Calculus in 5 Hours
Students often struggle to understand Calculus and get through their first Calculus course. And to make things worse, many popular textbooks reach a whopping 1,000 pages to introduce this crucial subject, needlessly frustrating and overwhelming students. Calculus in 5 Hours develops the confidence you need in approximately 124 pages.You may not realize it, but you're smarter than you think you are. The problem is that assigned textbooks give exhaustive explanations of every proof and theorem in Calculus. But too many details can impair learning - especially when you're learning something for the first time - creating doubt and uncertainty in your ability to understand. What's needed is a straightforward guide to give you the basic concepts.Calculus in 5 Hours is a good companion to any Calculus course and an excellent resource for refreshing your knowledge of the subject. Here's what it will do for you: Organize your understanding of Calculus for quick and easy recall on tests and homework assignmentsPresent straightforward drawings that demonstrate concepts with minimal effort on your partHighlight simple examples without burdening you with useless detailsCalculus in 5 Hours covers roughly 75% of a first-semester course and leaves out the extra material that adds little value in learning Calculus itself. So, if you need a comprehensive textbook that goes through every detail of Calculus, then this book is not for you.Instead, you'll get a straightforward and simple explanation of Calculus that can be absorbed in less than a day, strengthening your knowledge and confidence at the same time. This allows you to focus on what's truly important - gaining knowledge and achievement as fast as possible.Get Calculus in 5 Hours to shorten your learning curve and gain the understanding you need to be successful today.
Math is BAD
"Math is BAD" is a short text to demonstrate the strengths and weaknesses of mathematics in a simple manner. The book uses a significant number of credible sources and could provide a new angle of interpretation and appreciation of mathematics. Specifically, the modern era reveals another side of the truth that mathematics cannot formulate. That is to say, nothing is for sure. Such a vision has led to another branch of science, which requires relying on probabilistic effects. Statistics is the branch that employs mathematics while missing the absoluteness of mathematics. In simple terms, "MATH IS BAD" encourages us to listen to the sound of the cosmos and whatever it contains with more mindfulness while respecting its complexity and randomness. Moreover, "Math is Bad" briefly touches on the dark side of scientific literature and the way sources are altered for various purposes. The second edition has improved the content to include the most available up-to-date information and references.
Trig Identities Practice Workbook with Answers
This trigonometry workbook focuses on trig identities. The majority of the exercises let you derive a variety of trig identities by following similar examples. If you get stuck, helpful hints in the back of the book help walk you through the solution. Other exercises include applications, such as how to find the tangent of 15 degrees without a calculator or how to apply trig identities to solve equations. This book also serves as a handy list of numerous trig identities organized by topic. The answer to every problem can be found at the back of the book. The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his knowledge of trig identities.
An Elementary Course Of Mathematics Comprising Arithmetic, Algebra And Euclid
Clear, rigorous, unmistakably Victorian: a teaching voice that privileges method and habit over ornament. A timeless guide for learners. S. Hall's An Elementary Course of Mathematics comprising arithmetic, algebra and Euclid brings together practical instruction and geometric rigour in a single, thoughtfully ordered manual. As an elementary mathematics textbook it lays out foundational math concepts with step-by-step exposition, progressive examples and problems that train both calculation and thinking. Part arithmetic and algebra guide and part euclidean geometry course, the work balances numerical practice with the logical demands of proof, introducing mathematical problem solving alongside the geometry proofs basics that shaped nineteenth-century instruction. Carefully framed exercises and explanations make it a dependable math students resource, a compact choice for a homeschooling math curriculum and an indispensable beginner math collection for anyone starting serious study. The tone is direct and unadorned: concise definitions, worked problems and a steady march from simple arithmetic to algebraic manipulation and spatial reasoning. Learners benefit from clear progression; tutors and parents can pick discrete sections for focused study. For self-directed readers, the methodical layout makes independent revision straightforward; for classroom use it supplies the kind of disciplined training that underpins later mathematical reading. As a nineteenth century textbook it is also a document of Victorian era mathematics pedagogy, showing how clarity of statement and systematic demonstration were taught as moral and intellectual habits. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. Casual readers seeking structured guidance, parents and tutors planning a curriculum, and classic-literature collectors assembling a classic math reference will find equal reward here: a title that is at once practical, historically revealing and quietly luminous; useful both as a working primer in arithmetic and algebra and as an accessible euclidean geometry course that illuminates the roots of modern mathematical instruction.
Nature Intelligence
It's time to reset the global economy and the magnum opus book that will do the job is Nature Intelligence!Nature Intelligence (NI) is where every knowledge and learning -sciences, social sciences, technology, engineering, mathematics and art/humanities (STEMA) intersect. With NI, knowledge and learning are fun. Everything in the world feeds on nature such that wherever you are and whatever you are doing right now depends on nature. Nature is everything to the world hence we need to know about nature that makes living possible, habitable and livable for the fulfilment of life in time -the dress rehearsal for life in the timeless-zone. NI is the launch of the new but original economic system of the global economy known as octonomism -the retirement of capitalism, socialism and communism. NI is the launch of new physics known as existophysics -the goal of physics where physical reality and ultimate reality are defined and intersected. NI is the launch of new politics and political party known as octonomist -the true path of good governance. NI is a phenomenon in world affairs. In this trying times of the world where COVID-19 pandemic has distorted the working pattern of the global economy, there is the need for a shifting paradigm that will reset and reinvent the world from education to information gathering for the fulfilment of life in the world and that passionately needed reset and reinvention is NI which is good for parents, students, guardians, leaders of thoughts, and everyone to use at homes, in the offices, schools, hotels, streets, movies, marketplaces and anywhere humans are found in the world. NI is a daily application in all areas of life. Nothing gives more fun like nature and the fun is found in NI. Nature is a revolution in itself for nature changes the change that daily transforms the world from civilization to civilization. That revolution of nature is NI. So, welcome to NI revolution -the revolution of the wellbeing economy. NI is the book that unites the past, present and the future with ease and you being the ultimate beneficiary. NI, all interests covered, everyone wins. Knowledge is fun, learning is fun and life is fun -with NI.
Stephen of Pisa and Antioch: Liber Mamonis
Preface.- I. Introduction.- 1. Studies in Arabic Astronomy in the Early Crusader States.- 2. The Liber Mamonis, its author and his Main Source.- 3. Stephen's Version of On the Configuration.- 4. The Content and Purpose of Stephen's Commentary.- 5. Stephen's Astronomical Sources and his Los Regule Canonis.- II. Edition & Translation.- Book I.- Book II.- Book III.- Book IV.- A. Glossary.- B. Plates.
Modern Trends in Fuzzy Graph Theory
This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs to focus on advanced concepts such as planarity in fuzzy graphs, fuzzy competition graphs, fuzzy threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs, m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each chapter includes a number of key representative applications of the discussed concept. An authoritative, self-contained, and inspiring read on the theory and modern applications of fuzzy graphs, this book is of value to advanced undergraduate and graduate students of mathematics, engineering, and computer science, as well as researchers interestedin new developments in fuzzy logic and applied mathematics.
Matrici per Buchi Neri
Per evitare i metodi di Einstein, bench矇 siano descritti, l'autore introduce matrici 4x4 per ottenere gli stessi risultati, cio癡 per trovare posizioni di stelle ed anche i ben noti valori delle particelle fondamentali, includendo il bosone di Higgs. Un disco volante (fatto di aria ionizzata) appare lungo tre cerchi concentrici a causa di due forze oscillanti mutuamente ortogonali. Successivamente pu簷 essere immaginato come una ruota che rotola su un piano inclinato. Questo oggetto si 癡 formato a circa 3000m di altezza. L'allontanamento 癡 apparente: l'oggetto sta precipitando dalla parte del sole. La particella Ω(1672)MeV viene trovata con gli strumenti matematici adeguati; ma una nuova comprensione delle particelle si ha sviluppando argomentazioni di S. Sternberg, che predicono caratteristiche dipendenti dal gruppo dei quaternioni e da un gruppo diedrale. I decadimenti comprendenti il top quark, mostrati in questo libro, forniscono una spiegazione chiara e completa della descrizione data da Bellettini che sembra alquanto misteriosa. Alla fine del libro, il prodotto di due matrici unifica le particelle indicate da Chew, Gell'Mann e Rosenfeld lungo traiettorie di Regge.
Matrices for Black Holes
Per evitare i metodi di Einstein, bench矇 siano descritti, l'autore introduce matrici 4x4 per ottenere gli stessi risultati, cio癡 per trovare posizioni di stelle ed anche i ben noti valori delle particelle fondamentali, includendo il bosone di Higgs. Un disco volante (fatto di aria ionizzata) appare lungo tre cerchi concentrici a causa di due forze oscillanti mutuamente ortogonali. Successivamente pu簷 essere immaginato come una ruota che rotola su un piano inclinato. Questo oggetto si 癡 formato a circa 3000m di altezza. L'allontanamento 癡 apparente: l'oggetto sta precipitando dalla parte del sole. La particella Ω(1672)MeV viene trovata con gli strumenti matematici adeguati; ma una nuova comprensione delle particelle si ha sviluppando argomentazioni di S. Sternberg, che predicono caratteristiche dipendenti dal gruppo dei quaternioni e da un gruppo diedrale. I decadimenti comprendenti il top quark, mostrati in questo libro, forniscono una spiegazione chiara e completa della descrizione data da Bellettini che sembra alquanto misteriosa. Alla fine del libro, il prodotto di due matrici unifica le particelle indicate da Chew, Gell'Mann e Rosenfeld lungo traiettorie di Regge.
Abstract Intersections
Against the intricate backdrop of mathematics, Abstract Intersections stages a radically new portrayal of human emotions in the theater of life. Forged from passionate life experiences and the arduous journey of experiential mathematical learning, these poems lie at an unexpected crossroads: one which challenges the notion of separation between the intellectual stimulus provided by mathematics and experiences provoking deeply felt emotions. Placing a "favorite color" on a different footing than a "favorite mathematical object" is a controversy rather than an accepted reality in these verses. With topics ranging from elementary mathematics to advanced concepts from abstract algebra, statistics, real and complex analysis, and topology, these poems delineate the powerful emotions evoked throughout the experiential learning of celebrated theorems and concepts in mathematics. Using the language of mathematics, these poems take the reader through a surprising range of emotions and provoke deep philosophical contemplation. With mathematical and emotional context provided by the author for each poem, this poetry book caters to a wide audience, from the average intellectually curious high schooler, to seasoned members of the scientific community. A unique literary experiment, cloaked in philosophical revelation and shaped by mathematical insights, Abstract Intersections provides a profoundly original alternative in facing the challenges of life and mathematics, one where each is mirrored in the other.
Dynamic Geometry Computer Software in Geometry Classroom
The potential benefits of ICT have been identified by many countries in the world. Therefore, the essential requirement for schools and educational institutions have been made to expand teaching and learning environments and increasing the demand for education and training in most of the countries in the world. Geometry is a very significant study in the field of mathematics. It is a subset of the mathematics subject which associates with culture, history, art and design. Furthermore, geometry is commonly used to model the real-world concept which has many applications in solving practical problems. The methodical group geometrical knowledge of the ancient Greeks is one of the major successes of classical geometry. Learning geometry makes the secondary students develop some basic skills which include logical thinking abilities; spatial intuition about the universe; comparing and generalising; being careful and patient; as well as the reading and comprehension of geometrical concepts. The dynamic geometry computer software allows the users to construct geometry figures or shapes and to measure the variables of the shapes and determine the properties of them. It allows the users to; drag the figures through the screen, make geometric constructions and explain the facts about these constructions as well as test them so that the user will generalise the facts. The interactive learning environments of dynamic geometry computer software support the teaching and learning of abstract geometrical concepts in mathematics. The dynamic geometry computer software influenced students in gaining student-centered education and self-regulation. The integration of dynamic geometry computer software in learning geometry will enhance the construction knowledge in addition to the communication and dissemination of ideas in the geometry classroom.
An Elementary Course Of Mathematics Comprising Arithmetic, Algebra And Euclid
A clear, methodical introduction to the art of calculation and geometric thought. Simple rules, explained with care. S. Hall's An Elementary Course Of Mathematics is an elementary mathematics textbook that assembles arithmetic, algebra and Euclid into a coherent teaching sequence. As an arithmetic and algebra guide it unpacks foundational math concepts through plain, stepwise exposition, worked examples and progressive problems that train attention and skill in math problem solving. The Euclidean sections set out Euclidean geometry basics with direct proofs and diagrams that favour understanding over ornament. Measured in tone and practical in aim, the text functions as a student study resource for classroom use, self-study or the demands of a rigorous schooling scheme. Rooted in Victorian era mathematics, this nineteenth century textbook exemplifies the pedagogical clarity and moral seriousness of its time while retaining a surprisingly modern usefulness. Read as a classic math course, Hall's arrangement reveals how formulae, proof and practice were taught before modern curricular shifts - a window into both method and mindset. Surveying its pages gives a tangible sense of how mathematical instruction matured during the century and why foundational habits of thought - careful computation, algebraic manipulation and geometric proof - remained central. Casual readers will find the exposition brisk and instructive; classic-literature collectors will prize the work as a representative volume for a math education collection. Practical-minded educators and parents may adopt passages or problem sequences as part of a homeschooling math curriculum; historians and enthusiasts will value the book as a vintage math reference that illuminates the development of mathematical instruction. Whether returning to old lessons or discovering them for the first time, readers encounter patient explanation, crisp problems and a clarity that rewards careful study. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike.
Logic, Language, and Security
This Festschrift was published in honor of Andre Scedrov on the occasion of his 65th birthday. The 11 technical papers and 3 short papers included in this volume show the many transformative discoveries made by Andre Scedrov in the areas of linear logic and structural proof theory; formal reasoning for networked systems; and foundations of information security emphasizing cryptographic protocols. These papers are authored by researchers around the world, including North America, Russia, Europe, and Japan, that have been directly or indirectly impacted by Andre Scedrov. The chapter "A Small Remark on Hilbert's Finitist View of Divisibility and Kanovich-Okada-Scedrov's Logical Analysis of Real-Time Systems" is available open access under a CC BY 4.0 license at link.springer.com.
An Invitation to Abstract Mathematics
This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics.Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise.This second editionhas been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts.From reviews of the first edition: Bajnok's new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA ReviewsThe style of writing is careful, but joyously enthusiastic.... The author's clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
Graphs for the Analysis of Bipolar Fuzzy Information
This monograph discusses decision making methods under bipolar fuzzy graphical models with the aim of overcoming the lack of mathematical approach towards bipolar information-positive and negative. It investigates the properties of bipolar fuzzy graphs, their distance functions, and concept of their isomorphism. It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures. This book also presents the applications of mentioned concepts to real-world problems in areas of product manufacturing, international relations, psychology, global terrorism and more, making it valuable for researchers, computer scientists, social scientists and alike.
Kinetic Equations
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.
Origametry
Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.
Origametry
Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.
Analysis and Synthesis of Singular Systems
Analysis and Synthesis of Singular Systems provides a base for further theoretical research and a design guide for engineering applications of singular systems. The book presents recent advances in analysis and synthesis problems, including state-feedback control, static output feedback control, filtering, dissipative control, H∞ control, reliable control, sliding mode control and fuzzy control for linear singular systems and nonlinear singular systems. Less conservative and fresh novel techniques, combined with the linear matrix inequality (LMI) technique, the slack matrix method, and the reciprocally convex combination approach are applied to singular systems. This book will be of interest to academic researchers, postgraduate and undergraduate students working in control theory and singular systems.
Fantastische R瓣tsel Und Wie Sie Sie L繹sen K繹nnen
Die 49 verbl羹ffendsten, beliebtesten und interessantesten Mathematikr瓣tsel der Kolumne "The Riddler" auf der Nachrichtenseite "FiveThirtyEight" sind in diesem Buch f羹r das kleine (oder gr繹?ere) R瓣tselabenteuer zwischendurch gesammelt. Erforschen Sie dabei allt瓣gliche Vorkommnisse mit Mathematik und Verstand: Wie Sie am besten Ihr Smartphone fallen lassenK繹nnen Sie den unsteten Prinzen finden?Die Quadratur des QuadratsVorsicht mit dem Martini-Glas!K繹nnen Sie die Alien-Invasion stoppen?Besetzt oder nicht besetzt - das ist hier die FrageUnd wenn Roboter Ihre Pizza schneiden?Werden Sie (ja Sie!) die Wahl entscheiden? Und vieles mehr! Die einfachsten R瓣tsel erfordern blo? einen Geistesblitz, w瓣hrend Sie f羹r die schwierigsten schon ein gewisses Geschick in Analysis und Wahrscheinlichkeitstheorie ben繹tigen. Die "Fantastischen R瓣tsel" sind ein Muss f羹r jeden Mathematik- oder R瓣tselliebhaber!"Ein modernes, intelligentes R瓣tselbuch, wie ich es noch nie zuvor gesehen habe, dessen mathematische und logische Herausforderungen Ihr Gehirn auf neue Art und Weise fordern werden" - Will Shortz, New York Times, NPR-PuzzlemasterDer HerausgeberOliver Roeder war Redakteur bei FiveThirtyEight und Herausgeber der mathematischen Kolumne "The Riddler". Er hat in Wirtschaftswissenschaften mit Schwerpunkt Spieltheorie promoviert und war Nieman fellow an der Harvard University 2020. Er lebt in Brooklyn, New York.
Berechenbarkeit
In diesem essential werden wesentliche Konzepte der Berechenbarkeitstheorie er繹rtert. Zun瓣chst werden unterschiedliche Modelle der Berechenbarkeit eingef羹hrt und ihre semantische Gleichwertigkeit gezeigt. Dieses Resultat steht in Einklang mit der Church-Turing-These, nach der jede intuitiv berechenbare Funktion partiell-rekursiv ist. Neben zentralen Instrumenten der Berechenbarkeit, wie etwa der G繹delisierung von berechenbaren Funktionen und der Existenz universeller berechenbarer Funktionen, stehen unentscheidbare Probleme im Fokus, wie etwa das Halteproblem sowie das Wortproblem f羹r die Term-Ersetzung. Semi-entscheidbare Mengen werden beleuchtet und die zentralen S瓣tze von Rice und Rice-Shapiro werden skizziert.
The Maths Tutor
This book is for anyone studying Key Stage 3 Mathematics in Secondary School years 7, 8 and 9. The book will help you to overcome any difficulties or gaps in your knowledge. Parents or carers, you may wish to update your maths skills, in order to help your children with their homework. Maths tutors, you may find the exercise questions and answers a useful addition to your teaching.
Mechanics of Non-Homogeneous Anisotropic Materials
The meaning of Non-Homogeneous in this book is that the quality of materials is different from place to place. As shown in Figure 1, in the two dimensional X-Y coordinate or three dimensional X-Y-Z coordinate, depending on the location, the material characteristics or failure stresses are different, therefore it is complex in nature. In the strength of materials, we call it Non-Homogeneous. It is well explained in Figures 1 and 2. Also the meaning of Anisotropic is the material characteristics such as the elastic constants or failure stresses are different depending on the geometric direction. As a good example of anisotropic material, we can look at the reinforced concrete. The concrete is strong in compressive stresses but very weak in tensile stresses. To overcome the weakness, we insert steel bars, the reinforcing bars are very strong in the tensile forces. In other words, in the direction of reinforcing bars, the materials are strong and in the other direction, they are weak in the tensile strength. These kind of materials are named as diversified or Anisotropic Materials. Now is the era of aviation and aeronautics. Huge passenger aircrafts can fly around the earth non-stop.
Large Cardinals, Determinacy and Other Topics
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on 'Extensions of AD, models with choice', while Part VIII ('Other topics') collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.
Set Function T
Preliminaries.- The Set Function T.- Decomposition Theorems.- T-Closed Sets.- Continuity of T.- Images of T.- Applications.- Questions.- References.- Index.
Topics in Domination in Graphs
This volume comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The focus is on primary dominating sets such as paired domination, connected domination, restrained domination, dominating functions, Roman domination, and power domination. Additionally, surveys include known results with a sample of proof techniques for each parameter. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms; the second chapter provides an overview of models of domination from which the parameters are defined. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments in the field and proof techniques used.
Geometry And Trigonometry
Geometry And Trigonometry: a steady companion through proof and proportion. A patient teacher and exact reference. Clear, exact, and deeply practical. First-rate exposition guides readers from euclidean geometry basics to the richer terrain of trigonometric reasoning. As a geometry textbook for students it balances definition and demonstration; as a classic trigonometry guide it offers trigonometric functions explained with care, showing how sine, cosine and tangent serve measurement and insight. The book privileges geometric problem solving, supplying progressively demanding questions that sharpen method as much as memory. Explanations are concise, diagrams purposeful and the progression natural - suitable both for focused study and for those returning to core ideas after years away. Examples emphasise method over memorisation, so readers learn to craft proofs, estimate magnitudes, and approach unfamiliar problems with confidence. Rooted in twentieth century mathematics, this text occupies a distinctive place in academic math resource lists and in any mathematics reference collection. Readable enough to support the high school math curriculum and targeted enough for college entrance math prep, it also serves as an advanced math workbook for independent learners and tutors. The clear ordering supports lesson planning and the steady escalation of challenge suits focused revision as much as longer-term study. Its historical voice and method offer a window into how mathematical instruction matured through the century, while its clarity keeps it relevant alongside contemporary texts. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. For casual readers who enjoy the intellectual pleasure of clear argument and for classic-literature collectors seeking a cultural artefact, this edition is equally rewarding. Collectors value its restrained style and historical interest; casual readers value its clarity and practical problem focus. Practical, elegant and enduring, it returns core mathematics fundamentals study to student desks and the scholar's shelf.
Primzahlen. Algorithmen, Charakterisierungen und spezielle Typen
Diplomarbeit aus dem Jahr 2008 im Fachbereich Mathematik - Zahlentheorie, Note: 1,7, Universit瓣t zu K繹ln, Sprache: Deutsch, Abstract: Die Arbeit thematisiert das Themenfeld der Primzahlen. Neben den von Euklid gezeigten S瓣tzen werden zu Beginn der Arbeit andere zentrale Aussagen der Zahlentheorie bewiesen. Das anschlie?ende Kapitel liefert f羹r den Spezialfall, dass N - 1 leicht faktorisierbar ist, durch die von Lucas und Proth entwickelten klassischen Primzahltests eine Antwort. Als eine Art Komplement dazu werden danach mithilfe von Lucas-Folgen Tests hergeleitet, welche die Kenntnis der Primfaktoren von N + 1 erfordern. Dar羹ber hinaus werden zwei wichtige Teilfolgen von Lucas-Folgen, n瓣mlich die Fermat-Zahlen und die Mersenne-Zahlen behandelt. Des Weiteren werden zusammengesetzte Zahlen betrachtet, welche gewisse Eigenschaften mit den Primzahlen teilen. Wenn N keine spezielle Form aufweist, also weder N + 1 noch N - 1 leicht faktorisierbar sind, liefert das n瓣chste Kapitel einen Test, dessen Idee auf elliptischen Kurven basiert. Dieser Algorithmus hei?t Goldwasser-Kilian und ist der momentan schnellste allgemeine Primzahltest. Anschlie?end werden einige spezielle Primzahltypen vorgestellt.
A Compendium of Trending Research in Mathematical Sciences
This book is a worthwhile compilation of research articles written by a group of active research scholars working in various fields of Mathematics viz. Computational Mathematics, Modern Algebra, Number Theory, General Topology, Relativity, etc. The book consists of nine chapters, which includes some historical surveys of recent developments as well as some of the original works in the respective areas.
The Essence of Numbers
This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.
Fluiddynamik 2
Dieses 6-b瓣ndige Werk befasst sich mit den Anwendung von Differentialgleichungen in diversen Bereichen der Physik, Ingenieurwesen, Mathematik, Biologie und Soziologie. In jedem Buch wird die Theorie einleitend behandelt, dann werden die verschiedenen Anwendungen und Beispiele im Detail erkl瓣rt und diskutiert. B瓣nde 5 und 6 fokussieren auf Str繹mungen; Band 6 insbesondere auf turbulente Str繹mungen und Grenzschichttheorie.
Dimension Theory
This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Fast Track to Forcing
This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.
Games for Your Mind
A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt G繹del's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.
Uses of Technology in Upper Secondary Mathematics Education
This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes brought by technology in the interactions between environment, students and teachers, the interrelations between mathematical activities and technology, skills and competencies that must be developed in teacher education. Research shows that the use of some technologies may deeply change the solving processes and contribute to impact the learning processes. The questions are which technologies to choose for which purposes, and how to integrate them, so as to maximize all students' agency. In particular the role of the teacher in classrooms and the content of teacher education programs are critical for taking full advantage of technology in teaching practice. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Problem Solving in Mathematics Education
This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches - why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches - what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts - what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Theories in and of Mathematics Education
This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald D繹rfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Interdisciplinary Mathematics Education
This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field's relevant historical, conceptual and theoretical backgrounds, what "discipline" means and how inter-, trans-, and meta-disciplinary activities can be understood. Relevant theoretical perspectives from Marx, Foucault and Vygotsky are explained, along with key ideas in theory, e.g. boundaries, discourses, identity, and the division of labour in practice. Second, the book reviews research findings of mainly empirical studies on interdisciplinary work involving mathematics in education, in all stages of education that have become disciplined. For example, it reports that a common theme in studies in middle and high schools is assessing the motivational benefits for the learner of subsuming disciplinary motives and even practices to extra-academic problem-solving activities; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. These disciplinary boundaries are less obviously limitations in middle and primary schools, and in some vocational courses. Third and finally, it explores selected case studies that illustrate these concepts and findings, both in terms of the motivational benefits for learners and the institutional and other boundaries involved. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Teaching and Learning Mathematical Modelling
This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term "mathematical model" as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Problem Solving in Mathematics Education
This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches - why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches - what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts - what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Uses of Technology in Upper Secondary Mathematics Education
This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes brought by technology in the interactions between environment, students and teachers, the interrelations between mathematical activities and technology, skills and competencies that must be developed in teacher education. Research shows that the use of some technologies may deeply change the solving processes and contribute to impact the learning processes. The questions are which technologies to choose for which purposes, and how to integrate them, so as to maximize all students' agency. In particular the role of the teacher in classrooms and the content of teacher education programs are critical for taking full advantage of technology in teaching practice. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Application of Data Mining and Beyond
This is a collection of articles related to data mining and its application especially in education and banking industry, as well as the advantages of new technologies such as cloud computing and data science. Through the articles, the basic concepts, processes, historical development, as well as a review of the relevant literature are explained in detail. The book is intended for anyone who wants to get better acquainted with the above topics. It is written in simple vocabulary to bring scientific topics closer to the general population. Book Chapters: -Knowledge discovery in databases: relation to operations research-Case study in banking using neural networks-Determinants of Efficacy of Studying in the Republic Croatia: Comparing Neural Networks and Decision Trees: Research Framework Proposition-Application of educational data mining-Predicting students' success using Neural networks-Benefits of Educational Data Mining-Cloud computing ‐ Infrastructure as a service based on AWS-Data science: fundamental principles-Data science life cycle
International Comparative Studies in Mathematics
This open access book examines the cultural and educational factors that influence how successfully students learn mathematics; focuses on international comparative studies as a means of generating theories and improving students' learning; and discusses four valuable lessons that can be learned from international comparative studies with regard to improving students' learning. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Numerical Methods
Numerical methods are a specific form of mathematics that involve creating and use of algorithms to map out the mathematical core of a practical problem. Numerical methods naturally find application in all fields of engineering, physical sciences, life sciences, social sciences, medicine, business, and even arts. The common uses of numerical methods include approximation, simulation, and estimation, and there is almost no scientific field in which numerical methods do not find a use. Results communicated here include topics ranging from statistics (Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions) and Statistical software packages (dCATCH-A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS) to new approaches for numerical solutions (Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖
Relativistic Quantum Information
Relativistic quantum information is one of the most exciting fields of physics today. Not only does it open possibilities for new forms of computing but it also calls into question the peaceful coexistence between classical space-time and quantum physics with scenarios that reopen the relationships between locality and nonlocality in the foundational structure of physics. Curated by two international experts Ignazio Licata and Fabrizio Tamburini, this volume hosts a selection of particularly significant essays for the new territories, and is dedicated to the 60th anniversary of Prof. Ignazio Licata.
Interdisciplinary Mathematics Education
This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field's relevant historical, conceptual and theoretical backgrounds, what "discipline" means and how inter-, trans-, and meta-disciplinary activities can be understood. Relevant theoretical perspectives from Marx, Foucault and Vygotsky are explained, along with key ideas in theory, e.g. boundaries, discourses, identity, and the division of labour in practice. Second, the book reviews research findings of mainly empirical studies on interdisciplinary work involving mathematics in education, in all stages of education that have become disciplined. For example, it reports that a common theme in studies in middle and high schools is assessing the motivational benefits for the learner of subsuming disciplinary motives and even practices to extra-academic problem-solving activities; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. These disciplinary boundaries are less obviously limitations in middle and primary schools, and in some vocational courses. Third and finally, it explores selected case studies that illustrate these concepts and findings, both in terms of the motivational benefits for learners and the institutional and other boundaries involved. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Theories in and of Mathematics Education
This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald D繹rfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
History of the Theory of Numbers (Volume III) Quadratic and Higher Forms With A Chapter on the Class Number
A landmark in the evolution of mathematical theory, Leonard Eugene Dickson's "History Of The Theory Of Numbers (Volume III): Quadratic And Higher Forms With A Chapter On The Class Number" invites readers deep into the intricate world of quadratic forms and the mysteries of class number exploration. Every page reveals the intellectual ambition of early 20th-century mathematics, guiding both seasoned researchers and passionate newcomers through the pivotal concepts that shaped modern number theory. This volume stands as a foundational mathematics literature, meticulously tracing the development of quadratic forms study and the broader landscape of advanced number theory. Dickson's work, revered among academic mathematicians, offers a rare glimpse into the historical mathematics text tradition, where rigorous analysis meets the elegance of mathematical discovery. It is more than a chronicle; it is a mathematics researchers guide, illuminating the paths taken by pioneers and the enduring questions that continue to inspire. Republished by Alpha Editions in a careful modern edition, this volume preserves the spirit of the original while making it effortless to enjoy today - a heritage title prepared for readers and collectors alike. Whether you are delving into the works of Leonard Dickson for scholarly insight or seeking a collector's piece from the mathematical history series, this book stands as a cultural touchstone, bridging generations of inquiry and admiration.
