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.
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.
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!
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.
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.
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.
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.
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.
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.
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.
Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling
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.
Math Mammoth Grade 6-B Worktext
Math Mammoth Grade 6-B Worktext is the second student book in Math Mammoth grade 6 curriculum, meant for the latter half of 6th grade. This is the 2022 edition.The main areas of study in Math Mammoth Grade 6-B worktext are: prime factorization, GCF, and LCMfraction arithmetic with 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, histogramsChapter 6 first reviews prime factorization and then teaches students two new concepts: the greatest common factor and the least common multiple. We also apply those concepts factor to simplify fractions and to find common denominators for adding fractions.In Chapter 7, students first review addition, subtraction, and multiplication of fractions from fifth grade. Then we focus on a new topic: the division of fractions. The chapter also includes ample practice in solving problems with fractions.Chapter 8 introduces students to integers (signed numbers). They plot points in all four quadrants of the coordinate plane, reflect and translate simple figures, and learn to add and subtract with negative numbers. (Multiplication and division of integers will be studied in 7th grade.)The next chapter, Geometry, focuses on calculating the area of polygons. After a brief review of terminology for triangles and quadrilaterals and drawing fundamentals, this new topic is presented simply in a logical progression: first, the area of a right triangle; next, the area of a parallelogram; then, the area of any triangle; and finally, the area of a polygon. After that, students learn how to use nets of simple solids to calculate their surface area. Lastly, we turn to the concept of volume. Students have already learned to find the volumes of rectangular prisms in 5th grade. Now they calculate the volumes of rectangular prisms with fractional edge lengths.The final chapter is about statistics. Beginning with the concept of a statistical distribution, students learn about measures of center and measures of variability. They also learn how to make dot plots, histograms, boxplots, and stem-and-leaf plots as ways to summarize and analyze distributions.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.
Human-Like Decision Making and Control for Autonomous Driving
This book details research into human-like driving technology, utilising game theory to better suit a human and machine hybrid driving environment. Covering feature identification and modelling of human driving behaviours, the book explains how to design algorithms for decision making and control of autonomous vehicles in complex scenarios.
Smittestopp - A Case Study on Digital Contact Tracing
This open access book describes Smittestopp, the first Norwegian system for digital contact tracing of Covid-19 infections, which was developed in March and early April 2020. The system was deployed after five weeks of development and was active for a little more than two months, when a drop in infection levels in Norway and privacy concerns led to shutting it down. The intention of this book is twofold. First, it reports on the design choices made in the development phase. Second, as one of the only systems in the world that collected population data into a central database and which was used for an entire population, we can share experience on how the design choices impacted the system's operation. By sharing lessons learned and the challenges faced during the development and deployment of the technology, we hope that this book can be a valuable guide for experts from different domains, such as big data collection and analysis, application development, and deployment in a national population, as well as digital tracing.
Integer Sequences
This book discusses special properties of integer sequences from a unique point of view. It generalizes common, well-known properties and connects them with sequences such as divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, lifting properties, and so on. The book presents theories derived by using elementary means and includes results not usually found in common number theory books. Considering the impact and usefulness of these theorems, the book also aims at being valuable for Olympiad level problem solving as well as regular research. This book will be of interest to students, researchers and faculty members alike.
Waves in Flows
This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school "Waves in Flows", held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave-current interactionsWater-wave problemsGravity wave propagationFlow-acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
The Secret Lives of Numbers
We see numbers on automobile license plates, addresses, weather reports, and, of course, on our smartphones. Yet we look at these numbers for their role as descriptors, not as an entity in and unto themselves. Each number has its own history of meaning, usage, and connotation in the larger world. The Secret Lives of Numbers takes readers on a journey through integers, considering their numerological assignments as well as their significance beyond mathematics and in the realm of popular culture. Of course we all know that the number 13 carries a certain value of unluckiness with it. The phobia of the number is called Triskaidekaphobia; Franklin Delano Roosevelt was known to invite and disinvite guests to parties to avoid having 13 people in attendance; high-rise buildings often skip the 13th floor out of superstition. There are many explanations as to how the number 13 received this negative honor, but from a mathematical point of view, the number 13 is also the smallest prime number that when its digits are reversed is also a prime number. It is honored with a place among the Fibonacci numbers and integral Pythagorean triples, as well as many other interesting and lesser-known occurrences. In The Secret Lives of Numbers, popular mathematician Alfred S. Posamentier provides short and engaging mini-biographies of more than 100 numbers, starting with 1 and featuring some especially interesting numbers -like 6,174, a number with most unusual properties -to provide readers with a more comprehensive picture of the lives of numbers both mathematically and socially. ,
Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II
The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero.The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space.We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve inducesthe same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists.In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the 矇tale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
Transcendental Number Theory
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindzuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains
The Finite Element Method.- The Function Space.- Singularities and Graded Mesh Algorithms.- Error Estimates in Polygonal Domains.- Regularity Estimates and Graded Meshes in Polyhedral Domains.- Anisotropic Error Estimates in Polyhedral Domains.
Point-Counting and the Zilber-Pink Conjecture
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the Andr矇-Oort and Zilber-Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
