The Principles of Mathematics
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Treatise on Conic Sections
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Synopsis of Elementary Results in Pure Mathematics
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Fractional Calculus Operators and the Mittag-Leffler Function
This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag-Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others.
Festschrift for Martin Purvis. An Information Science "Renaissance Man"
Prof Dr Martin K Purvis spent most of his academic life with the Department of Information Science at the University of Otago, Aotearoa New Zealand. Former and current fellow academics and postgraduate students contributed to this collected volume of scholarly articles and reflections to honour the immensely productive career of Prof Purvis. This festschrift's breadth and depth of topics is indicative of Martin's expertise and interests and is a call for rejuvenating a "renaissance" view of information science and computing. We hope, that a wide range of scholarly readers will enjoy the topics covered and thoughts shared.
Stacks Project Expository Collection
The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne-Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.
Model and Mathematics: From the 19th to the 21st Century
How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes between 1830 and 1950. Introduction.- Knowing by Drawing: Geometric Material Models in 19th Century France.- Wilhelm Fiedler and his Models-the Polytechnic Side.- Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry.- Modeling Parallel Transport.- The great yogurt project: models and symmetry principles in early particle physics.- Interview with Myfanwy Evans: Entanglements on and Models of Periodic Minimal Surfaces.- The dialectics archetypes / types (universal categorical constructions / concrete models) in the work of Alexander Grothendieck.- 'Analogies, ' 'Interpretations, ' 'Images, ' 'Systems' and 'Models': Some Remarks on the History of Abstract Representation in the Sciences since the Nineteenth Century.- Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking circa 1900.- Thinking with Notations: Epistemic Actions and Epistemic Activities in Mathematical Practice.- Matrices - Compensating the Loss of Anschauung .- Interview with Anja Sattelmacher: Between Viewing and Touching - Models and Their Materiality.- Interview with Ulf Hashagen: Exhibitions and Mathematical Models in the 19th and 20th Centuries.- Interview with Andreas Daniel Matt: Real-Time Mathematics.
Analysis and Differential Equations (Second Edition)
The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.
Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert
Part 1: Essays.- 1 Renzo Caddeo and Athanase Papadopoulos, Introduction.- 2 Athanase Papadopoulos, Ancient geography: some markers.- 3 Athanase Papadopoulos, Euler and Maupertuis on the figure of the Earth.- 4 Charalampos Charitos, On the duration of the passage of a star from an almucantar to another.- 5 Charalampos Charitos, The differential equations in Euler's work on geography.- 6 Athanase Papadopoulos, Euler, Delisle and cartography.- 7 Charalampos Charitos and Athanase Papadopoulos, On Delisle's geographical projection.- 8 Charalampos Charitos, Lagrange's method for the construction of geographical maps.- 9 Athanase Papadopoulos, Some notes on the impact of Lagrange's memoir On the construction of geographical maps.- 10 Annette A'Campo-Neuen, Lambert's work on geographic map projections.- Part II: Sources.- 11 Vincent Alberge and Athanase Papadopoulos, Elements of spheroidal trigonometry drawn from the method of maxima and minima. Leonhard Euler.- 12 Renzo Caddeo, On the representation of the spherical surface on the plane. Leonhard Euler.- 13 Renzo Caddeo, On the geographical projection of the surface of the sphere. Leonhard Euler.- 14 Renzo Caddeo, On Delisle's geographical projection used for a general map of the Russian Empire. Leonhard Euler.- 15 Vincent Alberge and Athanase Papadopoulos, On the construction of geographical maps. Joseph-Louis Lagrange.- 16 Annette A'Campo-Neuen, Notes and comments on the composition of terrestrial and celestial maps. Johann Heinrich Lambert.
Developmental Education Preparation
Developmental Education Preparation suggests faculty development that can be used for teaching developmental education and corequisites courses, specifically in mathematics. Providing a look into the needs of students that may not be prepared for college level courses, the premise of the book is to prepare the faculty as much as possible to handle a developmental course. Complete with techniques, pedagogy, instructional skills, when combined all together, this book can help with developing meaningful professional development on any campus across the nation. The interviews presented in this book provide the reality of some faculty of developmental mathematics education and revealed common trends in the needs and characteristics of corequisite courses. Based on the themes found, professional development is suggested to aid in helping shift any negative components of those themes. The themes help better understand the needs of teaching these challenging courses. Student success should start with faculty making sure they are equipped with the tools and understanding of the students. Student's readiness starts with the faculty's readiness. Having the combined understanding of faculty and student needs can help to create a professional development plan that will enhance the developmental level mathematics courses in higher education.
Bayesian Predictive Inference and Related Asymptotics
Bayesian predictive inference is at the core of the mathematical theory of inductive reasoning. Nowadays, this field has become very attractive especially for its connections with algorithmic probability, machine learning and artificial intelligence. The complexity of both problems and algorithm represents a constant source of research of asymptotic techniques, which are necessary to handle vast datasets.The present book contains the 11 papers accepted and published in the Special Issue "Bayesian Predictive Inference and Related Asymptotics-Festschrift for Eugenio Regazzini's 75th Birthday" of the MDPI Mathematics journal. The topics of the paper focus, among others, on Bayesian nonparametrics, species sampling models, partial exchangeability and optimal stopping. Finally, as the title suggests, the Special Issue aims to celebrate the 75th birthday of Prof. Eugenio Regazzini, who has provided so many important contributions to the field of Bayesian inference.
Letters and Numbers
The book is letters and Numbers second edition it's a kids math book using alphabet letters and Numbers doing math adding subtracting multiplying and dividing and using Numbers too make a letter into a word. I'm from Medford and Somerville Massachusetts.
Mathematical Modeling
This book introduces modeling by a collection of ordinary differential or difference equations, calibrating the equations against data, checking quantitative predictions against events and understanding the qualitative patterns suggested by the model. One term of differential calculus is enough to get started and two terms are enough to finish. The topics covered are: Richardson's Model of Arms Races, Phase Portraits: Sketching the Phase Plane, Numerical Methods for Initial Value Problems, Modeling Population: Malthus' exponential model, growth rates, the Logistic Model, Discrete Time Reproduction Models, Overshoot and collapse models, Errors: Regression, Conditioning, Sensitivity and Predictability in Models, The Lotka-Volterra Model: Population Oscillations, Conservative Systems, Harvesting, General Models of Interacting Populations, Epidemics: SIR Models, Temporary Immunity, Latency and Asymptomatic Carriers, Persistent Oscillations: Limit cycles, Examples via polar coordinates, Poincar矇-Bendixon Theory, Hopf bifurcations, Oscillations in the Holling-Tanner Model: The Development of Predator-Prey Models, Analysis of the Holling-Tanner model, Testing the model, and Business Cycles: Business cycle theories, basic difficulties, Goodwin's model, Conclusions from Goodwin's model.
A Notebook
This book introduces some new fractal dimension concepts to calculate the center point elevation from a 3X3 grid of actual topographic data. The implications are that there is an order to natural systems that has been newly identified.The material is presented in the form of a notebook study. The innovative fractal-type equations and ancillary concepts are conceptually concise. The calculation framework to obtain the center point values uses the fractal and ancillary equations to construct what are termed "positive" and "negative" criteria, as well as a "position locator." The solution for the center point elevation is arrived at via a mathematical sieve of these three factors.There are 13 example datasets that are evaluated. In each analysis, only the data from the relevant 3X3 region was used. The topographic data is from the Red Deer River area in Alberta, Canada. The accuracy of the calculated elevations compared to the actual center point data in a notable number of cases is truly amazing, to the point of being essentially perfect.However, there appear to be limitations to the technique that have yet to be explored to any significant extent. With only 13 datasets investigated, it is expected that additional refinements to the various criteria will be required. A full and final theory will have a more rigorous mathematical foundation to formalize the criteria.The book includes code snippets of the various calculation methods, so that others may enjoy their own explorations. Ideas for additional studies and improvements are suggested. Predicting values in non-center-point situations would be one of the next steps.The material is primarily designed to be accessible to individuals with an undergraduate background in mathematics, physics or the sciences.Applications to other types of data would appear to be possible.
A Notebook
This book introduces some new fractal dimension concepts to calculate the center point elevation from a 3X3 grid of actual topographic data. The implications are that there is an order to natural systems that has been newly identified.The material is presented in the form of a notebook study. The innovative fractal-type equations and ancillary concepts are conceptually concise. The calculation framework to obtain the center point values uses the fractal and ancillary equations to construct what are termed "positive" and "negative" criteria, as well as a "position locator." The solution for the center point elevation is arrived at via a mathematical sieve of these three factors.There are 13 example datasets that are evaluated. In each analysis, only the data from the relevant 3X3 region was used. The topographic data is from the Red Deer River area in Alberta, Canada. The accuracy of the calculated elevations compared to the actual center point data in a notable number of cases is truly amazing, to the point of being essentially perfect.However, there appear to be limitations to the technique that have yet to be explored to any significant extent. With only 13 datasets investigated, it is expected that additional refinements to the various criteria will be required. A full and final theory will have a more rigorous mathematical foundation to formalize the criteria.The book includes code snippets of the various calculation methods, so that others may enjoy their own explorations. Ideas for additional studies and improvements are suggested. Predicting values in non-center-point situations would be one of the next steps.The material is primarily designed to be accessible to individuals with an undergraduate background in mathematics, physics or the sciences.Applications to other types of data would appear to be possible.
Thinking Programs
This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly think about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute from given inputs wanted outputs, and programs that describe continuously executing systems. The core message is that clear thinking about programs can be expressed in a single universal language, the formal language of logic. Apart from its universal elegance and expressiveness, this "logical" approach to the formal modeling of and reasoning about computer programs has another advantage: due to advances in computational logic (automated theorem proving, satisfiability solving, model checking), nowadays much of this process can be supported by software. This book therefore accompanies its theoretical elaborations by practical demonstrations of various systems and tools that are based on respectively make use of the presented logical underpinnings.
A Lambda Calculus Satellite
In 1936 the notion of intuitive computability was operationalized in two different ways: via Turing machines and via lambda-calculus. The difference consisted in manipulating beads (bits) for the former approach versus manipulating trees (rewriting lambda-terms) for the latter. Both proposals turned out to formalize the same notion of computability, and led to the Church-Turing Thesis, claiming that intuitive computability is captured in the correct way.This resulted in the foundation of imperative and functional programming. Variants of lambda-calculus are being used in another powerful field of applications, namely proof-checking, the basis for certifying mathematical theorems and thereby high tech industrial products. These two areas of research are still being actively investigated and make lambda-calculus a major tool in the present stages of science and of the industrial revolution.In this book lambda-calculus is considered from another angle: as a study of these tree-like structures, investigating the relation between their shape and their action. This is like studying numbers qualitatively, rather than for their applications dealing quantitatively with objects and phenomena in the world.Barendregt's book `The Lambda Calculus, its Syntax and Semantics' (1981/84), does treat the subject from the same methodological viewpoint, and includes several open conjectures. In the more than four decades that have passed, most - but not all - of these conjectures have been solved, sometimes in ingenious PhD theses. This `Satellite' to the aforementioned book presents these solutions in a uniform style and adds other topics of interest.
Two Trains Leave The Station
When her mother was diagnosed with Alzheimer's disease, Catherine Landis set out to do something to protect her own brain. Hoping to avoid a similar fate, she went searching for brain exercises and landed on math. Considering herself innumerate, she was flustered by the mere word. Could she relearn it? Could this source of embarrassment become an opportunity? TWO TRAINS LEAVE THE STATION: A Meditation on Age, Alzheimer's, and Arithmetic, is the story of how Catherine relearned math while grappling with her mother's illness and her own inevitable aging.
Have Fun with Numbers
Have fun with Numbers is an introduction to numbers from 1 to 10 by using images. Toddlers will learn to count in this book by using colorful images that will catch their attention. This book will also help kids write for the first time by tracing the numbers.
Introduction to Traveling Waves
This book focuses on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students.
Question Answering for the Curated Web
Question answering (QA) systems on the Web try to provide crisp answers to information needs posed in natural language, replacing the traditional ranked list of documents. QA, posing a multitude of research challenges, has emerged as one of the most actively investigated topics in information retrieval, natural language processing, and the artificial intelligence communities today. The flip side of such diverse and active interest is that publications are highly fragmented across several venues in the above communities, making it very difficult for new entrants to the field to get a good overview of the topic. Through this book, we make an attempt towards mitigating the above problem by providing an overview of the state-of-the-art in question answering. We cover the twin paradigms of curated Web sources used in QA tasks ‒ trusted text collections like Wikipedia, and objective information distilled into large-scale knowledge bases. We discuss distinct methodologies that have been applied to solve the QA problem in both these paradigms, using instantiations of recent systems for illustration. We begin with an overview of the problem setup and evaluation, cover notable sub-topics like open-domain, multi-hop, and conversational QA in depth, and conclude with key insights and emerging topics. We believe that this resource is a valuable contribution towards a unified view on QA, helping graduate students and researchers planning to work on this topic in the near future.
Data Through Movement
When you picture human-data interactions (HDI), what comes to mind? The datafication of modern life, along with open data initiatives advocating for transparency and access to current and historical datasets, has fundamentally transformed when, where, and how people encounter data. People now rely on data to make decisions, understand current events, and interpret the world. We frequently employ graphs, maps, and other spatialized forms to aid data interpretation, yet the familiarity of these displays causes us to forget that even basic representations are complex, challenging inscriptions and are not neutral; they are based on representational choices that impact how and what they communicate. This book draws on frameworks from the learning sciences, visualization, and human-computer interaction to explore embodied HDI. This exciting sub-field of interaction design is based on the premise that every day we produce and have access to quintillions of bytes of data, the exploration and analysis of which are no longer confined within the walls of research laboratories. This volume examines how humans interact with these data in informal (not work or school) environments, paritcularly in museums. The first half of the book provides an overview of the multi-disciplinary, theoretical foundations of HDI (in particular, embodied cognition, conceptual metaphor theory, embodied interaction, and embodied learning) and reviews socio-technical theories relevant for designing HDI installations to support informal learning. The second half of the book describes strategies for engaging museum visitors with interactive data visualizations, presents methodologies that can inform the design of hand gestures and body movements for embodied installations, and discusses how HDI can facilitate people's sensemaking about data. This cross-disciplinary book is intended as a resource for students and early-career researchers in human-computer interaction and the learning sciences, as well asfor more senior researchers and museum practitioners who want to quickly familiarize themselves with HDI.
Word Problems from Literature
You can help prevent math anxiety by giving your children the mental tools they need to conquer story problems. Young children expect to look at a word problem and instantly see the answer. But as they get older, their textbook math problems also grow in difficulty, so this solution-by-intuitive-leap becomes impossible. Too often the frustrated child concludes, "I'm just not good at math." But with practice, any student can learn to master word problems. Word Problems from Literature features math puzzles for elementary and middle school students inspired by classic books such as Mr. Popper's Penguins and The Hobbit. Denise Gaskins demonstrates step by step how to use the problem-solving tool of bar model diagrams, a type of pictorial algebra. For children who are used to playing with Legos or other blocks - or with computer games like Minecraft - this approach reveals the underlying structure of a math word problem. Students can make sense of how each quantity in the story relates to the others and see a path to the solution. And when you finish the puzzles in this book, Denise shows you how to create your own word problems from literature, using your child's favorite story worlds. Prepare your children for mathematical success. Order your copy of Word Problems from Literature today. * * * If you're using these word problems with your children, check out the companion Word Problems Student Workbook: Word Problems from Literature.
Trichometry (c)
Trichometry (c) The Study of the Geometrics of the 3-4-5-6 Golden Upright Right Triangle in Cartesian Coordinates is an informative book developed to explain in detail the innovative and in-depth mathematical operations involved in the Triological Science of Trichometry to create, explain, and model the internal and external dynamics of the 3-4-5-6 Golden Upright Right Triangle (or 3-4-5-6 GURT). Trichometry is the mathematical study of the geometrics of the 3-4-5-6 Golden Upright Right Triangle Model that is constructed from first quadrant Cartesian Coordinate mathematics. The Trichometry (c) book has been written in a manner that presents the geometrics in an explicative series of mathematical cyclical sequential formulae, descriptive Triostatistical models, step-by-step procedures, and explicative innovative in-depth terminology. This book has been designed to aid the reader in comprehending the unique Triological Sciences and their methodologies that will aid in the production of: conceptual models, problem-solving solutions, and innovative inventive inquiry.
Notable Modern Indian Mathematicians and Statisticians
Chapter 1. Historical Prelude and Introduction.- Chapter 2. Sir Asutosh Mookerjee (1864-1924).- Chapter 3. Syamadas Mukhopadhyay (1866-1937).- Chapter 4. Ganesh Prasad (1876-1935).- Chapter 5. Bibhuti Bhusan Datta (1888-1958).- Chapter 6. Prasanta Chandra Mahalanobis (1893-1972).- Chapter 7. Nikhil Ranjan Sen (1894-1963).- Chapter 8. Suddhodan Ghosh (1896-1976).- Chapter 9. Rabindranath Sen (1896-1974).- Chapter 10. Bibhutibhusan Sen (1898-1976).- Chapter 11. Raj Chandra Bose (1901-1987).- Chapter 12. Bhoj Raj Seth (1907-1979).- Chapter 13. . Subodh Kumar Chakrabarty (1909-1987).- Chapter 14. Manindra Chandra Chaki (1913-2007).- Chapter 15. Calyampudi Radhakrishna Rao (b. 10th September 1920).- Chapter 16. Anadi Sankar Gupta (1932-2012).- Chapter 17. Jyoti Das (1937-2015).- Chapter 18. Some Outstanding Minds from the Indian Statistical Institute.
Variational Calculus with Engineering Applications
VARIATIONAL CALCULUS WITH ENGINEERING APPLICATIONS A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.
Founding Mathematics on Semantic Conventions
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language - and specifically, the ability to institute conventions for the truth conditions of sentences.This philosophical stance leads to an alternative way of practicing mathematics: instead of "building" objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory.Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis.Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, thissolution also applies to Russell's paradox and the other mathematical paradoxes of self-reference.In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
The Spirit of Mathematics
What makes mathematics so special? Whether you have anxious memories of the subject from school, or solve quadratic equations for fun, David Acheson's book will make you look at mathematics afresh. Following on from his previous bestsellers, The Calculus Story and The Wonder Book of Geometry, here Acheson highlights the power of algebra, combining it with arithmetic and geometry to capture the spirit of mathematics. This short book encompasses an astonishing array of ideas and concepts, from number tricks and magic squares to infinite series and imaginary numbers. Acheson's enthusiasm is infectious, and, as ever, a sense of quirkiness and fun pervades the book. But it also seeks to crystallize what is special about mathematics: the delight of discovery; the importance of proof; and the joy of contemplating an elegant solution. Using only the simplest of materials, it conjures up the depth and the magic of the subject.
Hungarian Mathematical Olympiad (1964-1997)
This book is about a famous Hungarian mathematics competition that was founded in 1894, and thus, the oldest mathematics competition for secondary school students organized on a national scale. This book is based on Volumes III and IV of the Hungarian work by J獺nos Sur獺nyi, covering the years from 1964 to 1997.Hungary, along with Russia, has a well-deserved reputation for proposing important, instructive, and interesting problems. Here, the reader will find a treasure trove of over 100 of them. The solutions are written carefully, giving all the details, and keeping in mind at all times the overall logical structures of the arguments.An outstanding feature of this book is Part II: Discussion. Here, the problems are divided by topics into six groups. It contains a discussion of the topic in general, followed by the basic results, that precedes the discussions of the individual problems. When a student encounters some difficulty in a problem, this part of the book can be consulted without revealing the complete solution. As an alternative, a student can also start with this part to familiarize with the general topic before attempting any problems. Finally, almost 400 additional problems from the legendary K繹MaL (Secondary School Mathematics and Physics Journal) takes the student to mathematical topics beyond competitions.
Hungarian Mathematical Olympiad (1964-1997)
This book is about a famous Hungarian mathematics competition that was founded in 1894, and thus, the oldest mathematics competition for secondary school students organized on a national scale. This book is based on Volumes III and IV of the Hungarian work by J獺nos Sur獺nyi, covering the years from 1964 to 1997.Hungary, along with Russia, has a well-deserved reputation for proposing important, instructive, and interesting problems. Here, the reader will find a treasure trove of over 100 of them. The solutions are written carefully, giving all the details, and keeping in mind at all times the overall logical structures of the arguments.An outstanding feature of this book is Part II: Discussion. Here, the problems are divided by topics into six groups. It contains a discussion of the topic in general, followed by the basic results, that precedes the discussions of the individual problems. When a student encounters some difficulty in a problem, this part of the book can be consulted without revealing the complete solution. As an alternative, a student can also start with this part to familiarize with the general topic before attempting any problems. Finally, almost 400 additional problems from the legendary K繹MaL (Secondary School Mathematics and Physics Journal) takes the student to mathematical topics beyond competitions.
Maxwell's Equations in Periodic Structures
This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell's equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
Fast Track to Differential Equations
The second edition of this successful textbook includes a significantly extended chapter on Climate Change with an analysis of the CO2 budget. It also contains a completely new part on Epidemiology, treating the SEIR-model which describes the behavior and dynamics of epidemics. In particular, COVID-19 with actual data is discussed. This compact introduction to ordinary differential equations and their applications is aimed at anyone who in their studies is confronted voluntarily or involuntarily with this versatile subject. Numerous applications from physics, technology, biomathematics, cosmology, economy and optimization theory are given. Abstract proofs and unnecessary formalism are avoided as far as possible. The focus is on modelling ordinary differential equations of the first and second orders as well as their analytical and numerical solution methods, in which the theory is dealt with briefly before moving on to application examples. In addition, program codes show exemplarily how even more challenging questions can be tackled and represented meaningfully with the help of a computer algebra system. The first chapter deals with the necessary prior knowledge of integral and differential calculus. 103 motivating exercises together with their solutions round off the work. "I am happy to see such a book. It will serve as a support for many students, professors and faculty." Dr. Alessio Figalli, Professor at the ETH Z羹rich and Fields medalist 2018
New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus
This book focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems.It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention.
Applied Mathematics and Fractional Calculus
In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia.
Topological Dynamics of Enveloping Semigroups
This book introduces the theory of enveloping semigroups--an important tool in the field of topological dynamics--introduced by Robert Ellis. The book deals with the basic theory of topological dynamics and touches on the advanced concepts of the dynamics of induced systems and their enveloping semigroups. All the chapters in the book are well organized and systematically dealing with introductory topics through advanced research topics. The basic concepts give the motivation to begin with, then the theory, and finally the new research-oriented topics. The results are presented with detailed proof, plenty of examples and several open questions are put forward to motivate for future research. Some of the results, related to the enveloping semigroup, are new to the existing literature. The enveloping semigroups of the induced systems is considered for the first time in the literature, and some new results are obtained. The book has a research-oriented flavour in the field of topological dynamics.
Timed Division Drill Facts Grades 4-6
40+ reproducible drill worksheets. Strengthen students' speed and accuracy on their division facts.Each drill page concentrates on a specific area. In division fact recall, building students' skills as they progress from the easiest level to the most difficult. Each level has a daily practice page, a home practice page, an extra practice page, and a review test page. The extra practice drill sheet is to be used with students still having difficulty recalling facts quickly and accurately. It is a different approach to the timed drill method. This requires the student to complete the fact with its missing number. This different approach helps the students remember the facts more quickly.Supports Common Core Standards for Mathematics Gr. 4-5.The division fact drills have been designed to help strengthen students' speed and accuracy through practice during a specified time or each student could be timed individually.Some of the drills are shorter and are to be completed on a specified day. Each drill page concentrates on a specific area in division fact recall. The drills proceed from the easiest level to the most difficult level. Each level has a daily practise page, a home practise page, an extra practise page, and a review test page.The daily practice page is divided into five days. Each day of the week the student is tocomplete a drill, the date, score, and time it took to do the drill are to be recorded in each section. This page could be glued into the students' work books or kept in individual file folders.The home practice page is to be sent home to practice fact recall with parent supervision. Once completed, it is to be returned to school signed by a parent. A letter of explanation should be sent home with the first home practice page explaining how it is to be completed.The extra practice drill sheet is to be used with students who are still having difficultyrecalling facts quickly and accurately. It is a different approach to the time drill method. The student must complete the fact with its missing number.The review page or test page is to be used to test speed and accuracy within a given length of time. Begin with five minutes graduating down to one minute.Tell students when to begin and when to stop. Have the students circle the last completed question with a red crayon or red pencil crayon. The students are to exchange their papers and to mark each incorrect answer with a red dot as you read the answers aloud. Have the students count the number of correct answers. No credit is to be given for incomplete answers. The student is to record the number of correct answers, time, and date on each sheet where indicated. On each review test have all incomplete answers finished for extra practice after the completed answers have been marked.There are two timed review tests for each section that may be used after each section has been practiced successfully. These tests will evaluate students' speed and accuracy in each section.The final drill pages test all the division facts. These pages are to be used in the same manner as the other drills.The results of the various drills may be recorded on the Score Record Sheets provided in this book.
Timed Multiplication Drill Facts Grades 4-6
40+ reproducible drill worksheets. Strengthen students' speed and accuracy on their multiplication facts. Each drill page concentrates on a specific area. In multiplication fact recall, building students' skills as they progress from the easiest level to the most difficult.Each level has a daily practice page, a home practice page, an extra practice page, and a review test page.The extra practice drill sheet is to be used with students still having difficulty recalling facts quickly and accurately. It is a different approach to the timed drill method. This requires the student to complete the fact with its missing number. This different approach helps the students remember the facts more quickly.The multiplication fact drills have been designated to help strengthen students' speed and accuracy through practice during a specified time or each student could be timed individually. This practice will help to strengthen the process of memorization which is a skill needed to recall facts quickly.Some of the drills are shorter and are to be completed on a specified day. Each drill page concentrates on a specific area in multiplication fact recall. The drills proceed from the easiest level to the most difficult level. Each level has a daily practice page, a home practice page, an extra practice page, and a review test page.The daily practice page is divided into five days. Each day of the week the student is to complete a drill. The date, score, and time it took are to be recorded in each section. This page could be glued into the students' workbooks or kept in individual file folders.The home practice page is to be sent home to practice fact recall with parent supervision. Once completed it is to be returned to school and signed by a parent. A letter of explanation should be sent home with the first practice page explaining how it is to be completed.The extra practice drill sheet is to be used with students who are still having difficultyrecalling facts quickly and accurately. It is a different approach to the timed drill method. The student must complete the fact with its missing number. There is no extra practice page for multiplying with zero and one.The review page or test page is to be used to test the speed and accuracy within a given length of time. Begin with five minutes graduating down to one minute. Tell students when to begin and when to stop. Have the student circle the last completed question with a red crayon or a red pencil crayon. The students are to exchange their papers and to mark each incorrect answer with a red dot as you read the answers aloud. Have the students count the number of correct answers. No credit is to be given to incomplete answers. The student is to record the number of correct answers, the time, and the date on each sheet where indicated. On each review test have all incomplete answers finished for extra practice after the completed answers have been marked.There are two timed review tests for each section that may be used after each section has been practiced successfully. These test will evaluate students' speed and accuracy in each section.The final drill pages test all the facts in the multiplication tables. These pages are to be used in the same manner as the other drills.The results of the various drills may be recorded on the Score Record Sheets provided in this book.
Notes on Real Analysis and Measure Theory
Preface.- 1. Real-Valued Semicontinuous Functions.- 2. The Oscillations of Real-Valued Functions.- 3. Monotone and Continuous Restrictions of Real-Valued Functions.- 4. Bijective Continuous Images of Absolute Null Sets.- 5. Projective Absolutely Nonmeasurable Functions.- 6. Borel Isomorphisms of Analytic Sets.- 7. Iterated Integrals of Real-Valued Functions of Two Real Variables.- 8. The Steinhaus Property, Ergocidity, and Density Points.- 9. Measurability Properties of H-Selectors and Partial H-Selectors.- 10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets.- 11. Negligible Sets Versus Absolutely Nonmeasurable Sets.- 12. Measurability Properties of Mazurkiewicz Sets.- 13. Extensions of Invariant Measures on R.- A. A Characterization of Uncountable Sets in Terms of their Self-Mappings.- B. Some Applications of Peano Type Functions.- C. Almost Rigid Mathematical Structures.- D. Some Unsolved Problems in Measure Theory.- Bibliography.- Index.
Mirzakhani's Curve Counting and Geodesic Currents
1. Introduction.- 2. Read Me.- 3. Geodesic Currents.- 4. Train Tracks.- 5. Radallas.- 6. Subconvergence of Measures.- 7. Approximating the Thurston Measure.- 8. The Main Theorem.- 9. Counting Curves.- 10. Counting Square Tiled Surfaces.- 11. Statistics of Simple Curves.- 12. Sm繹rg疇sbord.- A. Radon Measures.- B. Computing Thurston Volumes.- References.- Index.
Landscape of 21st Century Mathematics
1 Number Theory.- 2 Combinatorics.- 3 Analysis.- 4 Algebra.- 5 Geometry and Topology.- 6 Probability and Statistics.- 7 Algorithms and Complexity.- 8 Logic and Set Theory.- References.- Index.
Making up Numbers
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis.Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of 'infinity' and its permissible uses in mathematics, number systems, and evolving views of the role of axioms.Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Making up Numbers
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis.Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of 'infinity' and its permissible uses in mathematics, number systems, and evolving views of the role of axioms.Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Solomon Golomb's Course on Undergraduate Combinatorics
0. Basic Tools.- 1. Combinations.- 2. Recurrence Relations and Generating Functions.- 3. Permutations.- 4. Special Numbers.- 5. Counting Under Symmetries.- 6. Combinatorial Structures.- A. Additional Exercises.- B. Additional Examples.- C. Solutions to Odd-numbered Exercises.- Bibliography.- Index.
Elementary Methods of Graph Ramsey Theory
This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner's overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Tur獺n numbers and communication channels, etc.
