Why Does Math Work ... If It's Not Real?
According to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless, ' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.
Graphs & Digraphs
Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.
Introduction to Real Analysis
The emphasis of this now classic text is on sequences of real numbers, compact subsets of IR, as well as real-valued functions.
Multiplicative Differential Equations
Multiplicative Differential Equations: Volume I is the first part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics.
Multiplicative Differential Equations
Multiplicative Differential Equations: Volume 2 is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics.
The Rule of Nine
"THE RULE OF NINE" IS A FASCINATING BOOK BY IYESIS MITCHELL-TIBERE THAT DELVES INTO THE MYSTICAL AND MATHEMATICAL SIGNIFICANCE OF THE NUMBER NINE. THE BOOK ARGUES THAT THE CREATOR'S SIGNATURE IS HIDDEN IN DIVINE MULTIPLICATION THROUGH THE RULE OF NINE, AND THAT BY UNDERSTANDING THE POWER OF THIS NUMBER, WE CAN UNLOCK LIMITLESS POTENTIAL WITHIN OURSELVES.IYESIS EXPLORES THE MANY WAYS IN WHICH THE NUMBER NINE APPEARS THROUGHOUT HISTORY AND OUR LIVES, FROM THE CYCLES OF NATURE TO THE STRUCTURE OF OUR BODIES. SHE ARGUES THAT THIS NUMBER IS NOT JUST A COINCIDENCE, BUT A FUNDAMENTAL ASPECT OF DESIGN.BY EXAMINING THE RULE OF NINE AND ITS VARIOUS MATHEMATICAL APPLICATIONS, THE AUTHOR SHOWS HOW WE CAN TAP INTO A DEEPER LEVEL OF UNDERSTANDING AND CONSCIOUSNESS. SHE EMPHASIZES THAT THIS UNDERSTANDING CAN HELP US ACHIEVE OUR FULL POTENTIAL AS INFINITE BEINGS AND RECOGNIZE THE LIMITLESS NATURE OF OUR OWN EXISTENCE.OVERALL, "THE RULE OF NINE" IS PROFOUNDLY INSPIRING AND THOUGHT-PROVOKING BOOK THAT ENCOURAGES READERS TO EXPLORE THE MYSTICAL AND MATHEMATICAL UNDERPINNINGS OF THE UNIVERSE. IT IS A MUST-READ FOR ANYONE INTERESTED IN THE INTERCONNECTION OF HISTORY, SCIENCE SPIRITUALITY, PERSONAL GROWTH, AND THE MYSTERIES OF THE COSMOS.
Why Does Math Work ... If It's Not Real?
According to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless, ' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.
Computational Mathematics and Applied Statistics
Rapid advances in modelling research have created new challenges and opportunities for statisticians. Statistical inference in observational studies and many other emerging fields have motivated statisticians worldwide to develop cutting-edge methods and analytical strategies.The aim of this book is to showcase the applications and methodological research in all fields of computational statistics. This book will provide a forum for computer scientists, mathematicians, and statisticians working in a variety of areas in statistics, including biometrics, econometrics, data analysis, graphics, and simulation.
Multivariate Calculus
This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students.
Special Functions with Applications to Mathematical Physics
This MDPI booklet lists the articles published in three Special Issues of the journal Mathematics devoted to special functions with applications in mathematical physics in the years 2020-2021.The call for papers considered theories and applications of high transcendental functions, including topics found mainly in the list of keywords: - Mittag-Leffler and related functions, and their applications in mathematical physics;- Wright and related functions and their applications in mathematical physics;- exponential integrals and their extensions with applications in mathematical physics;- generalized hypergeometric functions and their extensions with applicationsHowever, the Special Issues were not limited to the above list, for example, when the content of a paper was clearly related to some high transcendental functions and their applications.Special attention was reserved for distinct functions exhibiting some relevance in the framework of the theories and applications of the fractional calculus and in their visualization through illuminating plots.Both research and survey articles were included in this booklet, according to the content list.
Discrete Mathematics
Discrete Mathematics: A Gateway to the Mathematical Garden is an introduction to finite and discrete mathematics. This book includes all the important and foundational mathematics to support the student learning finite mathematics for the first time: logic, set theory, number theory, proofs, combinatorics, and graph theory. The exposition helps the student-reader learn to think logically and reasonably about mathematical structures. Discussions of cryptology, computer science, machine-readable codes, and operations research are used to give the student a sense of how the mathematics is applied. Throughout the book, examples illustrate the material and provide insight into the mathematical theory. The book is essentially self-contained. There are very few prerequistes aside from some mathematical maturity and familiarity with algebra. Problems to help the student master the concepts are included at the end of each section. Each chapter concludes with a set of supplementary problems and a set of sample test questions. Discrete Mathematics: A Gateway to the Mathematical Garden, Chuck Garner, paperback, color, first edition, 7.44in by 9.68 in, 217 pages, ISBN 978-1-312-71237-9, copyright 2023 Charles R. Garner Jr.
Differential Equations for Studies in Computational Electrophysiology
This open access text aims at giving you the simplest possible introduction to differential equations that are used in models of electrophysiology. It covers models at several spatial and temporal scales with associated numerical methods. The text demonstrates that a very limited number of fundamental techniques can be used to define numerical methods for equations ranging from ridiculously simple to extremely complex systems of partial differential equations. Every method is implemented in Matlab and the codes are freely available online. By using these codes, the reader becomes familiar with classical models of electrophysiology, like the cable equation, the monodomain model, and the bidomain model. But modern models that have just started to gain attention in the field of computational electrophysiology are also presented. If you just want to read one book, it should probably not be this one, but if you want a simple introduction to a complex field, it is worth considering the present text.
Temporal Logic: From Philosophy and Proof Theory to Artificial Intelligence and Quantum Computing
Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
Computing and Analysing Energy Minimisation Problems in Liquid Crystals: Implementation Using Firedrake
How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects?There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc.This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems.
Of Men and Numbers
Of Men and Numbers, first published in 1963, is a fascinating look at the lives and works of history's greatest mathematicians. Beginning with the early Egyptians and Greeks such as Pythagoras, Euclid and Archimedes, author Jane Muir then describes, in non-technical terms, the discoveries and personal stories of math greats such as Descartes, Pascal, and Newton, and continues with the important work of more recent mathematicians such as Nicholas Lobatchevsky, ?variste Galois, and Georg Cantor. Illustrated throughout with line drawings and figures.
Chatting with ChatGPT
This past April Ermes engaged ChatGPT in a wide variety of chats, ranging from philosophy to paradoxes to Canadian lit, to name just a few. Artificial intelligence is developing and improving very fast, so that no one should be surprised if a few years down the road one looks back at the ChatGPT responses given in this volume only to be amazed at the primitiveness and inaccuracy of some of the responses. For now, though, what stands out is ChatGPT's impressive ability to comment quickly and succinctly on any one of the given topics.
Mathfatuated
Mathfatuated includes unique poems representing math topics associated with the lovable subject, making it the perfect gift for the math lover. Creating a poetry book about math can be a unique way of exploring mathematical concepts that may seem boringly challenging to some. Poetry can give a fresh perspective and bring an imaginative approach to learning about math. It can also help people remember mathematical concepts better. Moreover, it can bridge the gap between math and art and appeal to a larger audience. Overall, a poetry book about math can be an appealing and creative way to engage with the subject.
A Textbook of Advanced Engineering Mathematics
Engineering is the practical application of science and technology. Mathematical models of these practical applications are obtained using various governing laws from science and technology. Most of the mathematical models lead to ordinary differential equations, partial differential equations or systems of partial or ordinary differential equations. The solution of these models plays a vital role in the analysis of the effect of parameters on the system. Solving the mathematical problem obtained by one of the many techniques covered in Engineering Mathematics. This book is a unique combination of differential equation theory and its fascinating application to "real-world" problems. The main aims of this book are: Elaborative discussion of the fundamental concepts of the relevant topicExtremely minute details have been addressed with sufficient justifications, and special care has been taken to make the explanation adequate, straightforward, and methodicalA large number of worked-out examples have been provided to aid in swiftly comprehending the subject matter and increasing self-confidence.Solution of engineering problem with detailed calculation.For more details, please visit https: //centralwestpublishing.com
Research in Computational Topology 2
This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariantsfor directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.
A Textbook of Advanced Engineering Mathematics
Integral transform and the Fourier series are two important concepts in the field of science and engineering. The understanding of these concepts at the graduate level plays a significant role, especially in the electrical and electronic communication fields.Periodic functions frequently appear in the field of engineering and science. Fourier series is the result of their representation in terms of simple periodic functions like sine and cosine. In the context of issues involving partial differential equations, the Fourier series is a particularly useful instrument. The study of the Fourier series is important in the field of electrical engineering and electronic communication.This book is a text and a reference book for undergraduate students and readers of mathematics, science, and engineering. A concerted effort has been made to offer practically all of the standard content, as well as some new material. This book is intended to serve as a fresh resource for both classical and contemporary topics involving integral transforms and their applications.For more details, please visit https: //centralwestpublishing.com
Chapters from G繹del's Unfinished Book on Foundational Research in Mathematics
Stochastic Integral and Differential Equations in Mathematical Modelling
The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes -- either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.
Combinatorics, Modeling, Elementary Number Theory
This book is mostly based on the author's 25 years of teaching combinatorics to two distinct sets of students: first-year students and seniors from all backgrounds. The prerequisites are kept to a minimum; essentially, only high school algebra is required. The design is to go quickly from zero knowledge to advanced themes and various applications with a lot of topics intended for additional reading and research projects. It contains an all-inclusive collection of 135 problems and 275 exercises with four difficulty levels: solutions, hints and answers are provided.Some themes of the book: Enumerative combinatorics and basic graph theory: Introduction to dimers, tilings, magic and Latin squares, permutations, combinations, generating functions, games of chance, random walks, binomial and Poisson distributions. Catalan numbers, their generalizations and applications, including roulette and pricing derivatives. Euler and Hamiltonian paths, linear and planar graphs, labeled trees and other topics on graphs; many of them are presented as exercises.Modeling: Linear recurrence relations, Fibonacci rabbits, population growth, tree growth, epidemic spread and reinfections, resonances and nuclear reactors, predator-prey relationships and stopping times.Elementary number theory: Residues, finite fields, Pisano periods, quadratic reciprocity, Pell's equation, continued fractions, and Frobenius coin problem. Applications to cryptography, designs and magic squares, error-correcting codes and nonattacking queens.
Logic
Logic: Deductive and Inductive, has been considered important throughout human history. In an effort to ensure that this work is never lost, we have taken steps to secure its preservation by republishing this book in a modern format for both current and future generations. This complete book has been retyped, redesigned, and reformatted. Since these books are not scans of the authors' original publications, the text is readable and clear.
Mathematical model for the biocontrol of vector-borne viral diseases in solanaceous vegetable plants
Doctoral Thesis / Dissertation from the year 2022 in the subject Mathematics - Applied Mathematics, Modibbo Adama University of Technology, Yola, language: English, abstract: This thesis treats the issue of Vector-Borne Virus Diseases (VBVDs) that are transmitted in solanaceous vegetable plants by incorporating three species of vectors (aphids, thrips and whiteflies). A mathematical model was developed that used lady beetles as biological control agents for controlling the spread of diseases in solanaceous vegetable plants through predation. The research adopted the linearization method. This research is restricted to a biological control of VBVDs of solanaceous vegetable plants using compartmental modeling approach. The model is a system of first order nonlinear ODEs. Additionally, the study is limited to three solanaceous plants (i.e. tomato, pepper and eggplant). This is because solanaceous plants are among the world's most cultivated crops and given proper conditions and regular maintenance, they are relatively easy to grow. We focused on viral diseases that affect solanaceous vegetable plants especially Yellow Leaf Curl Virus (YLCV), Spotted Wilt Virus (SWV) and Cucumber Mosaic Virus (CMV). It is a common knowledge that these plant viruses also require some sort of carrier, known as vectors to transmit the pathogen from plant to plant. Therefore, the study is demarcated to a class of aphids (green peach aphids), thrips (T. tabasi) and whiteflies (Bemisia tabasi) because these ones are reported as the common problem associated with solanaceous plants which can be controlled by natural predatory enemies - ladybugs (hippodamia convergens).
Approximation and Computation in Science and Engineering
In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.
In Situ Visualization for Computational Science
This book provides an overview of the emerging field of in situ visualization, i.e. visualizing simulation data as it is generated. In situ visualization is a processing paradigm in response to recent trends in the development of high-performance computers. It has great promise in its ability to access increased temporal resolution and leverage extensive computational power. However, the paradigm also is widely viewed as limiting when it comes to exploration-oriented use cases. Furthermore, it will require visualization systems to become increasingly complex and constrained in usage. As research efforts on in situ visualization are growing, the state of the art and best practices are rapidly maturing.Specifically, this book contains chapters that reflect state-of-the-art research results and best practices in the area of in situ visualization. Our target audience are researchers and practitioners from the areas of mathematics computational science, high-performance computing, and computer science that work on or with in situ techniques, or desire to do so in future.
Th矇orie des Fonctions Elliptiques
Th矇orie des Fonctions Elliptiques, a 矇t矇 consid矇r矇e comme importante tout au long de l'histoire de l'humanit矇. Dans un effort pour s'assurer que ce travail ne soit jamais perdu, nous avons pris des mesures pour assurer sa pr矇servation en republiant ce livre dans un format moderne pour les g矇n矇rations actuelles et futures. Ce livre complet a 矇t矇 retap矇, remani矇 et reformat矇. Comme ces livres ne sont pas des scans des publications originales des auteurs, le texte est lisible et clair.
Virginia Standards of Learning Grade 6 WorkBook
This book is your comprehensive workbook for 6th Grade Common Core Math.Practice makes it perfect. Practice questions on each concept helps the students master over the topic, Students get familiar with the state math aligned to common core standards and more.All our content is created by industry experts of over 30+ years of teaching experience and has been successfully used by students across various years.This book contains Multiple choice and free response questions. This 6th Grade Common Core Math Workbook includes the below.32 weeks of Math26 weeks of practice questions6 Assessments2500+ Math questionsChallenge QuestionsAligned to common core curriculumMultiple choice and Free response questionsDetailed notes on topics with solved examplesEnd of Year assessment onlineThis book has following topics covered: Number sense - Decimal Addition, Subtraction, Multiplication, DivisionNumber sense - Integer Addition, Subtraction, Multiplication, DivisionFactors & MultiplesGreatest Common Factor (GCF)Least Common Multiple (LCM)Number sense - Fraction Addition, Subtraction, Multiplication, DivisionAssessment #1RatiosPercentagesAssessment #2ExponentsLike term simplificationOrder of OperationsLinear variable substitutionsLinear variable expressionsOne and Two step EquationsAssessment #3Verbal InequalitiesOne and Two step InequalitiesAssessment #4Absolute valueArea of 2-D figures with mixed unitsPerimeter, Area of 2-DCo-ordinatesVolume& Surface Area: PrismsSimilar Ratio and NetsAssessment #5Dot plots, Box plots & Bar graphsHistograms, Line graphs, CirclesTransformationsAssessment #6END of YEAR ASSESSMENT #1 ( www.a4ace.com)Sharpening Minds Strengthening Skills Learn to Think with us
Beauty of Elementary Mathematics, The: And How to Teach It
Why is 2 times 3 equal to 3 times 2? One may think this is an axiom, but it has a proof, and a beautiful one at that. Elementary mathematics is as deep and as beautiful as higher mathematics. It includes some of the most important mathematical discoveries ever, for example the concept of the number, and the place-value method of representing numbers. We are so accustomed to this method, that we forget how clever and beautiful it is - resulting in its incredible efficacy.All this was a surprise for the author, a university professor of mathematics, when he went to teach in elementary school. He realized that good teaching of elementary mathematics requires understanding its fine points and conveying their beauty to the students. Sensing the beauty and understanding go hand in hand.The book outlines the material from kindergarten to grade 6 (with an excursion into algebra as well). It also discusses teaching principles, and their close relatives - thinking principles. Teachers and parents who imbue these principles are likely to convey the love of mathematics to the child.
Beauty of Elementary Mathematics, The: And How to Teach It
Why is 2 times 3 equal to 3 times 2? One may think this is an axiom, but it has a proof, and a beautiful one at that. Elementary mathematics is as deep and as beautiful as higher mathematics. It includes some of the most important mathematical discoveries ever, for example the concept of the number, and the place-value method of representing numbers. We are so accustomed to this method, that we forget how clever and beautiful it is -- resulting in its incredible efficacy.All this was a surprise for the author, a university professor of mathematics, when he went to teach in elementary school. He realized that good teaching of elementary mathematics requires understanding its fine points and conveying their beauty to the students. Sensing the beauty and understanding go hand in hand.The book outlines the material from kindergarten to grade 6 (with an excursion into algebra as well). It also discusses teaching principles, and their close relatives -- thinking principles. Teachers and parents who imbue these principles are likely to convey the love of mathematics to the child.
My Mathematical Life
This book is an autobiographical interview with Chinese Academician Yuan Wang on his experience in mathematical research. The book looks back on Wang's collaboration with his teacher Hua Loo-Keng and younger scholars, offering insights into fruitful cooperation in mathematical research.In this book, Yuan Wang's path of studying Goldbach conjecture is revealed in detail from motivation to method. Then his work on algebraic number theory is traced back in a separate chapter. The book ends with two chapters which introduce Wang's interest in history of mathematics and his hobbies outside of mathematical research. Wang shows how a mathematician can in the same time be a historical and popular science writer and, in particular, a well-received calligrapher. The book is intended for undergraduate and graduate students studying number theory. Researchers who are willing to learn from the experience of an established mathematician, as well as math amateurs and general audience who are interested in Yuan Wang's life story might also find this book appealing.
The Riordan Group and Applications
The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve asa text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.
The Irrationals
An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first century The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define-and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.
Boscawen-?n
Mathematician and essayist James Warren looks at the Cornish megalithic stone circle Boscawen-?n, nineteen granite or quartz menhirs arranged in a rough oval, with a single sloping stone in their midst. The monument was possibly laid-out in Chalcolithic times for unknown reasons. James Warren measures the layout from an aerial photograph. The plan is not circular and the author demonstrates that the whole array and indeed any choice of three or more component stones cannot mathematically lie on an arc of a circle. The author shows that the stone circuit is plausibly comprised of four elliptical arcs and that these were likely generated by dragging a taut loop of rope or chain around four posts driven at the corners of a square.
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.
What's Wrong with Math?
You see, our current system of math education is very efficient at creating math phobia. This systemic math phobia is the elephant in the room. Everyone knows it's there. Everyone knows it shouldn't be there. No one knows how it got there or how to get it to leave. In the end it gets left in the room year after year, decade after decade, generation after generation, because as a whole we haven't seen nor experienced what we are missing. As a whole we don't know what the room looks like without the elephant. Therefore I am writing this book from my corner of the room, to simply tell people about the part of the elephant I see from here, to lend my feeble voice in painting a clearer picture of what it is that we're missing, what it is that we need to do to move the elephant, and a suggestion or two on the ways we might get it done. My only goal is to give whatever I can offer for the future of an elephant-less room for all, and I invite all who are willing to help. Moving this elephant needs an orchestrated effort from a great many people.
Journal of Applied Logics - The IfCoLog Journal of Logics and their Applications - Volume 10, Issue 2, March 2023. Special issue
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Godel's Proof
Godel's Proof was first published in the US in 1958. In 1931 there appeared in a German scientific periodical a relatively short paper with the forbidding title "On Formally Undecidable propositions of Principia Mathematica and Related Systems". Its author was Kurt Godel, then a young mathematician of 25 at the University of Vienna who since 1938 was a permanent member of the Institute for Advanced Study at Princeton. The paper is a milestone in the history of logic and mathematics. When Harvard University awarded Godel an honorary degree, the citation described the work as one of the most important advances in logic in modern times. At the time of its appearance, however, neither the title of Godel's paper nor its content was intelligible to most mathematicians.
Zero and Pi
The book, divided into two major parts, discusses the evolution of the concept and symbols of zero and the history of pi. Both the topics are discussed from the Neolithic Age to the nineteenth century. The book also clears the assumption that Johann Heinrich Lambert (AD 1761) only invented the irrationality of pi by crediting Lambert jointly with Andr矇 Marie Legendre (AD 1794).Part 1, consisting of six stages spread in six chapters, meets a challenge to the authors as eminent scholars of the history of mathematics have diverse opinions based on conjectures. This part primarily discusses how the symbol O, in the Vedic religious practices, considered a replica of the universe prescribed for meditation on the unknown Brahman (conceived of as the space supreme in the Upanishads), was later transcended to the symbol of an unknown quantity in mathematics along with a dot for zero in an arena of atheism. It also highlights how the zero notation and the decimal system of Indian numerals embellished with the algebraic thoughts of Brahmagupta passed on to China and Europe via Arabia. Topics in this part have traced the development from the origin to the final form as seen today after the western practice and try to put an end to the long-standing debate over history. Appendices contain the Sanskrit verses (transliterated with meanings into English) along with the essential mathematical deduction referred to in the body of the part to help the reader to have a better understanding.Part 2 speaks of a novel idea of unveiling the nature of pi interwoven with threads of historical ups and downs in the world scenario. This part, containing five chapters, collects all available up-to-date data in every field of history to make the presentation complete in all respects. This part discusses the origin of the definition of pi as the rim of a wheel is thrice its diameter at the Indus Valley in the fourth millennium BC. This part also discusses the enlightenment of China in circle-squaring (classical method), Indian mathematics with astronomical knowledge along the Buddhist channel, and India's discovering circumference/diameter as a non-Euclidean number.
Rigorous State-Based Methods
This book constitutes the refereed proceedings of the 9th International Conference on Rigorous State-Based Methods, ABZ 2023, held in Nancy, France, in May 2023. The 12 full and 7 short papers included in this volume were carefully reviewed and selected from 47 submissions. The proceedings also include 4 PhD symposium contributions. They deal with state-based and machine-based formal methods, mainly Abstract State Machines (ASM), Alloy, B, TLA+, VDM, and Z.
Combinatorics on Words
This book constitutes the refereed proceedings of the 14th International Conference on Combinatorics on Words, WORDS 2023, held in Ume疇, Sweden, during June 12-16, 2023.The 19 contributed papers presented in this book were carefully reviewed and selected from 28 submissions. In addition, the volume also contains 3 invited papers. WORDS is the main conference series devoted to combinatorics on words. This area is connected to several topics from computer science and mathematics, including string algorithms, automated proofs, discrete dynamics, number theory and, of course, classical combinatorics
Calculus All-In-One for Dummies (＋ Chapter Quizzes Online)
Make calculus more manageable with simplified instruction and tons of practice Calculus All-in-One For Dummies pairs no-nonsense explanations of calculus content with practical examples and practice problems, so you can untangle the difficult concepts and improve your score in any calculus class. Plus, this book comes with access to chapter quizzes online. Dummies makes differentiation, integration, and everything in between more manageable, so you can crush calculus with confidence. Review the foundational basics, then dive into calc lessons that track your class. This book takes you through a full year of high-school calculus or a first semester of college calculus, only explained more clearly. Work through easy-to-understand lessons on everything in a typical calc class Get the score you want and need on standardized tests like AP Calculus Access online chapter quizzes for additional practice Untangle tricky problems and discover clever ways to solve themWith clear definitions, concise explanations, and plenty of helpful information on everything from limits and vectors to integration and curve-sketching, Calculus All-in-One For Dummies is the must-have resource for students who want to review for exams or just need extra help understanding the concepts from class.
Reactionary Mathematics
A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena. The nineteenth century opened with a major shift in European mathematics, and in the Kingdom of Naples, this occurred earlier than elsewhere. Between 1790 and 1830 its leading scientific institutions rejected as untrustworthy the "very modern mathematics" of French analysis and in its place consolidated, legitimated, and put to work a different mathematical culture. The Neapolitan mathematical resistance was a complete reorientation of mathematical practice. Over the unrestricted manipulation and application of algebraic algorithms, Neapolitan mathematicians called for a return to Greek-style geometry and the preeminence of pure mathematics. For all their apparent backwardness, Massimo Mazzotti explains, they were arguing for what would become crucial features of modern mathematics: its voluntary restriction through a new kind of rigor and discipline, and the complete disconnection of mathematical truth from the empirical world--in other words, its purity. The Neapolitans, Mazzotti argues, were reacting to the widespread use of mathematical analysis in social and political arguments: theirs was a reactionary mathematics that aimed to technically refute the revolutionary mathematics of the Jacobins. During the Restoration, the expert groups in the service of the modern administrative state reaffirmed the role of pure mathematics as the foundation of a newly rigorous mathematics, which was now conceived as a neutral tool for modernization. What Mazzotti's penetrating history shows us in vivid detail is that producing mathematical knowledge was equally about producing certain forms of social, political, and economic order.
Reactionary Mathematics
A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena. The nineteenth century opened with a major shift in European mathematics, and in the Kingdom of Naples, this occurred earlier than elsewhere. Between 1790 and 1830 its leading scientific institutions rejected as untrustworthy the "very modern mathematics" of French analysis and in its place consolidated, legitimated, and put to work a different mathematical culture. The Neapolitan mathematical resistance was a complete reorientation of mathematical practice. Over the unrestricted manipulation and application of algebraic algorithms, Neapolitan mathematicians called for a return to Greek-style geometry and the preeminence of pure mathematics. For all their apparent backwardness, Massimo Mazzotti explains, they were arguing for what would become crucial features of modern mathematics: its voluntary restriction through a new kind of rigor and discipline, and the complete disconnection of mathematical truth from the empirical world--in other words, its purity. The Neapolitans, Mazzotti argues, were reacting to the widespread use of mathematical analysis in social and political arguments: theirs was a reactionary mathematics that aimed to technically refute the revolutionary mathematics of the Jacobins. During the Restoration, the expert groups in the service of the modern administrative state reaffirmed the role of pure mathematics as the foundation of a newly rigorous mathematics, which was now conceived as a neutral tool for modernization. What Mazzotti's penetrating history shows us in vivid detail is that producing mathematical knowledge was equally about producing certain forms of social, political, and economic order.
Irish Mathematical Olympiad Manual
This is the third edition of the best-selling manual. It is A4-size, with larger type than the compact A5 second edition. It also incorporates a few corrections and some minor rearrangement of the material. This Manual was primarily written to assist Irish secondary-school students who are preparing to compete in the Irish Mathematical Olympiad (held in May each year) or the International Mathematical Olympiad (held each July). It has also proved useful in other countries, and is popular among people who simply enjoy mathematics. The Mathematical Olympiads are written examinations, based on what is called "second--level mathematics". There are significant variations between countries in the content of second--level programmes in Mathematics. Thus, Irish competitors find themselves faced with problems that require background knowledge that is not covered in the Senior Cycle programme for Irish schools. In order to have a reasonable chance of success, they need to master this material. The authors are academics who have many years experience as voluntary trainers of Olympiad contestants and in other mathematical enrichment activities for young people. The selection of material is based on this experience.
The Geometric Constants in Banach Spaces
The main purpose of this book is to present some old and new results in this research field. This book can be divided into two parts. The first part is the first chapter, in which we briefly introduce some basic concepts and results. It can help readers quickly learn about some of the classic research results in this field, as well as understand their research motivation and background. The remaining chapters can be considered as the second part. In these chapters, we will introduce in detail our relevant research results in recent years, which may help readers understand the main research content and motivation in this field today.
