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The Little Book of Bigger Primes
by Paulo RibenboimA deep understanding of prime numbers is one of the great challenges in mathematics. In this new edition, fundamental theorems, challenging open problems, and the most recent computational records are presented in a language without secrets. The impressive wealth of material and references will make this book a favorite companion and a source of inspiration to all readers. Paulo Ribenboim is Professor Emeritus at Queen's University in Canada, Fellow of the Royal Society of Canada, and recipient of the George Pólya Award of the Mathematical Association of America. He is the author of 13 books and more than 150 research articles. From the reviews of the First Edition: Number Theory and mathematics as a whole will benefit from having such an accessible book exposing advanced material. There is no question that this book will succeed in exciting many new people to the beauty and fascination of prime numbers, and will probably bring more young people to research in these areas. (Andrew Granville, Zentralblatt)
A Little Book of Martingales (Texts and Readings in Mathematics #86)
by Arup Bose Arijit Chakrabarty Rajat Subhra HazraThis concise textbook, fashioned along the syllabus for master’s and Ph.D. programmes, covers basic results on discrete-time martingales and applications. It includes additional interesting and useful topics, providing the ability to move beyond. Adequate details are provided with exercises within the text and at the end of chapters. Basic results include Doob’s optional sampling theorem, Wald identities, Doob’s maximal inequality, upcrossing lemma, time-reversed martingales, a variety of convergence results and a limited discussion of the Burkholder inequalities. Applications include the 0-1 laws of Kolmogorov and Hewitt–Savage, the strong laws for U-statistics and exchangeable sequences, De Finetti’s theorem for exchangeable sequences and Kakutani’s theorem for product martingales. A simple central limit theorem for martingales is proven and applied to a basic urn model, the trace of a random matrix and Markov chains. Additional topics include forward martingale representation for U-statistics, conditional Borel–Cantelli lemma, Azuma–Hoeffding inequality, conditional three series theorem, strong law for martingales and the Kesten–Stigum theorem for a simple branching process. The prerequisite for this course is a first course in measure theoretic probability. The book recollects its essential concepts and results, mostly without proof, but full details have been provided for the Radon–Nikodym theorem and the concept of conditional expectation.
The Little Book of Math into English
by George GrätzerThis colorful and concise little book is uniquely tailored for those who write mathematical texts at any level and are eager to improve their English writing skills. The easy-to-read guide focuses on helping the writer avoid common English mistakes in mathematical writing. With just a few minutes of engaging, light reading each day, the reader will learn to create clearer, more readable, math texts. The book covers 23 crucial topics, ranging from correct article and preposition usage to proper usage of dashes, conjunctions, and prepositions. It also addresses the construction of direct sentences, effective introductory phrases for formulas, and more. As a bonus to the reader, ‘Practice makes perfect’ exercises relating to each topic are freely accessible on this book’s Springer website. Appendix A gives a quick tutorial on grammatical terms and constructs. Appendix B looks at ChatGPT and the positive aspects of its powerful capabilities. Additionally, Paul Halmos’s article on ‘How to write mathematics’ is included in Appendix C. It deals with the mathematical aspects of writing.
A Little Guide for Teachers: Using Student Data (A Little Guide for Teachers)
by Richard SelfridgeStudent data can be one of the most powerful tools a teacher can use to help their students to learn. In this book, Richard Selfridge offers practical advice for teachers on how to gather useful student data in the classroom and how to use these findings effectively to enhance your teaching. The Little Guide for Teachers series is little in size but BIG on all the support and inspiration you need to navigate your day-to-day life as a teacher. Authored by experts in the field Easy to dip in-and-out of Interactive activities encourage you to write into the book and make it your own Read in an afternoon or take as long as you like with it!
A Little Guide for Teachers: Using Student Data (A Little Guide for Teachers)
by Richard SelfridgeStudent data can be one of the most powerful tools a teacher can use to help their students to learn. In this book, Richard Selfridge offers practical advice for teachers on how to gather useful student data in the classroom and how to use these findings effectively to enhance your teaching. The Little Guide for Teachers series is little in size but BIG on all the support and inspiration you need to navigate your day-to-day life as a teacher. Authored by experts in the field Easy to dip in-and-out of Interactive activities encourage you to write into the book and make it your own Read in an afternoon or take as long as you like with it!
A Little Guide for Teachers: Using Student Data (A Little Guide for Teachers)
by Richard SelfridgeStudent data can be one of the most powerful tools a teacher can use to help their students to learn. In this book, Richard Selfridge offers practical advice for teachers on how to gather useful student data in the classroom and how to use these findings effectively to enhance your teaching. The Little Guide for Teachers series is little in size but BIG on all the support and inspiration you need to navigate your day-to-day life as a teacher. Authored by experts in the field Easy to dip in-and-out of Interactive activities encourage you to write into the book and make it your own Read in an afternoon or take as long as you like with it!
Littlewood-Paley and Multiplier Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge #90)
by R. E. Edwards G. I. GaudryThis book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley theorem and of some of its applications, together with indications of its general significance in Fourier multiplier theory. We have striven to make the presentation self-contained and unified, and adapted primarily for use by graduate students and established mathematicians who wish to begin studies in these areas: it is certainly not intended for experts in the subject. It has been our experience, and the experience of many of our students and colleagues, that this is an area poorly served by existing books. Their accounts of the subject tend to be either ill-suited to the needs of a beginner, or fragmentary, or, in one or two instances, obscure. We hope that our book will go some way towards filling this gap in the literature. Our presentation of the Littlewood-Paley theorem proceeds along two main lines, the first relating to singular integrals on locally com pact groups, and the second to martingales. Both classical and modern versions of the theorem are dealt with, appropriate to the classical n groups IRn, ?L , Tn and to certain classes of disconnected groups. It is for the disconnected groups of Chapters 4 and 5 that we give two separate accounts of the Littlewood-Paley theorem: the first Fourier analytic, and the second probabilistic.
Liutex and Third Generation of Vortex Definition and Identification: An Invited Workshop from Chaos 2020
by Chaoqun Liu Yiqian WangThis book collects papers presented in the Invited Workshop, “Liutex and Third Generation of Vortex Definition and Identification for Turbulence,” from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference. Liutex is a new physical quantity introduced by Prof. Chaoqun Liu of the University of Texas at Arlington. It is a vector and could give a unique and accurate mathematical definition for fluid rotation or vortex. The papers in this volume include some Liutex theories and many applications in hydrodynamics, aerodynamics and thermal dynamics including turbine machinery. As vortex exists everywhere in the universe, a mathematical definition of vortex or Liutex will play a critical role in scientific research. There is almost no place without vortex in fluid dynamics. As a projection, the Liutex theory will play an important role on the investigations of the vortex dynamics in hydrodynamics, aerodynamics, thermodynamics, oceanography, meteorology, metallurgy, civil engineering, astronomy, biology, etc. and to the researches of the generation, sustenance, modelling and controlling of turbulence.
Living and Dying in the USA: Behavioral, Health, and Social Differentials of Adult Mortality
by Richard G. Rogers Robert A. Hummer Charles B. NamThe simplicity of using one data set in addressing the relationship of single variables to mortality distinguishes Living and Dying in the USA from other recent investigations of mortality. The authors use the recently released National Health Interview Survey and the National Death Index to make a definitive statement about demographics and mortality. By surveying demographic and sociocultural characteristics associated with mortality, socioeconomic effects, health-related conditions, and health status, they reveal connections among several factors related to mortality chances. Easily understood and cited, their study emphasizes the statistical methods underlying their revelations and invites readers to duplicate their results.Comprehensive coverage of US adult mortality differentialsBased on a new and innovative data setIncludes factors rarely examined in related mortality researchNot only documents mortality differentials, but explores explanations for themExtensive list of references associated with each chapterConsistent, straightforward methodology used throughout aids readers in both understanding the content and in comparing results from chapter to chapter
Living Longer and Healthier at Older Ages: A Longitudinal Analysis of Chinese Oldest Old’s Health and Its Determinants (Advances in Studies of Aging and Health #3)
by Li ZhangThis book analyzes data from eight waves (1998, 2000, 2002, 2005, 2008, 2011-12, 2014 and 2018) of the Chinese Longitudinal Healthy Longevity Surveys (CLHLS) to explore how health status of the Chinese oldest old has changed over time and across birth cohorts. It also intends to investigate how period and birth cohorts have played a role in the associations between Chinese oldest old’s health and a variety of demographic, socioeconomic, and lifestyle factors. The book applies the age-period-cohort (APC) approach and constructs cross-classified random-effects models (CCREMs) to carry out the analyses. The oldest old’s health is measured by self-rated health (SRH), chronic diseases, cognitive function and subjective wellbeing which is indicated by positive and negative feeling scores. The results show that Chinese oldest old’s health status has changed over time and across birth cohorts. Significant period and cohort effects are shown when linking Chinese oldest old’s health to various demographic, socioeconomic and health lifestyle covariates. In general, period effects surpass the cohort effects. Particularly, the oldest old’s subjective wellbeing is more likely to be influenced by period than cohort effects. Period changes caused by social events, such as economic hardship and natural disasters, have left strong imprints on Chinese oldest old’s mental than physical health status. Based on these findings, the book highlights some important policy implications and points out future research directions to improve the current study. It provides an interesting read for researchers in gerontology and public health studies. It is also of interest to general audience, including practitioners in health care and policy makers who are interested in old age care and healthy aging policies.
Living Standards Analytics: Development through the Lens of Household Survey Data (Statistics for Social and Behavioral Sciences)
by Dominique Haughton Jonathan HaughtonThe purpose of this book is to introduce, discuss, illustrate, and evaluate the colorful palette of analytical techniques that can be applied to the analysis of household survey data, with an emphasis on the innovations of the past decade or so.Most of the chapters begin by introducing a methodological or policy problem, to motivate the subsequent discussion of relevant methods. They then summarize the relevant techniques, and draw on examples – many of them from the authors’ own work – and aim to convey a sense of the potential, but also the strengths and weaknesses, of those techniques. This book is meant for graduate students in statistics, economics, policy analysis, and social sciences, especially, but certainly not exclusively, those interested in the challenges of economic development in the Third World. Additionally, the book will be useful to academics and practitioners who work closely with survey data. This is a book that can serve as a reference work, to be taken down from the shelf and perused from time to time.
LMIs in Control Systems: Analysis, Design and Applications
by Guang-Ren DuanAlthough LMI has emerged as a powerful tool with applications across the major domains of systems and control, there has been a need for a textbook that provides an accessible introduction to LMIs in control systems analysis and design. Filling this need, LMIs in Control Systems: Analysis, Design and Applications focuses on the basic analysis and d
Lmsst: 24 Lectures On Elliptic Curves (PDF) (London Mathematical Society Student Texts #24)
by J. W. S. Cassels C. M. Series J. W. BruceThe study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text.
Load Assumption for Fatigue Design of Structures and Components: Counting Methods, Safety Aspects, Practical Application
by Michael Köhler Sven Jenne Kurt Pötter Harald ZennerUnderstanding the fatigue behaviour of structural components under variable load amplitude is an essential prerequisite for safe and reliable light-weight design.For designing and dimensioning, the expected stress (load) is compared with the capacity to withstand loads (fatigue strength). In this process, the safety necessary for each particular application must be ensured. A prerequisite for ensuring the required fatigue strength is a reliable load assumption.The authors describe the transformation of the stress- and load-time functions which have been measured under operational conditions to spectra or matrices with the application of counting methods. The aspects which must be considered for ensuring a reliable load assumption for designing and dimensioning are discussed in detail. Furthermore, the theoretical background for estimating the fatigue life of structural components is explained, and the procedures are discussed for numerous applications in practice. One of the prime intentions of the authors is to provide recommendations which can be implemented in practical applications.
Loadings in Thermal Barrier Coatings of Jet Engine Turbine Blades: An Experimental Research and Numerical Modeling (SpringerBriefs in Applied Sciences and Technology)
by Tomasz Sadowski Przemysław GolewskiThis book discusses complex loadings of turbine blades and protective layer Thermal Barrier Coating (TBC), under real working airplane jet conditions. They obey both multi-axial mechanical loading and sudden temperature variation during starting and landing of the airplanes. In particular, two types of blades are analyzed: stationary and rotating, which are widely applied in turbine engines produced by airplane factories.
Lobachevsky Geometry and Modern Nonlinear Problems
by Andrey PopovThis monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed. The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry.
Lobbying, Political Uncertainty and Policy Outcomes
by Sebastian KoehlerThis book analyses interest group communication strategies in parliamentary political systems, and considers how political uncertainty, which emerges from the political process, shapes interest group communication strategies. It develops a formal model of lobbying in a bicameral legislature with strong party discipline, and discusses why interest groups choose public or private communication channels to influence political bargaining. The book tests its hypothesis in different policy contexts, including lobbying on major legislation in the field of labour and social policy.
Lobbying, Political Uncertainty and Policy Outcomes
by Sebastian KoehlerThis book analyses interest group communication strategies in parliamentary political systems, and considers how political uncertainty, which emerges from the political process, shapes interest group communication strategies. It develops a formal model of lobbying in a bicameral legislature with strong party discipline, and discusses why interest groups choose public or private communication channels to influence political bargaining. The book tests its hypothesis in different policy contexts, including lobbying on major legislation in the field of labour and social policy.
Local Algebra (Springer Monographs in Mathematics)
by Jean-Pierre SerreThis is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
Local Analytic Geometry: Basic Theory and Applications (Advanced Lectures in Mathematics)
by Theo de Jong Gerhard PfisterAuf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.
Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems: Results and Examples (Lecture Notes in Mathematics #1893)
by Heinz HanßmannThis book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems (Universitext)
by Mariana Haragus Gérard IoossAn extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
