First Math

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appe

This book describes a maximally simple market risk model that is still practical and main risk measures like the value-at-risk and the expected shortfall. It outlines the model's (i) underlying math, (ii) daily operation, and (iii) implementation, while stripping away statistical overhead to keep the concepts accessible. The author selects and weighs the various model features, motivating the choices under real-world constraints, and addresses the evermore important handling of regulatory requirements. The book targets not only practitioners new to the field but also experienced market risk operators by suggesting useful data analysis procedures and implementation details. It furthermore addresses market risk consumers such as managers, traders, and compliance officers by making the model behavior intuitively transparent.A very useful guide to the theoretical and practical aspects of implementing and operating a risk-monitoring system for a mid-size financial institution. It sets a com

WEBASSIGN: FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Twelfth Edition, is fully supported by WebAssign, the powerful online homework and course management system that engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.CAREFULLY-CRAFTED EXERCISE SETS: SECTION EXERCISE SETS include Self-Check Exercises that let students solve problems and check their work against worked-out solutions, Concept Exercises that let students gauge their understanding, and Exercise Sets with a mix of rote and applied problems. CHAPTER REVIEW EXERCISE SETS include Summary of Principal Formulas and Terms for easy reference, fill-in-the-blank Concept Review questions that reinforce chapter terms and concepts, Review Exercises, and Befo

Tough Test Questions? Missed Lectures? Not Enough Time? Textbook too pricey?Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.Schaum’s Outline of Linear Algebra, Sixth Edition features: • Updated content to match the

Tough Test Questions? Missed Lectures? Not Enough Time? Textbook too pricey?Fortunately, there's Schaum's. This all-in-one-package includes more than 500 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems—it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.Schaum’s Outline of Geometry, Sixth Edition features: • Over 500 problems, solved step by s

The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi–Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev–Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch–Gabber–Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics.

This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether–Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford–Tate groups and their associated domains, the Mumford–Tate varieties and generalization

Data structures are the fundamental building blocks of any computer program, used for storing, representing and manipulating data in a computer. This text presents the basic concepts of data structures as part of the art of writing computer programs. The author concentrates on the fundamentals of what should be done to solve a problem efficiently rather than technical implementation details. The text includes pseudocode and covers all the most common data structures, such as queues, stacks, trees, heaps, and hash tables, along with the basics of searching, sorting, and coding. This book can supplement any undergraduate algorithms or discrete math course and will also be accessible to students and researchers in other quantitative disciplines. No prerequisites beyond introductory programming and basic mathematics are required, and the accessible, conceptual presentation will appeal to undergraduates in many quantitative fields. Carefully designed problem sets with selected solutions wil

Data structures are the fundamental building blocks of any computer program, used for storing, representing and manipulating data in a computer. This text presents the basic concepts of data structures as part of the art of writing computer programs. The author concentrates on the fundamentals of what should be done to solve a problem efficiently rather than technical implementation details. The text includes pseudocode and covers all the most common data structures, such as queues, stacks, trees, heaps, and hash tables, along with the basics of searching, sorting, and coding. This book can supplement any undergraduate algorithms or discrete math course and will also be accessible to students and researchers in other quantitative disciplines. No prerequisites beyond introductory programming and basic mathematics are required, and the accessible, conceptual presentation will appeal to undergraduates in many quantitative fields. Carefully designed problem sets with selected solutions wil

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, includi

In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.

From the creators of Scratch comes ScratchJr, a programming language designed for young children (ages 5-7).The ScratchJr Book is the perfect addition to the free app and makes coding and computer science easy and fun for all ages!In The ScratchJr Book, kids learn by playing with programming blocks and building their own animated collages, interactive stories, and playable games.Thirty step-by-step activities help kids develop computational thinking, problem-solving, and design skills. Each chapter has several smaller activities that build on one other, culminating with a fun, final project. By the end of the book kids and parents will be ready for all sorts of new programming adventures.Each activity includes:step-by-step, easy-to-follow directionsliteracy and math connectiontips for grown ups and teachers creative challenges to explore and grow!

This book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the Navier–Stokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB® or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the b

原著書名為Introduction To Quantitative Finance—A Math Tool Kit，由MIT Press於2010年出版，同時還有一本學生使用手冊出版。本書涉及金融投資和定量金融，涵蓋適用於投資組合理論、投資銀行學、期權定價及投資、保險風險管理等領域所相關的重要數學理論及框架。因此本書適合作為高等院校，數量金融相關專業的教學參考書，以及希望強化數學技能與加深對投資、

Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive biblio

Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic di

In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at th

At the heart of this monograph is the Brunn–Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn–Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.

The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered.

The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive

The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know th

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

Randy likes space, robots, and baseball, but he can't ace everything . . . or can he? Chris Van Dusen knocks one out of the park with a comical ode to ingenuity.Randy Riley loves two things: science and baseball. When it comes to the solar system, the constellations, and all things robot, Randy is a genius. But on the baseball diamond? Not so much. He tries . . . but whiffs every time. Then, one night, Randy sees something shocking through his Space Boy telescope: it's a fireball, and it's headed right for his town! Randy does the math, summons all of his science smarts, and devises a plan that will save the day in a spectacular way. Once again, Chris Van Dusen winds up his visual humor, dizzying perspectives, perfect pacing, and rollicking rhyme and delivers a hit to make readers stand up and cheer.

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have sp

Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses.

Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science.

‧課外學習好幫手：活潑、趣味十足的標題，能引起孩子的好奇心。‧無限延伸想像力：跟著個性鮮明的可愛角色，遨遊妙趣橫生的數學王國。‧漫畫漫話一起來：以淺顯易懂的漫畫呈現學習內容及重點，理解更迅速。‧重要觀念一把抓：在每單元之中，以圖文區塊整理出重點，一目了然。‧學習成果知多少：從重要內容出題，馬上驗收學習成果，並能訓練答題的能力。‧解題金鑰匙：提示關鍵解題觀念，訓練分析及推理的能力。

‧課外學習好幫手：活潑、趣味十足的標題，能引起孩子的好奇心。‧無限延伸想像力：跟著個性鮮明的可愛角色，遨遊妙趣橫生的數學王國。‧漫畫漫話一起來：以淺顯易懂的漫畫呈現學習內容及重點，理解更迅速。‧重要觀念一把抓：在每單元之中，以圖文區塊整理出重點，一目了然。‧學習成果知多少：從重要內容出題，馬上驗收學習成果，並能訓練答題的能力。‧解題金鑰匙：提示關鍵解題觀念，訓練分析及推理的能力。

讀完這本書，讓你不再怕數學！ 本書特色： ‧課外學習好幫手：活潑、趣味十足的標題，能引起孩子的好奇心。‧無限延伸想像力：跟著個性鮮明的可愛角色，遨遊妙趣橫生的數學王國。‧漫畫漫話一起來：以淺顯易懂的漫畫呈現學習內容及重點，理解更迅速。‧重要觀念一把抓：在每單元之中，以圖文區塊整理出重點，一目了然。‧學習成果知多少：從重要內容出題，馬上驗收學習成果，並能訓練答題的能力。‧解題金鑰匙：提示關鍵解題

讀完這本書，讓你不再怕數學！ 本書特色： ‧課外學習好幫手：活潑、趣味十足的標題，能引起孩子的好奇心。‧無限延伸想像力：跟著個性鮮明的可愛角色，遨遊妙趣橫生的數學王國。‧漫畫漫話一起來：以淺顯易懂的漫畫呈現學習內容及重點，理解更迅速。‧重要觀念一把抓：在每單元之中，以圖文區塊整理出重點，一目了然。‧學習成果知多少：從重要內容出題，馬上驗收學習成果，並能訓練答題的能力。‧解題金鑰匙：提示關鍵解題

Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to abstraction – the most powerful tool for solving problems – rather than simply drilled in the practice of imitating solutions to given examples. The book is therefore ideal for students in mathematics and physics who require a more theoretical treatment than given in most introductory texts. Also designed with lecturers in mind, the fully modular presentation is easily adapted to a course of one-hour lectures, and a suggested 12-week syllabus is included to aid planning. Downloadable files for the hundreds of figures, hundreds of challenging exercises, and practice problems that appear in the book are available online, as are solutions.

Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to abstraction – the most powerful tool for solving problems – rather than simply drilled in the practice of imitating solutions to given examples. The book is therefore ideal for students in mathematics and physics who require a more theoretical treatment than given in most introductory texts. Also designed with lecturers in mind, the fully modular presentation is easily adapted to a course of one-hour lectures, and a suggested 12-week syllabus is included to aid planning. Downloadable files for the hundreds of figures, hundreds of challenging exercises, and practice problems that appear in the book are available online, as are solutions.

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

We are in the swirling center of the most life-changing technological revolution the Earth has ever known. In only 60 years, an eye-blink of human history, a single technological invention has launched the proverbial thousand ships, producing the most sweeping and pervasive set of changes ever to wash over humankind; changes that are reshaping the very core of human existence, on a global scale, at a relentlessly accelerating pace. And we are just at the very beginning. Silicon Earth introduces readers with little or no background to the many marvels of microelectronics and nanotechnology, using easy, non-intimidating language, with an intuitive approach using minimal math. The general scientific and engineering underpinnings of microelectronics and nanotechnology are addressed, as well as how this new technological revolution is transforming a broad array of interdisciplinary fields, and civilization as a whole. Special 'widget deconstruction' chapters address the inner workings of ub

We are in the swirling center of the most life-changing technological revolution the Earth has ever known. In only 60 years, an eye-blink of human history, a single technological invention has launched the proverbial thousand ships, producing the most sweeping and pervasive set of changes ever to wash over humankind; changes that are reshaping the very core of human existence, on a global scale, at a relentlessly accelerating pace. And we are just at the very beginning. Silicon Earth introduces readers with little or no background to the many marvels of microelectronics and nanotechnology, using easy, non-intimidating language, with an intuitive approach using minimal math. The general scientific and engineering underpinnings of microelectronics and nanotechnology are addressed, as well as how this new technological revolution is transforming a broad array of interdisciplinary fields, and civilization as a whole. Special 'widget deconstruction' chapters address the inner workings of ub

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy

本書簡要地概述了數學軟件，詳細介紹了目前使用最廣泛的幾種數學軟件：Math-ematuca、MATLAB及Maple。全書共分為數學軟件概述篇、Mathemstica篇、MATLAB篇和Maple篇四大部分。本書通過大量應用實例介紹這些軟件的使用方法，旨在使讀者對目前眾多數學軟件有更多的認識和了解，以便選擇自己適用的數學軟件，進一步學習掌握求解數學問題的實驗方法，達到理論和實踐的統一。 本書可作

This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them we