Rosenbrock--Wanner-Type Methods
This book discusses the development of the Rosenbrock--Wanner methods from the origins of the idea to current research with the stable and efficient numerical solution and differential-algebraic systems of equations, still in focus. The reader gets a comprehensive insight into the classical methods as well as into the development and properties of novel W-methods, two-step and exponential Rosenbrock methods. In addition, descriptive applications from the fields of water and hydrogen network simulation and visual computing are presented.
Algebraic Number Theory
This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.
Math Mammoth Grade 2-B Worktext
Math Mammoth Grade 2-B Worktext is the student book for the latter half of grade 2 mathematics studies. It covers three-digit numbers, measuring, regrouping in addition and subtraction, counting coins, and an introduction to multiplication.The "worktext" means it contains both the instruction ("text") and the exercises for the student ("work").This curriculum meets and exceeds the Common Core Standards. This is the full-color version; in other words, the inside pages are in full color. Please note this book does not contain an answer key.Features Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it. Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired. The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much. There is a strong emphasis on mental math and number sense. It requires very little teacher preparation, which is a big benefit to most teachers and parents.: ) The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material. After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Boundary and Interior Layers, Computational and Asymptotic Methods Bail 2018
This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.
Math Mammoth Grade 4 Answer Keys
Math Mammoth Grade 4 Answer Keys contains full answer keys to both Math Mammoth Grade 4-A and 4-B student worktexts, end-of-chapter tests, the end-of-year test, and the cumulative review lessons.
A Readable Introduction to Real Mathematics
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces.This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book.From the reviews of the first edition: "It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences." (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) "The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an 'appreciation of mathematics' course, among other possibilities." (G.A. Heuer, Mathematical Reviews, February, 2015)"Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers." (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)
The Fundamental Principle of Digits of a Number
The Fundamental Principle of Digits of a Number is a new mathematical idea for which the author received a copyright from the United States Library of Congress. Two related concepts make it easy to understand and apply the principle. The first concept is that a permutation of digits of a given number is an arrangement of the digits of the given number in any order such that the numerical quantity, which results from the arrangement of the digits of the given number, has the same digits and the same number of digits as the given number. The second concept is that the difference between two permutations of digits of a given number is governed by a mathematical law which guarantees that the difference is divisible by 9. One day, the number 12 suddenly appeared on the author's inner eye. It turned around and formed the number 21. The two numbers subtracted, and number 9 appeared. Then the three numbers disappeared from the author's inner eye. The motion of the numbers by their own power, as if they were birds in the sky, prompted Chibamba Mulenga to investigate this event with digits of other numbers, leading to his discovery of this mathematical principle.
52!
Do you see the elegant designs that are drawn on the back of the cards? Do you look right through the deck as they clutter the drawer and your mind wanders to other thoughts of the day? Do you think of the last time that you played a friendly game of Poker or Gin Rummy? Do you see more grains of rice than the richest king can afford to buy? Do you see an infinite number of monkeys typing nonsense on typewriters for all eternity? Do you see eggs lined up until they are in a galaxy far away? Do you ponder questions of life and sometimes simply "the reason for it all"? 52! is a journey to comprehend numbers that are relative to reality and the universe that we live in. It is a mathematical and a spiritual journey to understand the numbers behind life and perhaps more importantly shares the author's personal journey to find an axiom of faith.
Essence of Fractions
All you need to master fractions in one math workbook.Essence of Fractions is a textbook quality fraction workbook containingWell organized and comprehensive explanations of conceptsTables and visualizations for easy chunking of informationStep-by-step examplesPractice exercises at the end of each chapter with answers given in the appendixStudy questions in the appendix for reinforcing and gaining a more thorough understanding of key conceptsThe key concepts provided in this book includeHow a fraction is definedHow to compare fractionsHow to reduce fractions with a greatest common divisorHow to reduce fractions with prime factorizationHow to multiply fractionsHow to divide fractionsHow to add and subtract fractions with a common denominatorHow to add and subtract fractions with different denominatorsHow to simplify fractions containing variablesMinimal background knowledge of mathematics is necessary to make sense of the concepts presented in this book. Even if if you have not taken a math class in 20 years, you can learn and understand the principles presented in this book by paying close attention to the key concepts and how to use them.
Methods and Models in Mathematical Programming
This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.
Mathematics of Energy and Climate Change
The focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing planetary problems and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global challenges.Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has increased to the point where it influences the global climate, impacts the ability of the planet to feed itself and threatens the stability of these systems. Issues such as climate change, sustainability, man-made disasters, control of diseases and epidemics, management of resources, risk analysis and global integration have come to the fore.Written by specialists in several fields of mathematics and applied sciences, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Mathematics of Energy and Climate Change held in Lisbon, Portugal, in March 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book presents the state of the art in advanced research and ultimate techniques in modeling natural, economical and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences.
Advances in Non-Archimedean Analysis and Applications
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology.In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role - a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems - for instance, proteins - asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.
Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms
This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range of illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience.The book is intended for researchers and graduate students in number theory.
Integer Sequences
This book discusses special properties of integer sequences from a unique point of view. It generalizes common, well-known properties and connects them with sequences such as divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, lifting properties, and so on. The book presents theories derived by using elementary means and includes results not usually found in common number theory books. Considering the impact and usefulness of these theorems, the book also aims at being valuable for Olympiad level problem solving as well as regular research. This book will be of interest to students, researchers and faculty members alike.
Math Mammoth Grade 2-A Worktext
Math Mammoth Grade 2-A student worktext covers some review of 1st grade math, reading the clock, addition and subtraction facts within 18, adding two-digit numbers, geometry topics, and fractions. It is meant for the first half of grade 2. This student worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. The curriculum meets and exceeds the Common Core standards. This is the full-color version; in other words, the inside pages are in full color. Please note this is a student worktext and does not contain answers.
Hybrid High-Order Methods
This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.
Around the Unit Circle
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer's Problem (1933) and Boyd's Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov's proof of the Schinzel-Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson's Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book.One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted setsof polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Waves in Flows
This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school "Waves in Flows", held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave-current interactionsWater-wave problemsGravity wave propagationFlow-acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
Numerical Semigroups
This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere. The contents comprise the proceedings of the 2018 INdAM "International Meeting on Numerical Semigroups", held in Cortona, Italy. Talks at the meeting centered not only on traditional types of numerical semigroups, such as Arf or symmetric, and their usual properties, but also on related types of semigroups, such as affine, Puiseux, Weierstrass, and primary, and their applications in other branches of algebra, including semigroup rings, coding theory, star operations, and Hilbert functions. The papers in the book reflect the variety of the talks and derive from research areas including Semigroup Theory, Factorization Theory, Algebraic Geometry, Combinatorics, Commutative Algebra, Coding Theory, and Number Theory. The book is intended for researchers and students who want to learn about recent developments in the theory of numerical semigroups and its connections with other research fields.
Waves in Flows
This volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include: ChemorepulsionCompressible Navier-Stokes systemsNewtonian fluidsFluid-structure interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.
Smooth B矇zier Surfaces Over Unstructured Quadrilateral Meshes
With a foreword by T.J.R. Hughes Represents a step forward in Isogeometric Analysis and its applicationsProvides a bridge between Finite Element Methods and Isogeometric Analysis
Sequential Models of Mathematical Physics
The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence.FeaturesDescribes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physicsPresentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readersThe solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions
Pillars of Transcendental Number Theory
This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite-Lindemann-Weierstrass theorem, Gelfond-Schneider theorem, Schmidt's subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker's original results. This book presents Baker's original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of "Exercises" and interesting information presented as "Notes," intended to spark readers' curiosity.
New Sinc Methods of Numerical Analysis
This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.
Algorithmic Techniques for the Polymer Sciences
This new book-the first of its kind-examines the use of algorithmic techniques to compress random and non-random sequential strings found in chains of polymers. The book is an introduction to algorithmic complexity. Examples taken from current research in the polymer sciences are used for compression of like-natured properties as found on a chain of polymers. Both theory and applied aspects of algorithmic compression are reviewed. A description of the types of polymers and their uses is followed by a chapter on various types of compression systems that can be used to compress polymer chains into manageable units. The work is intended for graduate and postgraduate university students in the physical sciences and engineering.
Zero to Lazy Eight
From Simon & Schuster, Zero to Lazy Eight is Alexander Humez's exploration into the romance of numbers fit with free-forming essays related to folklore, idioms, and mathematical diversions. A collection of essays blending elements of linguistics and mathematics provides an educational glimpse into the social history and culture of common phrases and colloquial expressions.
An Introduction to Probabilistic Number Theory
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
A Key To The Western Calculator; Containing The Solution Of All The Examples And Questions For Exercise With Reference To The Pages Where They Stand To Which Is Added Some Useful Rules
A Key To The Western Calculator; Containing The Solution Of All The Examples And Questions For Exercise With Reference To The Pages Where They Stand To Which Is Added Some Useful Rules has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature.
Soft Computing Techniques for Engineering Optimization
This book covers the issues related to optimization of engineering and management problems using soft computing techniques with an industrial outlook. It covers a broad area related to real life complex decision making problems using a heuristics approach. It also explores a wide perspective and future directions in industrial engineering research on a global platform/scenario. The book highlights the concept of optimization, presents various soft computing techniques, offers sample problems, and discusses related software programs complete with illustrations.FeaturesExplains the concept of optimization and relevance to soft computing techniques towards optimal solution in engineering and management Presents various soft computing techniques Offers problems and their optimization using various soft computing techniques Discusses related software programs, with illustrations Provides a step-by-step tutorial on how to handle relevant software for obtaining the optimal solution to various engineering problems
Dynamical Systems
Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.
Spectral Methods in Geodesy and Geophysics
The text develops the principal aspects of applied Fourier analysis and methodology with the main goal to inculcate a different way of perceiving global and regional geodetic and geophysical data, namely from the perspective of the frequency, or spectral, domain rather than the spatial domain. The word "methods" in the title is meant to convey that the transformation of a geophysical signal into the spectral domain can be applied for purposes of analysis as well as rapid computation. The text is written for graduate students; however, Chapters 1 through 4 and parts of 5 can also benefit undergraduates who have a solid and fluent knowledge of integral and differential calculus, have some statistical background, and are not uncomfortable with complex numbers. Concepts are developed by starting from the one-dimensional domain and working up to the spherical domain, which is part of every chapter. Many concepts are illustrated graphically with actual geophysical data primarily from signals of gravity, magnetism, and topography.
B-Series
B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary differential equations, including approximate solutions. Through the formulation and manipulation of these series, properties of numerical methods can be assessed. Runge-Kutta methods, in particular, depend on B-series for a clean and elegant approach to the derivation of high order and efficient methods. However, the utility of B-series goes much further and opens a path to the design and construction of highly accurate and efficient multivalue methods. This book offers a self-contained introduction to B-series by a pioneer of the subject. After a preliminary chapter providing background on differential equations and numerical methods, a broad exposition of graphs and trees is presented. This is essential preparation for the third chapter, in which the main ideas of B-series are introduced and developed. In chapter four, algebraic aspects are further analysed in the context of integration methods, a generalization of Runge-Kutta methods to infinite index sets. Chapter five, on explicit and implicit Runge-Kutta methods, contrasts the B-series and classical approaches. Chapter six, on multivalue methods, gives a traditional review of linear multistep methods and expands this to general linear methods, for which the B-series approach is both natural and essential. The final chapter introduces some aspects of geometric integration, from a B-series point of view. Placing B-series at the centre of its most important applications makes this book an invaluable resource for scientists, engineers and mathematicians who depend on computational modelling, not to mention computational scientists who carry out research on numerical methods in differential equations. In addition to exercises with solutions and study notes, a number of open-ended projects are suggested. This combination makes the book ideal as a textbook for specialised courses on numerical methods for differential equations, as well as suitable for self-study.
![FSA Practice Grade 3 Math Test Prep for the Florida Standards Assessment [3rd Edition Book]](https://cdn.kingstone.com.tw/english/images/product/6546/9781637756546m.webp "FSA Practice Grade 3 Math Test Prep for the Florida Standards Assessment [3rd Edition Book]")
FSA Practice Grade 3 Math Test Prep for the Florida Standards Assessment [3rd Edition Book]
Test Prep Books' FSA Practice Grade 3 Math Test Prep for the Florida Standards Assessment [3rd Edition Book]Made by Test Prep Books experts for test takers trying to achieve a great score on the FSA Math Grade 3 exam.This comprehensive study guide includes: Quick Overview Find out what's inside this guide!Test-Taking Strategies Learn the best tips to help overcome your exam!Introduction Get a thorough breakdown of what the test is and what's on it!Operations and Algebraic Thinking Representing and Solving Problems Involving Multiplication and Division; Properties of Multiplication and the Relationship between Multiplication and Division; Multiplying and Dividing Within 100; and Solving Problems Involving the Four Operations, and Identifying and Explaining Patterns in ArithmeticNumber and Operations in Base Ten Using Place Value Understanding and Properties of Operations to Perform Multi-Digit ArithmeticNumber and Operations - Fractions Fractions as NumbersMeasurement and Data Solving Problems Involving Measurement and Estimation of Intervals of Time, Liquid Volumes, and Masses of Objects; Representing and Interpreting Data; Geometric Measurement: Understanding Concepts of Area and Relating Area to Multiplication and Addition; Geometric Measurement: Perimeter is an Attribute of Plane Figures; and Reasoning with Shapes and Their AttributesPractice Questions Practice makes perfect!Detailed Answer Explanations Figure out where you went wrong and how to improve!Studying can be hard. We get it. That's why we created this guide with these great features and benefits: Comprehensive Review: Each section of the test has a comprehensive review created by Test Prep Books that goes into detail to cover all of the content likely to appear on the test.FSA Math Grade 3 Practice Test Questions: We want to give you the best practice you can find. That's why the Test Prep Books practice questions are as close as you can get to the actual test.Answer Explanations: Every single problem is followed by an answer explanation. We know it's frustrating to miss a question and not understand why. The answer explanations will help you learn from your mistakes. That way, you can avoid missing it again in the future.Test-Taking Strategies: A test taker has to understand the material that is being covered and be familiar with the latest test taking strategies. These strategies are necessary to properly use the time provided. They also help test takers complete the test without making any errors. Test Prep Books has provided the top test-taking tips.Customer Service: We love taking care of our test takers. We make sure that you interact with a real human being when you email your comments or concerns.Anyone planning to take this exam should take advantage of this Test Prep Books study guide. Purchase it today to receive access to: FSA Math Grade 3 review materialsFSA Math Grade 3 practice test questionsTest-taking strategies
Computational Mathematics, Nanoelectronics, and Astrophysics
This book is a collection of original papers presented at the International Conference on Computational Mathematics in Nanoelectronics and Astrophysics (CMNA 2018) held at the Indian Institute of Technology Indore, India, from 1 to 3 November 2018. It aims at presenting recent developments of computational mathematics in nanoelectronics, astrophysics and related areas of space sciences and engineering. These proceedings discuss the most advanced innovations, trends and real-world challenges encountered and their solutions with the application of computational mathematics in nanoelectronics, astrophysics and space sciences. From focusing on nano-enhanced smart technological developments to the research contributions of premier institutes in India and abroad on ISRO's future space explorations-this book includes topics from highly interdisciplinary areas of research. The book is of interest to researchers, students and practising engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics to nanoelectronics, nanofabrications and astrophysics.
Bounded Gaps Between Primes
Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field.
Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics
This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, this book provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.
Structural Mechanics with a Pen
1 Idea and Derivation of the Method 2 Investigation of Rods in the Elastic Range 3 Investigation of Euler-Bernoulli Beams in the Elastic Range 4 Investigation of Timoshenko Beams in the Elastic Range 5 Consideration of Euler-Bernoulli Beams with Plastic Material Behavior 6 Answers to Supplementary Problems
Ho Math Chess Puzzles Sample Worksheets
If you have any comments or problems on this workbook, please email them to fho1928@gmail.com.Ho Math Chess(TM)= math + puzzles + chessFrank Ho, a Canadian math teacher, intrigued by math and chess relationships after teaching his son chess, started Ho Math Chess(TM) in 1995. His long-term devotion to research has led his son to become a FIDE chess master and Frank's publications of over 20 math workbooks. Today Ho Math Chess(TM) is the world's largest and the only franchised scholastic math, chess, and puzzles specialty learning centre worldwide. Ho Math Chess(TM) is a leading research organization in math, chess, and puzzles integrated teaching methodology. There are hundreds of articles already published showing chess benefits children and that math puzzles are an excellent way of improving brainpower. So, by integrating chess and mathematical chess puzzles, the learning effect is more significant. Parents send their children to Ho Math Chess(TM) because they like Ho Math Chess(TM) teaching philosophy - offering children problem-solving questions in various formats. The questions could be pure chess, chess puzzles, mathematical chess puzzles like logic, pattern, tree structure, Venn diagram, probability and many more math concepts. Ho Math Chess(TM) has developed a series of unique and high-quality math, chess, and puzzles integrated workbooks. Ho Math Chess(TM) produced the world's first workbook Learning Chess to Improve Math. This workbook is not only for learning chess but also for enriching math ability. This sets Ho Math Chess apart from other math learning centres, chess club, or chess classes. The teaching method at Ho Math Chess(TM) is to use math, chess, and puzzles integrated workbooks to teach children fun math. The purposes of Ho Math Chess(TM) teaching method and workbooks are to: -Improve math marks.-Develop problem-solving and critical thinking skills.-Improve logical thinking ability.-Boost brainpower. Testimonials, sample worksheets, reports, and franchise information can be found at www.homathchess.com.More information about Ho Math Chess(TM) can also be found from the following publications: 1. Why Buy a Ho Math Chess(TM) Learning Centre Franchise: A Unique Learning Centre?2.Ho Math Chess(TM) Sudoku Puzzles Sample Worksheets3.Introduction to Ho Math Chess(TM) and its Founder Frank HoThe above publications can be purchased from www.amazon.com.
Sofsem 2021: Theory and Practice of Computer Science
This book contains the invited and contributed papers selected for presentation at SOFSEM 2021, the 47th International Conference on Current Trends in Theory and Practice of Computer Science, which was held online during January 25-28, 2021, hosted by the Free University of Bozen-Bolzano, Italy.The 33 full and 7 short papers included in the volume were carefully reviewed and selected from 100 submissions. They were organized in topical sections on: foundations of computer science; foundations of software engineering; foundations of data science and engineering; and foundations of algorithmic computational biology. The book also contains 5 invited papers.
Quick Arithmetic
Master math at your own pace!Does working with numbers often frustrate you? Do you need to brush up on your basic math skills? Do you feel math stands between you and your career goals, or a better grade at school?Quick Arithmetic, Third Edition is the quickest and easiest way to teach yourself the basic math skills you need to advance on the job or in school. Using cartoons and a clear writing style, this practical guide provides a fresh start for learning or reviewing how to work with whole numbers, fractions, decimals, and percentages. The book's proven self-teaching approach allows you to work at your own pace and learn only the material you need. Previews and objectives at the beginning of each section help you determine your particular needs, while self-tests, practice problems, and a final exam let you measure your progress and reinforce what you've learned.For anyone who has ever felt intimidated by a page of numbers, Quick Arithmetic, Third Edition has the answers!
Srinivasa Ramanujan
This book offers a unique account on the life and works of Srinivasa Ramanujan-often hailed as the greatest "natural" mathematical genius. Sharing valuable insights into the many stages of Ramanujan's life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem. It also includes the list of Ramanujan's collected papers, letters and other material present at the Wren Library, Trinity College in Cambridge, UK. This book is a valuable resource for all readers interested in Ramanujan's life, work and indelible contributions to mathematics.
Multiplication Workbook Grade 3
Kickstart your child's learning and help them succeed with math!Are you searching for a new maths book to make learning fun? Do you want to make sure your child is up to date on their multiplication skills? Or are you looking for a way to supplement their learning with a practical workbook? Then keep reading!Designed to cover all the essential multiplication areas of a 3rd-grade education, this brilliant math workbook offers a wide selection of problems and equations that will test your child's skills and imbue them with a love of numbers.Containing a wealth of exercises including grids, real-life situations, puzzles and much more, now you can make sure your child succeeds in math. Perfect for homeschoolers, as an accompanying tool for homework, or for parents who just want to help their child strengthen their math skills, now you can discover how to make learning both practical and enjoyable!Here's just a little of what you'll discover inside: - A Wide Range of Math Problems and Equations Ideal For a 3rd Grade Level- Designed To Strengthen Kids' Multiplication Skills- Equations With a Ton of Grids, Shapes, Number Lines, Real-Life Problems and More- Engaging Puzzles To Instil Your Child With a Love of Math!- Questions In The Single Digits, Tens, and Even Hundreds- And So Much More!So don't wait! If you're looking for a way to make learning fun, or if you want to help your child get ahead in math, then this workbook is for you. Packed with tons of questions to challenge and inspire your child to master the world of multiplication, there's no better way to make sure their math skills are as strong as possible.
Fuzzy Recurrence Plots and Networks with Applications in Biomedicine
This book presents an original combination of three well-known methodological approaches for nonlinear data analysis: recurrence, networks, and fuzzy logic.After basic concepts of these three approaches are introduced, this book presents recently developed methods known as fuzzy recurrence plots and fuzzy recurrence networks. Computer programs written in MATLAB, which implement the basic algorithms, are included to facilitate the understanding of the developed ideas. Several applications of these techniques to biomedical problems, ranging from cancer and neurodegenerative disease to depression, are illustrated to show the potential of fuzzy recurrence methods. This book opens a new door to theorists in complex systems science as well as specialists in medicine, biology, engineering, physics, computer science, geosciences, and social economics to address issues in experimental nonlinear signal and data processing.
Research Schools on Number Theory in India
This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar-including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India. Research on number theory in India during modern times started with the advent of the iconic genius Srinivasa Ramanujan, inspiring mathematicians around the world. This book discusses the national and international impact of the research made by Indian number theorists. It also includes a carefully compiled, comprehensive bibliography of major 20th century Indian number theorists making this book important from the standpoint of historic documentation and a valuable resource for researchers of the field for their literature survey. This book also briefly discusses the importance of number theory in the modern world of mathematics, including applications of the results developed by indigenous number theorists in practical fields. Since the book is written from the viewpoint of the history of science, technical jargon and mathematical expressions have been avoided as much as possible.
Foundations of Analysis
1, 2, 3, 4, . . ., natural numbers. 0, zero. -1, -2, -3, -4, . . ., negative integers. Rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book. The book is intended to be a supplement to textbooks on the differential and integral calculus. Those who are studying the subject should read this book. However, prerequisites are kept minimum, challenging high school students are also welcome.This emended edition is newly typeset and corrected.The free PDF file available on the publisher's website www.bwpest2018.org
Foundations of Analysis
1, 2, 3, 4, . . ., natural numbers. 0, zero. -1, -2, -3, -4, . . ., negative integers. Rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book. The book is intended to be a supplement to textbooks on the differential and integral calculus. Those who are studying the subject should read this book. However, prerequisites are kept minimum, challenging high school students are also welcome.This emended edition is newly typeset and corrected.Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image.The free PDF file available on the publisher's website www.bwpest2018.org
Advances in Trefftz Methods and Their Applications
In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS). These are true meshless methods that have the advantage of avoiding the need to set up a mesh altogether, and therefore going beyond the reduction of the mesh to a boundary. These Trefftz methods have advantages in several engineering applications, for instance in inverse problems where the domain is unknown and some numerical methods would require a remeshing approach.Trefftz methods are also known to perform very well with regular domains and regular data in boundary value problems, achieving exponential convergence. On the other hand, they may also under certain conditions, exhibit instabilities and lead to ill-conditioned systems. This book is divided into ten chapters that illustrate recent advances in Trefftz methods and their application to engineering problems. The first eight chapters are devoted to the MFS and variants whereas the last two chapters are devoted to related meshless engineering applications. Part of these selected contributions were presented in the 9th International Conference on Trefftz Methods and 5th International Conference on the MFS, held in 2019, July 29-31, in Lisbon, Portugal.
Techniques for Designing and Analyzing Algorithms
Techniques for Designing and Analyzing Algorithms Design and analysis of algorithms can be a difficult subject for students due to its sometimes-abstract nature and its use of a wide variety of mathematical tools. Here the author, an experienced and successful textbook writer, makes the subject as straightforward as possible in an up-to-date textbook incorporating various new developments appropriate for an introductory course. This text presents the main techniques of algorithm design, namely, divide-and-conquer algorithms, greedy algorithms, dynamic programming algorithms, and backtracking. Graph algorithms are studied in detail, and a careful treatment of the theory of NP-completeness is presented. In addition, the text includes useful introductory material on mathematical background including order notation, algorithm analysis and reductions, and basic data structures. This will serve as a useful review and reference for students who have covered this material in a previous course. Features The first three chapters provide a mathematical review, basic algorithm analysis, and data structures Detailed pseudocode descriptions of the algorithms along with illustrative algorithms are included Proofs of correctness of algorithms are included when appropriate The book presents a suitable amount of mathematical rigor After reading and understanding the material in this book, students will be able to apply the basic design principles to various real-world problems that they may encounter in their future professional careers.
