Mathematics Books
CRC Press Theory of Stochastic Integrals
Book SynopsisIn applications of stochastic calculus, there are phenomena that cannot be analyzed through the classical Ità theory. It is necessary, therefore, to have a theory based on stochastic integration with respect to these situations.Theory of Stochastic Integrals aims to provide the answer to this problem by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales, such as Volterra Gaussian processes, or processes with bounded p-variation among which we can mention fractional Brownian motion and Riemann-Liouville fractional process.Features Self-contained treatment of the topic Suitable as a teaching or research tool for those interested in stochastic analysis and its applications Includes original results.
£75.99
CRC Press Chemistry Calculations for Beginners
Book Synopsis
£61.74
Taylor & Francis The Psychology of Collective Climate Action
Book SynopsisHow do we find the courage to act together against the climate crisis? This book weaves together real-life findings and examples from the socio-ecological movement with psychological research to show how motivation for collective climate action can be built.The book addresses two key questions: how can individuals be motivated to participate in collective climate action, and how can climate groups become resilient and effective? Specifically, it explores how individuals can foster their identification with climate action groups and the belief in their joint efficacy. It touches on a wide range of topics, covering anger, moral considerations, activist burnout, and the perception of protests, as well as general theories of socio-ecological change.This book is for anyone who is seeking the courage to act together and is curious about psychological insights. It will be essential reading for climate and environmental practitioners, climate activists and campaigners, climate change communicators, and anyone involved in socio-ecological change. It will also be of interest to students and researchers in the fields of environmental psychology, climate change, collective action, and political psychology.The Open Access version of this book, available at http://www.taylorfrancis.com, has been made available under a Creative Commons (CC BY) 4.0 license.
£29.99
CRC Press Optimal Estimation of Dynamic Systems
Book SynopsisOptimal Estimation of Dynamic Systems, Second Edition highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems. Accessible to engineering students, applied mathematicians, and practicing engineers, the text presents the central concepts and methods of optimal estimation theory and applies the methods to problems with varying degrees of analytical and numerical difficulty. Different approaches are often compared to show their absolute and relative utility. The authors also offer prototype algorithms to stimulate the development and proper use of efficient computer programs. MATLAB codes for the examples are available on the bookâs website.New to the Second EditionWith more than 100 pages of new material, this reorganized edition expands upon the best-selling original to include comprehensive developments and updates. It incorporates new theoretical re
£999.99
CRC Press Measure and Integral
Book SynopsisNow considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2 Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation
£54.14
CRC Press Set Theory
Book SynopsisContemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written and now considered to be âœclassicsâ decades ago are still prescribed for students today. These texts are not suitable for todayâs students. This text is meant for and written to todayâs mathematics students. Set theory is a pure mathematics endeavour in the sense that it seems to have no immediate applications; yet the knowledge and skills developed in such a course can easily branch out to various fields of both pure mathematics and applied mathematics.Rather than transforming the reader into a practicing mathematician this book is more designed to initiate the reader to what may be called âœmathematical thinkingâ while developing knowledge about foundations of modern mathematics. Without this insight, becoming a practicing mathematician is much more daunting.The main objective is twofold. The students will develop some fun
£999.99
CRC Press Number Systems
Book SynopsisNumber Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The authorâs motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.Features Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof Draws attention to connections with other areas of mathematics Plenty of exercises for students, both straightforward problems and more in-depth investigations Introduces many concepts that are required in more advanced topics in mathematicsNew to the second edition Complete solutions to all exercises, and hints for the in-depth investigations Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties A thorough correction of typos and errors across all chapters Updates to the bibliography
£50.34
CRC Press Applications of AI in Smart Technologies and Manufacturing
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£152.00
CRC Press Causal Analysis for Climate Study
Book SynopsisThis book offers the theory of causal analysis and its applications. The authors have developed this book in relation its applications to four climatological phenomena, to prove the theory of causal analysis in time sequential data analysis.Local Causal Test and the Partial Causal Test are used to study the theory of causal analysis. These are then applied to understand the climate effects of the eruption at Mt. Pinatubo, effect of the El Nino and Southern Oscillation (ENSO), and North Atlantic Oscillation (NAO). The reader learns about Test(S), a statistical test used to determine if the statistical properties of the data, such as mean and variance, remain constant over time within a local window. The authors also use the Stationary Test and Causality Test in time series to explore relationships within a localized subset of data as witnessed from the climate phenomenon. The book looks at the eruption at Mt. Pinatubo, ENSO and NAO and applies causal theory to study the result
£48.99
CRC Press Tensors For Inquiring Minds
£47.49
Springer Us Density Evolution Under Delayed Dynamics
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£80.99
Birkhäuser Classical Analysis in the Complex Plane
Table of ContentsPrerequisites and Preliminaries.- Curves, Connectedness and Convexity.- (Complex) Derivative and (Curvilinear) Integrals.- Power Series and the Exponential Function.- The Index and some Plane Topology.-Consequences of the Cauchy–Goursat Theorem—Maximum Principles and the Local Theory.- Schwarz' Lemma and its Many Applications.- Convergent Sequences of Holomorphic Functions.- Polynomial and Rational Approximation—Runge Theory.- The Riemann Mapping Theorem.- Simple and Double Connectivity.- Isolated Singularities.- Omitted Values and Normal Families.- Bibliography.- Name Index.- Subject Index.- Symbol Index.- Index of Series Summed and Integrals Evaluated.
£94.99
Springer Reading Writing and Proving
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£44.99
Cambridge University Press Descriptive Complexity Canonisation and Definable Graph Structure Theory 47 Lecture Notes in Logic Series Number 47
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£147.25
Cambridge University Press 3264 and All That
Book SynopsisThis book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique so that the student develops the ability to solve geometric problems. It also contains abundant examples, exercises and solutions.Trade Review'… the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry| and more generally, for every mathematician interested in concrete algebraic geometry.' Arnaud Beauville, MathSciNetTable of ContentsIntroduction; 1. Introducing the Chow ring; 2. First examples; 3. Introduction to Grassmannians and lines in P3; 4. Grassmannians in general; 5. Chern classes; 6. Lines on hypersurfaces; 7. Singular elements of linear series; 8. Compactifying parameter spaces; 9. Projective bundles and their Chow rings; 10. Segre classes and varieties of linear spaces; 11. Contact problems; 12. Porteous' formula; 13. Excess intersections and the Chow ring of a blow-up; 14. The Grothendieck–Riemann–Roch theorem; Appendix A. The moving lemma; Appendix B. Direct images, cohomology and base change; Appendix C. Topology of algebraic varieties; Appendix D. Maps from curves to projective space; References; Index.
£87.40
Cambridge University Press Normal Approximations with Malliavin Calculus From Steins Method to Universality 192 Cambridge Tracts in Mathematics Series Number 192
Book SynopsisStein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, BreuerâMajor theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wiTrade Review'This monograph is a nice and excellent introduction to Malliavin calculus and its application to deducing quantitative central limit theorems in combination with Stein's method for normal approximation. It provides a self-contained and appealing presentation of the recent work developed by the authors, and it is well tailored for graduate students and researchers.' David Nualart, Mathematical Reviews'The book contains many examples and exercises which help the reader understand and assimilate the material. Also bibliographical comments at the end of each chapter provide useful references for further reading.' Bulletin of the American Mathematical SocietyTable of ContentsPreface; Introduction; 1. Malliavin operators in the one-dimensional case; 2. Malliavin operators and isonormal Gaussian processes; 3. Stein's method for one-dimensional normal approximations; 4. Multidimensional Stein's method; 5. Stein meets Malliavin: univariate normal approximations; 6. Multivariate normal approximations; 7. Exploring the Breuer–Major Theorem; 8. Computation of cumulants; 9. Exact asymptotics and optimal rates; 10. Density estimates; 11. Homogeneous sums and universality; Appendix 1. Gaussian elements, cumulants and Edgeworth expansions; Appendix 2. Hilbert space notation; Appendix 3. Distances between probability measures; Appendix 4. Fractional Brownian motion; Appendix 5. Some results from functional analysis; References; Index.
£68.39
Cambridge University Press Bayesian Cognitive Modeling
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£94.04
Cambridge University Press Formal Languages in Logic
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£85.50
Cambridge University Press Sets of Finite Perimeter and Geometric
Book SynopsisThis engaging graduate-level introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. Explanatory pictures, detailed proofs, exercises and helpful remarks make it suitable for self-study and also a useful reference for researchers.Trade Review'The book is a clear exposition of the theory of sets of finite perimeter, that introduces this topic in a very elegant and original way, and shows some deep and important results and applications … Although most of the results contained in this book are classical, some of them appear in this volume for the first time in book form, and even the more classical topics which one may find in several other books are presented here with a strong touch of originality which makes this book pretty unique … I strongly recommend this excellent book to every researcher or graduate student in the field of calculus of variations and geometric measure theory.' Alessio Figalli, Canadian Mathematical Society Notes'The first aim of the book is to provide an introduction for beginners to the theory of sets of finite perimeter, presenting results concerning the existence, symmetry, regularity and structure of singularities in some variational problems involving length and area … The secondary aim … is to provide a multi-leveled introduction to the study of other variational problems … an interested reader is able to enter with relative ease several parts of geometric measure theory and to apply some tools from this theory in the study of other problems from mathematics … This is a well-written book by a specialist in the field … It provides generous guidance to the reader [and] is recommended … not only to beginners who can find an up-to-date source in the field but also to specialists … It is an invitation to understand and to approach some deep and difficult problems from mathematics and physics.' Vasile Oproiu, Zentralblatt MATHTable of ContentsPart I. Radon Measures on Rn: 1. Outer measures; 2. Borel and Radon measures; 3. Hausdorff measures; 4. Radon measures and continuous functions; 5. Differentiation of Radon measures; 6. Two further applications of differentiation theory; 7. Lipschitz functions; 8. Area formula; 9. Gauss–Green theorem; 10. Rectifiable sets and blow-ups of Radon measures; 11. Tangential differentiability and the area formula; Part II. Sets of Finite Perimeter: 12. Sets of finite perimeter and the Direct Method; 13. The coarea formula and the approximation theorem; 14. The Euclidean isoperimetric problem; 15. Reduced boundary and De Giorgi's structure theorem; 16. Federer's theorem and comparison sets; 17. First and second variation of perimeter; 18. Slicing boundaries of sets of finite perimeter; 19. Equilibrium shapes of liquids and sessile drops; 20. Anisotropic surface energies; Part III. Regularity Theory and Analysis of Singularities: 21. (Λ, r0)-perimeter minimizers; 22. Excess and the height bound; 23. The Lipschitz approximation theorem; 24. The reverse Poincaré inequality; 25. Harmonic approximation and excess improvement; 26. Iteration, partial regularity, and singular sets; 27. Higher regularity theorems; 28. Analysis of singularities; Part IV. Minimizing Clusters: 29. Existence of minimizing clusters; 30. Regularity of minimizing clusters; References; Index.
£74.09
Cambridge University Press The Physics of Dilute Magnetic Alloys
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£118.75
Cambridge University Press Understanding Process Dynamics and Control
Book SynopsisPresenting a fresh look at process control, this new text demonstrates state-space approach shown in parallel with the traditional approach to explain the strategies used in industry today. Modern time-domain and traditional transform-domain methods are integrated throughout and explain the advantages and limitations of each approach; the fundamental theoretical concepts and methods of process control are applied to practical problems. To ensure understanding of the mathematical calculations involved, MATLAB is included for numeric calculations and MAPLE for symbolic calculations, with the math behind every method carefully explained so that students develop a clear understanding of how and why the software tools work. Written for a one-semester course with optional advanced-level material, features include solved examples, cases that include a number of chemical reactor examples, chapter summaries, key terms, and concepts, as well as over 240 end-of-chapter problems, focused computatiTrade Review'Provides a fresh perspective through the integrated coverage of modern state-space and traditional transfer function approaches. The mathematical derivations are detailed and accessible, aiding clear understanding of the basic as well as the more advanced topics.' Prodromos Daoutidis, University of Minnesota'Breaking new ground in the crowded field of process control textbooks, this book provides the foundation for teaching a modern undergraduate process control course in the twenty-first century. It is exceptionally well written and organized, and includes numerous examples, making it a must-have for all process control researchers, students and engineers.' Panagiotis D. Christofides, University of California, Los AngelesTable of ContentsContents; Preface; 1. Introduction; 2. Dynamic Models for Chemical Process Systems; 3. First Order Systems; 4. Connections of First Order Systems; 5. Second Order Systems; 6. Linear Higher Order Systems; 7. Eigenvalue Analysis – Asymptotic Stability; 8. Transfer Function Analysis of the Input/Output Behavior; 9. Frequency Response; 10. The Feedback Control System; 11. Block Diagram Reduction and Transient Response Calculation in a Feedback Control System; 12. Steady-State and Stability Analysis of the Closed Loop System; 13. State Space Description and Analysis of the Closed Loop System; 14. Systems with Dead Time; 15. Parametric Analysis of Closed Loop Dynamics – Root Locus Diagrams; 16. Optimal Selection of Controller Parameters; 17. Bode and Nyquist Stability Criteria – Gain and Phase Margins; 18. Multiple-Input-Multiple-Output Systems; 19. Synthesis of Model-Based Feedback Controllers; 20. Cascade, Ratio and Feedforward Control; Appendix A; Appendix B.
£90.24
Cambridge University Press Vehicular Networking
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£89.29
Cambridge University Press Pericles Prince of Tyre The New Cambridge
Book SynopsisThe Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.Table of ContentsPreface; 1. Basic notions; 2. Capacity; 3. Boundary behavior; 4. Zero sets; 5. Multipliers; 6. Conformal invariance; 7. Harmonically weighted Dirichlet spaces; 8. Invariant subspaces; 9. Cyclicity; Appendix A. Hardy spaces; Appendix B. The Hardy–Littlewood maximal function; Appendix C. Positive definite matrices; Appendix D. Regularization and the rising-sun lemma; References; Index of notation; Index.
£60.79
Cambridge University Press Fluid Dynamics
Book SynopsisThis book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the NavierâStokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the bTable of Contents1. Introduction; 2. Eulerian and Lagrangian viewpoints, paths and streamlines; 3. Stream function; 4. Helmholtz decomposition; 5. Sources, sinks and vortices; 6. Doublets and their applications; 7. Complex potential; 8. Accelerating reference frames; 9. Fluids at rest; 10. Incompressibility and mass conservation; 11. Stress tensor - existence and symmetry; 12. Stress tensor in Newtonian fluids; 13. Navier–Stokes equation; 14. Thermodynamic considerations; 15. Energy equation; 16. Complete equations of motion; 17. Applications of Bernoulli's equation and control volumes; 18. Vorticity; 19. Applications to viscous flow; 20. Laminar boundary layers; 21. Some applications to convective heat and mass transfer.
£60.29
Cambridge University Press The Surprising Mathematics of Longest Increasing Subsequences 4 Institute of Mathematical Statistics Textbooks Series Number 4
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£80.75
Cambridge University Press Mathematical Methods in the Earth and
Book SynopsisThe Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB, this book supports readers in applying appropriate analytical or computational methods to solving real research questioTable of ContentsPreface; 1. Estimation and dimensional analysis; 2. Derivatives and integrals; 3. Series and summations; 4. Scalars, vectors, and matrices; 5. Probability; 6. Ordinary differential equations; 7. Vectors and calculus; 8. Special functions; 9. Fourier series and integral transforms; 10. Partial differential equations; 11. Tensors; Appendix A. Units and dimensions; Appendix B. Tables of useful formulae; Appendix C. Complex numbers; Notes; References; Index.
£52.24
Cambridge University Press Inside Mathforum.Org
Book SynopsisThe internet has dramatically transformed social space and time for many people in many different contexts. This dramatic warping of the social fabric has happened slowly over time as digital technologies have evolved and internet speeds have increased. While we are all aware of these changes, the impact is often little understood. There are few monographs about social groups made possible by the internet, and even fewer about educational communities made possible through digital technologies. Inside Mathforum.org details the ways that digital media are used to enhance the practices that teachers and students of mathematics engage in. The book also shows how different kinds of mathematical conversations and interactions become possible through the digital media. Unlike many other educational uses of digital media, the Math Forum''s community has provided online resources and sustained support for teachers and students, and it leads the way in showing the power of digital media for educTrade Review'This case study of The Math Forum highlights the contributions to mathematics education made by this online math resource center, making clear the essential components of the technology, invisible elements of the social structure its design invites and supports, and the cultural elements (e.g., values, ethos) that affected its original design and that have sustained its life over two decades. Shumar's analysis suggests lessons about building and sustaining communities of practice that have implications for teacher learning, online education more generally, and design of a wide range of other spaces for transformation.' Janet L. Kolodner, Chief Learning Scientist, Concord Consortium'One of the pleasures of reading Shumar's ethnography, Inside Mathforum.org, is the care he takes in portraying how larger neoliberal structures, digital technologies, and the affordances of the Math forum community unfold over the long term, almost twenty years. This portrait shows different strategic moments in the existence of Tthe Math Forum whose creative staff and online participants facilitate the emergence of community spaces both in spite of and because of the increasing commodification of the university. Rather than situate himself against some literature, his more intellectually generous approach is to use that literature to generate a sense of a broad interdisciplinary field where both structure, agency, and indeterminacy allow us to understand the potential for learning and pitfalls for organization faced by the Math Forum. Brilliant ideas and exegesis emerge on every page.' Jonathan Church, Arcadia University, Pennsylvania'Many years before Khan Academy, a distributed network of math educators were conducting Problems of the Week and inspiring learners. In my online learning communities courses, I've always enjoyed teaching with Wesley Shumar's ethnographic research writings on the pioneering Math Forum. This book now provides the ultimate resource on this seminal effort for spawning and sustaining community discourse about mathematics.' Roy Pea, Stanford University, California'Shumar presents a well-researched analysis of the political and cultural impacts to and the contributions of MathForum.org, as well as the broader scope of the internet in education. An ethnography in method and style, the book is organized in concise, yet dense, sections, offering a discussion that spans ethnography to neoliberalism. The inclusion of figures from the Forum, including the grading rubric and mentoring example, assist in transforming the community from an abstract idea to a tangible place of learning.' C. R. Hebert, ChoiceTable of Contents1. Introduction; 2. Ethnography with a leading internet-based educational center; 3. History of the Math Forum; 4. Possibilities and their foreclosure in the digital educational economy; 5. Mathematical conversations and mathematical thinking; 6. Mentoring students and faculty with digital technology; 7. Noticing and wondering in a mediated environment; 8. Space, affinity, and consciousness; 9. Identity and online interaction; 10. Conclusion; References; Index.
£999.99
Cambridge University Press Probability Theory and Statistical Inference
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£94.99
Cambridge University Press Fourier Analysis 85 London Mathematical Society Student Texts Series Number 85
Book SynopsisFourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course Trade Review'[Fourier Analysis: Volume l - Theory is] fabulous … Constantin structures his exercise sets beautifully, I think: they are abundant and long, covering a spectrum of levels of difficulty; each set is followed immediately by a section of hints (in one-one correspondence); finally the hints sections are followed by very detailed and well-written solutions (also bijectively). Can there be any clearer homage to the maxim that to learn mathematics one has to get one's hands really dirty? To boot, attention to detail is ubiquitous: it's everywhere in Constantin's presentation of proofs and arguments, as well as examples, all throughout the narrative itself. The entire presentation is very much to the point and the student who works through this book will come out knowing some real mathematics very well.' Michael Berg, MAA ReviewsTable of Contents1. Introduction; 2. The Lebesgue measure and integral; 3. Elements of functional analysis; 4. Convergence results for Fourier series; 5. Fourier transforms; 6. Multi-dimensional Fourier analysis; 7. A glance at some advanced topics; Appendix: historical notes; References; Index.
£42.74
Cambridge University Press The Prisoners Dilemma
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£26.99
Cambridge University Press Teaching Statistics
Book SynopsisStatistics has developed in parallel with the advances of technological and social change. Informed by the work of the Cambridge Mathematics team, this book outlines a new pedagogical approach to teaching statistics. It frames the interconnectedness of the subject around the experiences that students should have, rather than the specific techniques required. The book provides numerous examples and suggestions that teachers can incorporate in the classroom to help improve the way students understand statistics.Table of ContentsIntroduction; Part 1 A vision for statistics in schools: 1. What should all students understand and why is it important?; 2. The statistical cycle; 3. Exploratory data analysis; 4. Simulation; 5. Sampling and variation; 6. Signals and noise; 7. Informal inference; 8. Technology in the classroom; Part 2 Activities; 9. Activity for Chapter 2; 10. Activity for Chapter 3; 11. Activities for Chapter 4; 12. Activities for Chapter 5; 13. Activity for Chapter 6; 14. Activity for Chapter 7; Appendix 1; Appendix 2; Index.
£24.75
Cambridge University Press The Students Introduction to Mathematica and the
Book SynopsisThe unique feature of this compact student''s introduction to Mathematica and the Wolfram Language is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.Trade Review'This book is an easy-to-read introduction to Mathematica. It is interspersed with helpful hints that make interacting with Mathematica more efficient and examples to test the reader's comprehension. This book is good for learning how to use Mathematica to graph functions, perform algebraic manipulation, and approach topics from calculus and linear algebra. This new version shines some light on entity objects and accessing Wolfram's curated data which is needed because their structure is unintuitive and because of their growing prominence in the Wolfram ecosystem. The new final chapter on 3D printing gives readers the tools to quickly design and 3D print physical objects that embody mathematical surfaces. These two additions showcase recent advances in the Wolfram Language and ensure that the whole book remains relevant and up to date.' Christopher Hanusa, Queens College, City University of New York'Mathematica has the power to unravel some of the current mysteries of mathematics – but only if you know how to ask it the right questions. The 3rd edition of The Student's Introduction to Mathematica and the Wolfram Language can be your well-used guide for such exploration. Beginning and experienced Mathematica users will easily learn from the pages of this book especially given the recent changes to Mathematica. Even more, the 3rd edition moves into a new dimension, giving details on 3D printing! Grab one for yourself and another for a student you know.' Tim Chartier, Davidson College, North Carolina'This text, including the exercises and solutions, is written in a student-friendly style … Unlike most tutorial introductions to Mathematica, the authors go to significant lengths to provide explanations and rationales underlying what a newcomer would likely find confusing … I believe that this book would be a useful addition to any student's library in a college or university that uses Mathematica.' Marvin Schaefer, MAA ReviewsTable of ContentsPreface; 1. Getting started; 2. Working with Mathematica®; 3. Functions and their graphs; 4. Algebra; 5. Calculus; 6. Multivariable calculus; 7. Linear algebra; 8. Programming; 9. 3D printing; Index.
£44.64
Cambridge University Press Finite Elements
Book SynopsisWritten in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.Trade Review'The book is written in a very traditional and straightforward style of theory and proof. The organization of the material makes it accessible for the reader to gain a foundational understanding of the topics … This book provides a readable, concise introduction to finite elements. Summing Up: Recommended.' S. L. Sullivan, CHOICETable of ContentsPreface; 1. Sobolev spaces; 1.1. Banach and Hilbert spaces; 1.2. Weak derivatives; 1.3. Sobolev spaces; 2. Elliptic scalar problems; 2.1. A general elliptic problem of second order; 2.2. Weak solution; 2.3. Standard Galerkin method; 2.4. Abstract error estimate; 3. Finite element spaces; 3.1. Simplices and barycentric coordinates; 3.2. Simplicial finite elements and local spaces; 3.3. Construction of finite elements spaces; 3.4. The concept of mapped finite elements: affine mappings; 3.5. Finite elements on rectangular and brick meshes; 3.6. Mapped finite elements: general bijective mappings; 3.7. Mapped Qk finite elements; 3.8. Isoparametric finite elements; 3.9. Further examples of finite elements in C0 and C1; 4. Interpolation and discretization error; 4.1. Transformation formulas; 4.2. Affine equivalent finite elements; 4.3. Canonical interpolation; 4.4. Local and global interpolation error; 4.5. Improved L2 error estimates by duality; 4.6. Interpolation of less smooth functions; 5. Biharmonic equation; 5.1. Deflection of a thin clamped plate; 5.2. Weak formulation of the biharmonic equation; 5.3. Conforming finite element methods; 5.4. Nonconforming finite element methods; 6. Parabolic problems; 6.1. Conservation of energy; 6.2. A general parabolic problem of initial boundary value problems; 6.3. Weak formulation of initial boundary value problems; 6.4. Semidiscretization by finite elements; 6.5. Time discretization; 6.6. Finite elements for high-dimensional parabolic problems; 7. Systems in solid mechanics; 7.1. Linear elasticity; 7.2. Mindlin–Reissner plate; 8. Systems in fluid mechanics; 8.1. Conservation of mass and momentum; 8.2. Weak formulation of the Stokes problem; 8.3. Conforming discretizations of the Stokes problem; 8.4. Nonconforming discretizations of the Stokes problem; 8.5. The nonconforming Crouzeix–Raviart element; 8.6. Further inf–sup stable finite element pairs; 8.7. Equal order stabilized finite elements; 8.8. Navier–Stokes problem with mixed boundary conditions; 8.9. Time discretization and linearization of the Navier–Stokes problem; 9. Implementation of the finite element method; 9.1. Mesh handling and data structure; 9.2. Numerical integration; 9.3. Sparse matrix storage; 9.4. Assembling of system matrices and load vectors; 9.5. Inclusion of boundary conditions; 9.6. Solution of the algebraic systems; 9.7. Object-oriented C++ programming; Bibliography; Index.
£53.19
Cambridge University Press Geomathematics
Book SynopsisGeomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, covering the foundations of gravimetry, geomagnetics and seismology. Theorems and their proofs explain why physical realities in geoscience are the logical mathematical consequences of basic laws. The book also derives and analyzes the theory and numerical aspects of established systems of basis functions; and presents an algorithm for combining different types of trial functions. Topics cover inverse problems and their regularization, the Laplace/Poisson equation, boundary-value problems, foundations of potential theory, the Poisson integral formula, spherical harmonics, Legendre polynomials and functions, radial basis functions, the Biot-Savart law, decomposition theorems (orthogonal, Helmholtz, and Mie), basics of continuum mechanics, conservation laws, modelling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapter ends with review questions, with solutions for instructors available online, providing a valuable reference for graduate students and researchers.Table of Contents1. Introduction; 2. Required Mathematical Basics; 3. Gravitation and Harmonic Functions; 4. Basis Functions; 5. Inverse Problems; 6. The Magnetic Field; 7. Mathematical Models in Seismology; Appendix A. Hints for the Exercises; Appendix B. Questions for Understanding; References; Index.
£999.99
Cambridge University Press A First Course in Differential Geometry
a huge range and FREE tracked UK delivery on ALL orders.
£69.34
Cambridge University Press Electronic Structure
Book SynopsisThe study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.Trade Review'… this 2nd edition is … very welcome and timely, as it has been significantly expanded to cover the 'new' topics. The core of the book remains unchanged in scope, focusing on 'independent particle methods' such as DFT and Hartree-Fock theory, and their extensions. This is … a worthy … and is strongly recommended for anyone working in the field of electronic structure.' Matt Probert, Contemporary PhysicsTable of ContentsPreface; Acknowledgments; Notation; Part I. Overview and background topics: 1. Introduction; 2. Overview; 3. Theoretical background; 4. Periodic solids and electron bands; 5. Uniform electron gas and sp-bonded metals; Part II. Density functional theory: 6. Density functional theory: foundations; 7. The Kohn–Sham auxiliary system; 8. Functionals for exchange and correlation I; 9. Functionals for exchange and correlation II; Part III. Important preliminaries on atoms: 10. Electronic structure of atoms; 11. Pseudopotentials; Part IV. Determination of electronic structure: the basic methods: 12. Plane waves and grids: basics; 13. Plane waves and real space methods: full calculations; 14. Localized orbitals: tight-binding; 15. Localized orbitals: full calculations; 16. Augmented functions: APW, KKR, MTO; 17. Augmented functions: linear methods; 18. Locality and linear scaling O(N) methods; Part V. From Electronic Structure to Properties of Matter: 19. Quantum molecular dynamics (QMD); 20. Response functions: phonons, magnons, . . .; 21. Excitation spectra and optical properties; 22. Surfaces, interfaces, and lower dimensional systems; 23. Wannier functions; 24. Polarization, localization, and Berry phases; Part VI. Electronic Structure and Topology: 25. Topology of the electronic structure of a crystal: introduction; 26. Two band models: Berry phase, winding and topology; 27. Topological insulators I: Two dimensions; 28. Topological insulators II: Three dimensions; Part VII. APPENDICES: A. Functional equations; B. LSDA and GGA functionals; C. Adiabatic approximation; D. Perturbation Theory, response functions and Green's functions; E. Dielectric functions and optical properties; F. Coulomb interactions in extended systems; G. Stress from electronic structure; H. Energy and stress densities; I. Alternative force expressions; J. Scattering and phase shifts; K. Useful relations and formulas; L. Numerical methods; M. Iterative methods in electronic structure; N. Two-center matrix elements: expressions for arbitrary angular momentum l; O. Dirac equation and spin-orbit interaction; P. Berry phase, curvature and Chern numbers; Q. Quantum Hall effect and edge conductivity; R. Codes for electronic structure calculations for solids; References; Index.
£65.54
Cambridge University Press Stable Levy Processes via LampertiType
Book SynopsisStable Lévy processes lie at the intersection of Lévy processes and self-similar Markov processes. Processes in the latter class enjoy a Lamperti-type representation as the space-time path transformation of so-called Markov additive processes (MAPs). This completely new mathematical treatment takes advantage of the fact that the underlying MAP for stable processes can be explicitly described in one dimension and semi-explicitly described in higher dimensions, and uses this approach to catalogue a large number of explicit results describing the path fluctuations of stable Lévy processes in one and higher dimensions. Written for graduate students and researchers in the field, this book systemically establishes many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material. Topics explored include first hitting laws for a variety of sets, path conditionings, law-preserving path transformations, the distribution of eTrade Review'This treatise takes readers on a superb journey through the fascinating worlds of stable Lévy processes and of a rich variety of further naturally related random processes. Andreas Kyprianou and Juan Carlos Pardo masterfully deploy an arsenal of techniques, which are already interesting on their own right, to reveal many classical or more recent high level results on the distributions of functionals and on the path behaviours stable processes. It is indeed remarkable that their methods lead to so many explicit formulas, some amazingly simple, some more complex. The authors should be praised for making accessible as a coherent whole a vast literature that has been developed over several decades, including the latest developments.' Jean Bertoin, University of ZurichTable of Contents1. Stable distributions; 2. Lévy processes; 3. Stable processes; 4. Hypergeometric Lévy processes; 5. Positive self-similar Markov processes; 6. Spatial fluctuations in one dimension; 7. Doney–Kuznetsov factorisation and the maximum; 8. Asymptotic behaviour for stable processes; 9. Envelopes of positive self-similar Markov processes; 10. Asymptotic behaviour for path transformations; 11. Markov additive and self-similar Markov processes; 12. Stable processes as self-similar Markov processes; 13. Radial reflection and the deep factorisation; 14. Spatial fluctuations and the unit sphere; 15. Applications of radial excursion theory; 16. Windings and up-crossings of stable processes; Appendix.
£52.19
Cambridge University Press Algorithms for Convex Optimization
Book SynopsisIn the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.Trade Review'The field of mathematical programming has two major themes: linear programming and convex programming. The far-reaching impact of the first theory in computer science, game theory and engineering is well known. We are now witnessing the growth of the second theory as it finds its way into diverse fields such as machine learning, mathematical economics and quantum computing. This much-awaited book with its unique approach, steeped in the modern theory of algorithms, will go a long way in making this happen.' Vijay V. Vazirani, Distinguished Professor at University of California, Irvine'I had thought that there is no need for new books about convex optimization but this book proves me wrong. It treats both classic and cutting-edge topics with an unparalleled mix of clarity and rigor, building intuitions about key ideas and algorithms driving the field. A must read for anyone interested in optimization!' Aleksander Madry, Massachusetts Institute of Technology'Vishnoi's book provides an exceptionally good introduction to convex optimization for students and researchers in computer science, operations research, and discrete optimization. The book gives a comprehensive introduction to classical results as well as to some of the most recent developments. Concepts and ideas are introduced from first principles, conveying helpful intuitions. There is significant emphasis on bridging continuous and discrete optimization, in particular, on recent breakthroughs on flow problems using convex optimization methods; the book starts with an enlightening overview of the interplay between these areas.' László Végh, LSE'Recommended.' M. Bona, Choice ConnectTable of Contents1. Bridging continuous and discrete optimization; 2. Preliminaries; 3. Convexity; 4. Convex optimization and efficiency; 5. Duality and optimality; 6. Gradient descent; 7. Mirror descent and multiplicative weights update; 8. Accelerated gradient descent; 9. Newton's method; 10. An interior point method for linear programming; 11. Variants of the interior point method and self-concordance; 12. Ellipsoid method for linear programming; 13. Ellipsoid method for convex optimization.
£75.99
Cambridge University Press Modular Theory in Operator Algebras
Book SynopsisThe first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by S.V. Stratila and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu''s result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.Table of ContentsPreface to the second edition; Preface to the first edition; 1. Normal weights; 2. Conditional expectations and operator valued weights; 3. Groups of automorphisms; 4. Crossed products; 5. Continuous decompositions; 6. Discrete decompositions; Appendix; References; Subject Index; Notation Index.
£108.00
Cambridge University Press Mathematics and Its Logics
Book SynopsisIn these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman''s modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.Table of ContentsIntroduction; Part I. Structuralism, Extendability, and Nominalism: 1. Structuralism without Structures?; 2. What Is Categorical Structuralism?; 3. On the Significance of the Burali-Forti Paradox; 4. Extending the Iterative Conception of Set: A Height-Potentialist Perspective; 5. On Nominalism; 6. Maoist Mathematics? Critical Study of John Burgess and Gideon Rosen, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics (Oxford, 1997); Part II. Predicative Mathematics and Beyond: 7. Predicative Foundations of Arithmetic (with Solomon Feferman); 8. Challenges to Predicative Foundations of Arithmetic (with Solomon Feferman); 9. Predicativism as a Philosophical Position; 10. On the Gödel-Friedman Program; Part III. Logics of Mathematics: 11. Logical Truth by Linguistic Convention; 12. Never Say 'Never'! On the Communication Problem between Intuitionism and Classicism; 13. Constructive Mathematics and Quantum Mechanics: Unbounded Operators and the Spectral Theorem; 14. If 'If-Then' Then What?; 15. Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis.
£75.99
Cambridge University Press Stochastic Modelling of ReactionDiffusion Processes
a huge range and FREE tracked UK delivery on ALL orders.
£104.50
Cambridge University Press Zeta and LFunctions of Varieties and Motives
Book SynopsisZeta and L-functions have played a major part in the development of number theory. This book for graduate students and researchers presents a big picture of some key results and surrounding theory, whilst taking the reader on a journey through the history of their development.Trade Review'The book will be of interest to both young mathematicians and physicists as well as experienced scholars.' Nikolaj M. Glazunov, zbMATH OpenTable of ContentsIntroduction; 1. The Riemann zeta function; 2. The zeta function of a Z-scheme of finite type; 3. The Weil Conjectures; 4. L-functions from number theory; 5. L-functions from geometry; 6. Motives; Appendix A. Karoubian and monoidal categories; Appendix B. Triangulated categories, derived categories, and perfect complexes; Appendix C. List of exercises; Bibliography; Index.
£62.17
Cambridge University Press The Metaphysics and Mathematics of Arbitrary Objects
Book SynopsisBuilding 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. Hisbook 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.Trade Review'For the initiated reader, the book promises to add new life to research on arbitrary objects.' R. L. Pour, ChoiceTable of Contents1. Introduction; 2. Metaphysics of mathematics; 3. Arbitrary objects; 4. Mathematical objects as arbitrary objects; 5. Structure in mathematics; 6. Mathematical structures; 7. Kit fine; 8. Generic systems and mathematical structuralism; 9. Reasoning about generic w-sequences; 10. Probability and random variables; 11. Directions for future research.
£29.44
Cambridge University Press An Invitation to Applied Category Theory
Book SynopsisCategory theory reveals commonalities between structures of all sorts. This self-contained tour of applied category theory shows its potential in science, engineering, and beyond. Each chapter discusses a real-world application using category-theoretic tools, all of which are introduced in an accessible way with many examples and exercises.Trade Review'Category theory was always applied, but traditionally within pure mathematics. Now it is being used to clarify and synthesize a broad range of topics outside mathematics: from computer science to linguistics, from quantum theory to chemistry, and beyond. Charmingly informal yet crystal clear, Fong and Spivak's book does a wonderful job of demonstrating the power of category theory to beginners – even beginners without much background in pure mathematics.' John Baez, University of California, Riverside'The authors quite rightly describe category theory as a tool for thinking. So if your work requires thinking, this book is for you.' Bartosz Milewski, author of Category Theory for Programmers'This book provides a fantastic introduction to how category is not just abstract nonsense but can be applied to real-world engineering problems, pedagogical while still broad, and fun. A must read for all those entering the exciting emerging field of applied category theory by two key players of this community.' Bob Coecke, University of Oxford'An invitation to Applied Category Theory: Seven Sketches in Compositionality provides a grand tour of the fascinating emergent field of applied category theory that centers examples and use cases before gently introducing the accompanying abstract notions. Fong and Spivak should be congratulated for providing this accessible broad viewpoint to illustrate what category theory is all about vis-à-vis the real world.' Emily Riehl, The Johns Hopkins University'An Invitation to Applied Category Theory is clearly and entertainingly written, and provides a great entry into the world of applied category theory. It is chock full of concrete examples and illustrated with clear diagrams … Fong and Spivak will whet your appetite for learning about categories and how they - and the categorical way of thinking - can be applied in and beyond mathematics. And they will give you the means to do that in a self-contained text.' David Jaz Myers, MAA Reviews'Fong and Spivak's book is highly recommendable for anyone with even a passing interest in category theory in general. And it is mandatory reading for scholars aiming to apply category theory to real world problems.' Fernando A. Tohme, MathSciNet'The presentation is highly visual, employing graphs (nodes and edges), directed graphs, and hypergraphs. In addition, exercises intersperse each presentation, and the solutions to many of the exercises are included. Finally, the chapters include concluding summaries, with suggestions for further study. The book contains scores of references. In short, an excellent self-study resource for those interested in learning about applications of category theory to real-world problems.' J. T. Saccoman, Choice'… highly recommended.' Berthold Stoge, IUCr Journals CRYSTALLOGRAPHY JOURNALS ONLINETable of ContentsPreface; 1. Generative effects: orders and Galois connections; 2. Resource theories: monoidal preorders and enrichment; 3. Databases: categories, functors, and universal constructions; 4. Collaborative design: profunctors, categorification, and monoidal categories; 5. Signal flow graphs: props, presentations, and proofs; 6. Electric circuits: hypergraph categories and operads; 7. Logic of behavior: sheaves, toposes, and internal languages; Appendix. Exercise solutions; References; Index.
£41.79
Cambridge University Press Ontology and the Foundations of Mathematics
Book SynopsisThis Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem the problem of how knowable mathematical truths are identifiable with a reality independent of us as knowers. Specifically, if the only access problem acknowledged is the epistemological problem i.e. the problem of how we come to know mathematical truths then nothing is gained by the realist notion of an independent reality and in effect, nothing distinguishes realism from anti-realism in mathematics.Table of Contents1. What are we Talking about?; 2. Inter-translatability; 3. Two Access Problems; 4. Independence; 5. Justification.
£17.00
Cambridge University Press Applied Mixed Model Analysis
Book SynopsisThis book explains all aspects of mixed model analysis without mathematical jargon, so that non-statisticians can understand the basic principles, analyze their own data, and interpret the results with confidence. Worked examples are analyzed with STATA, and all datasets are available for download, equipping readers to replicate the methods.Table of Contents1. Introduction; 2. Basic principles of mixed model analysis; 3. What is gained by using mixed model analysis?; 4. Logistic mixed model analysis; 5. Mixed model analysis with other outcomes; 6. Explaining differences between groups; 7. Multivariable modelling; 8. Predictions based on mixed model analysis; 9. Mixed model analysis for longitudinal data; 10. Multivariate mixed model analysis; 11. Sample size calculations; 12. Some loose ends.
£47.49
Cambridge University Press Learning Scientific Programming with Python
Book SynopsisLearn to master basic programming tasks from scratch with real-life, scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to gain proficiency quickly. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving on to the NumPy, SciPy and Matplotlib libraries for numerical programming and data visualization, this textbook also discusses the use of Jupyter Notebooks to build rich-media, shareable documents for scientific analysis. The second edition features a new chapter on data analysis with the pandas library and comprehensive updates, and new exercises and examples. A final chapter introduces more advanced topics such as floating-pTable of ContentsAcknowledgments; 1. Introduction; 2. The core Python language I; 3. Interlude: simple plots and charts; 4. The core Python language II; 5. IPython and Jupyter Notebook; 6. NumPy; 7. Matplotlib; 8. SciPy; 9. Data analysis with pandas; 10. General scientific programming; Appendix A. Solutions; Appendix B. Differences between Python versions 2 and 3; Appendix C. SciPy's odeint ordinary differential equation solver; Glossary; Index.
£36.09
Cambridge University Press Coend Calculus
Book SynopsisThe language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.Table of ContentsPreface; 1. Dinaturality and (co)ends; 2. Yoneda and Kan; 3. Nerves and realisations; 4. Weighted (co)limits; 5. Profunctors; 6. Operads; 7. Higher dimensional (co)ends; Appendix A. Review of category theory; Appendix B; References; Index.
£55.09
