Introduction to Python Programming And Data Structure By Liang

Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.

This anthropological work of unusual historical depth describes the pattern of land tenure and resulting social structure in the Ceylonese village of Madagama. Dr Obeyesekere analyses the contemporary system in detail, and traces the evolution of every land holding and the correlated kinship pattern from the inception of the estate in 1790. The traditional cultivation and economy has been modified by land shortage, causing multiple division of shares, and by British rule which resulted in the introduction of Roman-Dutch law and the development of a cash economy. The practices of mortgaging and share speculation then became the basis of a new power structure derived from feudal norms of land ownership, and leading to radical reorganization of the traditional hamlet.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

When is a random network (almost) connected? How much information can it carry? How can you find a particular destination within the network? And how do you approach these questions - and others - when the network is random? The analysis of communication networks requires a fascinating synthesis of random graph theory, stochastic geometry and percolation theory to provide models for both structure and information flow. This book is the first comprehensive introduction for graduate students and scientists to techniques and problems in the field of spatial random networks. The selection of material is driven by applications arising in engineering, and the treatment is both readable and mathematically rigorous. Though mainly concerned with information-flow-related questions motivated by wireless data networks, the models developed are also of interest in a broader context, ranging from engineering to social networks, biology, and physics.

This book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincaré duality space with a local quadratic structure in the chain homotopy type of the universal cover. The difference between the homotopy types of manifolds and Poincaré duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic duality structures on chain complexes. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one. The book is designed as an introduction to the subject, accessible to graduate students in topology; no previous acquaintance with surgery theory is assumed, and every algebraic concept is justified by

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for comp

Recent advances in non-invasive sampling techniques have led to an increase in the study of hormones and behaviour. Behaviour is complex but can be explained to a large degree by interactions between various psychological and physiological components, such as the interplay between hormonal and psychological systems. This new textbook from Nick Neave offers a detailed introduction to the fascinating science of behavioural endocrinology from a psychological perspective, examining the relationships between hormones and behaviour in both humans and animals. Neave explains the endocrine system and the ways in which hormones can influence brain structure and function, and presents a series of examples to demonstrate how hormones can influence specific behaviours, including sexual determination and differentiation, neurological differentiation, parental behaviours, aggressive behaviours and cognition. This introductory textbook will appeal to second and third year social science undergraduate

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter.

Recent advances in non-invasive sampling techniques have led to an increase in the study of hormones and behaviour. Behaviour is complex but can be explained to a large degree by interactions between various psychological and physiological components, such as the interplay between hormonal and psychological systems. This new textbook from Nick Neave offers a detailed introduction to the fascinating science of behavioural endocrinology from a psychological perspective, examining the relationships between hormones and behaviour in both humans and animals. Neave explains the endocrine system and the ways in which hormones can influence brain structure and function, and presents a series of examples to demonstrate how hormones can influence specific behaviours, including sexual determination and differentiation, neurological differentiation, parental behaviours, aggressive behaviours and cognition. This introductory textbook will appeal to second and third year social science undergraduate

This accessible textbook provides a clear introduction to the sounds of Standard Chinese, designed for English-speaking students with no prior knowledge of linguistics. It explains from scratch the fundamentals of articulatory phonetics (the study of how speech sounds are produced) and phonology (the study of sound systems), and clearly applies them to the phonetic and phonological properties of Chinese. Topics covered include consonants, vowels, syllable structure, tone, stress, intonation, loan words and different varieties of Standard Chinese. Clear comparisons with English sounds are given wherever relevant, along with practical pronunciation advice. All the sounds described are demonstrated by native speakers in a set of web-based audio files, and over fifty graded exercises are provided, encouraging students to put their knowledge into practice. Building a solid understanding of how Chinese sounds work, this text will be invaluable to students of Chinese wishing to improve their

This book presents a wide-ranging introduction to the diatoms together with an illustrated description of over 250 genera. Diatoms are important as perhaps the commonest group of autotrophic plants on earth and are abundant in all waters and on soils and moist surfaces. The introduction describes the diatom cell in detail, the structure of the wall (often extremely beautiful in design), the cell contents and aspects of life cycle and cell division. The generic atlas section is the first account of diatom systematics since 1928 (Karsten in Engler and Prantl: Die Nauturlichen Pflanzenfamilien) and each generic description is accompanied by scanning electron micrographs to show the characteristic structure. Most of the latter have been prepared specially for this work from the authors' own collections. The Diatoms will be the standard reference work on the group for years to come and is an essential reference volume.

The New Cambridge Shakespeare appeals to students worldwide for its up-to-date scholarship and emphasis on performance. The series features line-by-line commentaries and textual notes on the plays and poems. Introductions are regularly refreshed with accounts of new critical, stage and screen interpretations. This second edition of The First Part of King Henry IV offers a theatrical perspective on the origins of Shakespeare's play and the history of its interpretation. In their introduction the editors, Herbert and Judith Weil, clarify the play's de-centred dramatic structure and call attention to the effects of civil war on a broad range of relationships. Falstaff's unpredictable vitality is also explored, together with such important contemporaneous values as honour, friendship, festivity and reformation. Lexical glosses make the rich wordplay accessible, while the notes provide a thorough commentary on Shakespeare's transformation of his sources. A supplementary section by Katharine

Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several

This book provides an introduction to Bluetooth programming, with a specific focus on developing real code. The authors discuss the major concepts and techniques involved in Bluetooth programming, with special emphasis on how they relate to other networking technologies. They provide specific descriptions and examples for creating applications in a number of programming languages and environments including Python, C, Java, GNU/Linux, Windows XP, Symbian Series 60, and Mac OS X. No previous experience with Bluetooth is assumed, and the material is suitable for anyone with some programming background. The authors place special emphasis on the essential concepts and techniques of Bluetooth programming, starting simply and allowing the reader to quickly master the basic concepts before addressing advanced features.

Analysis of variance (ANOVA) is a core technique for analysing data in the Life Sciences. This reference book bridges the gap between statistical theory and practical data analysis by presenting a comprehensive set of tables for all standard models of analysis of variance and covariance with up to three treatment factors. The book will serve as a tool to help post-graduates and professionals define their hypotheses, design appropriate experiments, translate them into a statistical model, validate the output from statistics packages and verify results. The systematic layout makes it easy for readers to identify which types of model best fit the themes they are investigating, and to evaluate the strengths and weaknesses of alternative experimental designs. In addition, a concise introduction to the principles of analysis of variance and covariance is provided, alongside worked examples illustrating issues and decisions faced by analysts.

Analysis of variance (ANOVA) is a core technique for analysing data in the Life Sciences. This reference book bridges the gap between statistical theory and practical data analysis by presenting a comprehensive set of tables for all standard models of analysis of variance and covariance with up to three treatment factors. The book will serve as a tool to help post-graduates and professionals define their hypotheses, design appropriate experiments, translate them into a statistical model, validate the output from statistics packages and verify results. The systematic layout makes it easy for readers to identify which types of model best fit the themes they are investigating, and to evaluate the strengths and weaknesses of alternative experimental designs. In addition, a concise introduction to the principles of analysis of variance and covariance is provided, alongside worked examples illustrating issues and decisions faced by analysts.

Written by one of the world's most eminent personality theorists, this book provides a simply written, comprehensive introduction to recent research about personality structure and the nature of indiv

In a rural community in Southern Ethiopia, there are two types of rituals performed by the same people. Historical evidence suggests that one has shown remarkable stability over the years, while the other has undergone massive transformations. External factors are the same, so how is this to be explained? In this 2002 book, Dena Freeman focuses on ethnographical and historical data from the Gamo Highlands of Southern Ethiopia to tackle the question of cultural change and transformation. She uses a comparative perspective and contrasts the continuity in sacrificial rituals with the rapid divergence and differentiation in initiations. Freeman argues that although external change drives internal cultural transformation, the way in which it does is greatly influenced by the structural organization of the cultural systems themselves. This insight leads to a rethinking of the analytic tension between structure and agency that is at the heart of contemporary anthropological theory.

Spray forming combines the metallurgical processes of metal casting and powder metallurgy to fabricate metal products with enhanced properties. This book provides an introduction to the various modelling and simulation techniques employed in spray forming, and shows how they are applied in process analysis and development. The author begins by deriving and describing the main models. He then presents their application in the simulation of the key features of spray forming. Wherever possible he discusses theoretical results with reference to experimental data. Building on the features of metal spray forming, he also derives common characteristic modelling features that may be useful in the simulation of related spray processes. The book is aimed at researchers and engineers working in process technology, chemical engineering and materials science.

Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transpo

Secondary data play an increasingly important role in epidemiology and public health research and practice; examples of secondary data sources include national surveys such as the BRFSS and NHIS, claims data for the Medicare and Medicaid systems, and public vital statistics records. Although a wealth of secondary data is available, it is not always easy to locate and access appropriate data to address a research or policy question. This practical guide circumvents these difficulties by providing an introduction to secondary data and issues specific to its management and analysis, followed by an enumeration of major sources of secondary data in the United States. Entries for each data source include the principal focus of the data, years for which it is available, history and methodology of the data collection process, and information about how to access the data and supporting materials, including relevant details about file structure and format.

Secondary data play an increasingly important role in epidemiology and public health research and practice; examples of secondary data sources include national surveys such as the BRFSS and NHIS, claims data for the Medicare and Medicaid systems, and public vital statistics records. Although a wealth of secondary data is available, it is not always easy to locate and access appropriate data to address a research or policy question. This practical guide circumvents these difficulties by providing an introduction to secondary data and issues specific to its management and analysis, followed by an enumeration of major sources of secondary data in the United States. Entries for each data source include the principal focus of the data, years for which it is available, history and methodology of the data collection process, and information about how to access the data and supporting materials, including relevant details about file structure and format.

This comprehensive volume authoritatively describes our understanding of the complex and fascinating jovian system. Written by a team of world experts, it brings together every aspect of the giant planetary system, from the deep interior of Jupiter to the distant tiny satellites and swarms of escaping gas and dust. Chapters present a synthesis of experimental data from the Voyager, Galileo and Cassini missions, from telescopes on the ground and in space, and from theoretical models on the different components that make up the Jupiter system. This book is a valuable introduction for graduate students and an indispensable resource for all researchers in planetary science.

The electroweak theory unifies two basic forces of nature: the weak force and electromagnetism. This 2007 book is a concise introduction to the structure of the electroweak theory and its applications. It describes the structure and properties of field theories with global and local symmetries, leading to the construction of the standard model. It describes the particles and processes predicted by the theory, and compares them with experimental results. It also covers neutral currents, the properties of W and Z bosons, the properties of quarks and mesons containing heavy quarks, neutrino oscillations, CP-asymmetries in K, D, and B meson decays, and the search for Higgs particles. Each chapter contains problems, stemming from the long teaching experience of the author, to supplement the text. This will be of great interest to graduate students and researchers in elementary particle physics.

Based on a wide array of data collected by the author, this book uses clear theoretically motivated economic analysis to explain the structure, performance, and influence of universal banks and securities markets on firms during industrialisation. The German universal banks played a significant but not overwhelming role in the ownership and control of corporate firms. Banks gained access to boards via a confluence of their underwriting and brokerage activities, the legal phenomena of bearer shares and deposited voting rights, and the flourishing securities markets of the turn of the twentieth century. In general, bank relationships had little impact on firm performance; stock market listings, or ownership structure, were more important. The findings show that securities markets can thrive within a civil-law, universal-bank system and suggest that financial system complexity can favour rapid industrial expansion.

Multiple-input multiple-output (MIMO) technology constitutes a breakthrough in the design of wireless communications systems, and is already at the core of several wireless standards. Exploiting multipath scattering, MIMO techniques deliver significant performance enhancements in terms of data transmission rate and interference reduction. This 2007 book is a detailed introduction to the analysis and design of MIMO wireless systems. Beginning with an overview of MIMO technology, the authors then examine the fundamental capacity limits of MIMO systems. Transmitter design, including precoding and space-time coding, is then treated in depth, and the book closes with two chapters devoted to receiver design. Written by a team of leading experts, the book blends theoretical analysis with physical insights, and highlights a range of key design challenges. It can be used as a textbook for advanced courses on wireless communications, and will also appeal to researchers and practitioners working

Increases in computer power and technology have rapidly advanced the applications of numerical modelling in environmental and earth sciences. The progress of numerical modelling in atmospheric, oceanic and geophysical sciences was the topic of an international conference held by the National Autonomous University of Mexico. The review articles and research papers in this volume constitute a wide-ranging account of modelling environmental and earth processes through a variety of numerical simulations. Sections are devoted to such topics as general circulation models and global change, methods of geophysical data assimilation, and mathematical and computational methods with geophysical applications. This book forms an excellent introduction and overview for graduate students as well as a critical update for researchers.

The sources and nature of China's transformation from a traditional to modern society - accelerated in the early twentieth century by the downfall of the Qing dynasty, the advent of foreign technology and increasing commercialization - are critical issues for the study of modern China. In this book, Xin Zhang uses the case of local elites and the power structure of Henan province in north-central China to demonstrate how local politics first transformed local society, challenged the state and eventually influenced change across China. Rather than focusing separately on elite mobility, social mobilization or state-making, Zhang observes changes in all three categories as interrelated aspects of a single, self-generating phenomenon of social change. Zhang's application of social science theory and rich, original, empirical data, sheds light on the sources of China's modernization, political and social identity, and the shifting relationship between the state and local elites.

Practical Plant Identification is an essential guide to identifying flowering plant families (wild or cultivated) in the northern hemisphere. Details of plant structure and terminology accompany practical keys to identify 318 families into which flowering plants are divided. Specifically designed for practical use, the keys can easily be worked backwards for checking identifications. Containing descriptions of families and listings of the genera within, it also includes a section on further identification to generic and specific levels. A successor to the author's bestselling The Identification of Flowering Plant Families, this guide is updated, and retains the same concise user-friendly approach. Cullen skillfully leads the reader from restrictive disciplines of older taxonomy, into an era of increasing numbers of plant families defined by DNA analysis. Aimed primarily at students of botany and horticulture, this is a perfect introduction to plant identification for anyone intereste

The most famous of the three canticles that comprise The Divine Comedy, Inferno describes Dante's descent in Hell midway through his life with Virgil as a guide. As he descends through nine concentric circles of increasingly agonizing torture, Dante encounters doomed souls that include the pagan Aeneas, the liar Odysseus, the suicidal Cleopatra, and his own political enemies, damned for their deceit. Led by leering demons, Dante must ultimately journey with Virgil to the deepest level of all-for it is only by encountering Satan himself, in the heart of Hell, that he can truly understand the tragedy of sin. BACKCOVER: "Kirkpatrick brings a more nuanced sense of the Italian and a more mediated appreciation of the poem's construction than nearly all of his competitors. . . . There is much to recommend here-certainly the intelligence, the energy, the linguistic range. . . . His introduction and canto-by-canto notes are remarkably level and lucid, as attentive to structure as to syntax, lan

Agreement in language relates to the correspondence between words in a sentence, in terms of gender, case, person, or number. For example, in the sentence 'he runs', the suffix -s 'agrees' in number with the singular pronoun 'he'. Patterns of agreement vary dramatically cross-linguistically, with great diversity in the way it is expressed and the types of variation permitted. This clear introduction offers an insight into how agreement works, and how linguists have tried to account for it. Comparing examples from a range of languages, with radically different agreement systems, it demonstrates agreement at work in a variety of constructions. It shows how agreement is influenced by the conflicting effects of sentence structure and meaning, and highlights the oddities of agreement in English. The first textbook devoted to the cross-linguistic study of the topic, Agreement will be essential reading for all those studying the structure and mechanisms of natural languages.

This study of reduplication in Afrikaans provides a unified and principled analysis of an unusual and highly complex word formation process, shedding new light on the scope and content of various fundamental lexicalist principles of word formation. Surprisingly, Rudolf Botha concludes that the principles involved in Afrikaans reduplication are not unique to Afrikaans, as has often been thought, and are used by many other languages. Moreover, the interpretation of Afrikaans reduplications depends on principles of conceptual structure that are restricted neither to Afrikaans nor to the interpretation of reduplications, thus supporting recent work on cognition and meaning undertaken by Ray Jackendoff and other scholars. In analysing the data, Professor Botha has also provided a concrete illustration of how the Galilean style of linguistic inquiry can fruitfully be applied in the study of word formation and meaning. The study thus represents an important theoretical and methodological adva

This volume identifies historical metrics as an important discipline within English studies and raises significant questions about the composition and transmission of early English verse. The chronological range of the book covers the Old English to the pre-Renaissance periods, while its theoretical range is multidisciplinary. The keynote introduction by Thomas Cable identifies major current issues within the field. The work concludes with an extensive and up-to-date bibliography which includes linguistics, philological and text-critical work. The distinguished team of contributors includes: Russom, McCully, and Obst (focusing on Old English, with a conspectus by Stockwell); Minkova (on the Ormulum and early Middle English); Borroff, Matonis, and Osberg (Middle English verse); Bunt and Duggan (editing and Middle English metrics); and Duffell and Youmans (the origin and structure of the Chaucerian long line).

The literature of Africa is dominated by accounts of crisis and gloom. But Thomas Bassett, a distinguished American geographer well known in the field of development, tells an unusual story of the growth of the cotton economy of West Africa. One of the few long-running success stories in African development, change was brought about by tens of thousands of small-scale peasant farmers. While the introduction of new strains of cotton in French West Africa was in part a result of agronomic research by French scientists, supported by an unusually efficient marketing structure, this is not a case of triumphant top-down 'planification'. Employing the case of Côte d'Ivoire, Professor Bassett shows agricultural intensification to result from the cumulative effect of decades of incremental changes in farming techniques and social organization. A significant contribution to the literature, the book demonstrates the need to consider the local and temporal dimensions of agricultural innovations. I

This 1992 book examines alternative methods for achieving optimality without all the apparatus of economic planning (such as information retrieval, computation of solutions, and separate implementation systems), or a vain reliance on sufficiently 'perfect' competition. All rely entirely on the self-interest of economic agents and voluntary contract. The author considers methods involving feedback iterative controls which require the prior selection of a 'criterion function', but no prior calculation of optimal quantities. The target is adjusted as the results for each step become data for the criterion function. Implementation is built in by the incentive structure, and all controls rely on consistency with the self-interest of individuals. The applicability of all the methods is shown to be independent of the form of ownership of enterprises: examples are given for industries which are wholly privately owned, wholly nationalized, mixed and labour-managed.

This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycles and intensionality. The resulting synthesis serves as a logical foundation for grammars, logic programming and constraint-based reasoning systems. A logical perspective is adopted which employs an attribute-value description language along with complete equational axiomatizations of the various systems of feature structures. At the same time, efficiency concerns are kept in mind and complexity and representability results are provided. The application of feature structures to phrase structure grammars is described and completeness results are shown for standard evaluation strategies. Definite clause logic programs are treated as a special case of phrase structure grammars. Constraint systems are introduced and an enumeration technique is developed for solving arbitrary

This introduction to the field of many-body atomic physics is suitable for researchers and graduate students. Drawing from three major subject areas, atomic structure, atomic photoionization, and electron-atom collisions, this book begins with an introduction to many-body diagrams, and continues with several chapters devoted to each subject area written by leading theorists in that field. Topics in atomic structure include the relativistic theory for highly charged atomic ions and calculations of parity nonconservation. Topics in atomic photoionization include single and double photoionization processes, and photoelectron angular distributions. Topics in electron-atom collisions include the theory of electron impact ionization, perturbation series methods, target dependence of the triply differential cross section, Thomas processes, R-matrix theory, close coupling, and distorted-wave theory. This coherent and carefully edited volume has been prepared by leading atomic physicists as a t

Deserts provide a harsh and inhospitable environment for plants and animals, and the ecosystem is correspondingly fragile and prone to disruption by a variety of external factors. The Mojave Desert is a winter-rainfall desert, experiencing drought in the summer months, and occasional rain during the cooler winter months. For many years, it has attracted the attention of ecologists and conservation biologists concerned to maintain the unique status of this region. This book provides a broad overview of plant and animal ecology in the Mojave Desert, presented with a focus on data from Rock Valley, Nevada. The data from many major research projects is synthesized into a description of community structure and dynamics in desert ecosystems.

Crystallization is an important purification process used in a broad range of industries, including pharmaceuticals, foods, and bulk chemicals. In recent years, molecular modeling has emerged as a useful tool in the analysis and solution of problems associated with crystallization. Modeling allows more focused experimentation based on structural and energetic calculations instead of intuition and trial and error. This book is the first to offer a general introduction to molecular modeling techniques and their application in crystallization. After explaining the basic concepts of molecular modeling and crystallization, the book goes on to discuss how modeling techniques are used to solve a variety of practical problems related to crystal size, shape, internal structure, and properties. With chapters written by leading experts and an emphasis on problem-solving, this book will appeal to scientists, engineers, and graduate students involved in research and the production of crystalline ma

The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book, first published in 2005, offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes and constructing phylogenies. The first part of this book consists of four chapters on the themes of Statistics, Computation, Algebra and Biology, offering speedy, self-contained introductions to the emerging field of algebraic statistics and its applications to genomics. In the second part, the four themes are combined and developed to tackle real problems in computational genomics. As the first book in the exciting and dynamic area, it wi