Numerus Computatio Balisticum
"Numerus Computatio Balisticum" is a fascinating book that explores the arcane discipline of number theory through the power of computation. With a deep passion for both computers and number theory, the author has spent years crafting elaborate algorithms to unlock the secrets of the integers. In this book, the author shares some of the most interesting and complex problems in number theory, from the history of the discipline to contemporary research. The book features chapters on topics such as Nash Goldbach Decompositions, Elliptic Curve Experiments, Alan Turing and Computers, the Collatz Conjecture, and Fermat's Factorization Method on Brilliant Numbers. Each chapter offers a unique glimpse into the intricate web of abstract concepts and elusive patterns that make up the fascinating world of computational number theory. Readers will also come across personal reflections that showcase the author's dedication and passion for the discipline. Despite the foreboding sense of mystery that surrounds the power of numbers, the author's aim is not to scare but to inspire. This book is perfect for anyone looking to explore the labyrinthine depths of mathematical thought and discover the wonders and terrors that lie within the shadowy realm of the integers. Whether you're a seasoned mathematician or a curious novice, this book is sure to ignite a spark of inspiration that drives you to investigate these problems for yourself. So, dive into this tome and behold the eerie and fascinating beauty of numbers!
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.
100+1 Problems in Advanced Calculus
This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination.In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l'Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found atthe end of each chapter.Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.
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.
Partial Differential Equations
This is a modern textbook on partial differential equations covering all the basic topics of a first course in PDEs. A balanced presentation introduces and practices all necessary problem-solving skills, yet is concise and friendly to the reader. The teaching-by-examples approach guides step-by-step learning of concepts and techniques.
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.
The Splendor and Squalor of Numbers
This captivating book on number theory explores the hidden beauty of numbers and the fascinating world of mathematics. The author's compulsion to analyze and contemplate the splendor (and squalor) of numbers leads him to seek out strange mathematical properties lurking within the platonic realm. The book covers a wide range of topics related to number theory, including compound interest, near misses of Fermat's last theorem, conjectures on twin primes, the mysterious qualities of zebra irrational numbers, and more. Readers will also enjoy a few fictional stories that feature numbers, which serve to further illuminate the beauty and wonder of mathematics (it's worth noting that the stories are entirely fictional, and any characters that might resemble real-life individuals (living or deceased) are entirely coincidental). The author's main goal is to inspire readers to engage in their own investigations of mathematical problems and discover the thrill of probing the integers to appreciate their mysterious and astounding qualities. Whether you're a seasoned mathematician or simply someone who enjoys contemplating the beauty of numbers, this book is sure to stimulate your mind and encourage you to think deeply about the fascinating world of mathematics. So come along for the ride as the author delves deep into the splendor (and squalor) of numbers, uncovering their hidden mysteries and inspiring readers to seek out the same.
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.
Excursions in Multiplicative Number Theory
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided "walks" invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin-Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at "higher ground", where they will find opportunities for extensions and applications, such asthe Selberg formula, Brun's sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.
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.
Theory of Games and Economic Behavior
John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.
Foundations of Quantitative Finance Book IV: Distribution Functions and Expectations
Published under the collective title of Foundations of Quantitative Finance, this set of 10 books develops the advanced topics in mathematics that finance professionals need to improve their careers. These books develop the theory most do not learn in graduate finance programs, finance mathematics undergraduate and graduate courses.
Learning Mathematics in the Context of 3D Printing
The volume presents a collection of articles on the use of 3D printing technology in mathematics education and in mathematics teacher training. It contains both basic research-oriented contributions as well as reflected descriptions of concrete developments for teaching. The authors of this compilation share a positive attitude towards the possibilities that the use of 3D printing technology (understood as an interplay of software and hardware) can unfold for mathematics education, but critically evaluate from a mathematics education research perspective when, where and how an application can enable an added value for the learning of a mathematical content.
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..
An Introduction to Optimization on Smooth Manifolds
Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.
An Introduction to Optimization on Smooth Manifolds
Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the 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.
Fractional Derivative Modeling in Mechanics and Engineering
This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.
Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents
This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(., .)-Navier-Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(., .) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner-Lebesgue spaces is not applicable. As a substitute for Bochner-Lebesgue spaces, variable Bochner-Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(., .)-Navier-Stokes equations under general assumptions.Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.
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.
The Conway-Maxwell-Poisson Distribution
While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.
Decentralized Insurance
The book offers an introduction to the technical foundation of decentralized insurance models, for advanced undergraduate students, graduate students and practitioners. The book is self-contained and anyone with a basic knowledge of probability and statistics should be able to follow through the entire book. It adopts a minimalist approach to describe the essential elements and first principles so that readers can get a gist of these models without being overwhelmed with too much technicality. It can be used as a reference for business model designs. The inclusion of exercises and practical examples makes the book suitable for advanced courses on decentralized insurance and risk sharing.There is a mix of industry practices and academic models presented in this book. The exposition starts with an overview of historic and current business practices and preliminaries on the mathematics and economics of risk and insurance. A bird's-eye view of traditional insurance isprovided as a benchmark for various topics to be used in contrast with decentralized insurance. The book then continues with decentralized insurance practices around the world, including online mutual aid originated in China, takaful from the Islamic world, peer-to-peer insurance in the West, catastrophe risk pooling for Carribean countries, etc. Theories of aggregate risk pooling and peer-to-peer risk exchanges are provided for readers to appreciate the mathematical foundation of risk sharing. A unified framework of decentralized insurance is presented to show a structured approach to the economic design of decentralized business models. The book ends with a technical review of blockchain and decentralized finance (DeFi) insurance applications.
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.
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.
Stochastic Finance
Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black-Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.
Magic & Rationality, Draft 2.3-RC-13
This book uses logic, philosophy, and whimsical storytelling to investigate the magic of succeeding by believing. In particular, we look at the "supposed" secret to success: if you believe you will succeed, then you will succeed. What happens when you adopt this belief? The logical consequences may be surprising. For example, under certain conditions, this supposed secret becomes a logical, self-fulfilling prophecy. Through a progression of 15 chapters, we follow a narrative-going deeper and deeper into the rabbit hole of the supposed secret. Most chapters include a short story to illustrate a logical concept relating to the supposed secret, and most chapters also include a rigorous analysis to satisfy the skeptics. My fundamental thesis is that "magicians" (those who believe in the supposed secret) are logically empowered by the supposed secret to success-even according to skeptical logic. Just a draft. Peer review appreciated.
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.
Fibonacci Cubes with Applications and Variations
Fibonacci Cubes have been an extremely popular area of research since the 1990s.This unique compendium features the state of research into Fibonacci Cubes. It expands the knowledge in graph theoretic and combinatorial properties of Fibonacci Cubes and their variants.By highlighting various approaches with numerous examples, it provides a fundamental source for further research in the field. This useful reference text surely benefits advanced students in computer science and mathematics and serves as an archival record of the current state of the field.
Associative Algebraic Geometry
Classical Deformation Theory is used for determining the completions of local rings of an eventual moduli space. When a moduli variety exists, the main result explored in the book is that the local ring in a closed point can be explicitly computed as an algebraization of the pro-representing hull, called the local formal moduli, of the deformation functor for the corresponding closed point.The book gives explicit computational methods and includes the most necessary prerequisites for understanding associative algebraic geometry. It focuses on the meaning and the place of deformation theory, resulting in a complete theory applicable to moduli theory. It answers the question 'why moduli theory', and gives examples in mathematical physics by looking at the universe as a moduli of molecules, thereby giving a meaning to most noncommutative theories.The book contains the first explicit definition of a noncommutative scheme, not necessarily covered by commutative rings. This definition does not contradict any previous abstract definitions of noncommutative algebraic geometry, but sheds interesting light on other theories, which is left for further investigation.
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
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
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.
Stochastic Finance
Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black-Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.
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
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
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
Algebra I for Beginners
The Only Book You Will Ever Need to Ace Algebra I Course!Algebra I for Beginners is a comprehensive guide for those just starting out in algebra. Designed for high school students or those looking to brush up on their skills, this book provides a clear and easy-to-follow approach to the subject. From solving linear equations to graphing quadratic functions, this book covers all the core concepts of Algebra I. With complete coverage of Algebra I topics, step-by-step explanations, and a wealth of examples and practice problems, Algebra I for Beginners offers the best education possible. Written by a math teacher and expert, the book is aligned with Algebra I courses and features an engaging writing style that makes it easy to understand and retain the material. Key Features: Step-by-Step Explanations: This comprehensive Algebra textbook employs a student-friendly approach to teaching Algebra I, with each concept broken down into digestible parts. Each algebraic concept is presented in a step-by-step manner, accompanied by lucid explanations and illustrative examples. This methodology not only simplifies complex ideas for beginners, but it also facilitates efficient and effective learning by presenting information in an organized, logical sequence.Rich Problem Sets: To solidify the understanding of the presented concepts, the book includes numerous problem sets right after each explanation. These practice exercises range in complexity, helping students apply the concepts they have learned in different contexts. Immediate application of theoretical knowledge through these problem sets strengthens understanding and encourages a proactive learning approach. Furthermore, solutions are provided for all problems, allowing students to check their answers and learn from any mistakes.Comprehensive Coverage: The book offers a thorough examination of all core Algebra 1 topics. Whether it's basic equations, inequalities, functions, or graphing, nothing is left untouched. This extensive coverage ensures a holistic learning experience, setting students on the path to mastering Algebra I. Each topic is discussed in depth, using straightforward language and explanations to ensure comprehension.Full-Length Practice Tests: To top it all off, the book concludes with two full-length Algebra I practice tests. These tests, designed to mirror the format and difficulty of the actual exam, provide a realistic testing experience for students. They offer an opportunity to apply the full range of Algebra I concepts, thereby bolstering readiness for course examinations or standardized tests. Fully worked-out solutions accompany these tests, providing insight into effective problem-solving strategies and aiding in the identification and rectification of any areas of weakness. These tests are a valuable tool for self-assessment and will give students a clear idea of what to expect in a real test scenario.Whether you're struggling with algebra or simply looking to improve your skills, this book is an excellent resource. Ideal for self-study or for use in the classroom, it will help you develop a strong foundation in the subject. Get ready for the Algebra I Exam with a perfect prep book from Effortless Math Education.
Advanced Algebra 1 vol 1
This book covers over 1000+ problems of practice in the core areas of1. Literal Equations2. Absolute value Equations and Inequalities3. Slope of a Straight line4. Parallel and Perpendicular lines5. Graphing Linear, Absolute value Equations and Inequalities6. Graphing System of Equations and InequalitiesVisit 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
