An Intellectual Arithmetic, Upon the Inductive Method
This book provides a comprehensive and detailed study of arithmetic, with a focus on the inductive method of reasoning. The author provides insightful commentary and analysis in a highly readable style. A must-read for educators and mathematicians.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.
Numerical Solutions Applied to Heat Transfer with the Sph Method
This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models. Techniques described in this book aim to speed up the convergence of numerical solutions and increase their accuracy by significantly reducing the discretization error.In their quest, the authors shed light on new sources of numerical error that are specific to the SPH method and, through them, they identify the characteristics of the solutions influenced by such errors. The accuracy of numerical solutions is also improved with the application of advanced tools like the repeated Richardson extrapolation (RRE) in quadruple precision, which was adapted to consider fixed or moving particles. The book finishes with the conclusion that the qualitative and quantitative verification of numerical solutions through coherence tests andmetrics are currently a methodology of excellence to treat computational heat transfer problems.Mathematicians in applied fields and engineers modelling and solving real physical phenomena can greatly benefit from this work, as well as any reader interested in numerical methods for differential equations.
Dual Arithmetic
This book offers a unique approach to arithmetic, using geometric shapes and colors to represent numbers and operations. It includes numerous examples and exercises to help readers master this innovative method. The publication provides a fascinating glimpse into the history and diversity of mathematical pedagogy. 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.
Readings for Sociology
Barnard's work provides a systematic introduction to the principles of arithmetic, with a focus on developing a deep understanding of the underlying concepts. Filled with examples and exercises, this book is an essential resource for math students and teachers alike.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.
Before You Go
First published in the mid-19th century, this classic textbook teaches arithmetic through a series of practical and relevant problems, such as measuring land, calculating interest, and making change. With clear explanations and plenty of practice exercises, this book is perfect for anyone looking to improve their numeracy skills.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.
Everyday Arithmetic; Volume 3
This textbook provides a comprehensive introduction to arithmetic for students of all ages. With clear explanations and practical exercises, it is an excellent resource for anyone seeking to improve their mathematical skills.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.
Masters' Ready Reckoner
This practical book is a comprehensive guide to everyday arithmetic. It includes information on measurements, weights and measures, and other important calculations. It is an excellent resource for students, professionals, and anyone else who needs to perform quick calculations on a regular basis.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.
Math Mammoth Foundational Word Problems
Math Mammoth Foundational Word Problems is a workbook intended for students in 3rd grade and above that need more practice with word problems. I especially aim to help students in 4th-7th grades who have trouble with word problems and who need to "go back to the beginning", so to speak, to learn to solve them.The problems are generally based on a knowledge of third grade math, such as regrouping in addition and subtraction, the multiplication tables, concept of division, and calculating change. The problems do not require long multiplication, long division, or calculations with fractions or decimals (with the exception of money amounts).The worksheets have examples and some instruction about common strategies for word problems. Students are often encouraged to write down the calculations they do. They are also encouraged to make a drawing or a sketch of the situation in the problem, to help them understand the situation and to see what math operation is involved.Overall, most of the problems require two or more steps; however, some problem sets focus on differentiating what math operation should be used, and those only require a single step.Several problem sets are designed to help students to master problems that involve equal-size groups. These questions either ask for the total (and are thus solved by multiplying), or they ask for the size of the group or for the quantity of the groups (one can write a missing number multiplication sentence, such as 3 ? ___ = 18 or use division).The book also includes word problems with fractions, with large numbers, with money, geometry word problems, and challenges in the form of puzzle corners.You can download sample pages from this link: https: //www.mathmammoth.com/word_problems/Foundational_Word_Problems_samples.pdf
Number Theory
This Book of Number Theory is a captivating exploration of one of the oldest branches of mathematics. From its ancient origins to modern-day breakthroughs, this book uncovers the patterns, properties, and relationships that lie at the heart of numbers. It delves into topics such as divisibility, prime numbers, modular arithmetic, Diophantine equations, prime number distribution, and sieve methods. With its comprehensive coverage and engaging explanations, The Book of Number Theory reveals the beauty and significance of this fascinating mathematical discipline.
Quaternion and Clifford Fourier Transforms
Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth.The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists, and engineers (signal and color image processing, electrical engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.).Features Intuitive real geometric approach to higher-dimensional Fourier transformations A comprehensive reference, suitable for graduate students and researchers Includes detailed definitions, properties, and many full step-by-step proofs Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information
The First Million Digits of Pi
Pi, the ratio of the circumference of a circle to its diameter, has been know to exist for thousands of years. Even before the common era, ancient mathematicians had found approximations for pi that were accurate to two digits (3.1). The Babylonians used 25/8 as an approximation of pi. The ancient Egyptians used 16/9 squared for pi. The next to improve the approximations for pi were Chinese mathematicians. The Chinese approximation was correct to seven digits (3.141592).In Greece, Archimedes used a polygon drawn outside a circle, and a polygon drawn inside a circle, and extended pi to three digits (3.14). Finally, when infinite series were developed, one could calculate pi with pen and paper to as many digits as one had time for. It was not until computers came along that it was practical to calculate pi to a million digits. Here, in this book, are the results."Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi"William L. Schaaf, Nature and History of Pi
The First Million Digits of Pi
Pi, the ratio of the circumference of a circle to its diameter, has been know to exist for thousands of years. Even before the common era, ancient mathematicians had found approximations for pi that were accurate to two digits (3.1). The Babylonians used 25/8 as an approximation of pi. The ancient Egyptians used 16/9 squared for pi. The next to improve the approximations for pi were Chinese mathematicians. The Chinese approximation was correct to seven digits (3.141592). In Greece, Archimedes used a polygon drawn outside a circle, and a polygon drawn inside a circle, and extended pi to three digits (3.14). Finally, when infinite series were developed, one could calculate pi with pen and paper to as many digits as one had time for. It was not until computers came along that it was practical to calculate pi to a million digits. Here, in this book, are the results."Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi"William L. Schaaf, Nature and History of Pi
Smooth-Automorphic Forms and Smooth-Automorphic Representations
This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider 'K-finite' automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of 'smooth-automorphic forms' is intrinsic to the group scheme G/F.This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.
The Indian Number System
This book presents well-established modern methods of representation and quantitative evaluation for a variety of entities, constants, functions, vectors, random quantities, fuzzy sets, and abstract entities such as relationships, cooperation, dependence, etc. and reveals striking similarities between these modern concepts and the Hindu-Arabic Decimal Number System. We regularly work with them without realizing these similarities perhaps because the centuries old Indian Number System became so commonplace today that these connections are not evidenced either by citations in the literature. It is hoped that this book will serve to throw some new light on the INS which is held in high esteem by great minds. The size of this book, its presentation in simple terms devoid of mystifying jargon, and its capture of the basic elements of the vast subject of mathematical concepts, especially in the field of systems and signals, are expected to be attractive to both teachers and students.
Classification of Musical Objects for Analysis and Composition
This book presents and discusses the fundamental topic of classification of musical objects, such as chords, motifs, and gestures. Their classification deals with the exhibition of isomorphism classes. Our structure types include local and global constructions, the latter being similar to global structures in geometry, such as differentiable manifolds. The discussion extends to the role, which classification plays for the creative construction of musical compositions. Our examples include references to classical compositions, such as Beethoven's sonatas, and some of the author's own compositions of classical and jazz styles. We also discuss software that enables the application of classification to musical creativity. The volume is addressed to an audience that would apply classification to programming and creative musical construction.
Numerical Analysis of Ordinary and Delay Differential Equations
This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering.One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.
The First Hundred Thousand Prime Numbers
A prime number is any integer greater than one which has only itself and one as factors. For example, 5 is prime since it does not have 2, 3, or 4 as a factor. 1 and 5 are the only factors of 5.Prime numbers have been studied since antiquity. Eratosthenes of Cyrene lived about 276 BCE to 194 BCE. He developed a method of finding prime numbers that is still taught today. It is called the Sieve of Eratosthenes.Prime numbers continue to fascinate mathematicians today. Prime numbers are used in number theory, and in cryptography.
Math Mammoth Grade 5 Skills Review Workbook Answer Key
Math Mammoth Grade 5 Skills Review Workbook Answer Key contains answers to all the worksheets in Math Mammoth Grade 5 Skills Review Workbook. The workbook itself is available separately. (This is the 2023 edition.)
Math Mammoth Grade 5 Skills Review Workbook
Some students benefit from spiral review, and that is exactly what Math Mammoth Grade 5 Skills Review Workbook offers! It has been designed to complement the lessons in Math Mammoth Grade 5 complete curriculum, providing spiral review of the concepts in the Grade 5 curriculum.Math Mammoth Grade 5 Skills Review Workbook is divided into chapters, which correspond to the chapters in Math Mammoth Grade 5 curriculum. It is meant to be used during the school year, alongside the main curriculum. Spiral reviewing means that after a particular concept or skill has been studied in the main curriculum, it is then reviewed repeatedly over time in several different worksheets of this book.You can choose exactly when to use the worksheets within the chapter, and how many of them to use. Not all students need all of these worksheets to help them keep their math skills fresh, so please vary the amount of worksheets you assign your student(s) according to their need.Each worksheet is designed to be one page, and includes a variety of exercises in a fun way without becoming too long and tedious.The answer key is available as a separate book.
Time Dependent Phase Space Filters
This book introduces an interesting and alternative way to design absorbing boundary conditions (ABCs) for quantum wave equations, basically the nonlinear Schr繹dinger equation. The focus of this book is the application of the phase space filter approach to derive accurate radiation conditions for Schr繹dinger equations.Researchers who are interested in partial differential equations and mathematical physics might find this book appealing.
Bridging Circuits and Fields
Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.
Computing With Fermat
"Computing with Fermat" is a fascinating collection of math articles that pay tribute to the great Pierre de Fermat, exploring various math problems using computational number theory that relate to his work. With chapters such as "On Fermat's Factorization Method," "Fun With the Sqrt(n) Primality Test," "Near-Misses of Fermat's Last Theorem," and "Marin Mersenne and the Power of Modern Computing," this book offers a comprehensive look at how computational number theory is changing the game in the world of mathematics. The author, who found solace in Simon Singh's book "Fermat's Enigma" during a difficult time in his life, was inspired to delve into the world of computational number theory. The book features the author's own papers related to Fermat's work, as well as two chapters from his book "The Lowbrow Experimental Mathematician" that explore certain Fermat-type problems in elementary number theory. "Computing with Fermat" is a must-read for anyone interested in the legacy of Pierre de Fermat and the fascinating world of computational number theory. With its accessible writing style and engaging content, this book is sure to inspire and entertain readers of all levels.
Tragic Encounters
Literary scholars largely agree that the Romantic period altered the definition of tragedy, but they have confined their analyses to Western European authors. Maksim Hanukai introduces a new, illuminating figure to this narrative, arguing that Russia's national poet, Alexander Pushkin, can be understood as a tragic Romantic poet, although in a different mold than his Western counterparts. Many of Pushkin's works move seamlessly between the closed world of traditional tragedy and the open world of Romantic tragic drama, and yet they follow neither the cathartic program prescribed by Aristotle nor the redemptive mythologies of the Romantics. Instead, the idiosyncratic and artistically mercurial Pushkin seized upon the newly unstable tragic mode to develop multiple, overlapping tragic visions. Providing new, innovative readings of such masterpieces as The Gypsies, Boris Godunov, The Little Tragedies, and The Bronze Horseman, Hanukai sheds light on an unexplored aspect of Pushkin's work, while also challenging reigning theories about the fate of tragedy in the Romantic period.
Math Mammoth Grade 6 Answer Keys
Math Mammoth Grade 6 Answer Keys contains answer keys to Math Mammoth Grade 6-A and 6-B student worktexts, chapter tests, the end-of-year test, and the cumulative review lessons. This is the 2022 edition.
Numerical Methods and Applications
This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.
Wave Phenomena
This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.
Searching for N
"Searching for N" is a captivating collection of articles that takes readers on a journey through the fascinating world of number theory and beyond. Written by a mathematics enthusiast, this book presents classic topics like prime numbers and divisibility, but also includes surprises like short stories, anecdotes, and informational articles on a variety of different subjects. Readers will find a diverse range of chapters that explore intriguing topics such as Concrete Calculator-Word Primes, Summation of Infinite Series, Zen Master Bodhidharma, Iteration Problems, Barbelo and Gnosticism, Artificial Intelligence, and more. Each chapter attempts to offer a unique perspective on number theory, and other subjects. By delving into apparently unrelated subjects, the author attempts to uncover the interconnectedness of mathematics with our surroundings. Whether you are a seasoned mathematician or simply curious about numbers, this book is sure to engage your mind and spark your imagination. But "Searching for N" is more than just a book on number theory. It is also a story of perseverance and passion for mathematics. The author, Fitzroy, struggled with the complexity of number theory and found himself unable to solve the most challenging problems. However, he refused to give up on his dream of contributing something to the world of mathematics. Determined to find his own path, Fitzroy turned to writing as a way to express his ideas and insights. He began crafting short stories that explored the mysteries of the human psyche, often incorporating abstract concepts and philosophical ideas into his writing. Despite his struggles with mathematical problem-solving, a few of his stories resonated with readers and were admired for their emotional power and insight. Join Fitzroy on his journey through "Searching for N" and discover the beauty and power of number theory, and the importance of perseverance and passion in pursuing one's dreams.
Numerus Computatio Balisticum
"Numerus Computatio Balisticum" is a fascinating book that explores the arcane discipline of number theory through the power of computation. With a deep passion for both computers and number theory, the author has spent years crafting elaborate algorithms to unlock the secrets of the integers. In this book, the author shares some of the most interesting and complex problems in number theory, from the history of the discipline to contemporary research. The book features chapters on topics such as Nash Goldbach Decompositions, Elliptic Curve Experiments, Alan Turing and Computers, the Collatz Conjecture, and Fermat's Factorization Method on Brilliant Numbers. Each chapter offers a unique glimpse into the intricate web of abstract concepts and elusive patterns that make up the fascinating world of computational number theory. Readers will also come across personal reflections that showcase the author's dedication and passion for the discipline. Despite the foreboding sense of mystery that surrounds the power of numbers, the author's aim is not to scare but to inspire. This book is perfect for anyone looking to explore the labyrinthine depths of mathematical thought and discover the wonders and terrors that lie within the shadowy realm of the integers. Whether you're a seasoned mathematician or a curious novice, this book is sure to ignite a spark of inspiration that drives you to investigate these problems for yourself. So, dive into this tome and behold the eerie and fascinating beauty of numbers!
The Splendor and Squalor of Numbers
This captivating book on number theory explores the hidden beauty of numbers and the fascinating world of mathematics. The author's compulsion to analyze and contemplate the splendor (and squalor) of numbers leads him to seek out strange mathematical properties lurking within the platonic realm. The book covers a wide range of topics related to number theory, including compound interest, near misses of Fermat's last theorem, conjectures on twin primes, the mysterious qualities of zebra irrational numbers, and more. Readers will also enjoy a few fictional stories that feature numbers, which serve to further illuminate the beauty and wonder of mathematics (it's worth noting that the stories are entirely fictional, and any characters that might resemble real-life individuals (living or deceased) are entirely coincidental). The author's main goal is to inspire readers to engage in their own investigations of mathematical problems and discover the thrill of probing the integers to appreciate their mysterious and astounding qualities. Whether you're a seasoned mathematician or simply someone who enjoys contemplating the beauty of numbers, this book is sure to stimulate your mind and encourage you to think deeply about the fascinating world of mathematics. So come along for the ride as the author delves deep into the splendor (and squalor) of numbers, uncovering their hidden mysteries and inspiring readers to seek out the same.
Excursions in Multiplicative Number Theory
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided "walks" invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin-Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at "higher ground", where they will find opportunities for extensions and applications, such asthe Selberg formula, Brun's sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.
Mathematical Essays and Recreations
Mathematical Essays and Recreations, has been acknowledged as a major work throughout human history, and we have taken precautions to assure its preservation by republishing this book in a modern manner for both present and future generations. This book has been completely retyped, revised, and reformatted. The text is readable and clear because these books are not created from scanned copies.
Advanced Problem Solving Using Maple
Advanced Problem Solving Using Maple(TM) Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. Scenarios are developed within the scope of the problem-solving process.The text focuses on discrete dynamical systems, optimization techniques, single-variable unconstrained optimization and applied problems, and numerical search methods. Additional coverage includes multivariable unconstrained and constrained techniques. Linear algebra techniques to model and solve problems such as the Leontief model, and advanced regression techniques including nonlinear, logistics, and Poisson are covered. Game theory, the Nash equilibrium, and Nash arbitration are also included.Features: The text's case studies and student projects involve students with real-world problem solving Focuses on numerical solution techniques in dynamical systems, optimization, and numerical analysis The numerical procedures discussed in the text are algorithmic and iterative Maple is utilized throughout the text as a tool for computation and analysis All algorithms are provided with step-by-step formats About the Authors: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his PhD at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles.William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM).
The Theory of Zeta-Functions of Root Systems
The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell-Tornheim multiple zeta-functions, and Euler-Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten's volume formula is provided. It is shown that various relations among special values of Euler-Zagier multiple zeta-functions-which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier's conjecture-are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.
Elliptic Curves
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer.Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work.The first three chapters develop the basic theory of elliptic curves.For this edition, the text has been completely revised and updated.
Women in Numbers Europe III
This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of collaborations started at the 3rd edition of the Women in Numbers Europe (WINE) conference between senior and mid-level faculty, junior faculty, postdocs, and graduate students. The contents of this book should be of interest to graduate students and researchers in number theory.
Fluids Under Control
This volume presents state-of-the-art developments in theoretical and applied fluid mechanics. Chapters are based on lectures given at a workshop in the summer school Fluids under Control, held in Prague on August 25, 2021. Readers will find a thorough analysis of current research topics, presented by leading experts in their respective fields. Specific topics covered include: Magnetohydrodynamic systemsThe steady Navier-Stokes-Fourier systemBoussinesq equationsFluid-structure-acoustic interactions Fluids under Control will be a valuable resource for students interested in mathematical fluid mechanics.
A First Course In Chaotic Dynamical Systems
The first text to introduce modern topics in dynamical systems at the undergraduate level, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. Now a classic, this new edition incorporates many new updates. The author also includes an emphasis on student research and experiment.
First sanctuaries - Jerusalem and Black Holes
Parte della scienza si limitava alla conoscenza dei calendari nel tempo antico. Per questa ragione, chi volesse indagare su qualunque civilt? del passato, trova qui tutti gli strumenti utili. L'autore ha introdotto l'uguaglianza 3402 = (30.24) 112.5, utile per isolare (30.24), che interviene col significato di rotazione di 360簞 lungo un cerchio. Inoltre 34.02 癡 anche impiegato per misurare ore alla ziggurat babilonese di Uruk (4000 a.C). Come si possa ricavare un calendario viene spiegato con la costruzione pratica di quello di Dionigi, scritto per ordine di un papa nei primi secoli del cristianesimo. Risulta importante la decifrazione di una tabella aritmetica egiziana, le cui cifre intervengono in vari contesti, dando la possibilit? di unificare tutte le misure di angoli. Nella riforma di Ezechiele compare un angolo di 72簞; e lo stesso an golo 癡 indispensabile anche per le galassie. In un libro di E. Fermi (No tes on Quantum Mechanics) 癡 dimostrato che ogni (quantit?) osservabile si descrive con un sistema di equazioni; cos穫 con la soluzione di un sistema abbiamo qui un metodo per controllare distanze di alcune galassie ad anche di stelle da punti considerati come sorgenti di forza, da cui dipendono. Se il lettore non vuol leggere qualche argomento pu簷 evitarlo passando oltre.
Math Mammoth Grade 5 Answer Keys
Math Mammoth Grade 5 Answer Keys contains the answer keys to Math Mammoth Grade 5-A and 5-B student worktexts, to all the chapter tests, the end-of-year test, and the cumulative review lessons.
Math Mammoth Grade 5-B Worktext
Math Mammoth Grade 5-B Worktext is the second student book in Math Mammoth grade 5 curriculum, meant for the latter half of 5th grade. This is the 2023 edition.The main areas of study in Math Mammoth Grade 5-B worktext are: decimal arithmeticfraction arithmetic (all operations with fractions)geometry: review of angles, area, and perimeter; drawing circles; classifying triangles & quadrilaterals; volume of rectangular prismsChapter 6 continues our study of decimals. The focus is on multiplying decimals by decimals, dividing decimals by decimals, and conversions between measuring units.Chapter 7 covers the addition and subtraction of fractions - another topic of focus for 5th grade, besides decimals. The most difficult topic of this chapter is adding and subtracting unlike fractions, which is done by first converting them to equivalent fractions with a common denominator.In chapter 8, we study the multiplication and division of fractions from various angles.Chapter 9 takes us to geometry, starting with a review of angles and polygons. From there, students will learn to classify triangles and quadrilaterals, and will study the concept of volume in the context of right rectangular prisms (boxes).FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.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.Very little teacher preparation is required. 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.This is the full-color version of the worktext. Please note that it does not include the answers; they are sold as a separate book.
Math Mammoth Grade 5 Tests and Cumulative Reviews
Math Mammoth Grade 5 Tests and Cumulative Reviews includes consumable student copies of the end-of-chapter tests, the end-of-year test, and additional cumulative review lessons, to match Math Mammoth Grade 5 curriculum.
Math Mammoth Grade 5-A Worktext
Math Mammoth Grade 5-A Worktext is the student book the first half of grade 5. 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. This is the 2023 edition.The main areas of study in the grade 5-A worktext are: the four operations with whole numbersplace value with large numbers and the judicious use of calculatorproblem solving & simple equationsdecimal arithmeticgraphing and the coordinate gridThe year starts out with a study of whole numbers and their operations. Students get to review multi-digit multiplication and learn long division with two-digit divisors. We also review divisibility and factors from fourth grade, and study prime factorization.In the second chapter, the focus is on large numbers and using a calculator. This is the first time a calculator is introduced in Math Mammoth complete curriculum-thus far, all calculations have been done mentally, or with paper and pencil. I want students to learn to be critical in their use of the calculator and use it with good judgment. Every exercise where calculator use is to be allowed is marked with a little calculator symbol.The third chapter is about equations and problem solving. We study simple equations with the help of a balance and bar models. The main idea is to get students used to the idea of an equation and what it means to solve an equation. Students also do a fair amount of problem solving using the visual bar model.The fourth chapter is about decimals and some of the operations with decimals (the rest will be studied in chapter 6). Fifth grade is the time when students learn all the basic operations with decimals. In this chapter, we focus on place value with decimals, addition and subtraction of decimals, and multiplication and division of decimals by whole numbers. Multiplying decimals by decimals and dividing decimals by decimals is covered in chapter 6.In chapter 5, we study graphing in the coordinate grid, line graphs, and average. Today's world has become increasingly complex with lots of data presented in the media, so our children need a good grasp of statistical graphs to be able to make sense of all of that information.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.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.Very little teacher preparation is required. 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.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.
Math Mammoth Grade 2 Tests and Cumulative Revisions, International Version (Canada)
Math Mammoth Grade 2 Tests and Cumulative Reviews includes consumable student copies of chapter tests, the end-of-year test, and additional cumulative review lessons to match Math Mammoth Grade 2 curriculum. This is the full-color version.
Advances in Number Theory and Applied Analysis
Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.
Math Mammoth Grade 6 Skills Review Workbook Answer Key
Math Mammoth Grade 6 Skills Review Workbook Answer Key contains answers to all the worksheets in Math Mammoth Grade 6 Skills Review Workbook. The workbook itself is available separately. (This is the 2022 edition.)
