Mathematics of Discrete Structures for Computer Science

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas by the principal figures in the history of the subject - Frege, Russell, Ramsey and Carnap - and in doing so illuminate current concerns about the nature of mathematical and theoretical knowledge. Issues addressed include the nature of arithmetical knowledge in the light of Frege's theorem; the status of realism about the theoretical entities of physics; and the proper interpretation of empirical theories that postulate abstract structural constraints.

In 1821, the French mathematician Augustin-Louis Cauchy published Cours d'Analyse de L'École Royale Polytechnique, a textbook designed to teach his students the basic theorems of calculus in as rigorous a way as possible. Cauchy was a pioneer of mathematical analysis, a branch of mathematics concerned with the idea of a limit, whether of a sequence or of a function. This book consists of 12 chapters that discuss real functions, infinitely small and large quantities, substitution groups, symmetrical functions, unknown variables, imaginary functions, and rational fractions in a recurrent series. It also provides formulas for solving various problems, such as converting the sine and cosine of a multiple polynomial arc and the Lagrange interpolation. Cauchy built on the work of Leibniz and Newton and is generally regarded as one of the greatest mathematicians in history. This is a reissue of one of his most important contributions.

The problem of ocean acoustic tomography is to infer from precise measurements of travel time, or other properties of acoustic propagation, the state of the ocean traversed by a sound field. Tomography takes advantage of two facts: that travel time and other measurable acoustic parameters are functions of temperature, water velocity, and other parameters of oceanographic interest, and can be interpreted to provide information about the intervening ocean using inverse methods; and that the ocean is virtually transparent to low-frequency sound, so that signals can be transmitted over distances of many thousands of kilometres. It is therefore possible to prepare a practical system of transmitters and receivers to interpret the behaviour of the oceans. This book gives a comprehensive presentation of the underlying oceanography and mathematics necessary to understand and develop such a system. It covers the forward and inverse tomography problem, as well as numerous models for data interpre

This book deals with vector algebra and analysis and with their application to three-dimensional geometry and the analysis of fields in three dimensions. While many treatments of the application of vectors have approached the fundamentals of the subject intuitively, assuming some prior knowledge of Euclidean and Cartesian geometry, Professor Chrisholm here bases the subject on the axioms of linear space algebra, which are fundamental to many branches of mathematics. While developing the properties of vectors from axioms, however, he continually emphasizes the geometrical interpretation of vector algebra in order to build up intuitive relations between the algebraic equations and geometrical concepts. Throughout, examples are used to illustrate the theory being developed; several sets of problems are incorporate in each chapter, and outline answers to many of these are given. Written primarily for undergraduate mathematicians in the early part of their courses, this lucidly written book

Twelve stories by science fiction master Stanisław Lem, nine of them never before published in English.Of these twelve short stories by science fiction master Stanisław Lem, only three have previously appeared in English, making this the first "new" book of fiction by Lem since the late 1980s. The stories display the full range of Lem's intense curiosity about scientific ideas as well as his sardonic approach to human nature, presenting as multifarious a collection of mad scientists as any reader could wish for. Many of these stories feature artificial intelligences or artificial life forms, long a Lem preoccupation; some feature quite insane theories of cosmology or evolution. All are thought provoking and scathingly funny.Written from 1956 to 1993, the stories are arranged in chronological order. In the title story, "The Truth," a scientist in an insane asylum theorizes that the sun is alive; "The Journal" appears to be an account by an omnipotent being describing the creation of inf

The first graphic novel adaptation of Dune, the groundbreaking science-fiction classic by Frank Herbert―now in a deluxe collector’s editionDune, Frank Herbert’s epic science-fiction masterpiece set in the far future amidst a sprawling feudal interstellar society, tells the story of Paul Atreides as he and his family accept control of the desert planet Arrakis. A stunning blend of adventure and mysticism, environmentalism, and politics, Dune is a powerful, fantastical tale that takes an unprecedented look into our universe, and is transformed by the graphic novel format. Brian Herbert and Kevin J. Anderson’s adaptation retains the integrity of the original novel, and Raúl Allén and Patricia Martín’s magnificent illustrations, along with cover art by Bill Sienkiewicz, bring the book to life for a new generation of readers. A national bestseller, Dune: The Graphic Novel, is now available in a deluxe collector's edition with an increased trim size of 7 1/2" x 11 1/4", printed on high-quali

Following the success of The Quantum Universe, first published in 1987, a host of exciting new discoveries have been made in the field of quantum mechanics. The New Quantum Universe provides an up-to-date and accessible introduction to the essential ideas of quantum physics, and demonstrates how it affects our everyday life. Quantum mechanics gives an understanding of not only atoms and nuclei, but also all the elements and even the stars. The book explains quantum paradoxes and the eventful life of Schroedinger's Cat, along with the Einstein–Podolsky–Rosen paradox and Bell's Inequality. It then looks ahead to the nanotechnology revolution, describing quantum cryptography, quantum computing and quantum teleportation, and ends with an account of quantum mechanics and science fiction. Using simple non-mathematical language, this book is suitable for final-year school students, science undergraduates, and anyone wishing to appreciate how physics allows the new technologies that are chang

The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.

The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and

Convex geometry is at once simple and amazingly rich. While the classical results go back many decades, during that previous to this book's publication in 1999, the integral geometry of convex bodies had undergone a dramatic revitalization, brought about by the introduction of methods, results and, most importantly, new viewpoints, from probability theory, harmonic analysis and the geometry of finite-dimensional normed spaces. This book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It continues the Israel GAFA Seminar series, which is widely recognized as the most useful research source in the area. The collection reflects the work done at the program in Convex Geometry and Geometric Analysis that took place at MSRI in 1996.

Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated 2004 book explores selected topics in depth in a way that makes contemporary mathematics accessible to an undergraduate audience. It can be used for upper-division courses, and assumes only knowledge of basic algebra and elementary topology. Together with standard topics, the book explains: polygonal and smooth presentations; the surgery equivalence of surfaces; the behaviour of invariants under factorisation and the satellite construction; the arithmetic of Conway's rational tangles; arc presentations. Alongside the systematic development of the main theory, there are discussion sections that cover historical aspects, motivation, possible extensions, and applications. Many examples and exercises are

This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.

Convex geometry is at once simple and amazingly rich. While the classical results go back many decades, during that previous to this book's publication in 1999, the integral geometry of convex bodies had undergone a dramatic revitalization, brought about by the introduction of methods, results and, most importantly, new viewpoints, from probability theory, harmonic analysis and the geometry of finite-dimensional normed spaces. This book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It continues the Israel GAFA Seminar series, which is widely recognized as the most useful research source in the area. The collection reflects the work done at the program in Convex Geometry and Geometric Analysis that took place at MSRI in 1996.

This book provides a practically based explanation of electronics which can be understood by any reader who has some knowledge of electrical circuits. Martin Hartley Jones presents a full account of the subject, starting with basic concepts such as amplification, and progressing to analogue and digital IC chip applications, including a lucid account of microcomputers. All the topics are effectively illustrated with stimulating experiments, and the mathematics is not permitted to obscure the electronic concepts, so the book remains very readable. This book is an ideal first text for degree and vocational course students in electronics. It will also be of use to those in other disciplines where electronics is a subsidiary subject. This highly successful text is now in its third edition, and builds on its predecessors by maintaining the style and logical development of the subject.

This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to

For readers of Giulia Enders’ Gut and Bill Bryson’s The Body, a surprising, witty and sparkling exploration of the teeming microbiome of possibility in human feces from microbiologist and science journalist Bryn Nelson.The future is sh*t: the literal kind. For most of human history we’ve been, well, disinclined to take a closer look at our body’s natural product―the complex antihero of this story―save for gleaning some prophecy of our own health. But if we were to take more than a passing look at our poop, we would spy a veritable cornucopia of possibilities. We would see potent medicine, sustainable power, and natural fertilizer to restore the world’s depleted lands. We would spy a time capsule of evidence for understanding past lives and murderous ends. We would glimpse effective ways of measuring and improving human health from the cradle to the grave, early warnings of community outbreaks like Covid-19, and new means of identifying environmental harm―and then reversing it.Flush is

Binary systems of stars are as common as single stars. Stars evolve primarily by nuclear reactions in their interiors, but a star with a binary companion can also have its evolution influenced by the companion. Multiple star systems can exist stably for millions of years, but can ultimately become unstable as one star grows in radius until it engulfs another. This volume, first published in 2006, discusses the statistics of binary stars; the evolution of single stars; and several of the most important kinds of interaction between two (and even three or more) stars. Some of the interactions discussed are Roche-lobe overflow, tidal friction, gravitational radiation, magnetic activity driven by rapid rotation, stellar winds, magnetic braking and the influence of a distant third body on a close binary orbit. A series of mathematical appendices gives a concise but full account of the mathematics of these processes.

Binary systems of stars are as common as single stars. Stars evolve primarily by nuclear reactions in their interiors, but a star with a binary companion can also have its evolution influenced by the companion. Multiple star systems can exist stably for millions of years, but can ultimately become unstable as one star grows in radius until it engulfs another. This volume, first published in 2006, discusses the statistics of binary stars; the evolution of single stars; and several of the most important kinds of interaction between two (and even three or more) stars. Some of the interactions discussed are Roche-lobe overflow, tidal friction, gravitational radiation, magnetic activity driven by rapid rotation, stellar winds, magnetic braking and the influence of a distant third body on a close binary orbit. A series of mathematical appendices gives a concise but full account of the mathematics of these processes.

The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.

Showcases the life of the first American woman in space, from her childhood, to her accomplishments as a tennis star, and her pioneering achievements as an astronaut and science educator.Explore Sally Ride’s life and contributions and understand the historical context of landmark events, movements, and women who paved the way for her success. Ride''s groundbreaking achievement represented a moment of triumph in an ongoing struggle for gender equality propelled by pivotal events such as the 1960''s Civil Rights Movement advocating for equal rights for all individuals, and the enactment of Title IX in 1972 ensuring gender equity in education. Written for students of American and women''s history, this examination of Ride''s life places each milestone in its historical context. This illuminates not only the world she lived in, but also her enduring significance to the contemporary challenges women and LGBTQ+ people continue to face in their efforts to pursue careers in STEM. A detailed ch

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. Brasses by J. S. M. Ward was first published in 1912. The book contains an engaging guide to monumental brasses, with information on historical classification and numerous illustrative figures.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. Geoffrey Smith's Primitive Animals, which was first published in 1911, contains an account of the chief groups in the animal kingdom and the evidence by which some of the main streams of animal evolution can be traced.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. The Flea by Harold Russell was first published in 1913. The text contains a variety of information regarding fleas, much of which had only recently been discovered by zoologists at the time of publication.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. Plato: Moral and Political Ideals by Adela Marion Adam, first printed in 1913, deals with the main substance of Plato's philosophy of ethics and politics, set within the context of his intellectual debt to Socrates.

Emotional intelligence is an important trait for success at work. IQ tests are biased against minorities. Every child is gifted. Preschool makes children smarter. Western understandings of intelligence are inappropriate for other cultures. These are some of the statements about intelligence that are common in the media and in popular culture. But none of them are true. In the Know is a tour of the most common incorrect beliefs about intelligence and IQ. Written in a fantastically engaging way, each chapter is dedicated to correcting a misconception and explains the real science behind intelligence. Controversies related to IQ will wither away in the face of the facts, leaving readers with a clear understanding about the truth of intelligence.

Emotional intelligence is an important trait for success at work. IQ tests are biased against minorities. Every child is gifted. Preschool makes children smarter. Western understandings of intelligence are inappropriate for other cultures. These are some of the statements about intelligence that are common in the media and in popular culture. But none of them are true. In the Know is a tour of the most common incorrect beliefs about intelligence and IQ. Written in a fantastically engaging way, each chapter is dedicated to correcting a misconception and explains the real science behind intelligence. Controversies related to IQ will wither away in the face of the facts, leaving readers with a clear understanding about the truth of intelligence.

With the global population expected to reach nine billion by 2050, our capacity to provide enough food, water and energy relies on our understanding and management of the complex interdependencies in the climate-energy-water nexus. This book presents a comprehensive and up-to-date analysis of the interdependencies between these sectors and the knock-on consequences of those interactions for other sectors, such as food production and biodiversity conservation. The interdisciplinary nature of the book across the three sectors of climate, energy and water means that it will be valuable for advanced students, researchers and policymakers across a broad range of fields, including environmental/energy/water/climate policy, environmental economics, climate science, hydrology, ecology and geography.

How do crystals nucleate and grow? Why and how do crystals form such a wide variety of morphologies, from polyhedral to dendritic and spherulitic forms? These are questions that have been posed since the seventeenth century, and are still of vital importance today both for modern technology, and to understand the Earth's interior and the formation of minerals by living organisms. In this book, Ichiro Sunagawa sets out clearly the atomic processes behind crystal growth, and describes case studies of complex systems from diamond, calcite and pyrite, to crystals formed through biomineralization, such as the aragonite of shells, and apatite of teeth. Essential reading for advanced graduates and researchers in mineralogy and materials science.

The important and rapidly emerging new field known as 'cyber threat intelligence' explores the paradigm that defenders of computer networks gain a better understanding of their adversaries by understanding what assets they have available for an attack. In this book, a team of experts examines a new type of cyber threat intelligence from the heart of the malicious hacking underworld - the dark web. These highly secure sites have allowed anonymous communities of malicious hackers to exchange ideas and techniques, and to buy/sell malware and exploits. Aimed at both cybersecurity practitioners and researchers, this book represents a first step toward a better understanding of malicious hacking communities on the dark web and what to do about them. The authors examine real-world darkweb data through a combination of human and automated techniques to gain insight into these communities, describing both methodology and results.

Bryophytes, especially mosses, represent a largely untapped resource for monitoring and indicating effects of climate change on the living environment. They are tied very closely to the external environment and have been likened to 'canaries in the coal mine'. Bryophyte Ecology and Climate Change is the first book to bring together a diverse array of research in bryophyte ecology, including physiology, desiccation tolerance, photosynthesis, temperature and UV responses, under the umbrella of climate change. It covers a great variety of ecosystems in which bryophytes are important, including aquatic, desert, tropical, boreal, alpine, Antarctic, and Sphagnum-dominated wetlands, and considers the effects of climate change on the distribution of common and rare species as well as the computer modeling of future changes. This book should be of particular value to individuals, libraries, and research institutions interested in global climate change.

Bryophytes, especially mosses, represent a largely untapped resource for monitoring and indicating effects of climate change on the living environment. They are tied very closely to the external environment and have been likened to 'canaries in the coal mine'. Bryophyte Ecology and Climate Change is the first book to bring together a diverse array of research in bryophyte ecology, including physiology, desiccation tolerance, photosynthesis, temperature and UV responses, under the umbrella of climate change. It covers a great variety of ecosystems in which bryophytes are important, including aquatic, desert, tropical, boreal, alpine, Antarctic, and Sphagnum-dominated wetlands, and considers the effects of climate change on the distribution of common and rare species as well as the computer modeling of future changes. This book should be of particular value to individuals, libraries, and research institutions interested in global climate change.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. The Individual in the Animal Kingdom by Julian Huxley was first published in 1912. The text contains an interdisciplinary discussion of individuality in nature, taking influence from both biology and philosophy.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. New Zealand by Robert Stout and J. Logan Stout was first published in 1911. The book contains information on New Zealand's social and political character, together with an account of its historical development.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. Coal Mining by T. C. Cantrill was first published in 1914. The text contains an account of the key principles involved in coal mining, together with information regarding its historical development.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. Published in 1913, F. B. Jevons's volume Comparative Religion offers a broad historical survey of various religious viewpoints ranging from ideas about magic and ancestor-worship to Buddhism and monotheism.

Originally published during the early part of the twentieth century, the Cambridge Manuals of Science and Literature were designed to provide concise introductions to a broad range of topics. They were written by experts for the general reader and combined a comprehensive approach to knowledge with an emphasis on accessibility. Earthworms and their Allies, written in 1912 by Frank E. Beddard, offers both an introduction to the principal facts about earthworms and an analysis of their distribution across the world.

As an historian and interloper in the Ivy League, I see the world through the lens of my unique identity, where the flow of history and personal struggles intertwine. Growing up in a poor foster family, Richard L. Davis carved an extraordinary path through academia to become a distinguished historian of ancient China. Despite facing significant challenges and exclusion, he secured advanced degrees and taught at some of the top universities—an achievement nearly impossible in his generation. Within predominantly white academic institutions, he—the interloper in the Ivy League—offers a fair yet compassionate judgment of elite universities undermined by systemic and structural flaws. He reveals how these remarkably homogenous institutions are biased power structures based on pedigree, race, and personal connections, which restrict opportunities for individuals from diverse backgrounds. More than a record of his academic path, the memoir acknowledges the deep impact of those wh

Fundamental tenets of colonial historiography are challenged by showing that US capital investment into this colony did not lead to the disappearance of the small farmer. Contrary to well-established narratives, quantitative data show that the increasing integration of rural producers within the US market led to differential outcomes, depending on pre-existing land tenure structures, capital requirements to initiate production, and demographics. These new data suggest that the colonial economy was not polarized into landless Puerto Rican rural workers on one side and corporate US capitalists on the other. The persistence of Puerto Rican small farmers in some regions and the expansion of local property ownership and production disprove this socioeconomic model. Other aspects of extant Puerto Rican historiography are confronted in order to make room for thorough analyses and new conclusions on the economy of colonial Puerto Rico during the early twentieth century.