Line Graphs and Line Digraphs
In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs.Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientistswho have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.
Ethereum for Beginners
Ethereum has received a lot of attention from the cryptocurrency and software communities, it's a blockchain based mix of currency and programming with seemingly endless and novel applications we are just starting to discover, it is also a complex and amazing technology. Here is a preview of what you'll learn...- What is ethereum- Technology behind ethereum- Ethereum mining- How to buy, sell and store ethereum- Should you invest in ethereum- Future of ethereum- And more.....The most important advantage of ethereum over bitcoin is that this cryptocurrency technology allows the computer applications to run on its network, not just ether by itself. The significant appeal of bitcoin lies in the fact that it can't be controlled by any single party and it is not running via a central server. Ethereum improves on that by allowing not only the currency but other things as well to be run inside the network.
Ethereum
This book is designed to give you step-by-step instructions on how to get started and join the ethereum bandwagon. Unlike bitcoin, ethereum is still very new in the cryptoworld, but it is growing fast. Learning some of the most successful strategies that have helped many to make their own fortunes could be your own ticket to financial freedom. After reading this book, the follow will have learned the following: - What ethereum is and how it can benefit your life- The pros and cons of ethereum technology to provide you with a complete picture- Tips on how to use ethereum to maximize your user experience- What smart contracts are and why they matter- The future potential of ethereum and why cryptocurrency mattersThe book then goes into what ethereum is and what you would need to start with this new cryptocurrency. As with any cryptocurrency, ethereum has its advantages and disadvantages. I go into detail explaining these as i've invested in bitcoin in the past. The book ends with final thoughts on where ethereum could go and some general projections about this exciting cryptocurrency.
The Golden Section
What was the great and golden secret known to Leonardo Da Vinci, Kepler, Plato, and the ancient magicians? Why were they forbidden to reveal it? Can there really be a key to nature and life itself? In this small but compact volume divine proportion, supersleuth Dr. Olsen unravels perhaps the greatest mystery of all time, a code that seems to underly life, the universe and everything, a pattern we instinctively recognize as beautiful, and which nature herself uses at every scale.
The Awakening of Numbers
The Awakening of NumbersBy: Mitchell E. FreemanAll numbers are a result of human imagination, and all numbers are not imagined the same way. The Awakening of Numbers contains examples of some of the ways numbers are imagined and some methods of utilization of the imagined numbers. Readers can take away the realization that the numbers humans use are a result of converting an imaginary concept into a written reality. About the AuthorMitchell E. Freeman's career spanned over 37 years in the Fleet Ballistic Missile Program. In addition to his FBM training, he has an AA and a BS with some master's work. He held numerous positions throughout his career that required the practical application of numbers. Freeman is a retired MCPO, a member of MENSA, American Legion, and a Signature Life Member of the Georgia Watercolor Society.
Adventures of a Mathematician
The true story that inspired the 2020 film. The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Fran癟oise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.
Twenty Key Ideas in Beginning Calculus
Twenty Key Ideas in Beginning Calculus is a color 174 page book written by a high school mathematics teacher who learned how to sequence and present ideas over a 30-year career of teaching grade school mathematics. It is intended to serve as a bridge for beginning calculus students to study independently in preparation for a traditional calculus curriculum or as supplemental material for students who are currently in a calculus class. It is highly visual with 40 supportive images, 100+ cartoons and other illustrations, 110 graphs, and 40+ data tables spread throughout its 174 pages. Comprehension and understanding of ideas is emphasized over symbol manipulation although the latter is covered. The main text, Chapters 1-14, teaches "intuitive calculus," while the appendices contain "traditional calculus" proofs allowing the reader to customize their learning experience according to their ability and interest for rigor. When appropriate, the reader is referred to correlative interactive applets that can be used to supplement the text.
Mathematische Weltbilder Weiter Denken
In dieser Studie wird untersucht, mit welchem schulisch gepr瓣gten Mathematikbild Studierende an die Universit瓣t kommen und wie sich dieses durch die Begegnung mit der universit瓣ren Mathematik ver瓣ndert. Zugleich wird die Wirksamkeit einer neu konzipierten hochschulmathematikdidaktischen Vorlesung auf die mathematischen Weltbilder der Lehramts-studierenden untersucht. Mathematische Weltbilder weiter zu denken ist hierf羹r gleicherma?en Anspruch wie Aufforderung: Mithilfe der entwickelten Skalen ist eine breitere Erfassung von Einstellungen gegen羹ber Mathematik m繹glich, sodass diese nun weiter gedacht werden k繹nnen als zuvor. Es wird gezeigt, dass sich Einstellungen zur Mathematik durch entsprechend gestaltete, fachmathematische Lehrveranstaltungen gezielt adressieren lassen. Dies erm繹glicht es, die Lehramtsausbildung mit Blick auf die Zukunft weiterzudenken: Lehrkr瓣fte sind gesellschaftliche Botschafter*innen f羹r Mathematik und m羹ssen 羹ber ein tragf瓣higes und facettenreiches Mathematikbild verf羹gen, um in einem modernen, kompetenzorientierten Unterricht die Relevanz der Mathematik und ihre Bedeutung als Kulturgut und Schl羹sseltechnologie vermitteln zu k繹nnen.
Rigorous State-Based Methods
This book constitutes the proceedings of the 8th International Conference on Rigorous State-Based Methods, ABZ 2021, which was planned to take place in Ulm, Germany, during June 6-11, 2021. The conference changed to an online format due to the COVID-19 pandemic. The 6 full and 8 short papers included in this volume were carefully reviewed and selected from 18 submissions. The proceedings also include 3 PhD symposium contributions. They deal with state-based and machine-based formal methods, mainly Abstract State Machines (ASM), Alloy, B, TLA+, VDM, and Z.
Higher-Order Lovelock Tensors and the Coefficients of Higher-Order Lovelock Lagrangians and Exterior Differential Forms Including Higher-Order Chern Forms and Their Coefficients Expressed in Terms of
This book presents general expressions for higher-order Lovelock tensors and the coefficients of higher-order Lovelock Lagrangians in terms of the Riemann-Christoffel and Ricci curvature tensors and Riemann curvature scalar and exterior differential forms including higher-order Chern forms and their coefficients expressed in terms of Pontrjagin's characteristic tensors of the second kind.
Creative Secondary School Mathematics
There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units - ranging from grades 7 through 12 - that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!
Advances in Differential Equations and Applications
The book contains a selection of contributions given at the 23th Congress on Differential Equations and Applications (CEDYA) / 13th Congress of Applied Mathematics (CMA) that took place at Castellon, Spain, in 2013. CEDYA is renowned as the congress of the Spanish Society of Applied Mathematics (SEMA) and constitutes the main forum and meeting point for applied mathematicians in Spain. The papers included in this book have been selected after a thorough refereeing process and provide a good summary of the recent activity developed by different groups working mainly in Spain on applications of mathematics to several fields of science and technology. The purpose is to provide a useful reference of academic and industrial researchers working in the area of numerical analysis and its applications.
Irregularity in Graphs
Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure. During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.
Matroid Decomposition
Matroids, first defined in 1935, are an abstract generalization of graphs and matrices. By now, there is a large body of matroid theory. The book covers the part of the theory dealing with composition and decomposition of matroids. The book is a revised version of the original publication of 1992. It does not assume any prior knowledge of matroid theory. Indeed, for the reader unfamiliar with matroid theory, the book may serve as an easy and intuitive introduction to that beautiful part of combinatorics. For the expert, the book is intended to provide a pleasant tour over familiar terrain.
Direct and Inverse Scattering for the Matrix Schr繹dinger Equation
The matrix Schr繹dinger equation and the characterization of the scattering data.- Direct scattering I.- Direct scattering II.- Inverse scattering.- Some explicit examples.- Mathematical preliminaries.
Einf羹hrung in Das Thema Schl羹sselkompetenzen
Schl羹sselkompetenzen spielen immer mehr eine entscheidende Rolle. In diesem essential werden ausgehend von dem allgemeinen Kompetenzbegriff Schl羹sselkompetenzen definiert. Es wird die Einteilung der Schl羹sselkompetenzen aufgezeigt. Der Kanon der Schl羹sselkompetenzen, definiert durch EU und OECD, wird dargelegt. Die Bestimmung der pers繹nlichen Auspr瓣gung und die Pr羹fungsmethode von Schl羹sselkompetenzen werden aufgezeigt. Ein Ausblick auf k羹nftige Erweiterungen des Spektrums der Schl羹sselkompetenzen wird diskutiert.
Understanding and Doing Math - Circle 1
This is the first in a series of math books intended for teenagers, young adults, or older who have acquired: certain calculating skills, dissatisfaction with their understanding of what they are calculating.If you are not satisfied with the mathematics you study at school, oryou are a student or a teacher who wants to understand mathematics better, orat some point in school, you ceased to understand mathematics in the way you would have liked to understand it, and if you would still like to have a fundamental understanding and working knowledge of mathematics, these are the books for you. We will start our journey with numbers. Numbers are the oldest mathematical idea but still also the most important one. We will go through the basics of numbers in a way that will give you the confidence to really understand numbers and know how to apply them, You will also learn all the essential elements of mathematics through the example of the world of numbers. Numbers will be used to illustrate what mathematical objects are, how they are applied, and what mathematical tools we use in their description and application. You can find out more about the book (including the excerpts from the book) on the web page https: //understandingmath.academy/math-circles/math-circle-1. You can meet me on Twitter: https: //twitter.com/doing_math.
Threshold Logic
Threshold Logic by Sze-Tsen Hu offers the first comprehensive treatment of logical elements based on the threshold principle, devices that had attracted growing attention in the wake of McCulloch and Pitts's 1943 neuron models and von Neumann's investigations into reliability. Threshold devices--including param矇trons, magnetic core switches, and Esaki diode circuits--function as complex logical units that extend well beyond the simplicity of "AND" and "OR" gates. Because a single device can generate relatively intricate switching functions, they hold the potential to increase the speed and efficiency of electronic digital computers while reducing the number of components required. This efficiency has made threshold logic a key subject in computing research during the postwar era, and the book situates the field at the intersection of mathematical theory, hardware design, and computational application. Hu's study surveys and advances work in three major areas: defining the conditions a switching function must meet to qualify as a threshold function, devising algorithms to test and implement these functions, and developing synthesis methods for networks composed of threshold gates. The book is designed both as a reference consolidating contributions from the previous decade and as a research monograph introducing Hu's own results, much of which had been confined to Lockheed Missiles and Space Company technical reports. The early chapters cover the theory of threshold functions and decision conditions; subsequent chapters detail algorithms for classification and realization; the concluding chapter presents Hu's mathematically rigorous process for constructing minimal threshold networks, moving beyond the heuristic techniques that had dominated the field. With an eye to accessibility, Hu deliberately emphasizes clarity in his proofs and explanations, ensuring that both engineers and mathematicians can use the book as a foundation for further exploration of threshold logic in the design of high-speed computing systems. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.
Threshold Logic
Threshold Logic by Sze-Tsen Hu offers the first comprehensive treatment of logical elements based on the threshold principle, devices that had attracted growing attention in the wake of McCulloch and Pitts's 1943 neuron models and von Neumann's investigations into reliability. Threshold devices--including param矇trons, magnetic core switches, and Esaki diode circuits--function as complex logical units that extend well beyond the simplicity of "AND" and "OR" gates. Because a single device can generate relatively intricate switching functions, they hold the potential to increase the speed and efficiency of electronic digital computers while reducing the number of components required. This efficiency has made threshold logic a key subject in computing research during the postwar era, and the book situates the field at the intersection of mathematical theory, hardware design, and computational application. Hu's study surveys and advances work in three major areas: defining the conditions a switching function must meet to qualify as a threshold function, devising algorithms to test and implement these functions, and developing synthesis methods for networks composed of threshold gates. The book is designed both as a reference consolidating contributions from the previous decade and as a research monograph introducing Hu's own results, much of which had been confined to Lockheed Missiles and Space Company technical reports. The early chapters cover the theory of threshold functions and decision conditions; subsequent chapters detail algorithms for classification and realization; the concluding chapter presents Hu's mathematically rigorous process for constructing minimal threshold networks, moving beyond the heuristic techniques that had dominated the field. With an eye to accessibility, Hu deliberately emphasizes clarity in his proofs and explanations, ensuring that both engineers and mathematicians can use the book as a foundation for further exploration of threshold logic in the design of high-speed computing systems. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.
Journal of Applied Logics - The IfCoLog Journal of Logics and their Applications
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 open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).
The 300 Sudoku Very Hard Difficult Challenging Extreme Expert Level Puzzles brain workout large print
300 New Sudoku puzzles from The Puzzle Publishing HouseSudoku is one of the World's most popular games, time and stress can feel like its melting away by working through these engaging puzzles.300 SudokuVery HardNo mercy editionMany hours of fun and challenge!Great gift for all Sudoku fansLarge print unlike most puzzle books, easy to read and fill out.Click on "Buy Now" to get your puzzle book in the post.
Philosophy of Mathematics
This book explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians into thinking about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.
The Laplace Transform
"Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there"-Marcus du SautoyLaplace transform is the integral transform which convert one function into another function. Like all transforms, the Laplace transform changes one signal into another according to some fixed set of rules or equations. The best way to convert differential equations into algebraic equations is the use of Laplace transformation. In this section, students get a step-by-step explanation for every concept and will find it extremely easy to understand this topic in a detailed way.
Speed Wheel Drills for Multiplication
This book is designed to help you learn your multiplication number facts. The goal is for you to have instant recall of each multiplication fact. The Speed Wheel Drills make learning fun! Use a timer and see how your speed and accuracy improve with each page. 1,440 Speed Wheel Drills Instant recall of number facts makes all math easier Learn them the fun, easy, FAST way Helps improve grades Easy to track progressBONUS! 21 Best Math Tips for All StudentsPlus a convenient Math Resource Center You will find that having instant recall of number facts will make ALL math easier for you!
Speed Wheel Drills for Addition
This book is designed to help you learn your addition number facts. The goal is for you to have instant recall of each addition fact. The Speed Wheel Drills make learning fun! Use a timer and see how your speed and accuracy improve with each page. 1,440 Speed Wheel DrillsInstant recall of number facts makes all math easierLearn them the fun, easy, FAST wayHelps improve gradesEasy to track progressBONUS! 21 Best Math Tips for All StudentsPlus a convenient Math Resource Center You will find that having instant recall of number facts will make ALL math easier for you!
Metastable Patterns for Multi-phase Field Models
The main objective of this work is to show the slow decay from metastable states of different phase-field models which stand for the dynamic phase transition between many different states (thus allowing the study mixtures of two or more components). By this way, we get a generalization of the existence of this kind of metastable solutions, given by other previous works, even when we consider the nonlinear diffusion.
Mathematics Practice Workbook Grade 8
Get the Targeted Practice You Need to Excel on the Math Section of the Mathematics Test Grade 8!Mathematics Practice Workbook Grade 8 is an excellent investment in your future and the best solution for students who want to maximize their score and minimize study time. Practice is an essential part of preparing for a test and improving a test taker's chance of success. The best way to practice taking a test is by going through lots of math questions.High-quality mathematics instruction ensures that students become problem solvers. We believe all students can develop deep conceptual understanding and procedural fluency in mathematics. In doing so, through this math workbook we help our students grapple with real problems, think mathematically, and create solutions. Mathematics Practice Workbook allows you to: Reinforce your strengths and improve your weaknessesPractice 2500+ realistic math practice questionsmath problems in a variety of formats that provide intensive practiceand study Two Full-length Practice Tests with detailed explanations ...and much more!This Comprehensive Math Practice Book is carefully designed to provide only that clear and concise information you need.Published By: The Math Notionwww.mathnotion.com
Talk With Me About Numbers, Mama
We talk with children about birds, flowers, lakes, stars, skies, bicycles, cars, and many other wonderful things. We should tell them about numbers as one of the beautiful aspects of our lives. Numbers can be observed and marveled at as much as birds and flowers. Sometimes they are as deep as lakes, but we can see only the surface. Sometimes they gleam and beckon, sending us mysterious light like stars. We can even ride them as a bicycle or a car if we learn to do so. Whether you are a parent or a teacher this book will help you start a conversation about numbers.
Bi-level Optimization in an Imprecise and Random Environment
In classical bi-level programming problems, coefficients of objective functions of the leader and the follower are crisp. But in real-life situations, uncertainties arise in almost every aspect. Thus, to include more realistic cases in classical bi-level programming problems, a fuzzy stochastic bi-level programming model has been developed using fuzzy random variable coefficients. A fuzzy random variable is a mathematical tool to deal with a sort of hybrid uncertainty. The novelty of the fuzzy random variable is that it contains the structure of twofold distribution which can carry a joint oneness of the simultaneous random and imprecise information which goes beyond the contrast of information contained in a random variable in probability theory and fuzzy variable in fuzzy set theory. Though the book deals to solve bi-level optimization models in the fuzzy or fuzzy random environment through a multi-stage decision-making approach. The main contribution of this book is twofold. It introduced the fuzzy stochastic and fuzzy rule-base bi-level optimization model to overcome the uncertainties present due to impreciseness and randomness.
Introduction to Mathematical Modeling
The book aims at providing a concise mathematical formulation of characteristic problems of real life with emphasis on quantitative aspects of the problems. It develops the basic concepts and methods in modeling focusing on forecasting relevant solutions to specified area problems. This book covers basic concepts and methods in modeling, dimensional analysis, graphical methods and applications, approximation and testing, consecutive equations, applications (growth and decay models, population growth model, interacting species, and population models, etc).
Optimal Mass Transport
In this book, we discuss the theory of optimal mass transport as first formulated by Gaspard Monge in 1781. We further discuss the important steps leading to the existence of solutions to the Monge's problem. Next, we formulate Brenier theorem which not only solves the Monge's problem for quadratic cost function but also provides a link to a class of the Monge-Ampere equations. Finally, we study the regularity of Brenier solution.
Topics in Algorithmic Graph Theory
Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.
Teach (Test) yourself...Introduction to Calculus
This book provides students with a tool to improve their knowledge in preparation to learning Calculus. This book is intended to be a good review of the introduction to Calculus. The book follows the main precalculus concepts needed in order to understand Calculus. It starts with the Cartesian System, Geometry and Trigonometric ratios, Algebra. From introduction to powers, and logarithms to polynomials, graphs of linear equations and quadratic equations. Then it follows Calculus I curriculum for high schools. Chapter 5 is a review of Functions. Chapter 6 is about Limits; Chapter 7 deals with Differentiation, and Chapter 8 is all about Integrals. Before each set of TESTS, a short review of the main theoretical concepts will be presented. There are examples given to help better understand and review the concepts. The TESTS apply the theory and concepts reviewed.
Philosophy of Mathematics
This book explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians into thinking about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.
Applications of Homogenization Theory to the Study of Mineralized Tissue
This book provides a thorough introduction to homogenization, a modeling procedure used to describe processes in complicated structures with known microstructures. It first presents the theoretical foundations of this powerful tool of analysis. Building on the theory, the authors explore various types of application problems, including flow in porous media, sound propagation in fluid saturated solids, acoustics of granular material, computational multiscale finite element methods, and interfaces in viscoelastic materials. The book also discusses results in which G-limits have different structures from the initial operators.
An Introduction to Metric Spaces
This book is designed to provide an extensive understanding of Metric spaces. It presents the basics of metric spaces in a natural way which encourages geometric thinking.
Essays on Early Medieval Mathematics
This book deals with the mathematics of the medieval West between ca. 500 and 1100, the period before the translations from Arabic and Greek had their impact. Four of the studies appear for the first time in English. Among the topics treated are: the Roman surveyors (agrimensores); recreational mathematics in the period of Bede and Alcuin; geometrical texts compiled in Corbie and Lorraine from Latin sources from late antiquity; the abacus at the time of Gerbert (pope Sylvester II.); and a board-game invented in the first half of the 11th century (the 'Rithmimachia') to help people to learn mathematics. Included in the volume are critical editions of several texts, e.g. that of Franco of Li癡ge on squaring the circle, Bede and Alcuin on recreational mathematics, and part of Pseudo-Boethius' Geometry I. The book opens with a survey of mathematics in the Middle Ages, and ends with a history of Rithmimachia up to the 17th century, when the game fell into disuse.
Laplace Transforms
This book is designed to cater the needs of the under graduate science and engineering students. It contains with the fundamental concepts related to Laplace Transformation and Inverse Laplace Transformation. The author utilized lucid style to explain the concepts. Also, the applications related to solving the Differential Equations, System of Differential Equations, Integral Equations and Partial Differential Equations are provided. The book contains with more number of examples and many exercise problems with key.
Fundamentals of Mathematical Analysis
Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and aims to achieve excellent breadth and depth and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.
Beyond Octonion Cosmology
Octonion Cosmology appears somewhat strange at first glance despite its clear consequences for Elementary Particle Physics. This book starts with octonionic spaces and proceeds to develop a Unified SuperStandard Theory for our universe with an exciting set of features that generalize The Standard Model to accommodate new phenomena such as leptoquark interactions via SU(4) and a Strong interaction connection for photons - both topics lately in the news. It provides a derivation of Octonion Cosmology from a substratum of eight postulates for the properties of space. These postulates lead directly to the eight spaces of Octonion Cosmology. The derivation is straightforward but somewhat complex. As a mathematical aside, a generalization of the important hypercomplex Cayley numbers is developed. Multidimensional Cayley arrays based on the Cayley-Dickson Construction are defined and their fundamental properties explored. This volume also contains Pioneering the Cosmos and Pioneering the Cosmos II God-Space in their entirety. Their purpose was to provide an almost complete Octonion Cosmology presentation and to serve as a ready reference for the derivation. Their descriptions follow.Description: Pioneering the Cosmos This book is the Second Edition of: From Octonion Cosmology to the Unified SuperStandard Theory of Particles. It presents a more detailed, complete Cosmology based on a spectrum of ten octonion spaces, a Superverse, and three spaces of functionals. Octonion Cosmology is a truly fundamental physical theory that "explains" space-time, internal symmetry groups, and elementary particles, and their associated, detailed phenomena. It provides a justification for the Unified SuperStandard Theory that the author previously derived from Logic considerations over the past twenty years (based on the author's extensions of Quantum Field Theory presented in papers in the 1970s.) There is a panoramic range from the most fundamental physical levels to current elementary particle physics experiments. Description: Pioneering the Cosmos II God-Space This book is Part II of Pioneering the Cosmos. It extends the presentation of features of Octonion Cosmology to make it a complete theory of the Cosmos. The beginning is the million dimension God-Space, from which the other octonion spaces (forming an octet), and their instances (particles), are derived. We show that the conventional form of symmetry breaking via the Higgs Mechanism is not sufficient. We introduce a new form of symmetry "splitting into factors" based on two types of inheritance. A view of the photon is presented showing that it is analogous to a frozen universe. Part of the photon "universe" connects to the ElectroWeak interactions; part of the photon universe connects to the Strong interaction and supports a ρ Vector Meson Dominance (VDM) connection.
Music, Math, and Mind
Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in the musical world as Dave Soldier, explains why the perception of music encompasses the physics of sound, the functions of the ear and deep-brain auditory pathways, and the physiology of emotion. He delves into topics such as the math by which musical scales, rhythms, tuning, and harmonies are derived, from the days of Pythagoras to technological manipulation of sound waves. Sulzer ranges from styles from around the world to canonical composers to hip-hop, the history of experimental music, and animal sound by songbirds, cetaceans, bats, and insects. He makes accessible a vast range of material, helping readers discover the universal principles behind the music they find meaningful. Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.
Emergence of Chaotic Dynamics from Singularities
This book is a journey through singularities, unfolding, bifurcations and strange attractors. The first stage isa walk through essential results in the context ofdiffeomorphisms. After that, we see how these results can beapplied to flows of vector fields via Poincar矇 return maps. Inthis way, the persistence of strange attractors in families ofdiffeomorphisms which unfold a homoclinic tangency lead to thepersistence of suspended strange attractors in families of vectorfields. We explain how these attractors are formed from homoclinicbifurcations, mostly around a Shilnikov homoclinic orbit or arounda bifocal homoclinic orbit, and from heteroclinic bifurcations as, for instance, in neighborhoods of Bykov cycles. All these globalconfigurations will be introduced later. These structures aredifficult to detect in a phase space, but we prove that they arisein generic unfoldings of certain singularities. As alreadymentioned, proceeding in this way, we provide results that allowto conclude the persistence of strange attractors from thepresence of certain singularities in a given family.
Music, Math, and Mind
Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in the musical world as Dave Soldier, explains why the perception of music encompasses the physics of sound, the functions of the ear and deep-brain auditory pathways, and the physiology of emotion. He delves into topics such as the math by which musical scales, rhythms, tuning, and harmonies are derived, from the days of Pythagoras to technological manipulation of sound waves. Sulzer ranges from styles from around the world to canonical composers to hip-hop, the history of experimental music, and animal sound by songbirds, cetaceans, bats, and insects. He makes accessible a vast range of material, helping readers discover the universal principles behind the music they find meaningful. Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.
Axiomatic Thinking II
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to G繹ttingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Mathematical Modelling in Biomedicine
Mathematical modelling in biomedicine is a rapidly developing scientific discipline at the intersection of medicine, biology, mathematics, physics, and computer science. Its progress is stimulated by fundamental scientific questions and by the applications to public health. This book represents a collection of papers devoted to mathematical modelling of various physiological problems in normal and pathological conditions. It covers a broad range of topics including cardiovascular system and diseases, heart and brain modelling, tumor growth, viral infections, and immune response. Computational models of blood circulation are used to study the influence of heart arrhythmias on coronary blood flow and on operating modes for left-ventricle-assisted devices. Wave propagation in the cardiac tissue is investigated in order to show the influence of tissue heterogeneity and fibrosis. The models of tumor growth are used to determine optimal protocols of antiangiogenic and radiotherapy. The models of viral hepatitis kinetics are considered for the parameter identification, and the evolution of viral quasi-species is investigated. The book presents the state-of-the-art in mathematical modelling in biomedicine and opens new perspectives in this passionate field of research.
Axiomatic Thinking I
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to G繹ttingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics
Preface.- Set Theory and Foundations of Mathematics.- On the Boundaries of Mathematics and Physics.- European Mathematics in Transition.- Mathematics and its History in Modern Cultures.- Traditional Chinese Mathematics.- Chinese Mathematics: Transmissions and Transformation.- Selected Bibliography of Joseph W. Dauben.- Bibliography.
When Least Is Best
A mathematical journey through the most fascinating problems of extremes and how to solve them What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes--with values becoming as small (or as large) as possible--and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.
