![Elementary Arithmetic [microform]](https://cdn.kingstone.com.tw/english/images/product/9912/9781015319912m.webp "Elementary Arithmetic [microform]")
Elementary Arithmetic [microform]
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![The Modern Development of Arithmetic [microform]](https://cdn.kingstone.com.tw/english/images/product/7558/9781015337558.webp "The Modern Development of Arithmetic [microform]")
The Modern Development of Arithmetic [microform]
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![Progressive Arithmetic [microform]](https://cdn.kingstone.com.tw/english/images/product/6612/9781015266612m.webp "Progressive Arithmetic [microform]")
Progressive Arithmetic [microform]
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![Saskatchewan Elementary Arithmetic for Public Schools [microform]](https://cdn.kingstone.com.tw/english/images/product/9815/9781015229815m.webp "Saskatchewan Elementary Arithmetic for Public Schools [microform]")
Saskatchewan Elementary Arithmetic for Public Schools [microform]
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Modern Arithmetic Through Discovery
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Paul and the Crucified
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Public School 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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![Mental Arithmetic [microform]](https://cdn.kingstone.com.tw/english/images/product/7300/9781015147300m.webp "Mental Arithmetic [microform]")
Mental Arithmetic [microform]
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
First Days in Number
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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Quadratic Number Fields
This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
Graph-Theoretic Concepts in Computer Science
This book constitutes the proceedings of the 47th International Workshop on Graph-Theoretic Concepts in Computer Science which was held during June 23-25, 2021. The conference was planned to take place in Warsaw, Poland, but changed to an online event due to the COVID-19 pandemic. The 30 full papers included in this volume were carefully reviewed and selected from 73 submissions. The conference aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science or by extracting new graph-theoretic problems from applications.Chapter "Bears with Hats and Independence Polynomials" is are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. Chapters 1, 6, and 22 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
The Genesis of the Langlands Program
Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.
Numerische Mathematik Kompakt
Dieses Lehrbuch behandelt in kompakter und 羹bersichtlicher Form die grundlegenden Themen der numerischen Mathematik. Es vermittelt ein solides Basiswissen der wichtigen Algorithmen und dazugeh繹rigen Fehler- und Aufwandsbetrachtungen, das zur L繹sung von zahlreichen in der Praxis auftretenden mathematischen Problemstellungen ben繹tigt wird. Die vorgestellten Resultate werden mit elementaren Methoden hergeleitet. F羹r die meisten der vorgestellten Verfahren werden Pseudo-Codes angegeben, die sich unmittelbar in Computerprogramme umsetzen lassen. Mit rund 200 ?bungsaufgaben und weiterf羹hrenden Literaturhinweisen ist das Buch f羹r das Selbststudium geeignet. Zahlreiche Abbildungen und 羹bersichtliche Schemata erleichtern dabei das Lernen. Das Lehrbuch ist ohne weitere Themenauswahl als Vorlage f羹r zwei jeweils vierst羹ndige einf羹hrende Vorlesungen 羹ber Numerik verwendbar.In der vorliegenden f羹nften Auflage sind Aktualisierungen, Korrekturen und stilistische ?nderungen vorgenommen worden. Au?erdem sind zahlreiche weitere ?bungsaufgaben und Beispiele aufgenommen worden, und landausche Symbole werden nun umfassender eingef羹hrt.InhaltPolynom- und Splineinterpolation, diskrete Fouriertransformation, Integration - Direkte und iterative L繹sung linearer Gleichungssysteme - Iterative Verfahren f羹r nichtlineare Gleichungssysteme - Numerische Behandlung von Anfangs- und Randwertaufgaben bei gew繹hnlichen Differenzialgleichungen - St繹rungstheorie und numerische Verfahren f羹r Eigenwertprobleme bei Matrizen - Approximationstheorie und RechnerarithmetikZielgruppen- Studierende der Mathematik und benachbarter F瓣cher an Universit瓣ten und Fachhochschulen- Hochschulabsolvent*innen in Industrie und Wirtschaft und an Forschungsinstituten aus den Fachrichtungen Mathematik, Informatik sowie Natur- und Ingenieurwissenschaften
A Pythagorean Introduction to Number Theory
Right triangles are at the heart of this textbook's vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many ofwhich are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader's appreciation of the final chapters.
Inverse Magnetometry
Introductory Remarks.- Basics of Magnetic Field Theory and Magnetization.- Dipole Potential Based Magnetometry.- Inverse Magnetometry.- Multi-Scale Inverse Mollifier Magnetometry.- Test Demonstrations.- Concluding Remarks.
Elementary Number Theory
Elementary Number Theory, Gove Effinger, Gary L. Mullen This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject. 　 Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter. 　 The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.
Zahlentheorie
Als die Aufgabe der elementaren Zahlentheorie kann die Aufsuchung der Beziehungen bezeichnet werden, welche zwischen allen rationalen ganzen oder gebrochenen Zahlen m einerseits und einer beliebig angenommenen festen Grundzahl g andererseits bestehen. Man kann dieser Aufgabe in ihrem weitesten Umfange dadurch gen羹gen, dass man alle diese Zahlen m in unendliche Reihen entwickelt. Nur durch die Betrachtung dieser vollst瓣ndigen Reihen erh瓣lt man eine vollkommene L繹sung unserer Aufgabe; beschr瓣nkt man sich dagegen auf gewisse Anfangsglieder derselben, wie dies gew繹hnlich in der Zahlentheorie geschieht, so erh瓣lt man angen瓣herte Resultate, welche f羹r bestimmte Zwecke nat羹rlich von gro?em Werte sein werden. Niemals aber k繹nnen durch solche Ann瓣herungen die Beziehungen der zu untersuchenden Zahlen m zu der Grundzahl g vollst瓣ndig und genau ergr羹ndet werden. Aus diesem Grund hat der Autor in dem vorliegenden Werk die Untersuchung g-adischer Zahlen mit Vorbedacht in den Vordergrund der Betrachtung gestellt.
Irrationality and Transcendence in Number Theory
Irrationality and Transcendence in Number Theory tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material.Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background
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.
Mersenne Numbers and Fermat Numbers
This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography.In Mathematics, a Mersenne number (named after Marin Mersenne, who studied them in the early 17-th century) is a number of the form Mn = 2n - 1 for positive integer n.In Mathematics, a Fermat number (named after Pierre de Fermat who first studied them) is a positive integer of the form Fn = 2k+ 1, k=2n, where n is a non-negative integer.Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular polygons etc.), numerous modern applications, long list of open problems allow us to provide a broad perspective of the Theory of these two classes of special numbers, that can be useful and interesting for both professionals and the general audience.
Quantification of Uncertainty: Improving Efficiency and Technology
1. Adeli, E. et al., Effect of Load Path on Parameter Identification for Plasticity Models using Bayesian Methods.- 2. Brugiapaglia S., A compressive spectral collocation method for the diffusion equation under the restricted isometry property.- 3. D'Elia, M. et al., Surrogate-based Ensemble Grouping Strategies for Embedded Sampling-based Uncertainty Quantification.- 4. Afkham, B.M. et al., Conservative Model Order Reduction for Fluid Flow.- 5. Clark C.L. and Winter C.L., A Semi-Markov Model of Mass Transport through Highly Heterogeneous Conductivity Fields.- 6. Matthies, H.G., Analysis of Probabilistic and Parametric Reduced Order Models.- 7. Carraturo, M. et al., Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains.- 8. Boccadifuoco, A. et al., Uncertainty quantification applied to hemodynamic simulations of thoracic aorta aneurysms: sensitivity to inlet conditions.- 9. Anderlini, A.et al., Cavitation model parameter calibration for simulations of three-phase injector flows.- 10. Hijazi, S. et al., Non-Intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: a Comparison and Perspectives.- 11. Bult矇, M. et al., A practical example for the non-linear Bayesian filtering of model parameters.
First Grade Math with Confidence Bundle
Math educator Kate Snow gives parents the tools they need to teach math with confidence. This scripted, open-and-go program leads parents and instructors step-by-step through teaching all the concepts first-graders need to master: counting, comparing, and writing numbers to 100 addition and subtraction facts to 20 addition and subtraction word problems beginning place-value and mental math shapes, money, time, and measurement. Short, lively lessons will hold a child's attention by incorporating movement, games, and real-life situations. Straightforward, colorful worksheets give students practice with new concepts and review previously-learned material. Snow makes math fun by including optional enrichment lessons, with suggestions for wonderful math picture books to enjoy together and application activities to make math come alive.Beyond just telling parents what to do, First Grade Math with Confidence also helps them understand why the lessons are designed the way they are, giving them the knowledge and confidence to help their children learn.Using First Grade Math with Confidence will allow parents to build a strong math foundation for their children.
Rationell aritmetik och algebrans grunder
Denna bok inneh疇ller portf繹ljer III(a)-(b) av den st繹rre studien och artikelsamlingen "Den f繹rsta matematiken". Del III(c) finns i tryck som en separat volym, "Den reella talsymbolens principer och hantverk". Portf繹lj III inneb瓣r en grundlig studie av element瓣r aritmetik och algebra ur ett mer teoretiskt-filosofiskt f疇gelperspektiv. B疇de intuitiva-疇sk疇dliga och logisk-algebraiska perspektiv p疇 begreppsbildningen lyfts fram. I artiklarna anv瓣nds en speciell layout och framst瓣llningsform f繹r matematik瓣mnet, som f繹rfattaren valt att kalla f繹r den holistiska. Boken riktar sig till studenter och l瓣rare i matematik, naturvetenskap, filosofi, med mera, men 瓣ven till en allm瓣n matematiskt eller filosofiskt intresserad publik.
Rosenbrock--Wanner-Type Methods
This book discusses the development of the Rosenbrock--Wanner methods from the origins of the idea to current research with the stable and efficient numerical solution and differential-algebraic systems of equations, still in focus. The reader gets a comprehensive insight into the classical methods as well as into the development and properties of novel W-methods, two-step and exponential Rosenbrock methods. In addition, descriptive applications from the fields of water and hydrogen network simulation and visual computing are presented.
Algebraic Number Theory
This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.
Math Mammoth Grade 2-B Worktext
Math Mammoth Grade 2-B Worktext is the student book for the latter half of grade 2 mathematics studies. It covers three-digit numbers, measuring, regrouping in addition and subtraction, counting coins, and an introduction to multiplication.The "worktext" means it contains both the instruction ("text") and the exercises for the student ("work").This curriculum meets and exceeds the Common Core Standards. This is the full-color version; in other words, the inside pages are in full color. Please note this book does not contain an answer key.Features Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it. Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired. The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much. There is a strong emphasis on mental math and number sense. It requires very little teacher preparation, which is a big benefit to most teachers and parents.: ) The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material. After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 4 Answer Keys
Math Mammoth Grade 4 Answer Keys contains full answer keys to both Math Mammoth Grade 4-A and 4-B student worktexts, end-of-chapter tests, the end-of-year test, and the cumulative review lessons.
Boundary and Interior Layers, Computational and Asymptotic Methods Bail 2018
This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.
A Readable Introduction to Real Mathematics
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces.This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book.From the reviews of the first edition: "It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences." (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) "The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an 'appreciation of mathematics' course, among other possibilities." (G.A. Heuer, Mathematical Reviews, February, 2015)"Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers." (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)
The Fundamental Principle of Digits of a Number
The Fundamental Principle of Digits of a Number is a new mathematical idea for which the author received a copyright from the United States Library of Congress. Two related concepts make it easy to understand and apply the principle. The first concept is that a permutation of digits of a given number is an arrangement of the digits of the given number in any order such that the numerical quantity, which results from the arrangement of the digits of the given number, has the same digits and the same number of digits as the given number. The second concept is that the difference between two permutations of digits of a given number is governed by a mathematical law which guarantees that the difference is divisible by 9. One day, the number 12 suddenly appeared on the author's inner eye. It turned around and formed the number 21. The two numbers subtracted, and number 9 appeared. Then the three numbers disappeared from the author's inner eye. The motion of the numbers by their own power, as if they were birds in the sky, prompted Chibamba Mulenga to investigate this event with digits of other numbers, leading to his discovery of this mathematical principle.
52!
Do you see the elegant designs that are drawn on the back of the cards? Do you look right through the deck as they clutter the drawer and your mind wanders to other thoughts of the day? Do you think of the last time that you played a friendly game of Poker or Gin Rummy? Do you see more grains of rice than the richest king can afford to buy? Do you see an infinite number of monkeys typing nonsense on typewriters for all eternity? Do you see eggs lined up until they are in a galaxy far away? Do you ponder questions of life and sometimes simply "the reason for it all"? 52! is a journey to comprehend numbers that are relative to reality and the universe that we live in. It is a mathematical and a spiritual journey to understand the numbers behind life and perhaps more importantly shares the author's personal journey to find an axiom of faith.
Essence of Fractions
All you need to master fractions in one math workbook.Essence of Fractions is a textbook quality fraction workbook containingWell organized and comprehensive explanations of conceptsTables and visualizations for easy chunking of informationStep-by-step examplesPractice exercises at the end of each chapter with answers given in the appendixStudy questions in the appendix for reinforcing and gaining a more thorough understanding of key conceptsThe key concepts provided in this book includeHow a fraction is definedHow to compare fractionsHow to reduce fractions with a greatest common divisorHow to reduce fractions with prime factorizationHow to multiply fractionsHow to divide fractionsHow to add and subtract fractions with a common denominatorHow to add and subtract fractions with different denominatorsHow to simplify fractions containing variablesMinimal background knowledge of mathematics is necessary to make sense of the concepts presented in this book. Even if if you have not taken a math class in 20 years, you can learn and understand the principles presented in this book by paying close attention to the key concepts and how to use them.
Methods and Models in Mathematical Programming
This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.
Mathematics of Energy and Climate Change
The focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing planetary problems and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global challenges.Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has increased to the point where it influences the global climate, impacts the ability of the planet to feed itself and threatens the stability of these systems. Issues such as climate change, sustainability, man-made disasters, control of diseases and epidemics, management of resources, risk analysis and global integration have come to the fore.Written by specialists in several fields of mathematics and applied sciences, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Mathematics of Energy and Climate Change held in Lisbon, Portugal, in March 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book presents the state of the art in advanced research and ultimate techniques in modeling natural, economical and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences.
Advances in Non-Archimedean Analysis and Applications
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology.In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role - a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems - for instance, proteins - asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.
Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms
This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range of illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience.The book is intended for researchers and graduate students in number theory.
Integer Sequences
This book discusses special properties of integer sequences from a unique point of view. It generalizes common, well-known properties and connects them with sequences such as divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, lifting properties, and so on. The book presents theories derived by using elementary means and includes results not usually found in common number theory books. Considering the impact and usefulness of these theorems, the book also aims at being valuable for Olympiad level problem solving as well as regular research. This book will be of interest to students, researchers and faculty members alike.
Math Mammoth Grade 2-A Worktext
Math Mammoth Grade 2-A student worktext covers some review of 1st grade math, reading the clock, addition and subtraction facts within 18, adding two-digit numbers, geometry topics, and fractions. It is meant for the first half of grade 2. This student worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. The curriculum meets and exceeds the Common Core standards. This is the full-color version; in other words, the inside pages are in full color. Please note this is a student worktext and does not contain answers.
Hybrid High-Order Methods
This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.
Around the Unit Circle
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer's Problem (1933) and Boyd's Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov's proof of the Schinzel-Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson's Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book.One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted setsof polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Waves in Flows
This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school "Waves in Flows", held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave-current interactionsWater-wave problemsGravity wave propagationFlow-acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
Numerical Semigroups
This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere. The contents comprise the proceedings of the 2018 INdAM "International Meeting on Numerical Semigroups", held in Cortona, Italy. Talks at the meeting centered not only on traditional types of numerical semigroups, such as Arf or symmetric, and their usual properties, but also on related types of semigroups, such as affine, Puiseux, Weierstrass, and primary, and their applications in other branches of algebra, including semigroup rings, coding theory, star operations, and Hilbert functions. The papers in the book reflect the variety of the talks and derive from research areas including Semigroup Theory, Factorization Theory, Algebraic Geometry, Combinatorics, Commutative Algebra, Coding Theory, and Number Theory. The book is intended for researchers and students who want to learn about recent developments in the theory of numerical semigroups and its connections with other research fields.
Waves in Flows
This volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include: ChemorepulsionCompressible Navier-Stokes systemsNewtonian fluidsFluid-structure interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.
Smooth B矇zier Surfaces Over Unstructured Quadrilateral Meshes
With a foreword by T.J.R. Hughes Represents a step forward in Isogeometric Analysis and its applicationsProvides a bridge between Finite Element Methods and Isogeometric Analysis
Sequential Models of Mathematical Physics
The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence.FeaturesDescribes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physicsPresentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readersThe solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions
Pillars of Transcendental Number Theory
This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite-Lindemann-Weierstrass theorem, Gelfond-Schneider theorem, Schmidt's subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker's original results. This book presents Baker's original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of "Exercises" and interesting information presented as "Notes," intended to spark readers' curiosity.
New Sinc Methods of Numerical Analysis
This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.
Algorithmic Techniques for the Polymer Sciences
This new book-the first of its kind-examines the use of algorithmic techniques to compress random and non-random sequential strings found in chains of polymers. The book is an introduction to algorithmic complexity. Examples taken from current research in the polymer sciences are used for compression of like-natured properties as found on a chain of polymers. Both theory and applied aspects of algorithmic compression are reviewed. A description of the types of polymers and their uses is followed by a chapter on various types of compression systems that can be used to compress polymer chains into manageable units. The work is intended for graduate and postgraduate university students in the physical sciences and engineering.
