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Lady Luck: The Theory of Probability
by Warren Weaver"Should I take my umbrella?" "Should I buy insurance?" "Which horse should I bet on?" Every day - in business, in love affairs, in forecasting the weather or the stock market questions arise which cannot be answered by a simple "yes" or "no." Many of these questions involve probability. Probabilistic thinking is as crucially important in ordinary affairs as it is in the most abstruse realms of science. This book is the best nontechnical introduction to probability ever written. Its author, the late Dr. Warren Weaver, was a professor of mathematics, active in the Rockefeller and Sloan foundations , an authority on communications and probability, and distinguished for his work at bridging the gap between science and the average citizen. In accessible language and drawing upon the widely diverse writings of thinkers like Kurt Godel, Susanne K.Langer, and Nicholas Bernoulli, Dr. Weaver explains such concepts as permutations, independent events, mathematical expectation, the law of averages, Chebychev's theorem, the law of large numbers, and probability distributions. He uses a probabilistic viewpoint to illuminate such matters as rare events and coincidences, and also devotes space to the relations of probability and statistics, gambling, and modern scientific research. Dr. Weaver writes with wit, charm and exceptional clarity. His mathematics is elementary, grasp of the subject profound, and examples fascinating. They are complemented by 49 delightful drawings by Peg Hosford. 13 tables. 49 drawings. Foreword. Index.
The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
by David SalsburgThis author brilliantly relates the history of statistics with colorful stories and intriguing details concerning the pioneers in the field.
Lagrangian and Hamiltonian Analytical Mechanics: Forty Exercises Resolved and Explained (UNITEXT for Physics)
by Vladimir PletserThis textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton – Jacobi Equations; and (6) Phase Integral and Angular FrequenciesEach chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics.Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.
Lagrangian and Hamiltonian Mechanics: A Modern Approach with Core Principles and Underlying Topics
by José Rachid MohallemThis book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks. Readers are provided with a clear understanding of topics that are usually inaccessible to the undergraduate level and that are critical to learning Lagrangian and Hamiltonian mechanics. Each chapter also includes worked problems and solutions, as well as additional exercises for readers to try. This book begins with the fundamentals of analytical mechanics, concisely introducing readers to the calculus of variations, Hamilton’s Principle, and Lagrange’s equations. While presenting readers with these core topics, the author uses an intuitive approach to delve into essential questions, such as where Galilean invariance lies in Lagrangian mechanics and how Hamilton’s Principle of Least Action encompasses Newton’s three laws, interesting conclusions that often go unnoticed. Infact, Hamilton’s principle is taken throughout as the very origin of classical physical laws, and the choice of appropriate Lagrangians in each case as the real theoretical challenge, meaning that forms of Lagrangian which differ from the standard one are not mere curiosities but, instead, the general rule. This book clarifies common misunderstandings that students face when learning the subject and formally rationalizes concepts that are often difficult to grasp. In addition, the final chapter provides an introduction to a Lagrangian field theory for those interested in learning more advanced topics. Ideal for upper undergraduate and graduate students, this book seeks to teach the intrinsic meaning of the principles and equations taught in an analytical mechanics course and convey their usefulness as powerful theoretical instruments of modern physics.
Lagrangian Floer Theory and Its Deformations: An Introduction to Filtered Fukaya Category (KIAS Springer Series in Mathematics #2)
by Yong-Geun OhA-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces. At the beginning of the 1990s, a similar structure was introduced by Fukaya in his categorification of Floer homology in symplectic topology. This structure plays a fundamental role in the celebrated homological mirror symmetry proposal by Kontsevich and in more recent developments of symplectic topology.A detailed construction of A-infinity algebra structure attached to a closed Lagrangian submanifold is given in Fukaya, Oh, Ohta, and Ono's two-volume monograph Lagrangian Intersection Floer Theory (AMS-IP series 46 I & II), using the theory of Kuranishi structures—a theory that has been regarded as being not easily accessible to researchers in general. The present lecture note is provided by one of the main contributors to the Lagrangian Floer theory and is intended to provide a quick, reader-friendly explanation of the geometric part of the construction. Discussion of the Kuranishi structures is minimized, with more focus on the calculations and applications emphasizing the relevant homological algebra in the filtered context.The book starts with a quick explanation of Stasheff polytopes and their two realizations—one by the rooted metric ribbon trees and the other by the genus-zero moduli space of open Riemann surfaces—and an explanation of the A-infinity structure on the motivating example of the based loop space. It then provides a description of the moduli space of genus-zero bordered stable maps and continues with the construction of the (curved) A-infinity structure and its canonical models. Included in the explanation are the (Landau–Ginzburg) potential functions associated with compact Lagrangian submanifolds constructed by Fukaya, Oh, Ohta, and Ono. The book explains calculations of potential functions for toric fibers in detail and reviews several explicit calculations in the literature of potential functions with bulk as well as their applications to problems in symplectic topology via the critical point theory thereof. In the Appendix, the book also provides rapid summaries of various background materials such as the stable map topology, Kuranishi structures, and orbifold Lagrangian Floer theory.
Lambda Calculus with Types
by Henk Barendregt Wil Dekkers Richard StatmanThe lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and has been treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), which are used to design and verify IT products and mathematical proofs. In this book, the author focuses on three classes of typing for lambda terms: simple types, recursive types and intersection types. Unexpected mathematical beauty is revealed in these three formalisms of terms and types. Numerous exercises are provided to deepen the reader's understanding and increase their confidence using types.
The Lambert W Function: Its Generalizations and Applications (Discrete Mathematics and Its Applications)
by Istvan MezoThis book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on. The first part of the book gives a full treatise of the W function from theoretical point of view. The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient. The third part presents a large number of applications from physics, biology, game theory, bacterial cell growth models, and so on. The second part presents the generalized Lambert functions based on the tools we had developed in the first part. In the third part familiarity with Newtonian physics will be useful. The text is written to be accessible for everyone with only basic knowledge on calculus and complex numbers. Additional features include the Further Notes sections offering interesting research problems and information for further studies. Mathematica codes are included. The Lambert function is arguably the simplest non-elementary transcendental function out of the standard set of sin, cos, log, etc., therefore students who would like to deepen their understanding of real and complex analysis can see a new “almost elementary” function on which they can practice their knowledge.
Land Use Dynamics in a Developing Economy
by Shahab FazalToday, India still remains a rural agricultural country although the share of urban population has also increased but these figures do not tell the whole story. There are evidences that urban growth is dispersed and urban sprawl promotes the spread of urban land use into the rural-urban fringe. Here the attempt is to investigate the land transformation and the driving forces which were influencing the land transformation. The present study was done on peri urban interface of Aligarh city, a relatively small city, but as other north Indian cities, it is also expanding rapidly. Moreover, it too is surrounded by a populous rural area with productive and rich agricultural hinterland. Such conditions give rise to many conflicts and mutually beneficial complementarities in the rural and urban spheres. The result shows that the demand for land is high which results in informal urban development fulfilling the requirements of many of the city's residents. Every piece of land is a tradable commodity, and the pursuit of short-term profits is the predominant ethic. The actors in PUI are strong because it is characterized by intermixing of rural and urban activities and interests as well as the number of actors are greater than in any other area. .
Landscape of 21st Century Mathematics: Selected Advances, 2001–2020
by Bogdan GrechukLandscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline.The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given.Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.
Landscapes of Time-Frequency Analysis: ATFA 2019 (Applied and Numerical Harmonic Analysis)
by Paolo Boggiatto Tommaso Bruno Elena Cordero Hans G. Feichtinger Fabio Nicola Alessandro Oliaro Anita Tabacco Maria VallarinoThis contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research. New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Topics covered include:Signal analysisQuantum theoryModulation space theoryApplications to the medical industryWavelet transform theoryAnti-Wick operatorsLandscapes of Time-Frequency Analysis: ATFA 2019 will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
Landscapes of Time-Frequency Analysis (Applied and Numerical Harmonic Analysis)
by Anita Tabacco Paolo Boggiatto Elena Cordero Maurice De Gosson Hans G. Feichtinger Fabio Nicola Alessandro OliaroThe chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include:Abstract harmonic analysis,Numerical harmonic analysis,Sampling theory,Compressed sensing,Mathematical signal processing,Pseudodifferential operators, andApplications of harmonic analysis to quantum mechanics.Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
Landslide: Application of Geostatistical and Geospatial Modeling (Advances in Natural and Technological Hazards Research #52)
by Rajib Shaw Uday Chatterjee Subodh Chandra Pal Gopal Krishna Panda Asish SahaThe book illustrates a geospatial and geostatistical approach to data analysis, modeling, risk assessment, and visualization, as well as landslide hazard management in the hilly region. This book investigates cutting-edge methodologies based on open source software and R statistical programming and modeling in current decision-making procedures, with a particular emphasis on recent advances in data mining techniques and robust modeling in torrential rainfall and earthquake induced landslide hazard.
Language and Automata Theory and Applications: 12th International Conference, Lata 2018, Ramat Gan, Israel, April 9-11, 2018, Proceedings (Lecture Notes in Computer Science #10792)
by Shmuel Tomi Klein Carlos Martín-Vide Dana ShapiraThis book constitutes the refereed proceedings of the 12th International Conference on Language and Automata Theory and Applications, LATA 2018, held in Ramat Gan, Israel, in April 2018.The 20 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 58 submissions. The papers cover fields like algebraic language theory, algorithms for semi-structured data mining, algorithms on automata and words, automata and logic, automata for system analysis and programme verification, automata networks, automatic structures, codes, combinatorics on words, computational complexity, concurrency and Petri nets, data and image compression, descriptional complexity, foundations of finite state technology, foundations of XML, grammars (Chomsky hierarchy, contextual, unification, categorial, etc.), grammatical inference and algorithmic learning, graphs and graph transformation, language varieties and semigroups, language-based cryptography, mathematical and logical foundations of programming methodologies, parallel and regulated rewriting, parsing, patterns, power series, string processing algorithms, symbolic dynamics, term rewriting, transducers, trees, tree languages and tree automata, and weighted automata.
Language and Automata Theory and Applications: 13th International Conference, LATA 2019, St. Petersburg, Russia, March 26-29, 2019, Proceedings (Lecture Notes in Computer Science #11417)
by Carlos Martín-Vide Alexander Okhotin Dana ShapiraThis book constitutes the refereed proceedings of the 13th International Conference on Language and Automata Theory and Applications, LATA 2019, held in St. Petersburg, Russia, in March 2019. The 31 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 98 submissions. The papers cover the following topics: Automata; Complexity; Grammars; Languages; Graphs, trees and rewriting; and Words and codes.
Language and Communication in Mathematics Education: International Perspectives (ICME-13 Monographs)
by Judit N. Moschkovich David Wagner Arindam Bose Jackeline Rodrigues Mendes Marcus SchütteThis book considers some of the outstanding questions regarding language and communication in the teaching and learning of mathematics – an established theme in mathematics education research, which is growing in prominence. Recent research has demonstrated the wide range of theoretical and methodological resources that can contribute to this area of study, including those drawing on cross-disciplinary perspectives influenced by, among others, sociology, psychology, linguistics, and semiotics. Examining language in its broadest sense to include all modes of communication, including visual and gestural as well as spoken and written modes, it features work presented and discussed in the Language and Communication topic study group (TSG 31) at the 13th International Congress on Mathematical Education (ICME-13). A joint session with participants of the Mathematics Education in a Multilingual and Multicultural Environment topic study group (TSG 32) enhanced discussions, which are incorporated in elaborations included in this book. Discussing cross-cutting topics it appeals to readers from a wide range of disciplines, such as mathematics education and research methods in education, multilingualism, applied linguistics and beyond.
Language Development 1a: Activities for Home
by Marion Nash Jackie LoweFirst Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
Language Development for Maths: Activities for Home
by Marion Nash Jackie LoweBuilding upon the successful 'spirals' programme this series of books addresses language development in three core areas of the curriculum. Linking the work done in school with the simple games and activities to be used at home. All activities have been tried and tested - proven effectiveness. the video CD with teachers' book contains explanations and demonstrations of the programme and its implementation, with comments from the staff who have used it.
Language Development for Maths: Circle Time Sessions to Improve Communication Skills in Maths
by Marion Nash Jackie LoweBuilding on the successful 'spirals' programme this series of books addresses language development in the three core areas of the curriculum. Linking the work done in school with simple games and activities to be used at home. All activities have been tried and tested - proven effectiveness. A video CD contains explanation and demonstration of the programme and its implementation, with commetns from staff who have used it.
Language, Logic, and Computation: 12th International Tbilisi Symposium, TbiLLC 2017, Lagodekhi, Georgia, September 18-22, 2017, Revised Selected Papers (Lecture Notes in Computer Science #11456)
by Peter Sutton Alexandra Silva Sam Staton Carla UmbachThis book constitutes the refereed proceedings of the 12th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2017, held in Lagodekhi, Georgia, in September 2017.The volume contains 17 full revised papers presented at the conference from 22 submissions. The aim of this conference series is to bring together researchers from a wide variety of fields in Natural language syntax, Linguistic typology, Language evolution, Logics for artificial intelligence and much more.
Language, Logic, and Mathematics in Schopenhauer (Studies in Universal Logic)
by Jens LemanskiThe chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.
The Language Lover's Puzzle Book: A World Tour Of Languages And Alphabets In 100 Amazing Puzzles (Alex Bellos Puzzle Books #0)
by Alex Bellos100 wonder-filled word puzzles that thrill and tantalize with the beauty, magic, and weirdness of world language Whether you’re a crossword solver, cryptogram fan, Scrabble addict, or Sudoku savant, The Language Lover’s Puzzle Book is guaranteed to tease your brain and twist your tongue. Puzzle master Alex Bellos begins in Japan, where we can observe some curious counting: boru niko = two balls tsuna nihon = two ropes uma nito = two horses kami nimai = two sheets of paper ashi gohon = five legs ringo goko = five apples sara gomai = five plates kaba goto = five hippos Now, how do the Japanese say “nine cucumbers”?* a) kyuri kyuhon b) kyuri kyuko c) kyuri kyuhiki d) kyuri kyuto Bellos finds the intrigue—and the human element—in a dizzying array of ancient, modern, and even invented tongues, from hieroglyphs to Blissymbolics, Danish to Dothraki. Filled with unusual alphabets, fascinating characters, and intriguing local customs for time-telling, naming children, and more, this is a bravura book of brainteasers and beyond—it’s a globe-trotting, time-traveling celebration of language. *The word endings depend on shape: Flat things end in -mai and spherical things end in -ko. Cucumbers are long things (like ropes and legs), so they end in -hon. The answer is (a)!
The Language of Algebra: Equations, Tables, and Graphs, Student Guide
by McGraw-HillMathScape(TM): Seeing and Thinking Mathematically is an NSF funded standards based program. This unique comprehensive curriculum encourages students to learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively increasing their understanding. MathScape(TM): Seeing and Thinking Mathematically is one of four middle school programs to receive a satisfactory rating from the American Association for the Advancement of Science (AAAS).
The Language of Mathematics
by Robert L. BaberA new and unique way of understanding the translation of concepts and natural language into mathematical expressionsTransforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process--not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work.Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding.The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
The Language Phenomenon
by K. Smith P. M. BinderThis volume contains a contemporary, integrated description of the processes of language. These range from fast scales (fractions of a second) to slow ones (over a million years). The contributors, all experts in their fields, address language in the brain, production of sentences and dialogues, language learning, transmission and evolutionary processes that happen over centuries or millenia, the relation between language and genes, the origins of language, self-organization, and language competition and death. The book as a whole will help to show how processes at different scales affect each other, thus presenting language as a dynamic, complex and profoundly human phenomenon.
Language Policy and Economics: The Language Question in Africa
by Nkonko M. KamwangamaluThis book addresses the perennial question of how to promote Africa's indigenous languages as medium of instruction in educational systems. Breaking with the traditional approach to the continent's language question by focusing on the often overlooked issue of the link between African languages and economic development, Language Policy and Economics argues that African languages are an integral part of a nation's socio-political and economic development. Therefore, the book argues that any language policy designed to promote these languages in such higher domains as the educational system in particular must have economic advantages if the intent is to succeed, and proposes Prestige Planning as the way to address this issue. The proposition is a welcome break away from language policies which pay lip-service to the empowerment of African languages while, by default, strengthening the stranglehold of imported European languages.