Mathematics Books
Cambridge University Press Harmonic Functions and Random Walks on Groups
Book SynopsisThe field of random walks on groups is re-emerging with many new ideas and exciting research. This book contains a comprehensive introduction for researchers new to the field. Despite dealing with cutting-edge research, it is accessible even to new graduate students, with worked examples, exercises, and open problems all included.
£56.99
Cambridge University Press An Introduction to Immersed Boundary Methods
£57.00
Cambridge University Press Optimal Mass Transport on Euclidean Spaces
Book SynopsisThis is a graduate-level introduction to the key ideas and theoretical foundation of the vibrant field of optimal mass transport in the Euclidean setting. Taking a pedagogical approach, it introduces concepts gradually and in an accessible way, while also remaining technically and conceptually complete.Trade Review'Francesco Maggi's book is a detailed and extremely well written explanation of the fascinating theory of Monge-Kantorovich optimal mass transfer. I especially recommend Part IV's discussion of the 'linear' cost problem and its subtle mathematical resolution.' Lawrence C. Evans, University of California, Berkeley'Over the last three decades, optimal transport has revolutionized the mathematical analysis of inequalities, differential equations, dynamical systems, and their applications to physics, economics, and computer science. By exposing the interplay between the discrete and Euclidean settings, Maggi's book makes this development uniquely accessible to advanced undergraduates and mathematical researchers with a minimum of prerequisites. It includes the first textbook accounts of the localization technique known as needle decomposition and its solution to Monge's centuries old cutting and filling problem (1781). This book will be an indispensable tool for advanced undergraduates and mathematical researchers alike.' Robert McCann, University of TorontoTable of ContentsPreface; Notation; Part I. The Kantorovich Problem: 1. An introduction to the Monge problem; 2. Discrete transport problems; 3. The Kantorovich problem; Part II. Solution of the Monge Problem with Quadratic Cost: the Brenier-McCann Theorem: 4. The Brenier theorem; 5. First order differentiability of convex functions; 6. The Brenier-McCann theorem; 7. Second order differentiability of convex functions; 8. The Monge-Ampère equation for Brenier maps; Part III. Applications to PDE and the Calculus of Variations and the Wasserstein Space: 9. Isoperimetric and Sobolev inequalities in sharp form; 10. Displacement convexity and equilibrium of gases; 11. The Wasserstein distance W2 on P2(Rn); 12. Gradient flows and the minimizing movements scheme; 13. The Fokker-Planck equation in the Wasserstein space; 14. The Euler equations and isochoric projections; 15. Action minimization, Eulerian velocities and Otto's calculus; Part IV. Solution of the Monge Problem with Linear Cost: the Sudakov Theorem: 16. Optimal transport maps on the real line; 17. Disintegration; 18. Solution to the Monge problem with linear cost; 19. An introduction to the needle decomposition method; Appendix A: Radon measures on Rn and related topics; Appendix B: Bibliographical Notes; Bibliography; Index.
£47.49
Cambridge University Press Four Open Questions for the NBody Problem
Book SynopsisThe N-body problem has been investigated since Isaac Newton, however vast tracts of the problem remain open. Showcasing the vibrancy of the problem, this book describes four open questions and explores progress made over the last 20 years. After a comprehensive introduction, each chapter focuses on a different open question, highlighting how the stance taken and tools used vary greatly depending on the question. Progress on question one, ''Are the central configurations finite?'', uses tools from algebraic geometry. Two, ''Are there any stable periodic orbits?'', is dynamical and requires some understanding of the KAM theorem. The third, ''Is every braid realised?'', requires topology and variational methods. The final question, ''Does a scattered beam have a dense image?'', is quite new and formulating it precisely takes some effort. An excellent resource for students and researchers of mathematics, astronomy, and physics interested in exploring state-of-the-art techniques and perspectives on this classical problem.
£33.24
Cambridge University Press Fourier Analysis
Book SynopsisFourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner''s 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.Trade Review'This is an extraordinary and very attractive book … I would like to see the book on the desk of every pure mathematician with an interest in classical analysis, and of every teacher of applied mathematics whose work involves analysis … This is how mathematics ideally should be presented, but too seldom is.' R. P. Boas, SIAM Review'This is a wonderful book … More than anything, this is just fun to read, to browse, to study. … Fourier Analysis is literate, lively and a true classic. I highly recommend it.' William J. Satzer, MAA ReviewsTable of ContentsForeword Terence Tao; Preface; 1. Fourier series; 2. Some differential equations; 3. Orthogonal series; 4. Fourier transforms; 5. Further developments; 6. Other directions; Appendices; Index.
£38.99
Cambridge University Press Enumerative Combinatorics Volume 2
Book SynopsisRichard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This updated edition provides the only comprehensive high-level treatment of enumerative combinatorics, including the theory of symmetric functions, with over 150 new exercises and solutions.Trade Review'This is one of the great books; readable, deep and full of gems. It brings algebraic combinatorics to life. I teach out of it and feel that if I can get my students to 'touch Stanley' I have given them a gift for life.' Persi Diaconis, Stanford University'It is wonderful to celebrate the completion of the second edition of Richard Stanley's Enumerative Combinatorics, one of the finest mathematical works of all time. He has added nearly 200 exercises, together with their answers, to what was already a uniquely masterful summary of a vast and beautiful theory. When paired with the second edition of Volume 1, his two classic volumes will surely be a timeless treasure for generations to come.' Donald E. Knuth, Stanford University'An updated classic with a mesmerizing array of interconnected examples. Through Stanley's masterful exposition, the current and future generations of mathematicians will learn the inherent beauty and pleasures of enumeration.' June Huh, Princeton University'I have used Richard Stanley's books on Enumerative Combinatorics numerous times for the combinatorics classes I have taught. This new edition contains many new exercises, which will no doubt be extremely useful for the next generation of combinatorialists.' Anne Schilling, University of California, Davis'Richard Stanley's Enumerative Combinatorics, in two volumes, is an essential reference for researchers and graduate students in the field of enumeration. Volume 2, newly revised, includes comprehensive coverage of composition and inversion of generating functions, exponential and algebraic generating functions, and symmetric functions. The treatment of symmetric functions is especially noteworthy for its thoroughness and accessibility. Engaging problems and solutions, and detailed historical notes, add to the value of this book. It provides an excellent introduction to the subject for beginners while also offering advanced researchers new insights and perspectives.' Ira Gessel, Brandeis UniversityTable of ContentsPreface to Second Edition; Preface; 5. Trees and the Composition of Generating Functions; 6. Algebraic Generating Functions; 7. Symmetric Functions; Appendices: References; Index.
£47.49
Cambridge University Press Islam and Science
Book SynopsisThis first Element in the series Islam and the Sciences is introductory and aims to give readers a general overview of the wide and rich scope of interactions of Islam with the sciences, including past disputes, current challenges, and future outlooks.Table of ContentsForeword; 1. Science, Religion/Islam, and how they relate; 2. The Islam & Science debates so far; 3. A field(s)/topic(al) map of the debates; 4. The new and future Islam & Science debates; 5. The Islam and Science topics in society/culture; 6. General Conclusions: Lessons and Prospects
£17.00
Cambridge University Press Underground Mathematics
Book SynopsisMorel tells the story of subterranean geometry, a forgotten discipline that developed in the silver mines of early modern Europe where mining and metallurgy were of great significance. Through vivid case studies, he illustrates how geometry was used in metallic mines, from surveying to map-making, by practitioners using esoteric manuscripts.
£28.49
Cambridge University Press Applied Longitudinal Data Analysis for Medical
Book SynopsisDiscusses methods available for longitudinal data analysis in non-technical language, allowing readers to apply techniques easily to their work. Aimed at non-statisticians and researchers working in medical science and utilising longitudinal studies, the interpretation of the results of various methods of analysis is emphasised.Table of Contents1. Introduction; 2. Continuous outcome variables; 3. Continuous outcome variables – regression based methods; 4. The modelling of time; 5. Models to disentangle the between- and within-subjects relationship; 6. Causality in observational longitudinal studies; 7. Dichotomous outcome variables; 8. Categorical and count outcome variables; 9. Outcome variables with floor or ceiling effects; 10. Analysis of longitudinal intervention studies; 11. Missing data in longitudinal studies; 12. Sample size calculations; 13. Software for longitudinal data analysis.
£47.49
Cambridge University Press Numerical Methods in Physics with Python
Book SynopsisBringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. The second edition of this introductory book features several new codes and 140 new problems (many on physics applications), as well as new sections on the singular-value decomposition, derivative-free optimization, Bayesian linear regression, neural networks, and partial differential equations. The last section in each chapter is an in-depth project, tackling physics problems that cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the numerical methods often used in the subject.Trade Review'A fantastic addition as an introductory textbook for computational physics. The book is timely, and the author made thoughtful and, in my view, many wise choices. The book is comprehensive and yet accessible to undergraduate students.' Shiwei Zhang, the Flatiron Institute and the College of William & Mary'Gezerlis' book Numerical Methods in Physics with Python is a beautiful example of how an established subject can be brought to the next level by making it very accessible and by introducing several insightful and interdisciplinary applications. This second edition considerably extends the set of exercises, resulting in an extremely useful resource for both students and teachers. Strongly recommended!' Sonia Bacca, Johannes Gutenberg-Universität Mainz'This new edition of Numerical Methods… is another great example of Gezerlis' passion for teaching and for doing so carefully and precisely. Especially welcome, in my view, are the addition of problems at the end of each chapter and the discussion of singular value decomposition (SVD) and Bayesian methods. The SVD is one of the crown jewels of linear algebra which modern students interested in machine learning will surely find beneficial. To physics, computer science, or engineering students mesmerized by the fast Fourier transform, Gezerlis' excellent explanation of it in Chapter 6 is likely to shed some light on the underlying divide-and-conquer algorithm, which is an essential classic.' Joaquin Drut, University of North Carolina at Chapel HillPraise for the first edition: 'I enthusiastically recommend Numerical Methods in Physics with Python by Professor Gezerlis to any advanced undergraduate or graduate student who would like to acquire a solid understanding of the basic numerical methods used in physics. The methods are demonstrated with Python, a relatively compact, accessible computer language, allowing the reader to focus on understanding how the methods work rather than on how to program them. Each chapter offers a self-contained, clear, and engaging presentation of the relevant numerical methods, and captivates the reader with well-motivated physics examples and interesting physics projects. Written by a leading expert in computational physics, this outstanding textbook is unique in that it focuses on teaching basic numerical methods while also including a number of modern numerical techniques that are usually not covered in computational physics textbooks.' Yoram Alhassid, Yale University'In Numerical Methods in Physics with Python by Gezerlis, one finds a resource that has been sorely missing! As the usage of Python has become widespread, it is too often the case that students take libraries, functions, and codes and apply them without a solid understanding of what is truly being done 'under the hood' and why. Gezerlis' book fills this gap with clarity and rigor by covering a broad number of topics relevant for physics, describing the underlying techniques, and implementing them in detail. It should be an important resource for anyone applying numerical techniques to study physics.' Luis Lehner, Perimeter Institute for Theoretical Physics'Gezerlis' text takes a venerable subject - numerical techniques in physics - and brings it up to date and makes it accessible to modern undergraduate curricula through a popular, open-source programming language. Although the focus remains squarely on numerical techniques, each new lesson is motivated by topics commonly encountered in physics and concludes with a practical hands-on project to help cement the students' understanding. The net result is a textbook which fills an important and unique niche in pedagogy and scope, as well as a valuable reference for advanced students and practicing scientists.' Brian Metzger, Columbia UniversityTable of ContentsPreface; 1. Idiomatic Python; 2. Numbers; 3. Derivatives; 4. Matrices; 5. Zeroes and minima; 6. Approximation; 7. Integrals; 8. Differential equations; Appendix A. Installation and setup; Appendix B. Number representations; Appendix C. Math background; Bibliography; Index.
£47.49
Cambridge University Press Graph Theory and Additive Combinatorics
Book SynopsisThis graduate level textbook covers classical and modern developments in graph theory and additive combinatorics, presenting arguments as a cohesive whole. Students will appreciate the chapter summaries, many figures and exercises, as well as the complementary set of lecture videos freely available through MIT OpenCourseWare.Trade Review'Yufei Zhao does great mathematics and has an uncanny ability to explain the deepest results with clear understandable prose. For anyone interested in the seminal ideas (and their interrelationships) of recent decades - pseudorandomness, graphons, graph regularity, to name a few - this is the book to read and savor.' Joel Spencer, New York University'This impeccable book should quickly become a classic text in discrete maths. A huge selection of topics is treated elegantly, with beautiful illustrations, and in just the `right' amount of detail to arouse the interest of the reader and leave them well placed to find out more. In particular, the second half of the book is a superb introduction to additive combinatorics, which I will happily recommend to any student in this area.' Ben Green, Oxford University'This charming text gives an accessible introduction to the connected topics of extremal graph theory and modern additive combinatorics. The focus is very strongly on presenting intuition and restricting attention to the simplest possible instances of methods or classes of results, rather than aiming for maximal generality or the strongest statements; instead, references are given for further reading, or for the proofs of important theorems that are only stated here. Being highly suitable for advanced undergraduates or beginning graduate students, it fills a niche that is currently not occupied by other texts in these highly active areas of current mathematical research.' Terry Tao, University of California, Los Angeles'A valuable and readable unified treatment of a fast-moving area of combinatorics from one of the world's experts - sure to become a standard resource.' Jordan Ellenberg, University of Wisconsin-Madison'Yufei Zhao's book is a wonderful book about graph theory, additive combinatorics, and their surprising connections, involving a major theme of modern mathematics: the interplay between structure and randomness. In both areas, the book can take the curious reader, whether an advanced undergraduate or a professional mathematician, on a joyous journey from the very basics to state-of-the-art research. Yufei Zhao himself is a major player in modern research in both these areas and his presentation is a tour de force.' Gil Kalai, Hebrew University of Jerusalem and Reichman University'This is a beautiful treatment of extremal graph theory and additive combinatorics, focusing on the fruitful interplay between the two. The book covers the classical results as well as recent developments in this active area. It is a fascinating manuscript that would appeal to students and researchers with an interest in discrete mathematics, theoretical computer number theory, and related areas.' Noga Alon, Princeton University'This is a wonderful, well-written account of additive combinatorics from the graph theoretic perspective. Zhao skillfully ties in this approach to the usual statements and gives a thorough development of the subject. This book is indispensable for any serious researcher in this area. Beginners will find a thorough account of the subject with plenty of motivation. The more experienced reader will appreciate the authors' insights and elegant development of some difficult ideas.' Andrew Granville, University of MontréalTable of ContentsPreface; Notation and Conventions; Appetizer: triangles and equations; 1. Forbidding a subgraph; 2. Graph regularity method; 3. Pseudorandom graphs; 4. Graph limits; 5. Graph homomorphism inequalities; 6. Forbidding 3-term arithmetic progressions; 7. Structure of set addition; 8. Sum-product problem; 9. Progressions in sparse pseudorandom sets; References; Index.
£52.24
Cambridge University Press Plato Was Not a Mathematical Platonist
Book SynopsisThis Element shows that Plato keeps a clear distinction between mathematical and metaphysical realism. It also shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability. This title is also available as Open Access on Cambridge Core.Trade Review'… Landry's response to the Platonic call for collaboration with his text opens up the possibility of very fruitful debates.' Susanna Saracco, MetascienceTable of Contents1. Introduction; 2. The interprative lay of the land; 3. The divided line; 4. Book 7; 5. The good in mathematics; 6. Mathematics versus metaphysics; References.
£16.15
Cambridge University Press Introducing String Diagrams
Book SynopsisThis is the first self-contained introduction to the use of string diagrams to reason in elementary category theory. Written in an informal expository style, it features hundreds of carefully chosen diagrams to aid understanding. With numerous worked examples and exercises, the text is ideal for graduate students and advanced undergraduates.Trade Review'String diagrams have proven an indispensable tool in modern category theory, enabling intuitive graphical reasoning while doing away with much of the bookkeeping that tends to bog down equational arguments. This textbook introduces category theory by way of string diagrams, making it an excellent choice both for beginners in category theory, as well as for more experienced category theorists seeking to add string diagrammatic reasoning to their repertoire.' Robin Kaarsgaard, University of Edinburgh'Well-chosen notation plays a vital role in constructive calculation because it facilitates the exploitation of algebraic properties. This book's exemplary use of string diagrams in category theory will inspire and invigorate the calculational method. Peruse and ponder its colourful beauty.' Roland Backhouse, University of NottinghamTable of ContentsPrologue; 1. Category theory; 2. String diagrams; 3. Monads; 4. Adjunctions; 5. Putting it all together; Epilogue; Appendix. Notation; References; Index.
£37.99
Cambridge University Press ADE
£26.99
Cambridge University Press Bayesian Social Science Statistics Volume 2
a huge range and FREE tracked UK delivery on ALL orders.
£17.00
Cambridge University Press Proven Impossible
Book SynopsisWritten for any motivated reader with a high-school knowledge of mathematics, and the discipline to follow logical arguments, this book presents the proofs for revolutionary impossibility theorems in an accessible way, with less jargon and notation, and more background, intuition, examples, explanations, and exercises.Trade Review'This unique and lovely book takes us on a grand tour of the limitations of science, mathematics, and of reason itself. To appreciate what is possible we must know the impossible, and such limitations define the boundary between the two. Gusfield offers well-explained gems illustrating various limitations, showing why they arise, giving their historical context, and in contrast to other similar books for a broad audience, presenting rigorous proofs requiring limited background.' Michael Sipser, MIT'There are impossible problems in many different fields (e.g., Physics, Mathematics). This book is an excellent exposition of these difference ways a problem can be impossible. Along the way, the reader will pick up the needed background which is interesting in itself.' William Gasarch, University of MarylandTable of ContentsPreface; 1. Yes you can prove a negative!; 2. Bell's impossibility theorem(s); 3. Enjoying Bell magic; 4. Arrow's (and friends') impossibility theorems; 5. Clustering and impossibility; 6. Gödel-ish impossibility; 7. Turing undecidability and incompleteness; 8. Chaitin's theorem: More devastating; 9. Gödel (for real, this time).
£26.59
Cambridge University Press Proven Impossible
Book SynopsisWritten for any motivated reader with a high-school knowledge of mathematics, and the discipline to follow logical arguments, this book presents the proofs for revolutionary impossibility theorems in an accessible way, with less jargon and notation, and more background, intuition, examples, explanations, and exercises.Trade Review'This unique and lovely book takes us on a grand tour of the limitations of science, mathematics, and of reason itself. To appreciate what is possible we must know the impossible, and such limitations define the boundary between the two. Gusfield offers well-explained gems illustrating various limitations, showing why they arise, giving their historical context, and in contrast to other similar books for a broad audience, presenting rigorous proofs requiring limited background.' Michael Sipser, MIT'There are impossible problems in many different fields (e.g., Physics, Mathematics). This book is an excellent exposition of these difference ways a problem can be impossible. Along the way, the reader will pick up the needed background which is interesting in itself.' William Gasarch, University of MarylandTable of ContentsPreface; 1. Yes you can prove a negative!; 2. Bell's impossibility theorem(s); 3. Enjoying Bell magic; 4. Arrow's (and friends') impossibility theorems; 5. Clustering and impossibility; 6. Gödel-ish impossibility; 7. Turing undecidability and incompleteness; 8. Chaitin's theorem: More devastating; 9. Gödel (for real, this time).
£56.99
Cambridge University Press A First Guide to Computational Modelling in
Book SynopsisThis hands-on text demystifies numerical modelling for early-stage physics and engineering students, with each chapter focusing on an intriguing physics problem. Developed over many years of teaching a computational modelling course, this stand-alone book gives students an essential numerical modelling toolkit for today's data-driven landscape.Table of ContentsPreface; How to use this book; First steps; 1. Rectangular finite quantum well – Stationary Schrödinger Equation in 1D; 2. Diffraction of light on a slit; 3. Pendulum as a standard unit of time; 4. Planetary system; 5. Gravitation inside a star; 6. Normal modes in a cylindrical waveguide; 7. Thermal insulation properties of a wall; 8. Cylindrical capacitor; 9. Coupled harmonic oscillators; 10. The Fermi-Pasta-Ulam problem; 11. Cold hydrogen star; 12. Rectangular quantum well filled with electrons – The idea of self-consistent calculations; 13. Time dependent Schrödinger Equation Dawid Dworzański; 14. Poisson equation in 2D; Appendices; Further Reading; Index.
£22.99
Cambridge University Press Metacognitive Artificial Intelligence
£52.24
Cambridge University Press Advanced Linear Algebra
Book SynopsisAn engaging textbook for advanced undergraduates and beginning graduates covering the core subjects in linear algebra, with a unique emphasis on ideas from analysis. This edition includes over 200 new exercises and in-depth coverage of contemporary applications, including quantum mechanics, machine learning, data science, and quantum information.
£37.99
Cambridge University Press Dynamics of Mechanical Systems
a huge range and FREE tracked UK delivery on ALL orders.
£56.99
LEGARE STREET PR Asymptotic Expansion of Multiple Integrals and
Book Synopsis
£21.56
Taylor & Francis Ltd Mathematica Beyond Mathematics
Book SynopsisAlthough many books have been written about Mathematica, very few of them cover the new functionality added to the most recent versions of the program. This thoroughly revised second edition of Mathematica Beyond Mathematics: The Wolfram Language in the Real World introduces the new features using real-world examples based on the experience of the author as a consultant and Wolfram certified instructor. The examples strike a balance between relevance and difficulty in terms of Mathematica syntax, allowing readers to incrementally build up their Mathematica skills as they go through the chapters While reading this book, you will also learn more about the Wolfram Language and how to use it to solve a wide variety of problems. The author raises questions from a wide range of topics and answers them by taking full advantage of Mathematica''s latest features. For example: What sources of energy does the world really use? Are our cities getting warmer? Is the novel ElTable of Contents1. Getting Started. 1.1. Mathematica, an Integrated Technical Computing System. 1.2. First Steps. 1.3. Editing Notebooks. 1.4. Basic Ideas. 1.5. From Graphics to Machine Learnings. 1.6. Additional Resources and Supplementary Materials. 2. Programming: The Beauty and Power of the Wolfram Language. 2.1. Mathematica’s Programming Language: The Wolfram Language. 2.2. Lists Operations. 2.3. Association and Dataset. 2.4. Matrix Operations. 2.5. Set, Set Delayed and Dynamic Variables. 2.6. Functional vs. Procedural Programming. 2.7. Apply, Map, and Other Related Functions. 2.8. Iterative Functions. 2.9. Pure Functions. 2.10. Global and Local Variables. 2.11. Conditional Expressions and Conditions. 2.12. Accuracy and Precision. 2.13. Choosing the Method of Computation. 2.14. Optimizing the Computation Time. 2.15. Cloud Deployment. 2.16. Package Development. 2.17. Additional Resources. 3. Interactive Applications, Image Processing, and More. 3.1. The Manipulate Function. 3.2. Creating Demonstrations. 3.3. Image Processing. 3.4. Image Manipulation. 3.5. Graphs and Networks. 3.6. Application: Finding the Period of a Pendulum. 3.7. Additional Resources. 4. Accessing Scientific and Technical Information. 4.1. The Wolfram Data Framework: Introducing Entities. 4.2. Computable Data Functions. 4.3. The Wolfram Data Repository. 4.4. Weather Data in Real Time. 4.5. Chemical and Physical Properties of Elements and Compounds. 4.6. Life Sciences and Medicine. 4.7. Earth Sciences and Geographic Data. 4.8. Additional Resources. 5. Data Analysis and Manipulation. 5.1. Importing/Exporting. 5.2. Statistical Analysis. 5.3. Probability Distributions. 5.4. Exploratory Data Analysis. 5.5. Bootstrapping and Confidence Estimates. 5.6. Curve Fitting. 5.7. Time Series Analysis. 5.8. Spatial Statistics. 6.9. Additional Resources. 6. Machine Learning and Neural Networks. 6.1. What is Machine Learning. 6.2. Classification. 6.3. Prediction. 6.4. Working with Neural Networks. 6.5. Additional Resources. 7. Calculating π and Other Mathematical Tales. 7.1. The Origins of π. 7.2. Archimedes’ Approximation. 7.3. π with More Than One Billion Decimals. 7.4. Buffon’s Method. 7.5. Application: Are the Decimal Digits of π Random? 7.6. The Strange Connection. 7.7. The Riemann Hypothesis. 7.8. Looking for the Magic Prime Formula. 7.9. Additional Resources. 8. Looking at the Sky. 8.1. A Short Astronomical Walk. 8.2. Solar Analemma. 8.3. Stargazing. 8.4. Application: Determining the Color of the Stars. 8.5. The Measurement of Distances Across the Universe. 8.6. Application: Binary Systems and the Search for Exoplanets. 8.7. Light Curves. 8.8. Additional Resources. 9. Nuclei and Radiations. 9.1. Nuclear and Particle Physics. 9.2. What are Isotopes? 9.3. Decay Constants, Decay Periods and Half-Lives. 9.4. Decay Chains. 9.5. Application: Modeling the Evolution of a Chain of Isotopes Over Time. 9.6. Application: Dating the History of Humankind. 9.7. Application: Calculating Binding Energies. 9.8. Radiation Attenuation. 9.9. Additional Resources. 10. Modeling: Applications in Biokinetics, Epidemiology and More. 10.1. Compartmental Modeling. 10.2. Epidemiological Models. 10.3. Physiological Modeling. 10.4. Fitting a Model. 10.5. Optimal Experimental Designs (OED). 10.6. BIOKMOD: The New Iodine OIR Model (ICRP 137). 10.7. Additional Modeling Examples. 10.8. Modeling Using PDEs. 10.9. Additional Resources. 11. Economic, Financial and Optimization Applications. 11.1. Accessing Economic Information. 11.2. Financial Information. 11.3. Financial Functions. 11.4. Optimization. 11.5. The Shortest Path Problem. 11.6. Optimum Flows. 11.7. Blockchains. 11.8. Additional Resources. 12. Faster, Further. 12.1. Parallel Computing. 12.2. Parallel Programming. 12.3. The Mandelbrot Set. 12.4. Comparing Organisms Genetically. 12.5. Compute Unified Device Architecture (CUDA). 12.6. Software Development with Wolfram Workbench. 12.7. Connecting with Other Programs and Devices. 12.8. Additional Resources.
£68.39
£46.54
Taylor & Francis Ltd Introduction to Number Theory
Book SynopsisIntroduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics.Aligning with the trend toward smaller, essential texts in mathematics, the author strives for clarity of exposition. Proof techniques and proofs are presented slowly and clearly.The book employs a versatile approach to the use of algebraic ideas. Instructors who wish to put this material into a broader context may do so, though the author introduces these concepts in a non-essential way.A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems helps students to realize unique factorization into primes is a more subtle idea than may at first appear; students will find this chapter interesting, fun and quite accTable of ContentsIntroduction. What is Number Theory? 1. Divisibility. 2. Congruences and Modular Arithmetic. 3. Cryptography: An Introduction. 4. Perfect Numbers. 5. Perfect Roots. 6. Quadratic Reciprocity. 7. Arithmetic Beyond Integers.
£39.99
CRC Press Predictive Modelling for Football Analytics
a huge range and FREE tracked UK delivery on ALL orders.
£45.59
CRC Press Differential Geometry of Curves and Surfaces
Book SynopsisThrough two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces.Requiring only multivariable calculus and linear algebra, it develops studentsâ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player.The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research.At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises.This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.
£54.14
CRC Press Feature Engineering and Selection
Book SynopsisThe process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results. Trade Review"The book is timely and needed. The interest in all things 'data science' morphed into everybody pretending to do, or know, Machine Learning. Kuhn and Johnson happen to actually know this—as evidenced by their earlier and still-popular tome entitled ‘Applied Predictive Modeling.’ The proposed ‘Feature Engineering and Selection’ builds on this and extends it. I expect it to become as popular with a wide reach as both a textbook, self-study material, and reference."~Dirk Eddelbuettel, University of Illinois at Urbana-Champaign"As a reviewer, it has been exciting and edifying to see this book develop into what is likely to become one of the foundational works on feature engineering. It is launching propitiously on the current tide of interest in both interpretable models and AutoML."~Robert Horton, Microsoft"In recent years, the statistics literature has featured new developments in modeling and predictive analytics. Approaches such as cross-validation and statistical/machine learning techniques have become widespread. The author's previous book ("Applied Predictive Modeling", APM) provided a wide-ranging introduction and integration of these methods and suggested a workflow in R to carry out exploratory and confirmation analyses. With this project, the authors have identified an important and interesting component of these methods that describes building better models by focusing on the predictors (feature engineering)…The authors focus on the variables that go into the model (and how they are represented) and argue that such issues are as important (or more important) than the particular methods that are applied to an analysis...The proposed book is likely to serve as a textbook (for a number of undergraduate and graduate courses in a variety of disciplines) and reference (for a large number of statisticians seeking principled and well-organized modeling)."~Nicholas Horton, Amherst College"I think this book is great and a joy to read…I like the pragmatic and practical approach taken in the book, and the examples given are very illustrative. The emphasis on how and when to use resampling is refreshing and something that the community needs to hear more." ~Andreas C. Muller, Columbia University"The book is timely and needed. The interest in all things 'data science' morphed into everybody pretending to do, or know, Machine Learning. Kuhn and Johnson happen to actually know this—as evidenced by their earlier and still-popular tome entitled ‘Applied Predictive Modeling.’ The proposed ‘Feature Engineering and Selection’ builds on this and extends it. I expect it to become as popular with a wide reach as both a textbook, self-study material, and reference."~Dirk Eddelbuettel, University of Illinois at Urbana-Champaign"As a reviewer, it has been exciting and edifying to see this book develop into what is likely to become one of the foundational works on feature engineering. It is launching propitiously on the current tide of interest in both interpretable models and AutoML."~Robert Horton, Microsoft"In recent years, the statistics literature has featured new developments in modeling and predictive analytics. Approaches such as cross-validation and statistical/machine learning techniques have become widespread. The author's previous book ("Applied Predictive Modeling", APM) provided a wide-ranging introduction and integration of these methods and suggested a workflow in R to carry out exploratory and confirmation analyses. With this project, the authors have identified an important and interesting component of these methods that describes building better models by focusing on the predictors (feature engineering)…The authors focus on the variables that go into the model (and how they are represented) and argue that such issues are as important (or more important) than the particular methods that are applied to an analysis...The proposed book is likely to serve as a textbook (for a number of undergraduate and graduate courses in a variety of disciplines) and reference (for a large number of statisticians seeking principled and well-organized modeling)."~Nicholas Horton, Amherst College"I think this book is great and a joy to read…I like the pragmatic and practical approach taken in the book, and the examples given are very illustrative. The emphasis on how and when to use resampling is refreshing and something that the community needs to hear more." ~Andreas C. Muller, Columbia UniversityTable of Contents1. Introduction. 2. Illustrative Example: Predicting Risk of Ischemic Stroke. 3. A Review of the Predictive Modeling Process. 4. Exploratory Visualizations. 5. Encoding Categorical Predictors. 6. Engineering Numeric Predictors. 7. Detecting Interaction Effects. 8. Handling Missing Data. 9. Working with Profile Data. 10. Feature Selection Overview. 11. Greedy Search Methods. 12. Global Search Methods.
£45.99
CRC Press C for Financial Mathematics
Book SynopsisIf you know a little bit about financial mathematics but donât yet know a lot about programming, then C++ for Financial Mathematics is for you.C++ is an essential skill for many jobs in quantitative finance, but learning it can be a daunting prospect. This book gathers together everything you need to know to price derivatives in C++ without unnecessary complexities or technicalities. It leads the reader step-by-step from programming novice to writing a sophisticated and flexible financial mathematics library. At every step, each new idea is motivated and illustrated with concrete financial examples.As employers understand, there is more to programming than knowing a computer language. As well as covering the core language features of C++, this book teaches the skills needed to write truly high quality software. These include topics such as unit tests, debugging, design patterns and data structures. The book teaches everything you neTrade Review"OOP in C++ remains a difficult programming language and paradigm to learn and develop. There remains a shortage of high-quality, easy to follow texts in C++ for mathematical finance. Dr Armstrong has successfully produced a self-contained publication that begins with the basics and patiently guides the student to advanced object-oriented C++ programming in a quant finance setting. The writing style is very user-friendly and immediately reassures the reader, while numerous exercises allow solid progression. The author’s extensive background in academia and as a practitioner is apparent throughout; the latter being a key accomplishment in setting the book apart from others. As a teacher of mathematical and computational finance, Armstrong’s book will feature at the top of my list of recommended textbooks."— Dr. Riaz Ahmad, The Fitch Group and University College London (Departments of Mathematics and Computer Science) "OOP in C++ remains a difficult programming language and paradigm to learn and develop. There remains a shortage of high-quality, easy to follow texts in C++ for mathematical finance. Dr Armstrong has successfully produced a self-contained publication that begins with the basics and patiently guides the student to advanced object-oriented C++ programming in a quant finance setting. The writing style is very user-friendly and immediately reassures the reader, while numerous exercises allow solid progression. The author’s extensive background in academia and as a practitioner is apparent throughout; the latter being a key accomplishment in setting the book apart from others. As a teacher of mathematical and computational finance, Armstrong’s book will feature at the top of my list of recommended textbooks."— Dr. Riaz Ahmad, The Fitch Group and University College London (Departments of Mathematics and Computer Science) Table of ContentsIntroduction. Getting Started. Basic Data Types and Operators. Functions. Flow of Control. Working with Multiple Files. Unit Testing. Using C++ Classes. User-Defined Types. Monte Carlo Pricing in C++. Interfaces. Arrays, Strings, and Pointers. More Sophisticated Classes. The Portfolio Class. Delta Hedging. Debugging and Development ToolsA Matrix Class. An Overview of Templates. The Standard Template Library. Function Objects and Lambda Functions. Threads. Next Steps. Appendix: Risk-Neutral Pricing
£45.99
CRC Press DevOps for Data Science
Book SynopsisData Scientists are experts at analyzing, modelling and visualizing data but, at one point or another, have all encountered difficulties in collaborating with or delivering their work to the people and systems that matter. Born out of the agile software movement, DevOps is a set of practices, principles and tools that help software engineers reliably deploy work to production. This book takes the lessons of DevOps and aplies them to creating and delivering production-grade data science projects in Python and R.This bookâs first section explores how to build data science projects that deploy to production with no frills or fuss. Its second section covers the rudiments of administering a server, including Linux, application, and network administration before concluding with a demystification of the concerns of enterprise IT/Administration in its final section, making it possible for data scientists to communicate and collaborate with their organizationâs security, networking,
£59.99
Taylor & Francis Ltd Galois Theory
Book SynopsisSince 1973, Galois theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for todayâs algebra students.New to the Fifth Edition Reorganised and revised Chapters 7 and 13 New exercises and examples Expanded, updated references Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel A new final chapter discussing other directions in which Galois theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representations This bestseller continues to deliver a rigorous, yet engaging, treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.Trade Review"In mathematics, the fundamental theorem of Galois theory connects field theory and group theory, enabling certain mathematical problems in field theory to be reduced to group theory, making the problems simpler and easier to understand. The fifth updated edition of the textbook Galois Theory is an invaluable teaching text and resource for instructors of undergraduate mathematics students. Featuring more than 200 exercises and historical notes to enhance understanding of the proofs, formulas, and theorems, the fifth edition of Galois Theory is a "must-have" for university library mathematics collections, and highly recommended for instructors or for self-study"- Midwest Books ReviewPraise for the Previous Editions"… this book remains a highly recommended introduction to Galois theory along the more classical lines. It contains many exercises and a wealth of examples, including a pretty application of finite fields to the game solitaire. … provides readers with insight and historical perspective; it is written for readers who would like to understand this central part of basic algebra rather than for those whose only aim is collecting credit points."—Zentralblatt MATH 1322"This edition preserves and even extends one of the most popular features of the original edition: the historical introduction and the story of the fatal duel of Evariste Galois. … These historical notes should be of interest to students as well as mathematicians in general. … after more than 30 years, Ian Stewart’s Galois Theory remains a valuable textbook for algebra undergraduate students."—Zentralblatt MATH, 1049"The penultimate chapter is about algebraically closed fields and the last chapter, on transcendental numbers, contains ‘what-every-mathematician-should-see-at-least-once,’ the proof of transcendence of pi. … The book is designed for second- and third-year undergraduate courses. I will certainly use it."—EMS NewsletterTable of Contents1. Classical Algebra. 1.1. Complex Numbers. 1.2. Subfields and Subrings of the Complex Numbers. 1.3. Solving Equations. 1.4. Solution by Radicals. 2. The Fundamental Theorem of Algebra. 2.1. Polynomials. 2.2. Fundamental Theorem of Algebra. 2.3. Implications 3. Factorisation of Polynomials. 3.1. The Euclidean Algorithm. 3.2 Irreducibility. 3.3. Gauss’s Lemma. 3.4. Eisenstein’s Criterion. 3.5. Reduction Modulo p. 3.6. Zeros of Polynomials. 4. Field Extensions. 4.1. Field Extensions. 4.2. Rational Expressions. 4.3. Simple Extensions. 5. Simple Extensions. 5.1. Algebraic and Transcendental Extensions. 5.2. The Minimal Polynomial. 5.3. Simple Algebraic Extensions. 5.4. Classifying Simple Extensions. 6. The Degree of an Extension. 6.1. Definition of the Degree. 6.2. The Tower Law. 6.3. Primitive Element Theorem. 7. Ruler-and-Compass Constructions. 7.1. Approximate Constructions and More General Instruments. 7.2. Constructions in C. 7.3. Specific Constructions. 7.4. Impossibility Proofs. 7.5. Construction From a Given Set of Points. 8. The Idea Behind Galois Theory. 8.1. A First Look at Galois Theory. 8.2. Galois Groups According to Galois. 8.3. How to Use the Galois Group. 8.4. The Abstract Setting. 8.5. Polynomials and Extensions. 8.6. The Galois Correspondence. 8.7. Diet Galois. 8.8. Natural Irrationalities. 9. Normality and Separability. 9.1. Splitting Fields. 9.2. Normality. 9.3. Separability. 10. Counting Principles. 10.1. Linear Independence of Monomorphisms. 11. Field Automorphisms. 11.1. K-Monomorphisms. 11.2. Normal Closures. 12. The Galois Correspondence. 12.1. The Fundamental Theorem of Galois Theory. 13. Worked Examples. 13.1. Examples of Galois Groups. 13.2. Discussion. 14. Solubility and Simplicity. 14.1. Soluble Groups. 14.2. Simple Groups. 14.3. Cauchy’s Theorem. 15. Solution by Radicals. 15.1. Radical Extensions. 15.2. An Insoluble Quintic. 15.3. Other Methods. 16. Abstract Rings and Fields. 16.1. Rings and Fields. 16.2. General Properties of Rings and Fields. 16.3. Polynomials Over General Rings. 16.4. The Characteristic of a Field. 16.5. Integral Domains. 17. Abstract Field Extensions and Galois Groups. 17.1. Minimal Polynomials. 17.2. Simple Algebraic Extensions. 17.3. Splitting Fields. 17.4. Normality. 17.5. Separability. 17.6. Galois Theory for Abstract Fields. 17.7. Conjugates and Minimal Polynomials. 17.8. The Primitive Element Theorem. 17.9. Algebraic Closure of a Field. 18. The General Polynomial Equation. 18.1. Transcendence Degree. 18.2. Elementary Symmetric Polynomials. 18.3. The General Polynomial. 18.5. Solving Equations of Degree Four or Less. 18.6. Explicit Formulas. 19. Finite Fields. 19.1. Structure of Finite Fields. 19.2. The Multiplicative Group. 19.3. Counterexample to the Primitive Element Theorem. 19.4. Application to Solitaire. 20. Regular Polygons. 20.1. What Euclid Knew. 20.2. Which Constructions are Possible? 20.3. Regular Polygons. 20.4. Fermat Numbers. 20.5. How to Construct a Regular 17-gon. 21. Circle Division. 21.1. Genuine Radicals. 21.2. Fifth Roots Revisited. 21.3. Vandermonde Revisited. 21.4. The General Case. 21.5. Cyclotomic Polynomials. 21.6. Galois Group of Q(ζ)= Q. 21.7. Constructions Using a Trisector. 22. Calculating Galois Groups. 22.1. Transitive Subgroups. 22.2. Bare Hands on the Cubic. 22.3. The Discriminant. 22.4. General Algorithm for the Galois Group. 23. Algebraically Closed Fields. 23.1. Ordered Fields and Their Extensions. 23.2. Sylow’s Theorem. 23.3. The Algebraic Proof. 24. Transcendental Numbers. 24.1. Irrationality. 24.2. Transcendence of e. 24.3. Transcendence of π. 25. What Did Galois Do or Know? 25.1. List of the Relevant Material. 25.2. The First Memoir. 25.3. What Galois Proved. 25.4. What is Galois Up To? 25.5. Alternating Groups, Especially A5. 25.6. Simple Groups Known to Galois. 25.7. Speculations about Proofs. 25.8. A5 is Unique. 26. Further Directions. 26.1. Inverse Galois Problem. 26.2. Differential Galois Theory. 26.3. p-adic Numbers.
£52.24
Taylor & Francis Ltd Real Analysis and Foundations
Book SynopsisThrough four editions this popular textbook attracted a loyal readership and widespread use. Students find the book to be concise, accessible, and complete. Instructors find the book to be clear, authoritative, and dependable. The primary goal of this new edition remains the same as in previous editions. It is to make real analysis relevant and accessible to a broad audience of students with diverse backgrounds while also maintaining the integrity of the course. This text aims to be the generational touchstone for the subject and the go-to text for developing young scientists. This new edition continues the effort to make the book accessible to a broader audience. Many students who take a real analysis course do not have the ideal background. The new edition offers chapters on background material like set theory, logic, and methods of proof. The more advanced material in the book is made more apparent.This new edition offers a new chapter onTable of ContentsPreface 0 Background Material 0.1 Number Systems 0.1.1 The Natural Numbers 0.1.2 The Integers 0.1.3 The Rational Numbers 02 Logic and Set 0.2.1 And” and “Or” 0.2.2 “not” and “if then”0.2.3 Contrapositive, Converse, and “Iff” 0.2.4 Quantifiers 0.2.5 Set Theory and Venn Diagrams 0.2.6 Relations and Functions 0.2.7 Countable and Uncountable Sets 1 Real and Complex Numbers 1.1 The Real Numbers Appendix: Construction of the Real Numbers 1.2 The Complex Numbers 2 Sequences 712.1 Convergence of Sequences 2.2 Subsequences 2.3 Limsup and Liminf 2.4 Some Special Sequences 3 Series of Numbers 3.1 Convergence of Series 3.2 Elementary Convergence Tests 3.3 Advanced Convergence Tests 3.4 Some Special Series 3.5 Operations on Series 4 Basic Topology 4.1 Open and Closed Sets 4.2 Further Properties of Open and Closed Sets 4.3 Compact Sets 4.4 The Cantor Set 4.5 Connected and Disconnected Sets 4.6 Perfect Sets 5 Limits and Continuity of Functions 5.1 Basic Properties of the Limit of a Function 5.2 Continuous Functions 5.3 Topological Properties and Continuity 5.4 Classifying Discontinuities and Monotonicity 6 Differentiation of Functions 6.1 The Concept of Derivative 6.2 The Mean Value Theorem and Applications 6.3 More on the Theory of Differentiation 7 The Integral7.1 Partitions and the Concept of Integral 7.2 Properties of the Riemann Integral 7.3 Change of Variable and Related Ideas 7.4 Another Look at the Integral 7.5 Advanced Results on Integration Theory 8 Sequences and Series of Functions 8.1 Partial Sums and Pointwise Convergence 8.2 More on Uniform Convergence 8.3 Series of Functions 8.4 The Weierstrass Approximation Theorem 9 Elementary Transcendental Functions 9.1 Power Series 9.2 More on Power Series: Convergence Issues 9.3 The Exponential and Trigonometric Functions 9.4 Logarithms and Powers of Real Numbers 10 Functions of Several Variables 10.1 A New Look at the Basic Concepts of Analysis 10.2 Properties of the Derivative 10.3 The Inverse and Implicit Function Theorems 11 Advanced Topics 11.1 Metric Spaces 11.2 Topology in a Metric Space 11.3 The Baire Category Theorem 11.4 The Ascoli-Arzela Theorem 12 Differential Equations 12.1 Picard’s Existence and Uniqueness Theorem 12.1.1 The Form of a Differential Equation 12.1.2 Picard’s Iteration Technique 12.1.3 Some Illustrative Examples 12.1.4 Estimation of the Picard Iterates 12.2 Power Series Methods 13 Introduction to Harmonic Analysis 13.1 The Idea of Harmonic Analysis 13.2 The Elements of Fourier Series 13.3 An Introduction to the Fourier Transform Appendix: Approximation by Smooth Functions 13.4 Fourier Methods and Differential Equations 13.4.1 Remarks on Different Fourier Notations 13.4.2 The Dirichlet Problem on the Disc 13.4.3 Introduction to the Heat and Wave Equations 13.4.4 Boundary Value Problems 13.4.5 Derivation of the Wave Equation 13.4.6 Solution of the Wave Equation 13.5 The Heat Equation Appendix: Review of Linear Algebra Table of Notation Glossary Bibliography Index
£80.74
Taylor & Francis Ltd The Elements of Advanced Mathematics
Book Synopsis
£54.14
CRC Press Multiple Imputation of Missing Data in Practice
Book SynopsisMultiple Imputation of Missing Data in Practice: Basic Theory and Analysis Strategies provides a comprehensive introduction to the multiple imputation approach to missing data problems that are often encountered in data analysis. Over the past 40 years or so, multiple imputation has gone through rapid development in both theories and applications. It is nowadays the most versatile, popular, and effective missing-data strategy that is used by researchers and practitioners across different fields. There is a strong need to better understand and learn about multiple imputation in the research and practical community.Accessible to a broad audience, this book explains statistical concepts of missing data problems and the associated terminology. It focuses on how to address missing data problems using multiple imputation. It describes the basic theory behind multiple imputation and many commonly-used models and methods. These ideas are illustrated by example
£51.29
Taylor & Francis Ltd An Introduction To Chaotic Dynamical Systems
Book SynopsisThere is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily. Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics.Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field.This is text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamicTable of ContentsI One Dimensional Dynamics1.A Visual and Historical Tour2.Examples of Dynamical Systems3.Elementary Definitions4.Hyperbolicity5.An Example: The Logistic Family6.Symbolic Dynamics7.Topological Conjugacy8.Chaos9.Structural Stability10.Sharkovsky's Theorem11.The Schwarzian Derivative 12.Bifurcations13.Another View of Period Three14.Period-Doubling Route to Chaos15.Homoclinic Points and Bifurcations16.Maps of the Circle17.Morse-Smale DiffeomorphismsII Complex Dynamics18.Quadratic Maps Revisited19.Normal Families and Exceptional Points 20.Periodic Points21.Properties of the Julia Set22.The Geometry of the Julia Sets23.Neutral Periodic Points24.The Mandelbrot Set25.Rational Maps26.The Exponential FamilyIII Higher Dimensional Dynamics27.Dynamics of Linear Maps28.The Smale Horseshoe Map29.Hyperbolic Toral Automorphisms30.Attractors31.The Stable and Unstable Manifold Theorem32.Global Results and Hyperbolic Maps33.The Hopf Bifurcation34.The Herron MapAppendix: Mathematical Preliminaries
£76.49
Taylor & Francis Ltd Quantum Continuous Variables
Book SynopsisQuantum Continuous Variables introduces the theory of continuous variable quantum systems, from its foundations based on the framework of Gaussian states to modern developments, including its applications to quantum information and forthcoming quantum technologies. This book addresses the theory of Gaussian states, operations, and dynamics in great depth and breadth, through a novel approach that embraces both the Hilbert space and phase descriptions.The second edition of this book has been revised throughout, and updated to include new topics, such as boson sampling, coherent feedback, nonlinear control, as well as several new solved problems.The volume includes coverage of entanglement theory and quantum information protocols, and their connection with relevant experimental set-ups. General techniques for non-Gaussian manipulations also emerge as the treatment unfolds and are demonstrated with specific case studies.This book willTable of ContentsChapter 1: Introduction. Chapter 2: Quantum Mechanics: Instructions for Use. Chapter 3: Gaussian States of Continuous Variable Systems. Chapter 4: Phase Space Methods. Chapter 5: Gaussian Operations. Chapter 6: Diffusive Dynamics and Continuous Monitoring. Chapter 7: Entanglement of Continuous Variable Systems. Chapter 8: Quantum Information Protocols with Continuous Variables. Chapter 9: A Grand Tour of Continuous Variable Platforms. Appendix A: A Note on Fermions. Appendix B: Some Notable Facts About the Symplectic Group. Appendix C: The Wiener Process. Appendix D: Selected Mathematical Lore on Quantum Channels. Appendix E: Classical and Quantum Estimation Bounds. References. Index.
£86.99
Taylor & Francis Ltd Occultism and the Origins of Psychoanalysis
Book SynopsisOccultism and the Origins of Psychoanalysis traces the origins of key psychoanalytic ideas back to their roots in hypnosis and the occult. Maria Pierri follows Freud’s early interest in ‘thought-transmission’, now known as telepathy. Trade Review"This book gives back to contemporary psychoanalysis the pleasure of exploring really little-known territories, fascinatingly restoring the connection between the past, present and "elsewhere" of communications between human beings, using the Freudian experience as its starting point, in order to reconsider in a reflective way the less visible, sometimes disorienting and mysterious levels of psychoanalytic practice. offers us an especially valuable reflection on the mysterious communicating paths which put individual and group unconsciouses in contact with each other, often bypassing in an apparently disconcerting manner the border controls." - Stefano Bolognini, past President of the IPA and the Italian Psychoanalytic Society"Following the thread of thought-transference, Maria Pierri goes through the events of the Freudian endeavour starting from its roots in hypnosis and occultism, through the dialogue with the masters, the pupils and the great female patients, the leading actresses of the cure. In his disquieting curiosity for telepathy, which he shared intimately with Ferenczi, Freud discovers that fortune-tellers, who do not know the future, can read the unconscious of their clients. But the "golden coin" of occultism, the generative mother-child communication, will be the great discovery of Ferenczi." - Luis J. Martin Cabré, Training analyst, past President Madrid Psychoanalytical Association."Today we know much about the polyphonic complex of contexts, experiences, relationships and ideas which made psychoanalysis possible and still nourish its current debates. We can be very grateful to Maria Pierri for bringing us up to date with the role and meaning of some little-known aspects of Freud’s life and work concerning occultism and the fascinating dialogue of the unconsciouses developed with Ferenczi: what the Author identifies as one of the matrices of the developments of contemporary psychoanalysis." - Marco Conci, MC, IPA Committee on the History of Psychoanalysis"This book gives back to contemporary psychoanalysis the pleasure of exploring really little-known territories, fascinatingly restoring the connection between the past, present and 'elsewhere' of communications between human beings, using the Freudian experience as its starting point, in order to reconsider in a reflective way the less visible, sometimes disorienting and mysterious levels of psychoanalytic practice. It offers us an especially valuable reflection on the mysterious communicating paths which put individual and group unconsciouses in contact with each other, often bypassing in an apparently disconcerting manner the border controls." - Stefano Bolognini, past president of the IPA and the Italian Psychoanalytic Society"Following the thread of thought-transference, Maria Pierri goes through the events of the Freudian endeavour starting from its roots in hypnosis and occultism, through the dialogue with the masters, the pupils and the great female patients, the leading actresses of the cure. In his disquieting curiosity for telepathy, which he shared intimately with Ferenczi, Freud discovers that fortune-tellers, who do not know the future, can read the unconscious of their clients. But the 'golden coin' of occultism, the generative mother-child communication, will be the great discovery of Ferenczi." - Luis J. Martin Cabré, training analyst, past president, Madrid Psychoanalytical Association"Today we know much about the polyphonic complex of contexts, experiences, relationships and ideas which made psychoanalysis possible and still nourish its current debates. We can be very grateful to Maria Pierri for bringing us up to date with the role and meaning of some little-known aspects of Freud’s life and work concerning occultism and the fascinating dialogue of the unconsciouses developed with Ferenczi: what the Author identifies as one of the matrices of the developments of contemporary psychoanalysis." - Marco Conci, MC, IPA Committee on the History of PsychoanalysisTable of ContentsIntroductionStefano BologniniPrologue: a result of character: the cocaine, this magical substance1. Vienna, Porta Orientis of the Unconscious The force of suggestion: the "wonderful somnambulists" HypnosisVienna, laboratory of modernity2. The Young FreudA passionate young researcher into natureFirst love Martha and Bertha: the languages of passion3. The Lesson of Jean Martin Charcot At the SalpêtrièreThe apparatus of language The magic of words4. The lesson of Josef Breuer and the "descent to the mothers"Studies on hysteriaA difficult separation: not all debts can be paidA foundation myth: a false pregnancy and a cure with a defect.5. Sigmund Freud’s lessonThe discovery of a false connection Irma’s throat and the feminine at the origin of psychoanalysis.Dream as desire 6. Fliess and the invention of psychoanalysis A secret correspondence My friend in BerlinFreud’s heart trouble7. The discovery of infantile sexualitySelf-analysis and the writing cure Cherchez la femme: the case of Emma Eckstein8. Original thought requires a ruptureThe "reader of thoughts" The accusation of plagiarism A future in the image of the past: predestination and superstition 9. Occultism made in the USASpiritualism Medium, media, and "mental telegraphy"First hypotheses about the unconscious10 Jung, spiritualism, and countertransference: the world of the deadJung, Poltergeist phenomena, and séances The arrival at Burghölzli First visit to ViennaEaster 1909: Jung’s spiritual complex and Sabina The dangerous fascination of the "beautiful Jewess"11. Ferenczi, the unclassifiableThe sultan and his "clairvoyant" A psychoanalyst "of a restless mind"Ferenczi and the hidden treasure of SpiritualismThe encounter with Freud: a postponed transferential appointment12. A journey to America Three men and an eventful, mutually analytic crossing: the outward journey… … and back again13. The Danaan gift The clairvoyant who reads Ferenczi’s mindThe patient who reads Ferenczi’s mindThe Palermo incident, or the interpretation of paranoiaThe psychic work of the clairvoyant: two unfulfilled prophecies14. An epistolary novelFerenczi and incestuous countertransferential storms: from mother to daughter What is still missing is the fatherly blessing: fatefulness and Oedipal coincidencesElma Pàlos, fragment of the analysis of a seduction The open wound in Ferenczi’s heart, a source of creativity 15. The Saturday goy: getting to know Dr Jones The Welsh liar Difficult beginnings Freud’s first pupil from BritainDr Jones’s stethoscope: rationalisation and censorship of excess countertransferenceA prescribed training analysis in Budapest 16. The intergenerational transmission of psychoanalysis Love and death: the three women of the three pupils"If you go to women, don't forget the whip"At school with Freud: the transmission of psychoanalysis17. The secret committeeThe transformations and the desertion of JungA missed meeting: the "Kreuzlingen gesture" The Committee: the Männerbund and the defence of the "Cause" (Die Sache)Totem and taboo: unconscious intelligence and intergenerational transmission of thought 18. 1913 - the year before the warThe last congress with JungA black tide of occultism The question of telepathyThe dialogues of the unconsciousEpilogue: a fortune-teller visits Freud in BerggasseCorrespondenceIndex
£29.99
Taylor & Francis Ltd Fuzzy Statistical Inferences Based on Fuzzy
Book SynopsisThis book presents the most commonly used techniques for the most statistical inferences based on fuzzy data. It brings together many of the main ideas used in statistical inferences in one place, based on fuzzy information including fuzzy data. This book covers a much wider range of topics than a typical introductory text on fuzzy statistics. It includes common topics like elementary probability, descriptive statistics, hypothesis tests, one-way ANOVA, control-charts, reliability systems and regression models. The reader is assumed to know calculus and a little fuzzy set theory. The conventional knowledge of probability and statistics is required.Key Features: Includes example in Mathematica and MATLAB. Contains theoretical and applied exercises for each section. Presents various popular methods for analyzing fuzzy data. The book is suitable for students and researchers in statistics, social science, engineering, and economics, and it can be used at graduate and P.h.D level.
£42.74
CRC Press An Invitation to Abstract Algebra
Book SynopsisStudying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout.The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galoisâ achievement in understanding how we canâand cannotârepresent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinksâperiod. This book is offered as a manual to a new way of thinking. The authorâs aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
£54.14
CRC Press Handbook of Complex Analysis
Book SynopsisIn spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. This Handbook presents contributed chapters by prominent mathematicians, including the new generation of researchers. More than a compilation of recent results, this book offers students an essential stepping-stone to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role. This book is also a reference and a source of inspiration for more seasoned mathematiciansboth specialists in complex analysis and others who want to acquaint themselves with current modes of thought.The chapters in this volume are authored by leading experts and gifted expositors. They are carefully crafted presentations of diverse aspects of the fiel
£71.24
CRC Press Data Integration Manipulation and Visualization
Book SynopsisData Integration, Manipulation and Visualization of Phylogenetic Trees introduces and demonstrates data integration, manipulation and visualization of phylogenetic trees using a suite of R packages, tidytree, treeio, ggtree and ggtreeExtra. Using the most comprehensive packages for phylogenetic data integration and visualization, contains numerous examples that can be used for teaching and learning. Ideal for undergraduate readers and researchers with a working knowledge of R and ggplot2.Key Features: Manipulating phylogenetic tree with associated data using tidy verbs Integrating phylogenetic data from diverse sources Visualizing phylogenetic data using grammar of graphics
£42.74
Taylor & Francis Ltd Modelling Survival Data in Medical Research
Book SynopsisModelling Survival Data in Medical Research, Fourth Edition, describes the analysis of survival data, illustrated using a wide range of examples from biomedical research. Written in a non-technical style, it concentrates on how the techniques are used in practice. Starting with standard methods for summarising survival data, Cox regression and parametric modelling, the book covers many more advanced techniques, including interval-censoring, frailty modelling, competing risks, analysis of multiple events, and dependent censoring.This new edition contains chapters on Bayesian survival analysis and use of the R software. Earlier chapters have been extensively revised and expanded to add new material on several topics. These include methods for assessing the predictive ability of a model, joint models for longitudinal and survival data, and modern methods for the analysis of interval-censored survival data.Features:Presents an accessible account oTable of Contents1. Survival analysis 2. Some non-parametric procedures 3. The Cox regression model 4. Model checking in the Cox regression model 5. Parametric regression models 6. Flexible parametric models 7. Model checking in parametric models 8. Time-dependent variables 9. Interval-censored survival data 10. Frailty models 11. Non-proportional hazards and institutional comparisons 12 Competing risks 13. Multiple events and event history modelling 14. Dependent censoring 15. Sample size requirements for a survival study 16. Bayesian survival analysis 17. Survival Analysis with R
£73.14
Taylor & Francis Ltd Bayesian Multilevel Models for Repeated Measures
Book SynopsisThis comprehensive book is an introduction to multilevel Bayesian models in R using brms and the Stan programming language. Featuring a series of fully worked analyses of repeated measures data, the focus is placed on active learning through the analyses of the progressively more complicated models presented throughout the book. In this book, the authors offer an introduction to statistics entirely focused on repeated measures data beginning with very simple two-group comparisons and ending with multinomial regression models with many random effects'. Across 13 well-structured chapters, readers are provided with all the code necessary to run all the analyses and make all the plots in the book, as well as useful examples of how to interpret and write up their own analyses. This book provides an accessible introduction for readers in any field, with any level of statistical background. Senior undergraduate students, graduate students, and experienced researchers looking Table of ContentsPrefaceAcknowledgments1. Introduction: Experiments and Variables2. Probabilities, Likelihood, and Inference3. Fitting Bayesian Regression Models with brms4. Inspecting a ‘Single Group’ of Observations using a Bayesian Multilevel Model5. Comparing Two Groups of Observations: Factors and Contrasts6. Variation in Parameters (‘Random Effects’) and Model Comparison7. Comparing Many Groups, Interactions, and Posterior Predictive Checks8. Varying Variances, More about Priors, and Prior Predictive Checks9. Quantitative Predictors and their Interactions with Factors10. Logistic Regression and Signal Detection Theory Models11. Multiple Quantitative Predictors, Dealing with Large Models, and Bayesian ANOVA12. Multinomial and Ordinal Regression13. Writing up Experiments: An investigation of the Perception of Apparent Speaker Characteristics from Speech Acoustics
£49.99
Taylor & Francis Ltd Thinking About Statistics
Book SynopsisSimply stated, this book bridges the gap between statistics and philosophy. It does this by delineating the conceptual cores of various statistical methodologies (Bayesian/frequentist statistics, model selection, machine learning, causal inference, etc.) and drawing out their philosophical implications. Portraying statistical inference as an epistemic endeavor to justify hypotheses about a probabilistic model of a given empirical problem, the book explains the role of ontological, semantic, and epistemological assumptions that make such inductive inference possible. From this perspective, various statistical methodologies are characterized by their epistemological nature: Bayesian statistics by internalist epistemology, classical statistics by externalist epistemology, model selection by pragmatist epistemology, and deep learning by virtue epistemology. Another highlight of the book is its analysis of the ontological assumptions that underpin statistical reasoning, sucTrade Review"Statistics are being used ever more widely in AI, climate studies, medicine and other areas. Yet they are hard to understand both mathematically and conceptually. Jun Otsuka has the answer to this problem. He has a remarkable ability to explain statistical techniques clearly and accurately with a minimal use of mathematics. At the same time he gives lucid discussions of why they work. He deals not only with the long-standing controversy between Bayesianism and classical statistics, but also with such recent topics as causality and deep learning by computers. His book is the perfect guide to those perplexed by statistics."Donald Gillies, University College London Table of ContentsIntroduction 1. The Paradigm of Modern Statistics 2. Bayesian Statistics 3. Classical Statistics 4. Model Selection and Machine Learning 5. Causal Inference 6. The Ontology, Semantics, and Epistemology of Statistics
£33.99
Taylor & Francis Ltd Models for NonModelers
Book SynopsisModels for Non-Modelers focuses not on how to design models but on how to understand and critically appraise them. Data and statistical models are widely used in disciplines such as epidemiology, climate science and systems design, but it can be difficult for those without the necessary training to understand and implement them.This book is for non-modelers, especially social scientists. Through extensive examination of some common models both in visual and text form, this book shows these non-modellers how to understand the problems, both in the logic and implementation of such models. It includes in-depth worked examples and boxed text for more technical aspects. It does not require the reader to have in-depth mathematical knowledge. Also working through some common models in epidemiology and climate change scholarship, it examines AI and the problem of causality.This book will be suitable for graduate students and researchers in the social sciences who woulTrade Review"Models for Non-Modelers is a very timely and up-to-date comment on a central theme of scientific work, the use of models. It helps the interested reader to better understand important challenges of knowledge production in an era of critical debate regarding the concept of truth. Furthermore, to understand the research community’s strengths and limitations to produce new knowledge, which can be useful for handling complex environmental, economic and societal challenges like climate change and pandemics. It is highly recommended for a broad audience spanning from the interested public to students and researchers in development studies, environmental sciences, public health, and many other fields of science." -- Per-Olof Östergren, Professor in Social Medicine, Lund University, Sweden"This is a mind-opening critical, and pedagogical, scrutiny of scientific reasoning about the fateful issues of our time, from "Limits to Growth" to climate change and artificial intelligence." --Göran Therborn, Professor Emeritus of Sociology, University of Cambridge, UK"Models walk a fine balance between simplicity and complexity to make it possible for us to summarize, make sense of, and sometimes predict a complicated world. How to illuminate the importance of models for scientists’ work and its communication to the public? Göran Djurfeldt’s answer is to ’teach by illustration.’ Occam’s razor of parsimony guides the author both in his style of presentation and in his approach to models themselves. This book is enlivened by both subject-specific and mathematical nuance at key intersections." -- Christopher Swader, Associate Professor of Sociology, Lund University, SwedenTable of Contents1. Limits to Growth: A Mother of all Models? 2. Epidemiological Models 3. Weather and Climate Models 4. Artificial Intelligence 5. Spatial Data and Models 6. Tragedy of the Commons 7. Conclusions: Whereto from Here?
£32.99
Taylor & Francis Ltd How to Think about Data Science
Book SynopsisThis book is a timely and critical introduction for those interested in what data science is (and isn't), and how it should be applied. The language is conversational and the content is accessible for readers without a quantitative or computational background; but, at the same time, it is also a practical overview of the field for the more technical readers. The overarching goal is to demystify the field and teach the reader how to develop an analytical mindset instead of following recipes. The book takes the scientist's approach of focusing on asking the right question at every step as this is the single most important factor contributing to the success of a data science project. Upon finishing this book, the reader should be asking more questions than I have answered. This book is, therefore, a practising scientist's approach to explaining data science through questions and examples.Trade Review"Data science is no longer the exclusive domain of computer scientists and engineers. The contributions of other stakeholders are required for taking a holistic approach to the problems that can be addressed by analysing a given dataset. Not only is this likely to lead to better solutions, but also a smoother journey to their implementation, validation and widespread adoption. However, in the same way that a computer scientist should at least gain an operational understanding of the tackled problem, the domain expert should also understand the foundations and correct use of the tools unveiling its solutions. In this context, How to Think about Data Science is an unusual book in that it provides an accessible introduction to this broad and booming discipline without sacrificing the understanding of key questions in data science. I can only recommend this book to those aspiring to acquire this knowledge and mindset."--Pedro J. Ballester, PhD, Senior Lecturer, Imperial College London; Wolfson Fellow, The Royal Society"What is the difference between a regular cook from a renowned chef? A regular cook may follow recipes and create edible dishes, but knowing which ingredients to use and how to combine them, how to cook each one and for how long, and how to finally present them is what makes all the difference. The tools and processes are important for sure, but what really provides value is being able to choose and integrate the right tools, ingredients and processes to create a terrific dish. In data science it is the same: anyone can execute a clustering or build a neural network with default parameters but what matters is to know, given a dataset, what questions can be answered, what algorithms we should use to answer each question and what ethical issues and privacy concerns should be considered; answering these questions would allow a data scientist not just to follow recipes, but to apply the right algorithms to answer the right questions while minimizing potentially discriminating outputs. This book focuses on these relevant questions. If you want to cook a terrific dish, this book will help you."--Jordi Conesa i Caralt, PhD, Associate Professor of Computer Science, Universitat Oberta de Catalunya"Today, big data influences nearly everything we do, and harnessing its enormous power remains a key driver of business analytics, research innovation, cultural revolution, and global politics. This book offers a great gateway to this broad and evolving subject by asking the right questions, introducing concepts clearly and succinctly, and making rational connections between computation and their wide ranging applications. The book also discusses important issues related to data bias, discrimination, data privacy, and security. The final chapter debates the limits of artificial intelligence and the computational, ethical, and philosophical conundrums it presents. Thought-provoking and refreshing – it is a must-read book!"-- Subhajyoti De, PhD, Associate Professor at the Center for Systems and Computational Biology, Rutgers, the State University of New JerseyTable of ContentsA bird’s-eye view and the art of asking questions. Descriptive Analytics. Predictive Analytics. How are predictive models trained and evaluated? Are our algorithms racist, sexist and discriminating? Personal data, privacy and cybersecurity. What are the limits of Artificial Intelligence?
£40.84
Taylor & Francis Ltd Discrete Mathematics with Coding
Book SynopsisThis book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simpli?ed using spreadsheet features and visualizing the data can make Table of Contents1. Introduction. 2. VBA Operators. 3. Conditional Statements. 4. Loops, 5. Arrays. 6. String Functions. 7. Grids. 8. Recursion. 9. Charts and Graphs, 10. Random Numbers. 11. Linear Equations. 12. Linear Programming. 13. Matrix Algebra. 14. Determinants. 15. Propositional Logic. 16. Switching Circuits. 17. Gates and Logic Circuits. 18. Sets. 19. Counting. 20. Probability. 21. Random Variables. 22. Markov Chains. 23. Divisibility and Prime Numbers. 24. Congruence. 25. The Enigma Machine. 26. Large Numbers.
£87.39
CRC Press The Mathematics of Politics
Book SynopsisIt is because mathematics is often misunderstood, it is commonlybelieved it has nothing to say about politics. The high schoolexperience with mathematics, for so many the lasting impressionof the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Thosebelieving this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoningabout politics. In the search for ideal ways to make certain kindsof decisions, a lot of wasted effort can be averted if mathematics can determine thatfinding such an ideal is actually impossible in the first place.In the first three parts of this book, we address the following threepolitical questions:Table of ContentsI VOTING Two Candidates Social Choice Functions Criteria for Social Choice Which Methods Are Good?Arrow’s Theorem Variations on a Theme Notes on Part I II: APPORTIONMENT Hamilton’s MethodDivisor Methods Criteria and Impossibility The Method of Balinski and Young Deciding among Divisor Methods History of Apportionment in the United StatesNotes on Part II III CONFLICTStrategies and OutcomesChance and Expectation Solving Zero-Sum Games Conflict and CooperationNash Equilibria The Prisoner’s DilemmaNotes on Part III IV THE ELECTORAL COLLEGEWeighted Voting Whose Advantage?Notes on Part IV Solutions to Odd-Numbered Exercises and Problems
£43.99
