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
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.
Mathematics Phase 5
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Informative Psychometric Filters
This book is a series of case studies with a common theme. Some refer closely to previous work by the author, but contrast with how they have been treated before, and some are new. Comparisons are drawn using various sorts of psychological and psychophysiological data that characteristically are particularly nonlinear, non-stationary, far from equilibrium and even chaotic, exhibiting abrupt transitions that are both reversible and irreversible, and failing to meet metric properties. A core idea is that both the human organism and the data analysis procedures used are filters, that may variously preserve, transform, distort or even destroy information of significance.
Geometry of Grief
In this profound and hopeful book, a mathematician and celebrated teacher shows how mathematics may help all of us--even the math-averse--to understand and cope with grief. We all know the euphoria of intellectual epiphany--the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief, mathematician Michael Frame draws on a career's worth of insight--including his work with a pioneer of fractal geometry Benoit Mandelbrot--and a gift for rendering the complex accessible as he delves into this twinning of understanding and loss. Grief, Frame reveals, can be a moment of possibility. Frame investigates grief as a response to an irrevocable change in circumstance. This reframing allows us to see parallels between the loss of a loved one or a career and the loss of the elation of first understanding a tricky concept. From this foundation, Frame builds a geometric model of mental states. An object that is fractal, for example, has symmetry of magnification: magnify a picture of a mountain or a fern leaf--both fractal--and we see echoes of the original shape. Similarly, nested inside great loss are smaller losses. By manipulating this geometry, Frame shows us, we may be able to redirect our thinking in ways that help reduce our pain. Small‐scale losses, in essence, provide laboratories to learn how to meet large-scale losses. Interweaving original illustrations, clear introductions to advanced topics in geometry, and wisdom gleaned from his own experience with illness and others' remarkable responses to devastating loss, Frame's poetic book is a journey through the beautiful complexities of mathematics and life. With both human sympathy and geometrical elegance, it helps us to see how a geometry of grief can open a pathway for bold action.
Clean Numerical Simulation
A new strategy to gain "clean" reliable numerical simulations of chaos and turbulence, namely the Clean Numerical Simulation (CNS), which can greatly reduce numerical noises to a tiny level much smaller than that of true solutions so numerical noises are negligible, and the corresponding numerical simulation is "clean" and thus reliable.
Differential and Low-Dimensional Topology
The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin research as quickly as possible. The only prerequisite assumed is an undergraduate algebraic topology course. The first half of the text reviews basic notions of differential topology and culminates with the classification of exotic seven-spheres. It then dives into dimension three and knot theory. There then follows an introduction to Heegaard Floer homology, a powerful collection of modern invariants of three- and four-manifolds, and of knots, that has not before appeared in an introductory textbook. The book concludes with a glimpse of four-manifold theory. Students will find it an exhilarating and authoritative guide to a broad swathe of the most important topics in modern topology.
Differential and Low-Dimensional Topology
The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin research as quickly as possible. The only prerequisite assumed is an undergraduate algebraic topology course. The first half of the text reviews basic notions of differential topology and culminates with the classification of exotic seven-spheres. It then dives into dimension three and knot theory. There then follows an introduction to Heegaard Floer homology, a powerful collection of modern invariants of three- and four-manifolds, and of knots, that has not before appeared in an introductory textbook. The book concludes with a glimpse of four-manifold theory. Students will find it an exhilarating and authoritative guide to a broad swathe of the most important topics in modern topology.
Real Harmonic Analysis
This book presents the material covered in graduate lectures delivered at The Australian National University in 2010. Real Harmonic Analysis originates from the seminal works of Zygmund and Calder籀n, pursued by Stein, Weiss, Fefferman, Coifman, Meyer and many others. Moving from the classical periodic setting to the real line, then to higher dimensional Euclidean spaces and finally to, nowadays, sets with minimal structures, the theory has reached a high level of applicability. This is why it is called real harmonic analysis: the usual exponential functions have disappeared from the picture. Set and function decomposition prevail.
Mathematics Phase 1
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 7
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 3
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 4
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 6
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Math Murder in Media Manufactured Madness
For 2.5 years since the declaration of the Covid-19 pandemic, people have felt extreme fear. Reason, rationality, basic math and logic have taken a severe beating. This book documents the math murder in the mad fear largely manufactured by relentless propaganda in the media. It is meant for those who want to reflect on the planet-wide panic surrounding Covid-19, to examine if it was justified, to sift truth from propaganda, to learn how we can possibly prevent such mistakes in the future. It is especially meant for the next generation, who were affected least by the virus itself, yet affected most by the irrational measures in the name of public health. They must know how the adults on the planet abandoned reason for madness, rationality for fear, and basic math for obvious absurdity. Most parts are meant to be understandable with only a secondary-school or high-school mathematics background.
Poetic Logic and the Origins of the Mathematical Imagination
This book treats eighteenth-century Italian philosopher Giambattista Vico's theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and N繳簽ez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics.The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its "modifications" (his term for "creations"); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts--including mathematics--the mind has allowed humans to establish "the world of civil society," Vico's term for culture and civilization.The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Al-Kashi's Miftah Al-Hisab, Volume III: Algebra
Jamshīd al-Kāshī's Miftāḥ al-Ḥisab (Key to Arithmetic) was largely unknown to researchers until the mid-20th century, and has not been translated to English until now. This is the third and final book in a multi-volume set that finally brings al-Kāshī's groundbreaking textbook to English audiences in its entirety. As soon as it was studied by modern researchers, Miftah changed some false assumptions about the history of certain topics in mathematics. Written as a textbook for students of mathematics, astronomy, accounting, engineering, and architecture, Miftah covers a wide range of topics in arithmetic, geometry, and algebra. By sharing al-Kāshī's most comprehensive work with a wider audience, this book will help establish a more complete history of mathematics, and extend al-Kāshī's influence into the 21st century and beyond. The book opens by briefly recounting al-Kāshī's biography, so as to situate readers in the work's rich historical context. His impressive status in the kingdom of Ulugh Beg is detailed, as well as his contributions to both mathematics and astronomy. As a master calculator and astronomer, al-Kāshī's calculations of 2π and sin(1⁰) were by far the most accurate for almost two centuries. His law of cosines is still studied in schools today. This translation contributes to the understanding and appreciation of al-Kāshī's esteemed place in the scientific world. A side-by-side presentation of the source manuscript--one of the oldest known copies--and the English translation is provided on each page. Detailed footnotes are also provided throughout, which will offer readers an even deeper look at the text's mathematical and historical basis. Researchers and students of the history of mathematics will find this volume indispensable in filling in a frequently overlooked time period and region. This volume will also provide anybody interested in the history of Islamic culture with an insightful look at one of the mathematical world's most neglected figures.
Mathematics for Computation (M4C)
The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
Complex Feedback Queue Network Models
Queuing theory has become most important discipline of Operation Research. In real world we are facing queues everywhere around us. Sometimes we see very complex type of queue networks. This book includes three complex types of queue network models. These queue network models has been analysed in stochastic environment with the facility of revisit for customer's satisfaction. Practical situations are also given at the end of every chapter. The applicability of these models is not limited to a specific situation; they are applicable to various fields. This book will be helpful for the researchers, who are working on queue network models in stochastic environment.
Dissipative Lattice Dynamical Systems
There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.
