Srinivasa Ramanujan
This book offers a unique account on the life and works of Srinivasa Ramanujan-often hailed as the greatest "natural" mathematical genius. Sharing valuable insights into the many stages of Ramanujan's life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem. It also includes the list of Ramanujan's collected papers, letters and other material present at the Wren Library, Trinity College in Cambridge, UK. This book is a valuable resource for all readers interested in Ramanujan's life, work and indelible contributions to mathematics.
Quantum Chemistry and Computing for the Curious
Acquire knowledge of quantum chemistry concepts, the postulates of quantum mechanics, and the foundations of quantum computing, and execute illustrations made with Python code, Qiskit, and open-source quantum chemistry packagesKey Features: Be at the forefront of a quest for increased accuracy in chemistry applications and computingGet familiar with some open source quantum chemistry packages to run your own experimentsDevelop awareness of computational chemistry problems by using postulates of quantum mechanicsBook Description: Explore quantum chemical concepts and the postulates of quantum mechanics in a modern fashion, with the intent to see how chemistry and computing intertwine. Along the way you'll relate these concepts to quantum information theory and computation. We build a framework of computational tools that lead you through traditional computational methods and straight to the forefront of exciting opportunities. These opportunities will rely on achieving next-generation accuracy by going further than the standard approximations such as beyond Born-Oppenheimer calculations.Discover how leveraging quantum chemistry and computing is a key enabler for overcoming major challenges in the broader chemical industry. The skills that you will learn can be utilized to solve new-age business needs that specifically hinge on quantum chemistryWhat You Will Learn: Understand mathematical properties of the building blocks of matterRun through the principles of quantum mechanics with illustrationsDesign quantum gate circuit computationsProgram in open-source chemistry software packages such as Qiskit(R)Execute state-of-the-art-chemistry calculations and simulationsRun companion Jupyter notebooks on the cloud with just a web browserExplain standard approximations in chemical simulationsWho this book is for: Professionals interested in chemistry and computer science at the early stages of learning, or interested in a career of quantum computational chemistry and quantum computing, including advanced high school and college students. Helpful to have high school level chemistry, mathematics (algebra), and programming. An introductory level of understanding Python is sufficient to read the code presented to illustrate quantum chemistry and computing
Swarm Intelligence
The notion of swarm intelligence was introduced for describing decentralized and self-organized behaviors of groups of animals. Then this idea was extrapolated to design groups of robots which interact locally to cumulate a collective reaction. Some natural examples of swarms are as follows: ant colonies, bee colonies, fish schooling, bird flocking, horse herding, bacterial colonies, multinucleated giant amoebae Physarum polycephalum, etc. In all these examples, individual agents behave locally with an emergence of their common effect.An intelligent behavior of swarm individuals is explained by the following biological reactions to attractants and repellents. Attractants are biologically active things, such as food pieces or sex pheromones, which attract individuals of swarm. Repellents are biologically active things, such as predators, which repel individuals of swarm. As a consequence, attractants and repellents stimulate the directed movement of swarms towards and away from the stimulus, respectively.It is worth noting that a group of people, such as pedestrians, follow some swarm patterns of flocking or schooling. For instance, humans prefer to avoid a person considered by them as a possible predator and if a substantial part of the group in the situation of escape panic (not less than 5%) changes the direction, then the rest follows the new direction, too. Some swarm patterns are observed among human beings under the conditions of their addictive behavior such as the behavior of alcoholics or gamers.The methodological framework of studying swarm intelligence is represented by unconventional computing, robotics, and cognitive science. In this book we aim to analyze new methodologies involved in studying swarm intelligence. We are going to bring together computer scientists and cognitive scientists dealing with swarm patterns from social bacteria to human beings. This book considers different models of simulating, controlling, and predicting the swarm behavior of different species from social bacteria to humans.
Effective Results and Methods for Diophantine Equations Over Finitely Generated Domains
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
Trilogy of Numbers and Arithmetic - Book 1: History of Numbers and Arithmetic: An Information Perspective
The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
The Basic Laws of Arithmetic
Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege's primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege's meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell. Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege's exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the system's semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege's precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege's ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance to modern philosophical inquiries into meaning and language. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.
Perfect and Amicable Numbers
This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians.The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions. Thus, for a perfect number n it holds σ(n) = 2n, where σ is the sum-of-divisors function, while for a pair of amicable numbers (n, m) it holds σ(n) = σ(m) = n + m. This is also an important part of the history of prime numbers, since the main formulas that generate perfect numbers and amicable pairs are dependent on the good choice of one or several primes of special form.Nowadays, the theory of perfect and amicable numbers contains many interesting mathematical facts and theorems, alongside many important computer algorithms needed for searching for new large elements of these two famous classes of special numbers.This book contains a list of open problems and numerous questions related to generalizations of the classical case, which provides a broad perspective on the theory of these two classes of special numbers. Perfect and Amicable Numbers can be useful and interesting to both professional and general audiences.
The Basic Laws of Arithmetic
Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege's primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege's meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell. Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege's exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the system's semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege's precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege's ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance to modern philosophical inquiries into meaning and language. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.
Teaching Mathematics at a Technical College
Not much has been written about technical colleges, especially teaching mathematics at one. Much had been written about community college mathematics. This book addresses this disparity. Mathematics is a beautiful subject worthy to be taught at the technical college level. The author sheds light on technical colleges and their importance in the higher education system. Technical colleges area more affordable for students and provide many career opportunities. These careers are becoming or have become as lucrative as careers requiring a four-year-degree. The interest in technical college education is likely to continue to grow. Mathematics, like all other classes, is a subject that needs time, energy, and dedication to learn. For an instructor, it takes many years of hard work and dedication just to be able to teach the subject. Students should not be expected to learn the mathematics overnight. As instructors, we need to be open, honest, and put forth our very best to our students so that they can see that they are able to succeed in whatever is placed in front of them.　This book hopes to encourage such an effort. A notable percentage of students who are receiving associate degrees will go through at least one of more mathematics, courses. These students should not be forgotten about-their needs are similar to any student who is required to take a mathematics course to earn a degree. This book offers insight into teaching mathematics at a technical college. It is also a source for students to turn toward when they are feeling dread in taking a mathematics course. Mathematics instructors want to help students succeed. If they put forth their best effort, and us ours, we can all work as one team to get the student through the course and onto chasing their dreams.　 Though this book focuses on teaching mathematics, some chapters expand to focus on teaching in general.　 The overall hope is the reader, will be inspired by the great work that is happening at technical colleges all around the country. Technical college can be, should be, and is the backbone of the American working class.
Teaching Mathematics at a Technical College
Not much has been written about technical colleges, especially teaching mathematics at one. Much had been written about community college mathematics. This book addresses this disparity.
Math Mammoth Grade 2-B Worktext, International Version (Canada)
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 contains both the necessary instruction and the problems & exercises, and is fairly self-teaching. Please note this is a student worktext and does not contain answers.Features of the curriculum: 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/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 we also offer 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.For addition and subtraction facts, you can use our online practice program (free). This Canadian version of the 2-B worktext is essentially the same as the U.S. version, but is customised for Canadian audiences in these aspects: The currency used in the chapter on money is the Canadian dollar.The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms to British international standards (British English).Page (paper) size is Letter.
Problems and Solutions in Mathematical Olympiad
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Problems and Solutions in Mathematical Olympiad (High School 2)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Problems and Solutions in Mathematical Olympiad (High School 1)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Problems and Solutions in Mathematical Olympiad (High School 1)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Transcendence and Linear Relations of 1-Periods
This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of π, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.
Math Mammoth Grade 4 Tests and Cumulative Reviews
Math Mammoth Grade 4 Tests and Cumulative Reviews includes consumable student copies of chapter tests, the end-of-year test, and additional cumulative review lessons to match the Math Mammoth Grade 4 curriculum.
Math Mammoth Grade 1 Tests and Cumulative Revisions, International Version (Canada)
Math Mammoth Grade 1 Tests and Cumulative Reviews includes consumable student copies of chapter tests, the end-of-year test, and additional cumulative revision lessons to match Math Mammoth Grade 1 curriculum (Canadian version). This is the full-color version.
Math Mammoth Grade 1 Answer Keys, International Version (Canada)
Math Mammoth Grade 1 Answer Keys (International version; Canada) contains answer keys to Math Mammoth Grade 1-A and 1-B student worktexts, chapter tests, the end-of-year test, and the cumulative review lessons. This is the full-color version; in other words, the inside pages are in full color.
Math Mammoth Grade 1-A Worktext, International Version (Canada)
Math Mammoth Grade 1-A worktext (Canadian version) is the student book for the first half of grade 1 mathematics. It covers addition within 0-10, subtraction within 0-10, and place value with two-digit numbers. The worktext contains both the necessary instruction and the problems & exercises, and is fairly self-teaching. Please note this is a student worktext and does not contain answers.Features of the curriculum: 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/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.For addition and subtraction facts, you can use our online practice program (free). Visit the pages for Single-digit Addition Facts online practice and Fact Families online practiceThis Canadian version of the 1-A worktext is essentially the same as the U.S. version, but is customised for Canadian audiences in these aspects: The spelling conforms to British international standards (British English).Page (paper) size is Letter.
Math Mammoth Grade 1-B Worktext, International Version (Canada)
Math Mammoth Grade 1-B worktext is the student book for the second half of grade 1 mathematics. It covers addition and subtraction facts within 0-10, telling time, shapes, measurement, addition and subtraction with two-digit numbers, graphs and coins. The worktext contains both the necessary instruction and the problems & exercises, and is fairly self-teaching. Please note this is a student worktext and does not contain answers.Features of the curriculum: 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/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.For addition and subtraction facts, you can use our online practice program (free). Visit the pages for Single-digit Addition Facts online practice and Fact Families online practiceThis Canadian version of the 1-B worktext is essentially the same as the U.S. version, but is customised for Canadian audiences in these aspects: The currency used in the chapter on money is the Canadian dollar.The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms to British international standards (British English).Page (paper) size is Letter.
B-Series
B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary differential equations, including approximate solutions. Through the formulation and manipulation of these series, properties of numerical methods can be assessed. Runge-Kutta methods, in particular, depend on B-series for a clean and elegant approach to the derivation of high order and efficient methods. However, the utility of B-series goes much further and opens a path to the design and construction of highly accurate and efficient multivalue methods. This book offers a self-contained introduction to B-series by a pioneer of the subject. After a preliminary chapter providing background on differential equations and numerical methods, a broad exposition of graphs and trees is presented. This is essential preparation for the third chapter, in which the main ideas of B-series are introduced and developed. In chapter four, algebraic aspects are further analysed in the context of integration methods, a generalization of Runge-Kutta methods to infinite index sets. Chapter five, on explicit and implicit Runge-Kutta methods, contrasts the B-series and classical approaches. Chapter six, on multivalue methods, gives a traditional review of linear multistep methods and expands this to general linear methods, for which the B-series approach is both natural and essential. The final chapter introduces some aspects of geometric integration, from a B-series point of view. Placing B-series at the centre of its most important applications makes this book an invaluable resource for scientists, engineers and mathematicians who depend on computational modelling, not to mention computational scientists who carry out research on numerical methods in differential equations. In addition to exercises with solutions and study notes, a number of open-ended projects are suggested. This combination makes the book ideal as a textbook for specialised courses on numerical methods for differential equations, as well as suitable for self-study.
Mathematical Foundations for Data Analysis
This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.
Problems and Solutions in Mathematical Olympiad (High School 3)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Problems and Solutions in Mathematical Olympiad (High School 3)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Computational Mathematics, Nanoelectronics, and Astrophysics
This book is a collection of original papers presented at the International Conference on Computational Mathematics in Nanoelectronics and Astrophysics (CMNA 2018) held at the Indian Institute of Technology Indore, India, from 1 to 3 November 2018. It aims at presenting recent developments of computational mathematics in nanoelectronics, astrophysics and related areas of space sciences and engineering. These proceedings discuss the most advanced innovations, trends and real-world challenges encountered and their solutions with the application of computational mathematics in nanoelectronics, astrophysics and space sciences. From focusing on nano-enhanced smart technological developments to the research contributions of premier institutes in India and abroad on ISRO's future space explorations-this book includes topics from highly interdisciplinary areas of research. The book is of interest to researchers, students and practising engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics to nanoelectronics, nanofabrications and astrophysics.
The Mordell Conjecture
The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell-Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole.
Essays on the Theory of Numbers
The contents of the book are as followsI. PROPERTIES OF RATIONAL NUMBERSII. COMPARISON OF THE RATIONAL NUMBERS WITH THE POINTS OF A STRAIGHT LINEIII. CONTINUITY OF THE STRAIGHT LINEIV. CREATION OF IRRATIONAL NUMBERSV. CONTINUITY OF THE DOMAIN OF REAL NUMBERSVI. OPERATIONS WITH REAL NUMBERSVII. INFINITESIMAL ANALYSIS.
Addition and Subtraction
First published in 1982, this work represents one of the first attempts to bring together the perspectives of a variety of different researchers investigating a specific, well defined content domain. It presents theoretical views and research findings investigating the early acquisition of addition and subtraction skills by young children.
Number Names; The Magic Square Divination of Cai Chen 蔡沈 (1167-1230)
In his Master Plan Cai Chen (1167-1230) created an original divination manual based on the Yijing and keyed it to an intricate series of 81 matrixes with the properties of "magic squares." Previously unrecognized, Cai's work is a milestone in the history of mathematics, and, in introducing it, this book dramatically expands our understanding of the Chinese number theory practiced by the "Image and Number" school within Confucian philosophy. Thinkers of that leaning devised graphic arrays of the binary figures called "trigrams" and "hexagrams" in the Yijing as a way of exploring the relationship between the random draws of divination and the classic's readings. Cai adapted this perspective to his 81 matrix series, which he saw as tracing the recurring temporal cycles of the natural world. The architecture of the matrix series is echoed in the language of his divination texts, which he called "number names"--hence, the book's title. This book will appeal to those interested in philosophy, the history of science and mathematics, and Chinese intellectual history. The divination text has significant literary as well as philosophical dimensions, and its audience lies both among specialists in these fields and with a general readership interested in recreational mathematics and topics like divination, Taiji, and Fengshui.
Steps Into Analytic Number Theory
This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest indeveloping problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
Women in Numbers Europe III
This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of collaborations started at the 3rd edition of the Women in Numbers Europe (WINE) conference between senior and mid-level faculty, junior faculty, postdocs, and graduate students. The contents of this book should be of interest to graduate students and researchers in number theory.
Square Roots of Numbers
Prime is very complex calculation which can not be entirely be understood by mathematics alone. With the help of a Spiritual Master to simplify Prime & at the same time turn it into a Fun game to play while learning. Prime itself shows how important the number one (1) is to existence & at the same time showing how special some numbers are without the availability of number one (1) is
Square Roots of Numbers
Prime is very complex calculation which can not be entirely be understood by mathematics alone. With the help of a Spiritual Master to simplify Prime & at the same time turn it into a Fun game to play while learning. Prime itself shows how important the number one (1) is to existence & at the same time showing how special some numbers are without the availability of number one (1) is
Soar to Excellence Primary 1 Mathematics 1A
The Soar to Excellence Primary 1 Mathematics 1A book follows Singapore's Ministry of Education syllabus to equip seven-year-old students with a solid foundation in Primary 1 Mathematics in a simple and effective way. This book is also suitable for students in other countries who wish to learn Mathematics based upon Singapore's renowned curriculum design and academic rigour. In each topic, students are taken through carefully structured concepts and examples to help them gain a clear understanding of the subject. Furthermore, practice questions help reinforce what they have learnt. Well-suited as an enrichment workbook or teaching material, here is a fuss-free resource for parents, tutors, and students, to help students Soar to Excellence.
Mathematical Modelling in Real Life Problems
This book is intended to be a useful contribution for the modern teaching of applied mathematics, educating Industrial Mathematicians that will meet the growing demand for such experts. It covers many applications where mathematics play a fundamental role, from biology, telecommunications, medicine, physics, finance and industry. It is presented in such a way that can be useful in Modelation, Simulation and Optimization courses, targeting master and PhD students. Its content is based on many editions from the successful series of Modelling Weeks organized by the European Consortium of Mathematics in Industry (ECMI). Each chapter addresses a particular problem, and is written in a didactic way, providing the description of the problem, the particular way of approaching it and the proposed solution, along with the results obtained.
Recent Progress on Topics of Ramanujan Sums and Cotangent Sums Associated with the Riemann Hypothesis
In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums -- which constitute a very classical domain of research in Number Theory -- as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bret癡che and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.
Research Schools on Number Theory in India
This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar-including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India. Research on number theory in India during modern times started with the advent of the iconic genius Srinivasa Ramanujan, inspiring mathematicians around the world. This book discusses the national and international impact of the research made by Indian number theorists. It also includes a carefully compiled, comprehensive bibliography of major 20th century Indian number theorists making this book important from the standpoint of historic documentation and a valuable resource for researchers of the field for their literature survey. This book also briefly discusses the importance of number theory in the modern world of mathematics, including applications of the results developed by indigenous number theorists in practical fields. Since the book is written from the viewpoint of the history of science, technical jargon and mathematical expressions have been avoided as much as possible.
Irrationality and Transcendence in Number Theory
This book 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, etc.
Approximation and Online Algorithms
This book constitutes the thoroughly refereed workshop post-proceedings of the 19th International Workshop on Approximation and Online Algorithms, WAOA 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 16 revised full papers presented in this book were carefully reviewed and selected from 31 submissions. The papers focus on the design and analysis of algorithms for online and computationally hard problems.
Uncertainty Quantification in Variational Inequalities
The primary objective of this book is to present a comprehensive treatment of uncertainty quantification in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields.
Computational Cryptography
The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lov獺sz lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.
Key to Fish's Arithmetic Number Two for Teachers and Private Learners; 2
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.
![A Concise Introduction to Practical Arithmetic [microform]](https://cdn.kingstone.com.tw/english/images/product/8885/9781013648885m.webp "A Concise Introduction to Practical Arithmetic [microform]")
A Concise Introduction to Practical 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.
Learning and Intelligent Optimization
This book constitutes the refereed post-conference proceedings on Learning and Intelligent Optimization, LION 15, held in Athens, Greece, in June 2021. The 30 full papers presented have been carefully reviewed and selected from 35 submissions. LION deals with designing and engineering ways of "learning" about the performance of different techniques, and ways of using past experience about the algorithm behavior to improve performance in the future. Intelligent learning schemes for mining the knowledge obtained online or offline can improve the algorithm design process and simplify the applications of high-performance optimization methods. Combinations of different algorithms can further improve the robustness and performance of the individual components.
