Elements Of Mathematics
John Muller's textbook provides an introduction to various branches of mathematics, including algebra, geometry, and trigonometry. Written for the Royal Academy of Artillery at Woolwich, this book is a comprehensive guide to the mathematical principles needed for military training. Both students and instructors will find this textbook helpful.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Advanced Part of A Treatise on the Dynamics of a System of Rigid Bodies
The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies is a foundational text in the field of mechanics. Written by Edward John Routh, one of the great mathematicians of the 19th century, this book is essential reading for anyone interested in the history and development of this field.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Practical Railway Spiral
This practical guide provides formulas, tables, and examples for railway spirals. It covers the deflection angles necessary for a spiral track and offers numerous illustrative examples. This is an essential reference for engineers and railway professionals.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Institutiones Calculi Integralis; Volume 3
Euler's groundbreaking work on calculus is presented in its entirety in this comprehensive book. A must-have for any mathematician, this book is a fascinating look at the development of calculus and its importance in modern 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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Treatise of Trigonometry, Plane and Spherical, Theoretical and Practical ...
This treatise is both theoretical and practical, and includes a section on stereographick and orthographick projection of the sphere. It is a detailed analysis of the subject, supported by numerous illustrations and examples.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Primary Arithmetic
Master the fundamentals of arithmetic with this comprehensive textbook, designed for graded schools. Featuring engaging exercises, colorful illustrations, and clear explanations, this book is an essential resource for students and educators alike.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Practical Mathematics For Home Study
This mathematics book is tailored for home study and covers arithmetic, geometry, algebra, and trigonometry.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Mathematical Gazette, Volume 1, Issues 1-6
This collection of the first six issues of The Mathematical Gazette includes articles on everything from elementary algebra to geometry to the use of logarithms. It's a fascinating look at the world of mathematics in the late 19th century.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Elementary Treatise on Geometrical Optics
This classic text provides a clear and concise introduction to the principles of geometrical optics. Heath's lucid explanations and helpful diagrams make this book an ideal resource for students and professionals in the field. Whether you are interested in the physics of light or practical applications of optics, this book will provide you with a solid foundation in the subject.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Martyrs of Florida (1513-1616) / by Luis Gero? nimo De Ore? ...translated With Biographical Introduction and Notes, by Maynard Geiger.
This historical account tells the story of the Catholic martyrs who were killed by the indigenous people of Florida in the sixteenth century. The book includes a biographical introduction to the author, Luis Ger籀nimo de Ore穩, as well as notes and annotations to provide historical context for the events described in the text.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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Enumerative Combinatorics: Volume 2
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson-Schensted-Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood-Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
How to Write∧Edit Your Scientific Article
Publications are the currency of academia. And yet, many people in the sciences, and especially mathematics, are never actually taught how to write. More specifically, they are not taught how to edit, redraft and revise their material so that the presentation is optimal for the reader. Most academic articles are appallingly written, even by native English speakers. One of the core problems is that most scientists hate writing and put only the bare minimum of effort into it. Furthermore, academic articles too often read like a first draft, with little understanding that all writing is editing. However, academic writing is a skill like any other that can be broken down into stages. This book will go through the detailed process of assembling an article, from first drafts to writing abstracts to revision to responding to reviewers, illustrated with multiple versions of worked examples as well as what not to do.
How to Write∧Edit Your Scientific Article
Publications are the currency of academia. And yet, many people in the sciences, and especially mathematics, are never actually taught how to write. More specifically, they are not taught how to edit, redraft and revise their material so that the presentation is optimal for the reader. Most academic articles are appallingly written, even by native English speakers. One of the core problems is that most scientists hate writing and put only the bare minimum of effort into it. Furthermore, academic articles too often read like a first draft, with little understanding that all writing is editing. However, academic writing is a skill like any other that can be broken down into stages. This book will go through the detailed process of assembling an article, from first drafts to writing abstracts to revision to responding to reviewers, illustrated with multiple versions of worked examples as well as what not to do.
Mathematical Imagining
Imagine a plastic cup lying on the floor. Give the cup a nudge so that it begins to roll.
The Semantic Conception of Logic
This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
Multiplicative Partial Differential Equations
This book presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs.
Problem Posing and Solving for Mathematically Gifted and Interested Students
Mathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights.
Reachability Problems
This book constitutes the refereed proceedings of the 17th International Conference on Reachability Problems, RP 2023, held in Nice, France, during October 11-13, 2023.The 13 full papers included in this book were carefully reviewed and selected from 19 submissions. They present recent research on reachability problems to promote the exploration of new approaches for the modeling and analysis of computational processes by combining mathematical, algorithmic, and computational techniques.
Optimal Fractionation in Radiotherapy
This monograph provides a mathematically rigorous overview of optimal fractionation in cancer radiotherapy, which seeks to address the fundamental tradeoff of maximizing tumor-kill while protecting nearby healthy tissue from toxic effects. Most mathematical research on exact solutions to this problem is scattered across journals in applied mathematics, operations research, radiobiology, medicine, and medical physics. These works rarely include rigorous proofs or detailed derivations of their methodologies. Moreover, computer programs utilized for conducting numerical experiments seldom accompany these publications, thereby jeopardizing reproducibility. This monograph aims to provide a comprehensive pedagogical reference that brings researchers up to speed on optimal fractionation, utilizing and illustrating analytical techniques from linear algebra, calculus, linear programming, quadratic and nonlinear programming, robust optimization, and inverse optimization. Its purpose is to help readers understand the mathematics behind the optimal fractionation problem, empowering them to contribute original work to this field.
Essays in Constructive Mathematics
This collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it. All definitions and proofs are based on finite algorithms, which pave illuminating paths to nontrivial results, primarily in algebra, number theory, and the theory of algebraic curves. The second edition adds a new set of essays that reflect and expand upon the first. The topics covered derive from classic works of nineteenth-century mathematics, among them Galois's theory of algebraic equations, Gauss's theory of binary quadratic forms, and Abel's theorems about integrals of rational differentials on algebraic curves. Other topics include Newton's diagram, the fundamental theorem of algebra, factorization of polynomials over constructive fields, and the spectral theorem for symmetric matrices, all treated using constructive methods in the spirit of Kronecker. In this second edition, the essays of the first edition are augmented with newessays that give deeper and more complete accounts of Galois's theory, points on an algebraic curve, and Abel's theorem. Readers will experience the full power of Galois's approach to solvability by radicals, learn how to construct points on an algebraic curve using Newton's diagram, and appreciate the amazing ideas introduced by Abel in his 1826 Paris memoir on transcendental functions. Mathematical maturity is required of the reader, and some prior knowledge of Galois theory is helpful. But experience with constructive mathematics is not necessary; readers should simply be willing to set aside abstract notions of infinity and explore deep mathematics via explicit constructions.
The Shape of Knowledge
The Shape of Knowledge is the outcome of a meaningful experience that occurred in 2012. In it are developed the foundations of a new science of philosophy, which promises to provide a solution to the disparity preventing our discourse from progress. Through the language of the Western canon, The Shape of Knowledge exposes the ubiquitous structure that conditions our capacity to reason the truth for our world. Then, through an investigation of the phenomenon of self-reference, in both the processes and products of thought, this structure is shown to necessitate its own existence. Underscoring it all is a principle of complementarity, which arises as the modality of the rationalisation of paradox. Experience is shown to be a relative process of making sense of the nonsensical nature of reality, and the emergence of paraphilosophy is our means of reconciling the present war of opposites--having now served its purpose--with the nondual nature of self-consciousness. Paraphilosophy is not an idea to be believed--it is the idea of the idea, which is our creative spirit. So this work is at root an inquiry into oneself.
Core Mathematics for High Schools
Core Mathematics for High School gives a fresh and easy approach for solving difficult high school level mathematics problems. By going through basic concepts in algebra, numbers, trigonometry, kinematics and more, this book allows the student to gradually build on their understanding and confidence in tackling tricky mathematics problems, regardless of the topic. Each chapter has several practice questions that will ensure the student has a clear understanding of key concepts and a variety of approaches to solving problems. Finally, at the back of the book there are step-by-step solutions to all practice questions so that the student can verify their answers.
Advances on Mathematical Modeling and Optimization with Its Applications
Advances on Mathematical Modeling and Optimization with Its Applications discusses optimization, equality, and inequality constraints and their application in the versatile optimizing domain. It further covers non-linear optimization methods such as global optimization, and gradient-based non-linear optimization, and their applications. Discusses important topics including multi-component differential equations, geometric partial differential equations, and computational neural systems Covers linear integer programming and network design problems, along with an application of the mixed integer problems Discusses constrained and unconstrained optimization, equality, and inequality constraints, and their application in the versatile optimizing domain Elucidates the application of statistical models, probability models, and transfer learning concepts Showcases the importance of multi-attribute decision modeling in the domain of image processing and soft computing The text is primarily for senior undergraduate and graduate students, and academic researchers in the fields of mathematics, statistics, and computer science.
Symmetric Cycles
This original research monograph concerns various aspects of how (based on the decompositions of vertices of hypercube graphs with respect to their symmetric cycles) the vertex sets of related discrete hypercubes, as well as the power sets of the corresponding ground sets, emerge from rank 2 oriented matroids, from underlying rank 2 systems of linear inequalities, and thus literally from arrangements of straight lines crossing a common point on a piece of paper. It reveals some beautiful and earlier-hidden fragments in the true foundations of discrete mathematics. The central observation made and discussed in the book from various viewpoints consists in that 2t subsets of a finite t-element set Et, which form in a natural way a cyclic structure (well, just t subsets that are the vertices of a path in the cycle suffice), allow us to construct any of 2t subsets of the set Et by means of a more than elementary voting procedure expressed in basic linear algebraic terms. The monograph will be of interest to researchers, students, and readers in the fields of discrete mathematics, theoretical computer science, Boolean function theory, enumerative combinatorics and combinatorics on words, combinatorial optimization, coding theory, and discrete and computational geometry.
The Splendors and Miseries of Martingales
Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler's holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally invarious applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.
Pre-Calculus All-In-One for Dummies
The easy way to understand and retain all the concepts taught in pre-calculus classes Pre-Calculus All-in-One For Dummies is a great resource if you want to do you best in Pre-Calculus. Packed with lessons, examples, and practice problems in the book, plus extra chapter quizzes online, it gives you absolutely everything you need to succeed in pre-calc. Unlike your textbook, this book presents the essential topics clearly and concisely, so you can really understand the stuff you learn in class, score high on your tests (including the AP Pre-Calculus exam!), and get ready to confidently move ahead to upper-level math courses. And if you need a refresher before launching into calculus, look no further--this book has your back. Review what you learned in algebra and geometry, then dig into pre-calculus Master logarithms, exponentials, conic sections, linear equations, and beyond Get easy-to-understand explanations that match the methods your teacher uses Learn clever shortcuts, test-taking tips, and other hacks to make your life easierPre-Calculus All-in-One For Dummies is the must-have resource for students who need to review for exams or just want a little (or a lot of!) extra help understanding what's happening in class.
The Equation of Knowledge
This book introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. .
Lesson Study with Mathematics and Science Preservice Teachers
This insightful volume offers an overview of the fundamentals of lesson student practice in US teacher education as well as examples from math and science teacher educators using lesson study in their local contexts.The number of teacher educators using lesson study with preservice teachers is small but growing. This book is aimed at teacher educators who may want to try lesson study in university contexts without the challenge of translating the practice from the K-12 context on their own. In this volume, lesson study is broadly overviewed, attention is given to its constituent steps, and examples of lesson study in preservice contexts are shared. Given the broad array of teacher education program designs, numerous contingencies guide teacher educators in their implementation of lesson study, given their contextual affordances and limitations. The lesson study descriptions and cases in this book will support teacher educators and scholars across subject specialities and geographic lines, as they seek instructional frameworks to advance their pedagogical goals.
The Fate of AI Society
Hackers who exploit binary computers become expert cybercriminals. A vicious cycle of undetected attacks by criminal gangs, spies, and foreign enemies fuels skilled staff shortages and escalating costs. Ken Hamer-Hodges, explains why outdated computers cannot stop malware and how democracy is undermined by corrupt dictators. Digital convergence subverts yesterday's binary computer, allowing advanced malware, pervasive cameras, misinformation, AI, and deep-fakes to destroy our culture and civilization. His inspiring examples explain the perfection of computer science that all can grasp. How malware thrives and why operating systems lead to Orwellian dictatorship. To prevent catastrophe computer hardware must catch up with software progress, preventing malware and stopping AI breakout. He explains how to transition to a well engineered, crime free, global cybersociety. How machine code achieves Alonzo Church's vision of networked function abstractions that avoid disaster by accelerating scientific progress. Plotting the path for radical improvement is vital for civilization to flourish as democratically controlled, AI-empowered, global cyber societies. Ken shows how science drives high performance with high reliability for independent applications needed in a world run by superhuman software. Join the author as he explores the fix to computer science. He shows how nations can thrive in a world run by dubious software, governed by superhuman AI, working as functional democracies kept safe from criminals, spies, and dictators.
Data Analysis
Data analysis has been a hot topic for a number of years, and many future data scientists have backgrounds that are relatively light in mathematics. This slim volume provides a very approachable guide to the techniques of the subject, designed with such people in mind. Formulae are kept to a minimum, but the book's scope is broad, introducing the basic ideas of probability and statistics and more advanced techniques such as generalised linear models, classification using logistic regression, and support-vector machines. An essential feature of the book is that it does not tie to any particular software. The methods introduced in this book could also be implemented using any other statistical software and applying any major statistical package. Academically, the book amounts to a first course, practical for those at the undergraduate level, either as part of a mathematics/statistics degree or as a data-oriented option for a non-mathematics degree. The book appeals to would-be data scientists who may be formula shy. However, it could also be a relevant purchase for statisticians and mathematicians, for whom data science is a new departure, overall appealing to any computer-literate reader with data to analyse.
Logics for AI and Law. Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, September 8-9 and
This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of logic in these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law.
The Second Story of Meno; A Continuation of Socrates’ Dialogue with Meno in Which the Boy Proves Root 2 is Irrational
The Second Story of Meno; A Continuation of Socrates' Dialogue with Meno in Which the Boy Proves Root 2 is Irrational, a classical book, has been considered essential throughout the human history, and so that this work is never forgotten we at Alpha Editions have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies of their original work and hence the text is clear and readable.
The philosophy of mathematics
The philosophy of mathematics, a classical book, has been considered essential throughout the human history, and so that this work is never forgotten we at Alpha Editions have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies of their original work and hence the text is clear and readable.
Solving Ordinary Differential Equations in Python
This open access volume explains the foundations of modern solvers for ordinary differential equations (ODEs). Formulating and solving ODEs is an essential part of mathematical modeling and computational science, and numerous solvers are available in commercial and open source software. However, no single ODE solver is the best choice for every single problem, and choosing the right solver requires fundamental insight into how the solvers work. This book will provide exactly that insight, to enable students and researchers to select the right solver for any ODE problem of interest, or implement their own solvers if needed. The presentation is compact and accessible, and focuses on the large and widely used class of solvers known as Runge-Kutta methods. Explicit and implicit methods are motivated and explained, as well as methods for error control and automatic time step selection, and all the solvers are implemented as a class hierarchy in Python.
Axiomatic Thinking I
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to G繹ttingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Axiomatic Thinking II
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to G繹ttingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Elementary Methods of Graph Ramsey Theory
This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner's overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Tur獺n numbers and communication channels, etc.
Maurer-Cartan Methods in Deformation Theory
Covering an exceptional range of topics, this text provides a unique overview of the Maurer--Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Graph Theory and Additive Combinatorics
Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemer矇di, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Tur獺n problem, Szemer矇di's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.
Taking the "Oof!" Out of Proofs
This book introduces readers to the art of doing mathematical proofs.
Perplexing Paradoxes
Why does it always seem like the elevator is going down when you need to go up? Is it really true that 0.99999 . . . with an infinite number of 9s after the decimal point, is equal to 1? What do tea leaves and river erosion have in common, per Albert Einstein? Does seeing a bed of red flowers help prove that all ravens are black? Can we make sense of a phrase like "this statement is unprovable"? Exploring these questions and many more, George G. Szpiro guides readers through the puzzling world of paradoxes, from Socratic dialogues to the Monty Hall problem. Perplexing Paradoxes presents sixty counterintuitive conundrums drawn from diverse areas of thought--not only mathematics, statistics, logic, and philosophy but also social science, physics, politics, and religion. Szpiro offers a brisk history of each paradox, unpacks its inner workings, and considers where one might encounter it in daily life. Ultimately, he argues, paradoxes are not simple brain teasers or abstruse word games--they challenge us to hone our reasoning and become more alert to the flaws in received wisdom and common habits of thought. Lighthearted, witty, and conversational, Perplexing Paradoxes presents sophisticated material in an accessible way for all readers interested in the world's boundless possibilities--and impossibilities.
MotivPoetry
Do you know poetry can be motivational? Poetry has great power. Let MotivPoetry by Walter the Educator motivate you to be a great Mathematician! Creating a poetry book about being a great mathematician can be a unique and creative way to explore the intersection of two seemingly different disciplines. It allows you to bridge the gap between the logical, analytical world of mathematics and the expressive, imaginative world of poetry. By combining these two disciplines, you can showcase the beauty and elegance of mathematics through the power of language and emotions. Poetry can help to humanize the often abstract and complex concepts of mathematics, making them more relatable and accessible to a wider audience. Furthermore, a poetry book about being a great mathematician can inspire and encourage others to pursue and appreciate the subject. It can showcase the creative and artistic aspects of mathematics, breaking stereotypes and showing that the field is not just about calculations and formulas, but also about creativity, intuition, and innovation. Overall, creating a poetry book about being a great mathematician allows you to celebrate both the logical and creative sides of your identity, and to share your passion for both disciplines in a unique and compelling way.
Research in History and Philosophy of Mathematics
This volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include: A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schemaA quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematiciansThe depiction and perception of ?milie Du Ch璽telet's scientific contributions as viewed through the frontispieces designed for books written by or connected to herA study of the Cambridge Women's Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth centuryAn examination of the researchand writing process of mathematicians by looking at their drafts and other preparatory notesA global history of al-Khwārāzmī's Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentariesWritten by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
Nonlinear Systems and Their Remarkable Mathematical Structures
The third volume consists of a collection of contributions by world-leading experts in the subject of nonlinear DE and nonlinear dynamical systems (both continuous and discrete), but in this instance only featuring contributions by leading Chinese scientists who also work in China.
Common Core Math Workbook
6th Grade Common Core Math: Practice Workbook Practice Questions, Answers & Explanations Recommended by Teachers Ace Academic PublishingBased on Common Core State Standards: Similar to a standardized exam, you can find questions of all types, including multiple-choice, fill-in-the-blank, true or false, match the correct answer, and free-response questions.High Standards of Questions: Each of these questions is divided into Chapters and Sub-Topics. The contents of this Math workbook include multiple chapters and units covering all the required Common Core Standards for this grade level.Recommended by Teachers: These carefully written questions aim to help students reason abstractly and quantitatively using various models, strategies, and problem-solving techniques.Identifying trouble spots and fixing them: This workbook will help students overcome any deficiencies in their understanding of critical concepts and also will help you identify the specific topic that students may require additional practice.Practice all types of questions including free response: The book is comprised of multiple tests for each topic so that your child can have an abundant amount of tests on the same topic.Includes 2 Comprehensive Full-Length Tests: to practice the entire syllabus to prepare for the common core standardized exams.Includes detailed step-by-step answers: The detailed answer explanations in the back of the book help the students understand the topics and gain confidence in solving similar problems and take the Common Core Standardized Exam with Confidence.
Common Core Math Workbook
8th Grade Common Core Math: Practice Workbook Practice Questions, Answers & Explanations Recommended by Teachers Ace Academic PublishingBased on Common Core State Standards: Similar to a standardized exam, you can find questions of all types, including multiple-choice, fill-in-the-blank, true or false, match the correct answer, and free-response questions.High Standards of Questions: Each of these questions is divided into Chapters and Sub-Topics. The contents of this Math workbook include multiple chapters and units covering all the required Common Core Standards for this grade level.Recommended by Teachers: These carefully written questions aim to help students reason abstractly and quantitatively using various models, strategies, and problem-solving techniques.Identifying trouble spots and fixing them: This workbook will help students overcome any deficiencies in their understanding of critical concepts and also will help you identify the specific topic that students may require additional practice.Practice all types of questions including free response: The book is comprised of multiple tests for each topic so that your child can have an abundant amount of tests on the same topic.Includes 2 Comprehensive Full-Length Tests: to practice the entire syllabus to prepare for the common core standardized exams.Includes detailed step-by-step answers: The detailed answer explanations in the back of the book help the students understand the topics and gain confidence in solving similar problems and take the Common Core Standardized Exam with Confidence.
