A Complete System of Mensuration of Superficies and Solids, of All Regular Figures, Calculated for the Use of Schools, Academies, and Private Learners
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Topology of Manifolds. --
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Practical Analysis
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Meta - Ecosystem Dynamics
This book presents current meta-ecosystem models and their derivation from classical ecosystem and metapopulation theories. Specifically, it reviews recent modelling efforts that have emphasized the role of nonlinear dynamics on spatial and food web networks, and which have cast their implications within the context of spatial synchrony and ecological stoichiometry. It suggests that these recent advances naturally lead to a generalization of meta-ecosystem theories to spatial fluxes of matter that have both a trophic and non-trophic impact on species. Ecosystem dynamics refers to the cycling of matter and energy across ecological compartments through processes such as consumption and recycling. Spatial dynamics established its ecological roots with metapopulation theories and focuses on scaling up local ecological processes through the limited movement of individuals and matter. Over the last 15 years, theories integrating ecosystem and spatial dynamics have quickly coalesced into meta-ecosystem theories, the focus of this book. The book will be of interest to graduate students and researchers who wish to learn more about the synthesis of ecosystem and spatial dynamics, which form the foundation of the theory of meta-ecosystems.
Chasing Rabbits
Curiouser and Curiouser . . .Mainstream math education over the last century has concretized an approach to mathematics that is rote, anxiety-producing, and far too focused on outcomes rather than the journey of discovery. In Chasing Rabbits, educator Sunil Singh offers an approach to mathematics that advocates getting lost, slowing down, feeling bewildered and disoriented, and even failing. Engaging with math in this way, he argues, can not only accomplish greater buy-in and enjoyment from math learners, but it can also affirm our sense of humanity and wellness overall. Singh invites the reader to explore his philosophy of mathematics through relating math to other disciplines, and to figures as diverse as MC Escher and Anthony Bourdain. Singh also delves into variously complex mathematical problems to offer concrete examples of what doing math differently looks and feels like. Mathematics, Singh demonstrates, ought to be a site not of stress and anxiety, but of wonder and joy.Endorsements"If you want to learn about what it's like to live a mathematical life by sitting around the campfire with a mug of cocoa, listening to a great storyteller who has done just that, this book is for you. It's superb. I loved it."-Keith Devlin, Stanford University"This book is a fascinating journey that illuminates the wonder, joy, and beauty of mathematics!"-Trena Wilkerson, NCTM president"Sunil Singh is a powerful storyteller who paints a vivid picture of mathematical wellness."-Mona Toncheff, NCSM president"Insightful introspections, rich rumination, and unexpected metaphors abound in this book!"-Francis Su, author of Mathematics for Human Flourishing
Basic Trigonometry In One Week
Basic Trigonometry In One Week: With an introduction to brain based learning (BBL)This book is not a complete solution to all learning problems. But it is certainly a beginning in the right direction. It stands out from its competitors due to its radical approach to the principles and techniques of learning.The book starts off by presenting what it is and what it isn't. Then challenges the reader to self examine who they are."Are you fast learner, or a slow learner. Are you good at math, or having a hard time with it"It goes on to discuss fast learning vs slow learning, also detailing the procedures involved in an effective learning process with an exposition on Brain Based Learning (BBL).Learning techniques like spaced repetition and active recalling using flash cards are discussed in great detail.It also discusses the benefits of meditation methods to achieve a focused mindset necessary for learning.The trigonometry part is divided into 7 chapters-"The Seven Days", each consisting of 3 sessions, making a total of 21 sessions.In addition to numerous examples and problems, the chapters contain explanations on some basic questions in mathematics like: Why can't we divide by zero?Why a complete rotation is 360 degrees?What is the difference between an equation and an identity? etc.Problem solving is regarded with high importance, since entire sessions are dedicated to them.The book features topics like: Angles and its unitsTrigonometric functionsPythagoras TheoremTrigonometric IdentitiesProving IdentitiesQuadrants and sign conventionAllied anglesDouble and triple angle formulaeTips and tricks for memorizing formulae at the end of each chapter.Final Quiz for final brush upAnd many more...
Introduction to Trigonometry
The branch of mathematics which studies the relationship between side lengths and angles of triangles is known as trigonometry. This field of study is considered to be the foundation of all applied geometry. The real functions which relate an angle of a right-angled triangle to ratios of two side lengths are called trigonometric functions. They have a wide range of applications in astronomy, music theory, electronics, medical imaging and optics. Astronomy uses the trigonometric technique of triangulation to measure the distance to nearby stars. A few important concepts within trigonometry are triangle identities and trigonometric identities. This book presents the complex subject of trigonometry in the most comprehensible and easy to understand language. It will prove to be immensely beneficial to students and researchers in this field. Coherent flow of topics and extensive use of examples make this book an invaluable source of knowledge.
Wavelet Theory: Developments and Applications
Wavelets are functions fulfilling certain mathematical requirements and used in representing data or other functions. The application of wavelet transformation to examine the behavior of complex systems from several fields has begun to be widely identified and applied successfully during the past few decades. The book selectively deals with two major aspects of Wavelet Transformation such as Image Processing and Applications in Engineering. One of the important characteristics of this book is that the wavelet concepts that are applied in engineering, physics and technology have been discussed from a point of view that is recognizable to researchers from different branches of science and engineering. The book is worth utility to a large number of readers interested in the field of study.
Essential Concepts in Mathematics
Mathematics is a vast field of study with applications in all major fields of science, engineering, business, economics, computer science and many more. Mathematics uses the tools of measurement, calculations, algebra, etc. to study concepts such as shape, quantity, structure and change. Some of the major branches of mathematics are algebra, calculus, geometry, topology, number theory, probability and statistics. The chapters included herein explore all the important aspects of mathematics in the present day scenario. It strives to provide a fair idea about this discipline and to help develop a better understanding of the latest advances within this field. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of knowledge.
Finite Element Analysis: Biomedical Aspects
Finding approximate solutions to partial differential equations and integral equations, allowing numerical assessment of complicated structures based on their material properties is best represented by the mathematical method of Finite Element Analysis. This book presents varied topics on the utilization of Finite Elements in biomedical engineering under two sections on "Dentistry, Dental Implantology and Teeth Restoration" and "Cardiovascular and Skeletal Systems". The structure and language of the book has been so written that it is useful for graduate students learning applications of finite element and also encompasses topics and reference material useful for research and professionals who want to gain a deeper knowledge of finite element analysis.
Computational and Applied Mathematics: Volume I
This book attempts to understand the multiple branches and research projects that fall under the field of computational mathematics and how such research can be useful in our lives. The various projects that are constantly contributing towards advancing technologies and the evolution of this field are looked at in detail here. Those in search of information to further their knowledge of this field will be greatly assisted by this book.
Computational and Applied Mathematics: Volume III
This book attempts to understand the multiple branches and research projects that fall under the field of computational mathematics and how such research can be useful in our lives. The various projects that are constantly contributing towards advancing technologies and the evolution of this field are looked at in detail here. Those in search of information to further their knowledge of this field will be greatly assisted by this book.
Integrated Applications of Cellular Automata
This book describes the integrated applications of cellular automata with the help of valuable information. Cellular automata have become an important topic in the sciences of complexity due to their conceptual simplicity, easiness of implementation for computer simulation and ability to exhibit a wide variety of intricate behavior. These attributes of cellular automata have drawn attention of researchers from a multitude of various fields of science. This book describes some exceptionally innovative cellular automata applications. It highlights the versatility of cellular automata as a model for a diversity of complex systems. This book is an attempt to bring across the efforts of engineers and scientists about the application of cellular automata for solving practical problems in diverse disciplines. All the authors have made substantial contributions in the diverse topics of cellular automata covered in this book.
Stochastic Chemical Reaction Systems in Biology
This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.
Fuzzy Systems: Theory and Applications
A control system which operates on fuzzy logic is known as a fuzzy system or a fuzzy control system. Fuzzy logic is a mathematical system which does not operate on absolute binary values of 0 or 1, but instead analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1. Fuzzy systems have found a variety of uses in different fields, from vacuum cleaners to autofocusing cameras and air conditioners. The design of the fuzzy control system is based on empirical methods, which is basically a methodical approach to trial and error. Fuzzy control systems is an upcoming field of science that has undergone rapid development over the past few decades. The extensive content of this book provides the readers with a thorough understanding of the subject.
Computational and Applied Mathematics: Volume IV
This book attempts to understand the multiple branches and research projects that fall under the field of computational mathematics and how such research can be useful in our lives. The various projects that are constantly contributing towards advancing technologies and the evolution of this field are looked at in detail here. Those in search of information to further their knowledge of this field will be greatly assisted by this book.
Mathematical and Scientific Analysis Handbook
In simple terms, analysis refers to the breaking down of complex data, materials, compounds, topics or any other substance to derive a simpler form. From chemistry to business, espionage and computer science, analysis has applications in almost all walks of life. Though as a concept, analysis is relatively new. Constant research is happening across the globe which has broadened the horizon of study of this discipline. This book takes a look at various aspects of analysis and the related advancements happening in diverse fields. It is a compilation of materials sent forth by experts in different subjects and domains.
Computational and Applied Mathematics: Volume V
This book attempts to understand the multiple branches and research projects that fall under the field of computational mathematics and how such research can be useful in our lives. The various projects that are constantly contributing towards advancing technologies and the evolution of this field are looked at in detail here. Those in search of information to further their knowledge of this field will be greatly assisted by this book.
Calculus: The Basics
The mathematical study of continuous change is known as calculus. There are two major divisions of calculus, known as differential calculus and integral calculus. The instantaneous rates of change and the slope of curves is studied under differential calculus. Integral calculus deals with the accumulation of quantities and areas between and under the curves. The link between these two branches is known as the fundamental theorem of calculus. This theorem states that differentiation and integration are inverse operations. Calculus finds its application in every field where a problem can be mathematically modeled and where an optimal solution is sought. Therefore, it is used in all branches of physical science, actuarial science, computer science, statistics, engineering and a variety of other disciplines. The topics covered in this extensive book deal with the core aspects of calculus. It is appropriate for students seeking detailed information in this area as well as for experts. The book will serve as a valuable source of reference for graduate and post graduate students.
Fuzzy Systems: Theory and Researches
The scope of Fuzzy Systems is now being expanded as it is now being incorporated in different scientific researches. This book contains researches concerning the theory and applications of fuzzy subsets and systems. This book on fuzzy systems is a collective contribution of a highly advanced group of international authors. Different approaches, evaluations, methodologies and advanced studies on fuzzy systems have been included in this book. The numerous applications of fuzzy systems in different areas of science such as medical science and environmental science have also been included in this book.
Computational and Applied Mathematics: Volume II
This book attempts to understand the multiple branches and research projects that fall under the field of computational mathematics and how such research can be useful in our lives. The various projects that are constantly contributing towards advancing technologies and the evolution of this field are looked at in detail here. Those in search of information to further their knowledge of this field will be greatly assisted by this book.
Bifurcation and Chaos in Science and Engineering
The bifurcation and chaos in science and engineering has been elaborately discussed in this up-to-date book. The aim of this book is to introduce both theoretical and application oriented approaches in science and engineering. It is intended to assist scientists, engineers, teachers, researchers, as well as graduate and post-graduate students either engaged or interested in this field.
Industrial Aspects of Finite Element Analysis
Finding approximate solutions to partial differential equations, and integral equations, allowing numerical assessment of complicated structures based on their material properties is best represented by the mathematical method of Finite Element Analysis. This book presents varied topics on the utilization of Finite Elements, varying from manufacturing technology to industrial developments. The structure and language of the book has been so written that it is useful for graduate students learning 'applications of finite element modeling and analysis' and also encompasses topics and reference material useful for research and professionals who want to gain a deeper knowledge of finite element analysis.
Fractional Calculus: Theory and Applications
Fractional calculus falls under the domain of mathematical analysis. It focuses on the study of the differentiation operator in terms of real and complex number powers. Fractional calculus has various applications across other scientific fields such as polymer chemistry through structural damping models, in quantum theory through the analysis of Schr繹dinger's equation, etc. This book elucidates new techniques and their applications in a multidisciplinary manner. The chapters provide significant information of this field to help develop a good understanding of fractional calculus and related fields. It also attempts to understand the multiple branches that fall under this discipline and how such concepts have practical applications. It aims to serve as a resource guide for students and experts alike as well as contribute to the growth of the discipline.
Matrix And Determinants In One Week
Matrix And Determinants In One Week -With an introduction to brain based learning (BBL)This book is not a complete solution to all learning problems. But it is certainly a beginning in the right direction. It stands out from its competitors due to its radical approach to the principles and techniques of learning.The book starts off by presenting what it is and what it isn't. Then challenges the reader to self examine who they are."Are you fast learner, or a slow learner. Are you good at math, or having a hard time with it"It goes on to discuss fast learning vs slow learning, also detailing the procedures involved in an effective learning process with an exposition on Brain Based Learning (BBL).Learning techniques like spaced repetition and active recalling using flash cards are discussed in great detail.It also discusses the benefits of meditation methods to achieve a focused mindset necessary for learning.The Matrix part is divided into 7 chapters-"The Seven Days", each consisting of 3 sessions, making a total of 21 sessions.In addition to numerous examples and problems, the chapters contain explanations on some basic questions in mathematics like: Why can't we divide by zero?What exactly is a determinant?Where do matrices come from? etc..Problem solving is regarded with high importance, since entire sessions are dedicated to them.The book features topics like: Vectors and MatricesMatrix additionMatrix multiplicationRow Echelon formElementary Row OperationsInverse of a matrixLinear SystemsGaussian eliminationCramer's ruleRank of a matrixMinors, cofactors and adjointsShortcuts for finding determinants and inversesFinal Quiz for final brush upAnd many more..Visit: Neo Learning Books on google.
The Construction of Mathematics
Is mathematics created or discovered? The answer has been debated for centuries. This book answers the question clearly and decisively by applying the concept of language games, invented by the philosopher Wittgenstein to solve difficult philosophical issues. Using the results of modern brain science, the book also explains how it is possible that eminent mathematicians and scientists offer diametrically opposed answers to the question of creation vs. discovery. Interested in the topic but intimidated by mathematics? Not to worry. If you are familiar with the elementary operations of addition, subtraction, multiplication, and division, you can follow the arguments of this book.
Tales of Impossibility
A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems-squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle-have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs-which demonstrated the impossibility of solving them using only a compass and straightedge-depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Vi癡te, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.
An Analytical Technique to Solve the System of Non-Linear Korteweg-De Vries Equation (KdV), FPDE
Bachelor Thesis from the year 2021 in the subject Mathematics - Miscellaneous, Federal Urdu University, language: English, abstract: Dive into the complex world of nonlinear dynamics with a groundbreaking exploration of fractional calculus and its application to solving some of the most challenging equations in mathematical physics. This book introduces a novel analytical method, a beacon of innovation in the field of fractional partial differential equations (FPDEs), specifically targeting the elusive solutions of nonlinear fractional Korteweg-de Vries (KdV) systems. By masterfully weaving together the classical power of the Laplace transform with a fresh, cutting-edge analytical approach, this study unveils a new pathway for understanding and solving these intricate equations. At the heart of this methodology lies the Caputo fractional derivative, a cornerstone of fractional calculus, enabling a more accurate and nuanced modeling of real-world phenomena. The journey begins with a comprehensive introduction to fractional calculus, contrasting it with its integer-order counterpart and tracing its historical roots from the early inquiries of Leibniz and L'Hopital to the pivotal contributions of Laplace and Liouville. Discover how the KdV equation, a fundamental model for solitary waves, finds new life through the lens of fractional calculus. This book meticulously constructs the theoretical framework, defining essential mathematical tools such as the Gamma function and rigorously establishing the properties of the Laplace transform. A detailed convergence analysis provides a solid foundation for the practical application of this method. Explore worked examples that showcase the method's efficacy and illuminate the path for researchers and students alike. This book is an invaluable resource for those seeking to push the boundaries of knowledge in fractional calculus, nonlinear systems, and the development of novel analytical techniques for solving FPDEs. Unlock the se
G繹del's Theorems and Zermelo's Axioms
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of G繹del's classical completeness and incompleteness theorems. In particular, the book includes a full proof of G繹del's second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo's axioms, containing a presentation of G繹del's constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
K繹nnen Hunde Rechnen?
Wenn auch Sie sich zum Beispiel schon oft gefragt haben, ob Hunde rechnen k繹nnen, wie man das Gewicht eines Schweines berechnet oder worin der Unterschied zwischen gro?en und riesengro?en Zahlen liegt, finden Sie in diesem Buch, in seiner aktualisierten und erweiterten Auflage, die mathematischen L繹sungen. Au?erdem ist ein komplett neues Kapitel 羹ber Mathematik und Corona hinzugekommen, in dem das Ph瓣nomen des exponentiellen Wachstums mit Hilfe von Schachbrettern und Haien genauer unter die Lupe genommen wird. Entdecken Sie auf humorvolle Weise, welche 羹berraschenden Erkl瓣rungen Ihnen die Mathematik f羹r allt瓣gliche Fragen zu bieten hat.
Selected Topics from Contemporary Logics
As used by professional logicians today, is the name of their chosen subject singular or plural, "logic" or "logics"? This is a special case of a more general question. For instance, an algebraist might write a book entitled "Algebra", which is about algebras. Though many mathematicians are not aware of it, logic today most decidedly has its plural aspect. Indeed, it always did. Classical logic, which mathematicians often tend to identify with the entirety of logic, was in place roughly by the beginning of the twentieth century. Since then a wide range of so-called non-classical logics have been developed. But indeed, before the creation of classical logic, there were multiple versions of logic, some of them more-or-less formalized. The current growing interest in medieval and ancient European and Asian logics has brought much of this back to modern awareness. Perhaps a later volume in this series will look at the history from a contemporary viewpoint. But that is not our task here.This is the second volume in a series called Landscapes in Logic. The intention of the series is to present reports illustrating the interplay between contemporary work in logic and mainstream mathematics. Of course this is both vague and overly ambitious, and must result in heterogeneous collections. The first volume in the series, Contemporary Logic and Computing, appeared in 2020. The contents divided plausibly into topics from contemporary logic, and from contemporary computing. The present volume is more diverse, and includes articles about both classical and non-classical logics, sometimes from the semantic side and sometimes from the proof-theoretic side. Some articles are primarily technical, often algebraic, while others are more philosophical in nature. Many fit into multiple categories. This multiplicity should not be seen as a defect. The papers here do not just explore logics house by house, but say something about their general neighborhoods as well.
Non-Standard Analysis
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Introduction to Partial Differential Equations
The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.
The Search for Mathematical Roots, 1870-1940
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schr繹der, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and G繹del. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and G繹deI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
The Mathematical Career of Pierre de Fermat, 1601-1665
Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.
Lectures on Hermite and Laguerre Expansions. (Mn-42), Volume 42
The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.
Introduction to Ergodic Theory
Based on lectures in Erevan, this exposition of ergodic theory contains a rich collection of examples well chosen to introduce the reader to the main themes of the subject. Topics discussed include existence of invariant measures, geodesic flows on Riemannian manifolds, ergodic theory of an ideal gas, and entropy of dynamical systems.
McGraw-Hill Dictionary of Mathematics
Derived from the content of the respected McGraw-Hill Dictionary of Scientific and Technical Terms Sixth Edition, each title provides thousands of definitions of words and phrases encountered in a specific discipline. All include: * Pronunciation guide for every term * Acronyms, cross-references, and abbreviations * Appendices with conversion tables; listings of scientific, technical, and mathematical notation; tables of relevant data; and more * A convenient, quick-find format
The Concise Oxford Dictionary of Mathematics
With over 4,000 entries, this informative A to Z provides clear, jargon-free definitions on a wide variety of mathematical terms. Its entries cover both pure and applied mathematics, and include key theories, concepts, methods, programmes, people, and terminology. For this sixth edition, around 800 new terms have been defined, expanding on the dictionary's coverage of topics such as algebra, differential geometry, algebraic geometry, representation theory, and statistics. Among this new material are articles such as cardinal arithmetic, first fundamental form, Lagrange's theorem, Navier-Stokes equations, potential, and splitting field. The existing entries have also been revised and updated to account for developments in the field. Numerous supplementary features complement the text, including detailed appendices on basic algebra, areas and volumes, trigonometric formulae, and Roman numerals. Newly added to these sections is a historical timeline of significant mathematicians lives and the emergence of key theorems. There are also illustrations, graphs, and charts throughout the text, as well as useful web links to provide access to further reading.
Mathematics and Plausible Reasoning
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Textbook of Mathematics
The discipline of mathematics is concerned with the study of topics such as quantity, space, change and structure. It uses patterns for the formulation of new conjectures. Pure mathematics and applied mathematics are two of the major domains of mathematics. Pure mathematics focuses on the study of mathematical concepts such as quantity and structure. Applied mathematics deals with the application of mathematical concepts in different fields such as computer science, engineering, business, science and industry. Some of the other subdisciplines within this field are arithmetic, geometry, algebra and analysis. The concepts included in this book on mathematics are of utmost significance and bound to provide incredible insights to readers. Some of the diverse topics covered herein address the varied branches that fall under this category. Those with an interest in this field would find it helpful.
Calculus: An Introduction
Calculus refers to the mathematical study of continuous change. The major branches of calculus are differential calculus and integral calculus. Differential calculus is concerned with the immediate rate of change and the slopes of curves. Integral calculus focuses on the accumulation of quantities and the areas under and between curves. Both branches are connected by the fundamental theorem of calculus. They utilize the fundamental concepts of convergence of infinite sequences and infinite series to a well-defined limit. Calculus is used in various branches of physical sciences, computer science, statistics, engineering, economics, business, actuarial science and demography. It is also used in various other fields where a problem is capable of being mathematically modeled and where an optimal solution is required. This textbook outlines the processes and applications of calculus in detail. It presents this complex subject in the most comprehensible and easy to understand language. The book will serve as a reference to a broad spectrum of readers.
Boundary Layer Flows: A Mathematical Approach
The layer of fluid wherein the effects of viscosity are significant and which exists in the immediate vicinity of a bounding surface is known as a boundary layer. Boundary layer equations such as Bernoulli's equation, Prandtl's transposition theorem, energy integral, Von Mises transformation, and Crocco's transformation equations are necessary for the understanding of boundary layer flows. They are also a vital point of fluid dynamics. In mathematical analysis of fluid dynamics, one of the central problems is the asymptotic limit of the fluid flow as viscosity becomes zero. This book unravels the recent studies in the field of boundary layer flows. It will also provide interesting topics for research which interested readers can take up. This book is a vital tool for all researching or studying about boundary layer flows as it gives incredible insights into emerging trends and concepts.
Math Workshop for Children - D, Teacher's Guide; Level D, Teacher's Guide
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
High School Mathematics, Second Course; 1
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Digest of High School Mathematics ..
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lectures_on_the_philosophy_of_mathematics
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Contextualized Mathematics
Whether you are an educator, student, researcher, or administrator, it has become even more critical now more than ever to understand what contextualized math curriculum is and how it can be applied inside an online or face-to-face math classroom. What is contextualized mathematics? What are the foundational research underpinnings of contextualized math curriculum? What have we learned about contextualized math curriculum that will improve math education in the future? These questions build the foundation for a reader to begin a journey with Dr. Valenzuela on this crucial topic for math education and for our society
