Applications highlights the transformative potential of Fourier Transform methodologies in solving complex scientific and engineering challenges.
AP Calculus Study Guide AP 微积分 AB/BC 指导用书
本书是一部系统全面的微积分教程，涵盖了从基础概念到高级应用的完整内容。书中包括了极限与连续性、微分及其基本性质、复合函数的微分、积分及其累积变化、微分方程和积分应用等主题。内容结构清晰，循序渐进，辅以大量的例题和解析，帮助学生理解并掌握微积分的核心概念及解题技巧，特别适用于准备AP微积分的学习者。这部书为学生提供了深入的理论知识和实用的数学工具，使其能更好地理解和应用微积分于实际问题中。This book is a systematic and comprehensive calculus tutorial that covers a complete range of content from basic concepts to advanced applications. The book includes topics such as limits and continuity, differentiation and its basic properties, differentiation of composite functions, integration and its cumulative change, differential equations, and applications of integration. With a clear content structure and a step-by-step approach, it is supplemented by a large number of examples and analyses to help students understand and master the core concepts of calculus and problem-solving techniques. It is especially suitable for learners preparing for AP Calculus. This book provides students with in-depth theoretical knowledge and practical mathematical tools, enabling them to better understand and apply calculus to practical problems.
The Geometry of Equilibrium
James Clerk Maxwell is one of the giants of scientific thought, and whilst his groundbreaking contributions to electromagnetism and statistical physics are well known, his profound insights into the theory of structures are appreciated less widely. Maxwell's approach was deeply geometrical, and this richly illustrated book reveals his astute perception of the remarkable dualities that exist between the form of a structure and the forces it can carry, with understandings that will surprise contemporary readers. Early chapters introduce the background in which Maxwell was working, followed by contributions by leading researchers describing the latest applications of these ideas. Subsequent chapters introduce the many subtopics that this work embraces. The book ends with Maxwell's original papers on structural mechanics, each annotated to highlight and explain the ideas therein. This is a wonderful resource for mathematicians, scientists, engineers, and designers to enter this rich and underexplored aspect of the genius of Maxwell.
Mathematica
A fascinating look into how the transformative joys of mathematical experience are available to everyone, not just specialists Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet the greatest mathematicians throughout history, from Ren矇 Descartes to Alexander Grothendieck, have insisted that this is not the case. Like Albert Einstein, who famously claimed to have "no special talent," they said that they had accomplished what they did using ordinary human doubts, weaknesses, curiosity, and imagination. David Bessis guides us on an illuminating path toward deeper mathematical comprehension, reconnecting us with the mental plasticity we experienced as children. With simple, concrete examples, Bessis shows how mathematical comprehension is integral to the great learning milestones of life, such as learning to see, to speak, to walk, and to eat with a spoon. Focusing on the deeply human roots of mathematics, Bessis dispels the myths of mathematical genius. He offers an engaging initiation into the experience of math not as a series of discouragingly incomprehensible logic problems but as a physical activity akin to yoga, meditation, or a martial art. This perspective will change the way you think not only about math but also about intelligence, intuition, and everything that goes on inside your head.
A Little History of Mathematics
A lively, accessible history of mathematics throughout the ages and across the globe Mathematics is fundamental to our daily lives. Science, computing, economics--all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from? In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad's House of Wisdom, and sangaku geometrical theorems at Japanese shrines. Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy Noether and Maryam Mirzakhani.
HESI Math Workbook
Over 200 HESI A2(R) practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! You have arrived!Here is everything you need to pass the HESI(R) Math! We have helped thousands of students and we can help you!Complete HESI Math workbook, prepared by exam experts, with over 200 questions. Basic MathSolving Word ProblemsSolve Algebra EquationsMetric ConversionData InterpretationWhy Us?The Complete Test Preparation Team has been publishing high quality study materials since 2005, with a catalogue of over 145 titles, in English, French and Chinese, as well as ESL curriculum for all levels.You have come to the right place.If you want to spend your valuable study time where it will help you the most - we've got you covered today and tomorrow.You can pass the HESI with a great score! Here is how! You already know that Practice Makes Perfect! The more questions you see, and the more you practice - the better your HESI score! HESI A2(R) Math practice questions, easy-to-read tutorials explaining everything in plain language, exam tips and tricks, math shortcuts, and multiple choice strategies! Everything you need, complied by a dedicated team of experts with everything you need all in one place! Please note that HESI(R) is a registered trademark of the Health Education Systems Inc., which was not involved in the production of, and does not endorse, this product. Practice Really Does Make Perfect! The more questions you see, the more likely you are to pass the test. And between our study guide and practice tests, you'll have over 200 practice questions that cover every category. Our practice test questions have been developed by our dedicated team of experts. All the material in the study guide, including every practice question, are designed to engage your critical thinking skills needed to pass the test! Heard 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! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Solution of Initial-Boundary Value Problems
Methods for solving problems of mathematical physics can be divided into the following four classes. Analytical methods (the method of separation of variables, the method of characteristics, the method of Green's functions, etc.) methods have a relatively low degree of universality, i.e. focused on solving rather narrow classes of problems. Approximate analytical methods (projection, variational methods, small parameter method, operational methods, various iterative methods) are more versatile than analytical ones. Numerical methods (finite difference method, direct method, control volume method, finite element method, etc.) are very universal methods. Probabilistic methods (Monte Carlo methods) are highly versatile. Can be used to calculate discontinuous solutions. However, they require large amounts of calculations and, as a rule, they lose with the computational complexity of the above methods when solving such problems to which these methods are applicable. Comparing methods for solving problems of mathematical physics, it is impossible to give unconditional primacy to any of them. Any of them may be the best for solving problems of a certain class. The proposed method of moving nodes for boundary value problems of differential equations combines a combination of numerical and analytical methods. In this case, we can obtain, on the one hand, an approximately analytical solution of the problem, which is not related to the methods listed above. On the other hand, this method allows one to obtain compact discrete approximations of the original problem. Note that obtaining an approximately analytical solution of differential equations is based on numerical methods. The nature of numerical methods also allows obtaining an approximate analytical expression for solving differential equations
Carleman Estimates in Mean Field Games
This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems. MFG theory can govern a range of societal phenomena, including finance, sociology, machine learning, and economics. The focus is on the system of two coupled nonlinear parabolic partial differential equations (PDEs) that define the Mean Field Games System. The book covers key theoretical topics such as solution stability and uniqueness, with a particular emphasis on Carleman estimates, which are used to estimate solution errors based on noise in the input data. It also introduces the theory of Ill-Posed and Inverse Problems within MFG theory. Both theoretical and numerical aspects of forward and inverse problems are explored through Carleman estimates, offering a rigorous foundation for researchers and practitioners in applied mathematics and related fields. This book offers a rigorous approach to Carleman estimates, a key element of Mean Field Games theory, making it an essential resource for researchers, graduate students, and professionals looking to apply this powerful framework to complex, real-world systems.
Multivariable Calculus
Foundations of Multivariable Functions: Provide a comprehensive introduction to functions of multiple variables, including definitions, graphical interpretations, and basic properties. Cover topics such as partial derivatives, gradient vectors, and the concept of differentiability for functions of several variables.Multiple Integration Techniques: Explore techniques for evaluating multiple integrals, including double and triple integrals. Discuss applications of multiple integrals in calculating areas, volumes, and other physical quantities. Include methods for changing variables, such as polar, cylindrical, and spherical coordinates.Vector Calculus and Field Theory: Examine key concepts in vector calculus, including vector fields, line integrals, surface integrals, and flux. Discuss fundamental theorems such as Green's Theorem, Stokes' Theorem, and the Divergence Theorem, and their applications in physics and engineering.Optimization and Constrained Optimization: Discuss methods for optimization in multivariable settings, including finding local and global extrema of functions. Cover techniques such as Lagrange multipliers for constrained optimization problems and the use of Hessian matrices for analyzing critical points.Applications and Advanced Topics: Address various applications of multivariable calculus in fields such as physics, engineering, economics, and computer science. Include advanced topics such as differential forms, manifold theory, and the applications of multivariable calculus in differential equations and dynamical systems.
Introductory Discrete Mathematics
Fundamental Concepts: Provide an overview of foundational concepts in discrete mathematics, including sets, relations, functions, and basic logic. Explain how these concepts form the basis for more advanced topics in discrete mathematics.Combinatorics and Counting: Explore combinatorial methods and counting principles, including permutations, combinations, the pigeonhole principle, and inclusion-exclusion principles. Discuss their applications in solving counting problems and understanding discrete structures.Graph Theory: Introduce the basics of graph theory, including definitions and properties of graphs, types of graphs (e.g., directed, undirected, weighted), and key concepts such as paths, cycles, connectivity, and graph coloring.Applications of Discrete Mathematics: Explore the practical applications of discrete mathematics in computer science, including its role in cryptography, network design, coding theory, and algorithm design. Discuss how discrete mathematics provides tools for solving real-world problems in these areas.
Handbook of Calculus of Variations for Absolute Beginners
The book aims at endowing any student with a survival toolkit to start safely diving into the realm of Calculus of Variations. In summary, the latter is a part of mathematical analysis devoted to minimization/maximization problems. A great effort has been made to present the themes and methods considered in the book in the simplest possible way: the reader will not find here general statements or proofs based on general abstract theories. In contrast, the main focus of the book is on introducing some key concepts "from scratch", by means of simple and meaningful explicit examples (including for instance, the classical isoperimetric and brachistocrone problems, as well as the boundary value problem for harmonic functions). In particular, the book is mainly (but not exclusively) designed to smoothly introduce the reader to the so-called Direct Method of the Calculus of Variations, which is a central concept in the field. Accordingly, a good part of the book is devoted to discussing spaces of weakly differentiable functions (i.e., Sobolev and Lipschitz functions), which are essential tools of the Direct Method. A long list of problems will guide the student through the study of the subject. Almost all the problems come with their fully detailed solutions. The book is complemented by four appendices, which contribute to making it self-contained, as well as to deepening the study of certain parts. Despite being designed for students, even the researchers in the field could find a reading of the book profitable, at least for certain parts concerning the properties of Sobolev spaces, functional inequalities of the Sobolev-Poincar矇 type, tricks to handle nonlinear elliptic PDEs, and a gentle introduction to some techniques of modern regularity theory for elliptic PDEs.
Mathematical Modeling and Control of COVID-19 and Its Variants
In this book, we developed a new hybrid deterministic model, we do this by considering several essential properties of the pandemic COVID-19, such as the existence of individuals tested positive for COVID-19 with severe, mild, or asymptomatic symptoms, and dividing infectious compartment into two essential compartments of hospitalized individuals and those in intensive care units. The content of this book is divided into 3 chapters: In the first chapter, we study the stability properties of the solutions of a proposed nonlinear mathematical model with nine compartments, namely, susceptible-exposed infectious with severe symptoms-infectious with mild symptoms-asymptomatic infectious-hospitalized intensive care unit-dead infectious corpses-recovered to investigate the current outbreak of coronavirus disease (COVID-19) in Morocco and beyond. In the second chapter, we employed the control theory procedure to better understand the ways to maintain the progression of the COVID-19 outbreak and its variant Omicron in a case study of Morocco by designing optimal disease intervention strategies.The third chapter is devoted to expand the proposed nonlinear model into a fractional-order COVID.
Vector Calculus
It strives to present the material in a clear and accessible manner, with a focus on providing practical examples and applications to various fields such as physics, engineering, computer graphics, and more.Covers the essential concepts of vectors in three-dimensional Euclidean space and explains vector operations, including addition, subtraction, scalar multiplication, and dot product.Discusses partial derivatives, gradient vectors, directional derivatives, and tangent planes and also provides a comprehensive introduction to double and triple integrals.Demonstrates techniques for evaluating integrals using different coordinate systems and covers line integrals and their relationship to work and circulation.This book serves as a valuable resource for students studying mathematics, physics, engineering, and related disciplines. It also serves as an excellent reference for professionals seeking a concise and practical guide to vector calculus.
Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications
This Special Issue of Axioms entitled "Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking, and Their Applications" consists of a collection of ten papers written by eminent mathematicians and experts in their fields, covering numerous different areas of fuzzy MCDM, hybrid methods, ranking methods, and/or their applications. The objective of this Special Issue is to provide a platform for researchers to publish their recent work, delve deeper into various problems, and solve them mathematically.
Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups
An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields Exponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck's creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne's theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions. This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.
