Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.

With its intuitive yet rigorous approach to machine learning, this text provides students with the fundamental knowledge and practical tools needed to conduct research and build data-driven products. The authors prioritize geometric intuition and algorithmic thinking, and include detail on all the essential mathematical prerequisites, to offer a fresh and accessible way to learn. Practical applications are emphasized, with examples from disciplines including computer vision, natural language processing, economics, neuroscience, recommender systems, physics, and biology. Over 300 color illustrations are included and have been meticulously designed to enable an intuitive grasp of technical concepts, and over 100 in-depth coding exercises (in Python) provide a real understanding of crucial machine learning algorithms. A suite of online resources including sample code, data sets, interactive lecture slides, and a solutions manual are provided online, making this an ideal text both for graduate courses on machine learning and for individual reference and self-study.

Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems - and apply these principles to their own projects. A clear and self-contained introduction to linear algebra demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance. Requiring only a basic understanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and rigor, it enables students to quickly understand the material, without being overwhelmed by complex mathematics. Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and relevant examples from diverse fields including engineering, data science, economics, finance, and management, this is the perfect introduction to optimization for undergraduate and graduate students.

Behavioural observations from both the field and captivity indicate that same-sex sexual interactions are widespread throughout the animal kingdom, and occur quite frequently in certain non-human species. Proximate studies of these phenomena have yielded important insights into genetic, hormonal and neural correlates. In contrast, there has been a relative paucity of research on the evolutionary aspects. Homosexual Behaviour in Animals seeks to redress this imbalance by exploring animal same-sex sexual behaviour from an evolutionary perspective. Contributions focus on animals that routinely engage in homosexual behaviour and include birds, dolphin, deer, bison and cats, as well as monkeys and apes, such as macaques, gorillas and bonobos. A final chapter looks at human primates. This book will appeal to graduate students and researchers in evolutionary biology, biological anthropology, zoology, evolutionary psychology, animal behaviour and anyone interested in the current state of knowledge in this area of behavioural studies.

In this account of one of the least known parts of South Asia, Eaton recounts the history of the Deccan plateau in southern India from the fourteenth century to the rise of European colonialism. He does so through the lives of eight Indians who lived at different times during this period, and who each represented something particular about the Deccan. In the first chapter, for example, the author describes the demise of the regional kingdom through the life of a maharaja. In the second, a Sufi sheikh illustrates Muslim piety and state authority. Other characters include a merchant, a general, a slave, a poet, a bandit and a female pawnbroker. Their stories are woven together into a rich narrative tapestry, which illumines the most important social processes of the Deccan across four centuries.

"Iran entered the twentieth century with oxen and wooden plough. It exited with steel mills, one of the world's highest automobile accident rates, and, to the consternation of many, a nuclear program. This book narrates the dramatic transformation that has taken place in twentieth-century Iran. Since the main engine of this transformation has been the central government, the book focuses on the state, on how it was created and expanded, and how its expansion has had profound repercussions not only on the polity and economy, but also on the environment, culture, and, most important of all, wider society. Some repercussions were intended; others, especially protest movements and political revolutions, were not. This book may appear somewhat quaint and even insidious to those convinced that the state is inherently a part of the problem rather than solution of contemporary dilemmas. But since this book is about major transformations, and these transformations in Iran have been initiated invariably by the central government, it will focus on the latter hopefully without falling into the Hegelian-Rankean pitfalls of glorifying the state"--

The Third Edition of this popular and engaging text consolidates the interdisciplinary streams of cognitive science to present a unified narrative of cognitive science as a discipline in its own right. It teaches students to apply the techniques and theories of the cognitive scientist's 'toolkit' - the vast range of methods and tools that cognitive scientists use to study the mind. Thematically organized, Cognitive Science underscores the problems and solutions of cognitive science rather than more narrowly examining individually the subjects that contribute to it - psychology, neuroscience, linguistics, and so on. The generous use of examples, illustrations, and applications demonstrates how theory is applied to unlock the mysteries of the human mind. Drawing upon cutting-edge research, the text has been substantially revised, with new material on Bayesian approaches to the mind and on deep learning. An extensive on-line set of resources is available to aid instructors and students alike. Sample syllabi show how the text can support a variety of courses, making it a highly flexible teaching and learning resource at both the undergraduate and graduate levels. Instructor and student resources available at https://www.bermudezcogsci.com/
> Offers a popular and highly readable text that consolidates the interdisciplinary streams of cognitive science into a unified introduction to the field
> Provides a strong focus on dynamical systems, situated cognition and robotics, and mindreading
> Thought-provoking exercises within the chapters enable students to test and apply their understanding
> Includes new chapters on Bayesian approaches to cognitive science and machine learning/deep learning

What do you know, if you know that a language has 'Object Verb' structure rather than 'Verb Object'? Answering this question and many others, this book provides an essential guide to the syntactic structure of German. It examines the systematic differences between German and English, which follow from this basic difference in sentence structure, and presents the main results of syntactic research on German. Topics covered include the strict word order in VO vs word order variation in OV, verb clustering, clause union effects, obligatory functional subject position, and subject-object asymmetries for extractions. Through this, a cross-model and cross-linguistic comparison evolves, highlighting the immediate implications for non-Germanic OV languages, and creating a detailed and comprehensive description of the syntactic differences that immediately follow from an OV type in contrast with a VO type like English. It will be of interest to all those interested in syntax and Germanic languages.

Understanding Chinese politics has become more important than ever. Some argue that China's political system is 'institutionalized' or that 'win all/lose all' struggles are a thing of the past, but, Joseph Fewsmith argues, as in all Leninist systems, political power is difficult to pass on from one leader to the next. Indeed, each new leader must deploy whatever resources he has to gain control over critical positions and thus consolidate power. Fewsmith traces four decades of elite politics from Deng to Xi, showing how each leader has built power (or not). He shows how the structure of politics in China has set the stage for intense and sometimes violent intra-elite struggles, shaping a hierarchy in which one person tends to dominate, and, ironically, providing for periods of stability between intervals of contention.

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

Richard Bird is famed for the clarity and rigour of his writing. His new textbook, which introduces functional programming to students, emphasises fundamental techniques for reasoning mathematically about functional programs. By studying the underlying equational laws, the book enables students to apply calculational reasoning to their programs, both to understand their properties and to make them more efficient. The book has been designed to fit a first- or second-year undergraduate course and is a thorough overhaul and replacement of his earlier textbooks. It features case studies in Sudoku and pretty-printing, and over 100 carefully selected exercises with solutions. This engaging text will be welcomed by students and teachers alike.

Originally published in 1988, this book presents an introduction to lambda-calculus and combinators without getting lost in the details of mathematical aspects of their theory. Lambda-calculus is treated here as a functional language and its relevance to computer science is clearly demonstrated. The main purpose of the book is to provide computer science students and researchers with a firm background in lambda-calculus and combinators and show the applicabillity of these theories to functional programming. The presentation of the material is self-contained. It can be used as a primary text for a course on functional programming. It can also be used as a supplementary text for courses on the structure and implementation of programming languages, theory of computing, or semantics of programming languages.

Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.

Combinatory logic and λ-calculus were originally devised in the 1920s for investigating the foundations of mathematics using the basis concept of 'operation' instead of 'set'. They have since evolved into important tools for the development and study of programming languages.<br /><br />The authors' previous book <i>Introduction to Combinators and λ-Calculus</i> served as the main reference for introductory courses on λ-calculus for over 20 years: this long-awaited new version offers the same authoritative exposition and has been thoroughly revised to provide a fully up-to-date account of the subject.<br /><br />The grammar and basic properties of both combinatory logic and λ-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. λ-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth.<br /><br />The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most of them at the end of the book.

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Between 838 and 1403 CE, there was a six-century lapse in diplomatic relations between present day China and Japan. This hiatus in what is known as the tribute system has led to an assumption that there was little contact between the two countries in this period. Yiwen Li debunks this assumption, arguing instead that a vibrant Sino-Japanese trade network flourished in this period as Buddhist monks and merchants fostered connections across maritime East Asia. Based on a close examination of sources in multiple languages, including poems and letters, transmitted images and objects, and archaeological discoveries, Li presents a vivid and dynamic picture of the East Asian maritime world. She shows how this Buddhist trade network operated outside of the framework of the tribute system and, through novel interpretations of Buddhist records, provides a new understanding of the relationship between Buddhism and commerce.

Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day.

The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.