Answers, Or, A Key To Nearly Three Thousand Questions In Addition, Subtraction, Multiplication And Division
This handy reference book provides easy-to-use answers to a wide range of mathematical questions. P. B. Templeton provides a comprehensive guide to arithmetic operations, with step-by-step solutions to common problems in addition, subtraction, multiplication, and division. This book is a must-have resource for students and teachers, and is suitable for all levels of mathematical ability.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.
Analytic Methods in Number Theory
There is no surprise that arithmetic properties of integral ('whole') numbers are controlled by analytic functions of complex variable. At the same time, the values of analytic functions themselves happen to be interesting numbers, for which we often seek explicit expressions in terms of other 'better known' numbers or try to prove that no such exist. This natural symbiosis of number theory and analysis is centuries old but keeps enjoying new results, ideas and methods.The present book takes a semi-systematic review of analytic achievements in number theory ranging from classical themes about primes, continued fractions, transcendence of π and resolution of Hilbert's seventh problem to some recent developments on the irrationality of the values of Riemann's zeta function, sizes of non-cyclotomic algebraic integers and applications of hypergeometric functions to integer congruences.Our principal goal is to present a variety of different analytic techniques that are used in number theory, at a reasonably accessible -- almost popular -- level, so that the materials from this book can suit for teaching a graduate course on the topic or for a self-study. Exercises included are of varying difficulty and of varying distribution within the book (some chapters get more than other); they not only help the reader to consolidate their understanding of the material but also suggest directions for further study and investigation. Furthermore, the end of each chapter features brief notes about relevant developments of the themes discussed.
Algebraic Groups and Number Theory
The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.
Learning and Intelligent Optimization
This book constitutes the refereed proceedings of the 17th International Conference on Learning and Intelligent Optimization, LION-17, held in Nice, France, during June 4-8, 2023.The 40 full papers presented have been carefully reviewed and selected from 83 submissions. They focus on all aspects of unleashing the potential of integrating machine learning and optimization approaches, including automatic heuristic selection, intelligent restart strategies, predict-then-optimize, Bayesian optimization, and learning to optimize.
Hamilton’s Essentials of Arithmetic; Volume 2
Hamilton's Essentials of Arithmetic is an indispensable guide to the fundamental principles of mathematics. Written by Samuel Hamilton, an experienced teacher and mathematician, this book covers all the essential topics in arithmetic, from basic operations and fractions to percentages, algebra and geometry. With clear explanations and worked examples, as well as a wide range of practice exercises and quizzes, Hamilton's Essentials of Arithmetic is an ideal textbook for students of all ages and abilities.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.
Cockers Arithmetick, Perused by J. Hawkins
First published in 1678, Edward Cocker's Arithmetick is a classic text that has been used for centuries to teach the principles of mathematics. This edition, perused by J Hawkins, includes helpful explanations and examples that make even the most complex concepts easy to grasp. Whether you're a student, a teacher, or just someone who loves numbers, this book is sure to become a favorite.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.
Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws
The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods.
Aritm矇tica Elemental
Un manuel d'arithm矇tique clair et complet destin矇 aux 矇tudiants de tous niveaux, avec des exemples et des exercices pratiques pour aider les 矇l癡ves ? ma簾triser les concepts de base et ? progresser en math矇matiques.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.
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.
Mathematical Thinking
This textbook invites readers to explore mathematical thinking by finding the beauty in the subject. With an accessible tone and stimulating puzzles, the author will convince curious non-mathematicians to continue their studies in the area. It has an expansive scope, covering everything from probability and graph theory to infinities and Newton's method. Many examples of proofs appear as well, offering readers the opportunity to explore these topics with the amount of rigor that suits them. Programming exercises in Python are also included to show how math behaves in action.Mathematical Thinking is an ideal textbook for transition courses aimed at undergraduates moving from lower level to more advanced topics, as well as for math recruitment and invitational courses at the freshman or sophomore level. It may also be of interest in computer science departments and can be used as a supplemental text for courses in discrete mathematics and graph theory.
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.
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.
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
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.
All That Math!
Prophetess Dr. Kemba Jarena Lucas (PK), founder and chief visionary officer of Daughters of Destiny International (DOD), is celebrating the organization's jade anniversary by supporting her tribe and any Christian woman willing to help children ages 4-8 overcome their math learning gaps. As a Christian educator who began preaching at the age of 12, she offers a one-of-a-kind, Christ-centered approach to assisting her brilliant crew in growing closer to God, overcoming challenges, and progressing in their math skill sets without the pressure of completing a task in a specific time frame because everyone grows differently. Her brilliant mathematicians are guided by their Auntie-Prophetess, a fifteen-year veteran homeschool parent, to gain confidence while conquering the learning obstacles that they will face from time to time without shame and by asking for help. In "All That Math!: A Kembativity Mathematics Workbook for Ages 4-8 featuring 'The Parsonage Tales of Kemba Jarena, God's Little Prophet Series' Fam," PK, along with a few characters from her children's series, inspires her brilliant nieces and nephews to close learning gaps day by day, starting today. By purchasing this book, you are financially supporting Daughters of Destiny International's Build Her Global Project, which is co-sponsored by KJL Design + Build, KEMBA IC partners, and other faith-based organizations around the world. This global project will provide borehole wells, butterfly meditation gardens, Gchapels, prayer walls, exterior remodeling, landscaped campuses, and hospitable built environments to foster community within a harmonized sacred space of divinity, humanity, and nature, thereby catalyzing educational, economic, and communal growth, particularly for women and girls.
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.
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.)
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.
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.
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.
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.
Number Fields
Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.Part I of the book contains topics in basic algebraic number theory as they may be presented in a beginning master course on algebraic number theory. It includes the classification of abelian number fields by groups of Dirichlet characters. Class field theory is treated in Part II: the more advanced theory of abelian extensions of number fields in general. Full proofs of its main theorems are given using a 'classical' approach to class field theory, which is in a sense a natural continuation of the basic theory as presented in Part I. The classification is formulated in terms of generalized Dirichlet characters. This 'ideal-theoretic' version of class field theory dates from the first half of the twentieth century. In this book, it is described in modern mathematical language. Another approach, the 'id癡lic version', uses topological algebra and group cohomology and originated halfway the last century. The last two chapters provide the connection to this more advanced id癡lic version of class field theory. The book focuses on the abstract theory and contains many examples and exercises. For quadratic number fields algorithms are given for their class groups and, in the real case, for the fundamental unit. New concepts are introduced at the moment it makes a real difference to have them available.
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.
