Number Stories
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.
Theory of Groups of Finite Order
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.
Cubic Forms and the Circle Method
- 1. Cubic Forms Over Local Fields. - 2. Waring's Problem for Cubes. - 3. Cubic Forms via Weyl Differencing. - 4. Norm Forms Over Number Fields. - 5. Diagonal Cubic Forms Over Function Fields. - 6. Lines on Cubic Hypersurfaces.
Numerical Methods for Elliptic and Parabolic Partial Differential Equations
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Ray's New Intellectual Arithmetic
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.
The Earliest Arithmetics in English
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 Elementary Treatise on Arithmetic Taken Principally From the Arithmetic of S. Fran癟ois Lacroix
An Elementary Treatise on Arithmetic Taken Principally From the Arithmetic of S. Fran癟ois Lacroix
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.
The Earliest Arithmetics in English
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.
Arithmetic Village Presents Arithmetic Village
In Arithmetic Village, there are only two rules: be kind to each other and share all the jewels. This first book in a series of five which use characters, rhyme and color to introduce the basic math concepts. This book explains number placement with easy to understand symbols: One jewel = 1, a golden bag represents 10, and a treasure chest equals 100. Number placement is a vital part of understanding future math concepts. This gentle math book is suitable for all children.
The Thorndike Arithmetics, Book 1
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.
The Anderson Arithmetic, Book One
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A High School Arithmetic (Wentworth & Hill's Practical Arithmetic)
The American Tutor's Assistant Revised, Or, a Compendious System of Practical Arithmetic
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.
Short-Cut Math
Clear, concise compendium of about 150 time-saving math short-cuts features faster, easier ways to add, subtract, multiply, and divide. Each problem includes an explanation of the method, a step-by-step solution, the short-cut solution, and proof, as well as an explanation of why it works. No special math ability needed.
Arithmetic Village Presents Linus Minus
Linus Minus, the third book in the ]Arithmetic Village] series, teaches subtraction simply and quickly through characters and rhyme. Linus playfully introduces the concept, while joyfully losing jewels throughout the village. For more information visit www.arithmeticvillage.com
Arithmetic Village Presents King David Divide
King David Divide is mighty and wise, sharing jewels equally is what he decides. This is the last book in a picture book series, ]Arithmetic Village] which teaches math simply and gently though characters, color and rhyme. King David introduces the concept of division by equally distributing jewels throughout the village. His dog, Rover gets the remainder. For more information visit arithmeticvillage.com
The Arithmetic Primer
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
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.
The Arithmetic Primer
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.
Integral Equation Methods for Evolutionary Pde
1 Some examples of causal convolutions.- 2 Convolution quadrature for hyperbolic symbols.- 3 Algorithms for CQ: linear multistep methods.- 4 Acoustic scattering in the time domain.- 5 Runge-Kutta CQ.- 6 Transient electromagnetism.- 7 Boundary-field formulations.- 8 Parabolic problems.- 9 Data sparse methods and other topics.
Teaching Multiplication Using LEGO(R) Bricks
In Teaching Multiplication Using LEGO(R) Bricks, Dr. Shirley Disseler has developed activities that work to help students learn the basics of multiplication, using a common toy available in most classrooms and homes-LEGO(R) bricks!Multiplication is not simply the rote memorization of times tables. Students need to understand multiplication concepts. LEGO(R)bricks are the perfect manipulative to help students model, utilizing their creative and logical processes together.In this book, the hands-on activities using LEGO(R) bricks help students learn: - the meaning of multiplication as repeated addition- the vocabulary of multiplication- basic multiplication facts- one-digit multiplication- two-digit and larger multiplicationThe book starts at the most basic concepts and focuses on a specific topic in each chapter. Most students learn these concepts between grades 2 - 5.Using LEGO(R) bricks to model math provides a universal language. Children everywhere recognize this manipulative.It's fun to learn when you're using LEGO(R) bricks!
Krylov Subspace Methods for Linear Systems
Introduction to Numerical Methods for Solving Linear Systems.- Some Applications to Computational Science and Data Science.- Classification and Theory of Krylov Subspace Methods.- Applications to Shifted Linear Systems.- Applications to Matrix Functions.
Homogenization Theory for Multiscale Problems
The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.
Progressive Maths For School
Progressive Maths For Schools is a book about whole number. The book is for all children. It is illustrated and can be written on. Needless to say the child will love the book. There's colouring in it and join the dots.
From Great Discoveries in Number Theory to Applications
Foreword.- 1. Divisibility and Congruence.- 2. Prime and Composite Numbers.- 3. Properties of Prime Numbers.- 4. Special Types of Primes.- 5. On a Connection of Number Theory with Graph Theory.- 6. Pseudoprimes.- 7. Fibonacci and Lucas Numbers.- 8. Further Special Types of Integers.- 9. Magic and Latin Squares.- 10. The Mathematics Behind Prague's Horologe.- 11. Applications of Primes.- 12. Further Applications of Number Theory.- Tables.- References.
illpha Math Book (Level 2)
The 2nd book of illpha series for learning Children writing numbers and counting With fun and interesting way For children from 4 to 5 years old.
Multivariate Data Analysis on Matrix Manifolds
This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.
New Sinc Methods of Numerical Analysis
This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.
Introduction to the Tools of Scientific Computing
The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike standard approaches, it does not focus on any specific language, but aims to explain the underlying ideas.Typically, new concepts are first introduced in the particularly user-friendly Python language and then transferred and extended in various programming environments from C/C++, Julia and MATLAB to Maple and Mathematica. This includes various approaches to distributed computing. By examining and comparing different languages, the book is also helpful for mathematicians and practitioners in deciding which programming language to use for which purposes.At a more advanced level, special tools for the automated solution of partial differential equations using the finite element method are discussed. On a more experimental level, the basic methods of scientific machine learning in artificial neural networks are explained and illustrated.
Anisotropic Hp-Mesh Adaptation Methods
Introduction.- Metric Based Mesh Representation.- Interpolation Error Estimates for Two Dimensions.- Interpolation Error Estimates for Three Dimensions.- Anisotropic Mesh Adaptation, h-Variant.- Anisotropic Mesh Adaptation Method, hp-Variant.- Framework of the Goal-Oriented Error Estimates.- Goal-Oriented Anisotropic Mesh Adaptation.- Implementation Aspects.- Applications.
Approximation and Online Algorithms
This book constitutes revised selected papers from the thoroughly refereed workshop proceedings of the 20th International Workshop on Approximation and Online Algorithms, WAOA 2022, which was colocated with ALGO 2022 and took place in Potsdam, Germany, in September 2022.The 12 papers included in these proceedings were carefully reviewed and selected from21 submissions. They focus on topics such as graph algorithms, network design, algorithmic game theory, approximation and online algorithms, etc.
Continued Fractions and Signal Processing
Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony's problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.
Data Science for Public Policy
This textbook presents the essential tools and core concepts of data science to public officials, policy analysts, and economists among others in order to further their application in the public sector. An expansion of the quantitative economics frameworks presented in policy and business schools, this book emphasizes the process of asking relevant questions to inform public policy. Its techniques and approaches emphasize data-driven practices, beginning with the basic programming paradigms that occupy the majority of an analyst's time and advancing to the practical applications of statistical learning and machine learning. The text considers two divergent, competing perspectives to support its applications, incorporating techniques from both causal inference and prediction. Additionally, the book includes open-sourced data as well as live code, written in R and presented in notebook form, which readers can use and modify to practice working with data.
Mathematical and Computational Models of Flows and Waves in Geophysics
- Geostrophic Turbulence and the Formation of Large Scale Structure. - Ocean Surface Waves and Ocean-Atmosphere Interactions. - A 3D Two-Phase Conservative Level-Set Method Using an Unstructured Finite-Volume Formulation. - The Physics of Granular Natural Flows in Volcanic Environments. - Cooperative Gravity and Full Wave form Inversion: Elastic Case. - Modelling the 3D Electromagnetic Wave Equation: Negative Apparent Conductivities and Phase Changes.
Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling
Weighted Automata, Formal Power Series and Weighted Logic
The main objective of this work is to represent the behaviors of weighted automata by expressively equivalent formalisms: rational operations on formal power series, linear representations by means of matrices, and weighted monadic second-order logic. First, we exhibit the classical results of Kleene, B羹chi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the B羹chi-Elgot-Trakhtenbrot Theorem addressing formulas, whereas the original statement concerns only sentences. Then we use the language-theoretic methods as starting point for our investigations regarding power series. We establish Sch羹tzenberger's extension of Kleene's Theorem, referred to as Kleene-Sch羹tzenberger Theorem. Moreover, we introduce a weighted version of monadic second-order logic, which is due to Droste and Gastin. By means of this weighted logic, we derive an extension of the B羹chi-Elgot-Trakhtenbrot Theorem. Thus, we point out relations among the different specification approaches for formal power series. Further, we relate the notions and results concerning power series to their counterparts in Language Theory. Overall, our investigations shed light on the interplay between languages, formal power series, automata and monadic second-order logic.
The Characterization of Finite Elasticities
This book develops a new theory in convex geometry, generalizing positive bases and related to Carath矇ordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.
Numerical Methods for Mixed Finite Element Problems
This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations. Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system. A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models. An account of the mixed formulation for Dirichlet's boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints. This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.
The Eigenbook
​This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory.For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs.Written in an engaging and educational style, the book also includes exercises and provides their solution.
Introduction to Number Theory
Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics.
Introduction to Number Theory
Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics.
Mind Math
Math class can be a frustrating place for many children, but it doesn't have to be that way. When a student understands the fundamentals of math, the classroom transforms from a place of stress and anger into a place full of exciting adventures. The confidence students earn from this book can be used each year as they conquer new math topics.Thank you so much for taking the time to check out my book. I know you're going to absolutely love it, and i can't wait to share my knowledge and experience with you on the inside! Here is a small sample methods you will learn: Add/multiply /subtract/divide numbers at a faster paceCalculate the square root of a number like 1496 in less than 5 secondsSolve algebraic equations at a lighting speedFind the cube root of a number like 46,656 in less than 5 secondsFind the percentage of a number at a rapid paceAnd much, much moreCan advanced mathematics demonstrate the mind's inner workings? Yes, according to mathematician and author robert paster. The mit and harvard graduate has studied theories of quantum physics related to cognition for more than twenty years, and now he has applied that knowledge to digital mind math, the innovative framework that mathematically models the way we think.
Perfect Numbers and Fibonacci Sequences
In this book, we first review the history and current situation of the perfect number problem, including the origin story of the Mersenne primes, and then consider the history and current situation of the Fibonacci sequence. Both topics include results from our own research. In the later sections, we define the square sum perfect numbers, and describe for the first time the secret relationships connecting the square sum perfect numbers, the Fibonacci sequence, the Lucas sequence, the twin prime conjecture, and the Fermat primes. Throughout, we raise various interesting questions and conjectures.
Math Mammoth Grade 6-A Worktext
Math Mammoth Grade 6-A Worktext is the student book for the first half of grade 6 mathematics. 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 2022 edition.The main areas of study in Math Mammoth Grade 6-A are: review of the basic operations with whole numbersbeginning algebra topics: expressions, equations, and inequalitiesreview of all decimal arithmeticintroduction to ratios and percentprime factorization, GCF, and LCMa review of fraction arithmetic from 5th grade, plus a focus on division of fractionsthe concept of integers, coordinate grid, addition & subtraction of integersgeometry: review of quadrilaterals & drawing problems; area of triangles & polygons; volume of rectangular prisms with fractional edge lengths; surface areastatistics: concept of distribution, measures of center, measures of variation, boxplots, stem-and-leaf plots, histogramsThis book starts out with a review of the four operations with whole numbers (including long division), place value, and rounding. Students are also introduced to exponents and do some problem solving.Chapter 2 starts the study of algebra topics, delving first into expressions and equations. Students practice writing expressions in many different ways, and use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. We also study briefly inequalities and using two variables.In chapter 3 we review all of decimal arithmetic, just using more decimal digits than in 5th grade. Students also practice conversions of measurement units.Ratios (chapter 4) is a new topic for sixth grade. Students are already familiar with finding fractional parts of quantities from earlier grades, and now it is time to advance that knowledge into the study of ratios, which arise naturally from dividing a quantity into many equal parts. We study such topics as rates, unit rates, equivalent ratios, and problem solving using bar models.In chapter 5, the goal is to develop a basic understanding of percent, to see percentages as decimals, and to learn to calculate discounts.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.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.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 6 Tests and Cumulative Reviews
Math Mammoth Grade 6 Tests and Cumulative Reviews includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 6 curriculum.
