Mathematics Phase 5
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Informative Psychometric Filters
This book is a series of case studies with a common theme. Some refer closely to previous work by the author, but contrast with how they have been treated before, and some are new. Comparisons are drawn using various sorts of psychological and psychophysiological data that characteristically are particularly nonlinear, non-stationary, far from equilibrium and even chaotic, exhibiting abrupt transitions that are both reversible and irreversible, and failing to meet metric properties. A core idea is that both the human organism and the data analysis procedures used are filters, that may variously preserve, transform, distort or even destroy information of significance.
Geometry of Grief
In this profound and hopeful book, a mathematician and celebrated teacher shows how mathematics may help all of us-even the math-averse-to understand and cope with grief. We all know the euphoria of intellectual epiphany-the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief, mathematician Michael Frame draws on a career's worth of insight-including his work with a pioneer of fractal geometry Benoit Mandelbrot-and a gift for rendering the complex accessible as he delves into this twinning of understanding and loss. Grief, Frame reveals, can be a moment of possibility. Frame investigates grief as a response to an irrevocable change in circumstance. This reframing allows us to see parallels between the loss of a loved one or a career and the loss of the elation of first understanding a tricky concept. From this foundation, Frame builds a geometric model of mental states. An object that is fractal, for example, has symmetry of magnification: magnify a picture of a mountain or a fern leaf-both fractal-and we see echoes of the original shape. Similarly, nested inside great loss are smaller losses. By manipulating this geometry, Frame shows us, we may be able to redirect our thinking in ways that help reduce our pain. Small‐scale losses, in essence, provide laboratories to learn how to meet large-scale losses. Interweaving original illustrations, clear introductions to advanced topics in geometry, and wisdom gleaned from his own experience with illness and others' remarkable responses to devastating loss, Frame's poetic book is a journey through the beautiful complexities of mathematics and life. With both human sympathy and geometrical elegance, it helps us to see how a geometry of grief can open a pathway for bold action.
Clean Numerical Simulation
A new strategy to gain "clean" reliable numerical simulations of chaos and turbulence, namely the Clean Numerical Simulation (CNS), which can greatly reduce numerical noises to a tiny level much smaller than that of true solutions so numerical noises are negligible, and the corresponding numerical simulation is "clean" and thus reliable.
Differential and Low-Dimensional Topology
The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin research as quickly as possible. The only prerequisite assumed is an undergraduate algebraic topology course. The first half of the text reviews basic notions of differential topology and culminates with the classification of exotic seven-spheres. It then dives into dimension three and knot theory. There then follows an introduction to Heegaard Floer homology, a powerful collection of modern invariants of three- and four-manifolds, and of knots, that has not before appeared in an introductory textbook. The book concludes with a glimpse of four-manifold theory. Students will find it an exhilarating and authoritative guide to a broad swathe of the most important topics in modern topology.
Real Harmonic Analysis
This book presents the material covered in graduate lectures delivered at The Australian National University in 2010. Real Harmonic Analysis originates from the seminal works of Zygmund and Calder籀n, pursued by Stein, Weiss, Fefferman, Coifman, Meyer and many others. Moving from the classical periodic setting to the real line, then to higher dimensional Euclidean spaces and finally to, nowadays, sets with minimal structures, the theory has reached a high level of applicability. This is why it is called real harmonic analysis: the usual exponential functions have disappeared from the picture. Set and function decomposition prevail.
Mathematics Phase 7
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 3
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 4
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 6
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Mathematics Phase 1
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Differential and Low-Dimensional Topology
The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin research as quickly as possible. The only prerequisite assumed is an undergraduate algebraic topology course. The first half of the text reviews basic notions of differential topology and culminates with the classification of exotic seven-spheres. It then dives into dimension three and knot theory. There then follows an introduction to Heegaard Floer homology, a powerful collection of modern invariants of three- and four-manifolds, and of knots, that has not before appeared in an introductory textbook. The book concludes with a glimpse of four-manifold theory. Students will find it an exhilarating and authoritative guide to a broad swathe of the most important topics in modern topology.
Math Murder in Media Manufactured Madness
For 2.5 years since the declaration of the Covid-19 pandemic, people have felt extreme fear. Reason, rationality, basic math and logic have taken a severe beating. This book documents the math murder in the mad fear largely manufactured by relentless propaganda in the media. It is meant for those who want to reflect on the planet-wide panic surrounding Covid-19, to examine if it was justified, to sift truth from propaganda, to learn how we can possibly prevent such mistakes in the future. It is especially meant for the next generation, who were affected least by the virus itself, yet affected most by the irrational measures in the name of public health. They must know how the adults on the planet abandoned reason for madness, rationality for fear, and basic math for obvious absurdity. Most parts are meant to be understandable with only a secondary-school or high-school mathematics background.
Poetic Logic and the Origins of the Mathematical Imagination
This book treats eighteenth-century Italian philosopher Giambattista Vico's theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and N繳簽ez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics.The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its "modifications" (his term for "creations"); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts--including mathematics--the mind has allowed humans to establish "the world of civil society," Vico's term for culture and civilization.The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Al-Kashi's Miftah Al-Hisab, Volume III: Algebra
Jamshīd al-Kāshī's Miftāḥ al-Ḥisab (Key to Arithmetic) was largely unknown to researchers until the mid-20th century, and has not been translated to English until now. This is the third and final book in a multi-volume set that finally brings al-Kāshī's groundbreaking textbook to English audiences in its entirety. As soon as it was studied by modern researchers, Miftah changed some false assumptions about the history of certain topics in mathematics. Written as a textbook for students of mathematics, astronomy, accounting, engineering, and architecture, Miftah covers a wide range of topics in arithmetic, geometry, and algebra. By sharing al-Kāshī's most comprehensive work with a wider audience, this book will help establish a more complete history of mathematics, and extend al-Kāshī's influence into the 21st century and beyond. The book opens by briefly recounting al-Kāshī's biography, so as to situate readers in the work's rich historical context. His impressive status in the kingdom of Ulugh Beg is detailed, as well as his contributions to both mathematics and astronomy. As a master calculator and astronomer, al-Kāshī's calculations of 2π and sin(1⁰) were by far the most accurate for almost two centuries. His law of cosines is still studied in schools today. This translation contributes to the understanding and appreciation of al-Kāshī's esteemed place in the scientific world. A side-by-side presentation of the source manuscript--one of the oldest known copies--and the English translation is provided on each page. Detailed footnotes are also provided throughout, which will offer readers an even deeper look at the text's mathematical and historical basis. Researchers and students of the history of mathematics will find this volume indispensable in filling in a frequently overlooked time period and region. This volume will also provide anybody interested in the history of Islamic culture with an insightful look at one of the mathematical world's most neglected figures.
Complex Feedback Queue Network Models
Queuing theory has become most important discipline of Operation Research. In real world we are facing queues everywhere around us. Sometimes we see very complex type of queue networks. This book includes three complex types of queue network models. These queue network models has been analysed in stochastic environment with the facility of revisit for customer's satisfaction. Practical situations are also given at the end of every chapter. The applicability of these models is not limited to a specific situation; they are applicable to various fields. This book will be helpful for the researchers, who are working on queue network models in stochastic environment.
Mathematics for Computation (M4C)
The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
Dissipative Lattice Dynamical Systems
There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.
Generalized Radon Transforms and Imaging by Scattered Particles
A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.
Basic Topology 3
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
Mathematical Logic
This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene's theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht- Fra簿ss矇 game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and G繹del's incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic. Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style and topics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including G繹del's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
An Introduction to the Math of Voting Methods
Some modern political discussions are focused on electoral reform and the mechanics of democracy. For instance, Maine and Alaska recently adopted new procedures for statewide elections that involve Ranked Choice Voting, while a similar ballot measure in Massachusetts was only narrowly defeated. Meanwhile, countries all over the world use other voting methods with runoffs or scores. It's important for people to be aware of how different voting methods work in practice so that we can have productive debates about which to use in various situations.​Accordingly, this book will teach you about a variety of voting methods through concrete examples and clear explanations. Each chapter illustrates a different type of voting method using basic definitions, real-world examples, a list of pros and cons, and detailed practice problems with solutions. No prior mathematical or political knowledge is assumed. In fact, the prose is designed for a wide audience, making this book ideal for a general education mathematics course or anyone else who is curious to learn about different methods of voting.
Gauss Nodes Revolution
Radical insight into how and why Gauss nodes work using alternative non-polynomial vectors presented in a simple argument. In fact, the Runge-vector solution (arguably the most important solution presented in GNR), is fully accessible to high school mathematics. And conventional Gauss-Legendre nodes generate as one of an infinite number of approaches to the Runge-vector solution.
Stem Education Now More Than Ever
In response to "these unconventional and uncertain years," veteran educator Rodger W. Bybee has written a book that's as thought-provoking as it is constructive. Now more than ever, he writes, America needs reminders of both the themes that made it great in the first place and STEM's contributions to its citizens." Science educators must address STEM issues at local, national, and global levels. And teachers should help students tackle today's problems with new approaches to STEM learning that complement traditional single-discipline programs. STEM Education Now More Than Ever addresses these themes through four wide-ranging sections. Parts of the book are what you might expect from a longtime thought leader in science education. In light of the 2016 election and recent assaults on science's validity, Bybee strongly asserts the need for a new case for STEM education. Other parts may not seem typical for a book on STEM. He writes about the Enlightenment, the U.S. Constitution, democracy, and citizenship as reminders of the effects of STEM disciplines on America's foundational ideas and values. In the end, Bybee ties it all together with positive, practical recommendations. A major one involves newer, faster ways to help teachers develop STEM units that address contemporary challenges in their classes. Another involves the importance of strong leadership from teachers and the STEM education community--leadership Bybee believes we need now more than ever.
The Making of Mathematics
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of G繹del's incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem provingby the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Star-Critical Ramsey Numbers for Graphs
This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists.This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges.The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.
The Mathematical Field
While writing this book, I felt intuitively that readers would want to know whether the Creator knew about the Mathematical Field. I have answered the question in one section of this book. Unfortunately, I do not know whether you will agree with me because as I mention in the book, human beings have free will. The book shows the beauty and purity of the Mathematical Field, particularly how the numbers follow specific rules to form different systems like Binary, Octal, Decimal, Duodecimal, and Hexadecimal, where they can have different place values. It is significant that the decimal system suits human beings and our design of 10 fingers and 10 toes for counting seems to be no accident. The rules of the decimal system allows the numbers to be easily added, subtracted, multiplied and divided. Even the higher functions of calculating square roots, cube roots, Sine, Cosine, Tan, logarithms, and exponentials can be easily calculated using a simple calculating machine. The numbers form sequences and series. The arithmetic and geometric series enable easy calculation of numbers using formulae. All the periodic functions like Sine, Cosine, Tan, and ex can be expressed as a series. The Algebraic Arm has shown us how lines and curves can be expressed as simple equations, which we can visualise on the Cartesian Plane in two dimensions. Through differentiation and integration, we can sketch curves and calculate areas and volumes. In the Geometric Arm, we can visualise the points forming lines and the lines forming different slopes and different angles. Geometry also shows the different formations the lines can take-three lines to form triangles, four lines to form quadrilaterals, five lines to form pentagons, and many other shapes with more lines. Geometry also shows the purity of the conic sections forming hyperbolas, ellipses, parabolas, and circles with specific equations and characteristics that enable them to be easily sketched. The manner in which the two foci of the ellipse can come together to form the beautiful circle with one centre and one radius is amazing. Although the Cartesian Plane is more of an algebraic way of showing points in terms of x and y coordinates from an origin of (0,0), the Geometric Arm has shown that points can be described geometrically, as a distance and an angle from an origin. Geometry has also shown us how points around a circle can be drawn as Sine and Cosine waves, which generate the numerous trigonometric identities. The Mathematical Field shows the importance of measurements, which has led to standardisation and mass production of goods and services. This has obviously made things easy for the large populations supported in the cities and towns all over the world. The Mathematical Field has also made it possible to draw and design objects before manufacture and construction; this eliminates errors and wastage. Numbers are essentially pure producing the same results when put in equations and formulae. Human beings and the Fields of Knowledge can produce uncertain results because of the free will issue. Mathematics allows for this in Probability Theory, a branch of Arithmetic Arm. The Sporting Field is full of probability associated with the results. If five horses are running in a race, there is only a certain probability that a particular horse will win. Also, if one tossed a coin, there is only a 50% chance of getting a head and a 50% chance of not getting a head. Probability Theory shows how to calculate the chances of certain events occurring. Finally, the Mathematical Field shows us how to sort the data accumulated in many of Fields of Knowledge to produce useful statistical data and generate formulae and applications in many other Fields of Knowledge, some of which will be considered in my next book.
Operation Research
Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.The concept of operations research arose during World War II by military planners. After the war, the techniques used in their operations research were applied to addressing problems in business, the government and society.
Solving Diophantine Problems
The name Diophantus has long been attached to what we call under-determined algebraic problems with more unknowns than information. He himself was short of good methods of attack but his work has been the jump off point for a great and hugely productive range of mathematical developments. His choice of word problems remains a source of fascination to this day and that is the topic of this book..
A Brief Quadrivium
Mathematics occupies a central place in the traditional liberal arts. The four mathematical disciplines of the quadrivium-arithmetic, geometry, music, and astronomy-reveal their enduring significance in this work, which offers the first unified, textbook treatment of these four subjects. Drawing on fundamental sources including Euclid, Boethius, and Ptolemy, this presentation respects the proper character of each discipline while revealing the relations among these liberal arts, as well as their connections to later mathematical and scientific developments.This book makes the quadrivium newly accessible in a number of ways. First, the careful choice of material from ancient sources means that students receive a faithful, integral impression of the classical quadrivium without being burdened or confused by an unwieldy mass of scattered results. Second, the terminology and symbols that are used convey the real insights of older mathematical approaches without introducing needless archaism. Finally, and perhaps most importantly, the book is filled with hundreds of exercises. Mathematics must be learned actively, and the exercises structured to complement the text, and proportioned to the powers of a learner to offer a clear path by which students make quadrivial knowledge their own.Many readers can profit from this introduction to the quadrivium. Students in high school will acquire a sense of the nature of mathematical proof and become confident in using mathematical language. College students can discover that mathematics is more than procedure, while also gaining insight into an intellectual current that influenced authors they are already reading: authors such as Plato, Aristotle, Augustine, Thomas Aquinas, and Dante. All will find a practical way to grasp a body of knowledge that, if long neglected, is never out of date.
Teaching the Quadrivium
Reviving an educational tradition involves a double task. A new generation of students must be taught, and at the same time the teachers themselves must learn. This book addresses the teachers who seek to hand on the quadrivium-the four mathematical liberal arts of arithmetic, geometry, music, and astronomy-at the same time as they acquire it.Two components run in parallel throughout the book. The first component is practical. Weekly overviews and daily lesson plans explain how to complete the study of A Brief Quadrivium in the course of a single school year, and suggestions for weekly assessments make it easy to plan tests and monitor student progress. The second component is directed to the continuing education of the teacher. Short essays explore the history, philosophy, and practice of mathematics. The themes of these essays are coordinated with the simultaneous mathematical work being done by students, allowing the teacher to instruct more reflectively.Some users of this book are confident in their grasp of mathematics and natural science. For them, the essays will clarify the unity of mathematical activity over time and reveal the old roots of new developments. Other users of this book, including some parents who school their children at home, find mathematics intimidating. The clear structure of the lesson plans, and the support of the companion essays, give them the confidence to lead students through a demanding but doable course of study.The British mathematician John Edensor Littlewood remarked that one finds in the ancient mathematicians not "clever schoolboys" but rather "Fellows of another College." This guide invites all teachers of the quadrivium to join the enduring mathematical culture of Littlewood and his predecessors, and to witness for themselves the significance and vitality of a tradition as old as Pythagoras.
Random Graphs and Networks: A First Course
Networks surround us, from social networks to protein-protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs - component structure, matchings and Hamilton cycles, connectivity and chromatic number - before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Random Graphs and Networks: A First Course
Networks surround us, from social networks to protein-protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs - component structure, matchings and Hamilton cycles, connectivity and chromatic number - before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Mental Maths
This series on Mental Maths has been developed to improve mathematical skills of young children. The books include various mathematical problems and the correct methodology for solving them, several illustrative examples and many unsolved problems for practice which will help strengthen the basic concepts of mathematics.
Mental Maths
This series on Mental Maths has been developed to improve mathematical skills of young children. The books include various mathematical problems and the correct methodology for solving them, several illustrative examples and many unsolved problems for practice which will help strengthen the basic concepts of mathematics.
Mental Maths
This series on Mental Maths has been developed to improve mathematical skills of young children. The books include various mathematical problems and the correct methodology for solving them, several illustrative examples and many unsolved problems for practice which will help strengthen the basic concepts of mathematics.
Numerical Modelling and Simulation of Fractals in C++
In Euclidean Geometry, the simplest and best known figures are studied, such as: straight lines, squares, circles, cones, pyramids, among others. In this context, many phenomena and shapes are found in nature, which cannot be explained in the conventional mathematical molds, requiring a special theory to explain and characterize them, known as fractal geometry. According to (TRICOT, 1955) fractal means "broken", which are geometric shapes with some special characteristics that define and distinguish them from other shapes, such as self-similarity at different levels of scale. Currently, fractal geometry, especially the fractal dimension, has been used in several areas of knowledge, such as the study of chaotic systems, image analysis and pattern recognition, texture analysis, among others. This book presents numerical simulation along with mathematical concepts with object oriented programming languages, allowing the topological representation of fractals.
On Cantor and the Transfinite
A set in mathematics is just a collection of elements; an example is the set of natural numbers {1, 2, 3, ...}. Simplifying somewhat, the theory of sets can be regarded as the foundation on which the whole of mathematics is built; and the founder of set theory is the German logician and mathematician Georg Cantor (1845-1918). However, the aspect of Cantor's work that's most widely known-or most controversial, at any rate-isn't so much set theory in general, but rather those parts of that theory that have to do with infinite sets in particular. Cantor claimed among other things that the infinite set of real numbers contains strictly more elements than the infinite set of natural numbers. From this result, he concluded that there's more than one kind of infinity; in fact, he claimed that there are an infinite number of different infinities, or transfinite numbers. (He also believed these results had been communicated to him by God.) The aim of this book is to explain and investigate these claims of Cantor's in depth (and question them, where appropriate). It's not a textbook, though; instead, it's a popular account-it tells a story-and the target audience is interested lay readers, not mathematicians or logicians. What little mathematics is needed to understand the story is explained in the book itself.
Basic Algebra 1
This book covers over 1000+ problems of practice in the core areas of1. Verbal expressions and Equations2. Variable Expressions3. Variable Equations4. Variable Inequalities5. Least Common Multiples6. Simplification of ExponentsVisit www.math-knots.com for more books.Questions?e-mail: mathknots.help@gmail.comMastering the concepts is a very important part of the academic excellence of students.1000+ problems to practice and master the concepts
Fractions
This book reinforces the concepts of Fractions. This is the basic block for mastering elementary mathThis book containsAdditions of FractionsSubtractions of FractionsMultiplications of FractionsDivisions of FractionsMixed NumbersVisit www.math-knots.com for more books.Questions? e-mail: mathknots.help@gmail.com Mastering the concepts is a very important part of the academic excellence of students.1000+ problems to practice and master the concept
Decimals
This book reinforces the concepts of Decimal numbers: 1. Additions2. Subtractions3. Multiplications4. Divisions5. Rounding a place value6. Write in words and numbersMastering the concepts is a very important part of the academic excellence of students.
Geometry
This book covers over 1000+ problems of practice in the core areas of 1. Various types of Angles2. Finding a missing Angle3. Areas of 2-D figures4. Volumes of 3-D figures5. Total surface Areas of 3-D figures Visit www.math-knots.com for more books.Questions? e-mail: mathknots.help@gmail.com Mastering the concepts is a very important part of the academic excellence of students.1000+ problems to practice and master the concepts
Pre-Algebra
The Pre-Algebra practice sets are developed to help teachers and counselors make informed decisions about the initial placement of students in the secondary mathematics curriculum.Math-Knots Pre-Algebra Books, designed to harnesses a child's Pre-Algebra skills.Math-Knots Pre-Algebra Work Book Includes: Topics covering Pre-algebra skills extensively1000 + questionsAnswer key is included.The content has been successfully used by many kids over the years to ace the test.Also availablePre-Algebra Work book - Vol 1a4ace offers an online comprehensive test prep course for students .The most effective online test prep course for boosting your Pre-Algebra skillsPractice test series with 9, 12, 21 or 32 practice testsVarious packages to chooseDetailed step by step solutionsStrategies to improve speed & accuracy on the testStudents can practice as many times as they needTime based assessments simulating the real test.Many of our students got highest scoresVisit https: //a4ace.comPurchase ONLY our latest edition books. If you see any issues, please email us mathknots.help@gmail.com. For more practice tests visit www.a4ace.com
Pre-Algebra
The Pre-Algebra practice sets are developed to help teachers and counselors make informed decisions about the initial placement of students in the secondary mathematics curriculum.Math-Knots Pre-Algebra Books, designed to harnesses a child's Pre-Algebra skills.Math-Knots Pre-Algebra Work Book Includes: Topics covering Pre-algebra skills extensively1000 + questionsAnswer key is included.The content has been successfully used by many kids over the years to ace the test.Also availablePre-Algebra Work book - Vol 2a4ace offers an online comprehensive test prep course for students .The most effective online test prep course for boosting your Pre-Algebra skillsPractice test series with 9, 12, 21 or 32 practice testsVarious packages to chooseDetailed step by step solutionsStrategies to improve speed & accuracy on the testStudents can practice as many times as they needTime based assessments simulating the real test.Many of our students got highest scoresVisit https: //a4ace.comPurchase ONLY our latest edition books. If you see any issues, please email us mathknots.help@gmail.com. For more practice tests visit www.a4ace.com
Hyers-Ulam Stability of Function Equations and Fractional Differential Equations
The main purpose of this book is to present some of the old and recent results on Hyers-Ulam stability of function equations and differential equations in Banach spaces, quasi-Banach spaces, F-spaces and group. The book provides a survey of both the latest and new results especially on the following topics: (1)Stability theory for several new functional equations in Banach spaces.(2)Stability of some functional equations and some properties of groups.(3)Hyers-Ulam Stability of functional differential equations and partial differential equations.(4)Stability of nonlinear fractional differential equations.(5)Stability of differential equations on time scales
