Maths for scientists Books

Book SynopsisThis highly acclaimed undergraduate textbook teaches all the mathematics for undergraduate courses in the physical sciences. Containing over 800 exercises, half come with hints and answers and, in a separate manual, complete worked solutions. The remaining exercises are intended for unaided homework; full solutions are available to instructors.Trade ReviewFrom reviews of previous editions: '…a great scientific textbook. It is a tour de force … to write mathematical sections that are both complete and at an appropriate academic level. The authors have clearly succeeded in this challenge, making this a remarkable pedagogical book … The choice of exercises is excellent and possibly the best feature of the book. In summary, this textbook is a great reference at undergraduate levels, particularly for those who like to teach or learn using lots of examples and exercises.' R. Botet, European Journal of Physics'… the book provides scientists who need to use the tool of mathematics for practical purposes with a single, comprehensive book. I recommend this book not only to students in physics and engineering sciences, but also to students in other fields of natural sciences.' P. Steward, Optik'… suitable as a textbook for undergraduate use … this is a book that in view of its content and its modest softcover price, will find its way on to many bookshelves.' Nigel Steele, The Times Higher Education Supplement'Riley et al. has clear, thorough and straightforward explanations of the subjects treated. It rigorously adopts a three-stage approach throughout the book: first a heuristic, intuitive introduction, then a formal treatment, and finally one or two examples. This consistent presentation, the layout, and the print quality make the book most attractive … and value for money. It contains a thousand pages, there are plenty of exercises with each chapter.' J. M. Thijssen, European Journal of PhysicsThis is a valuable book with great potential use in present-day university physics courses. Furthermore, the book will be useful for graduate too, and researchers will find it useful for looking up material which they have forgotten since their undergraduate days.' J. M. Thijssen, European Journal of Physics'This textbook is a well-written, modern, comprehensive, and complete collection of topics in mathematical methods ranging from a review of differential and integral calculus to group and representation theory, probability, the calculus of variations, and tensors.' Science Books and Films'This is a very comprehensive textbook suitable for most students enrolling on undergraduate degree courses in engineering. It contains 31 stand-alone chapters of mathematical methods which enable the students to understand the principles of the basic mathematical techniques and the authors have produced a clear, thorough and straightforward explanation of each subject. … finding a single textbook which covers the engineering student's need throughout their entire course is by no means an easy task. I believe the authors have achieved it … complete fully worked solutions … which I think is a useful asset for both students and lecturers.' Civil Engineering' ... this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics ever likely to be needed for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics covered and many worked examples, it contains more than 800 exercises.' L'enseignement mathematiqueTable of ContentsPrefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Read more less

Book SynopsisExam Board: SQALevel: HigherSubject: ChemistryFirst Teaching: September 2014First Exam: Summer 2015Ideal practice material for one of the most challenging areas for Higher Chemistry candidates.This edition of Test Your Higher Chemistry Calculations provides:> Extensive overview of all types of questions likely to be tested> Exploration of the theory behind each topic in each chapter> Worked examples and problems

Read more less

Book SynopsisA refreshing, student-focused introduction to the use of statistics in the study of the biosciences. Emphasising why statistical techniques are essential tools for bioscientists, Biomeasurement removes the stigma attached to statistics by giving students the confidence to use key techniques for themselves.Trade ReviewReview from previous edition Biomeasurement does a wonderful job of keeping the biology the focus of analysis, and highlighting the fact that statistics is simply another useful tool to help biological understanding. * Dr Shane Richards, Biological and Biomedical Sciences, University of Durham, UK *This book represents the best I have seen for teaching undergraduate biologists statistics. * Dr Chris Venditti, Department of Biological Sciences, University of Hull, UK *It demystifies and clarifies topics that students can normally find confusing and challenging. It is a must for biologists! * Dr Maria G. Tuohy, School of Natural Sciences, National University of Ireland, Galway *This book was a blessing when I got it for my first year, and I'm still finding it helpful in my second year! It is so easy to navigate; you can read it cover to cover if you are very confused, or just dip into the topics you need. I would definitely recommend it to any students doing a bioscience degree which involves statistical elements. * Bethany Richmond, student at the University of Warwick *As a student with limited mathematical ability, new to statistics who believed I would not be able to pass this module, I read this book chapter by chapter prior to my weekly lectures and everything fell into place without a struggle. A 100% necessary purchase. A 100% necessary read. The book is appealing and very easy to navigate. I have tried to read other statistics books aimed at beginners but this was the only book which I clearly understood. * Julie Carter, student at Anglia Ruskin University *Table of Contents1: Why am I reading this book?2: Getting to grips with the basics3: Describing a single sample4: Inferring and estimating5: Choosing the right test and graph6: Overview of null hypothesis significance testing7: Tests on frequencies8: Tests of difference: two unrelated samples9: Tests of difference: two related samples10: Tests of difference: more than two samples11: Tests of relationship: regression12: Tests of relationship: correlation13: Introducing the generalized linear model: general linear model14: More on the generalized linear model: logistic and loglinear modelsAppendix I How to enter data into SPSSAppendix II Statistical tables of critical valuesAppendix III Summary guidance on reporting statistical resultsAppendix IV Statistics and experimental designRelated Titles

Read more less

Book SynopsisIf your students struggle with standard deviation, statistical tests and logarithmic functions, this is the book for them. This textbook companion will help improve their essential maths skills for biology, whichever awarding body specification you''re following. You can use it throughout the course, whenever you feel they need some extra help.- Develop understanding of both maths and biology with all worked examples and questions within a biology context- Improve confidence with a step-by-step approach to every maths skill- Measure progress with guided and non-guided questions - Understand misconceptions with full worked solutions to every question - Feel confident in expert guidance from experienced teacher and former Senior Examiner Dan Foulder

Read more less

Book SynopsisMathematical science communication, as well as the field of science communication in general, has gained momentum over the last few decades. Mathematical science communication aims to inform the public about contemporary research, enhance factual and methodological knowledge, and foster a greater interest and support for the science of mathematics. This enables the public to apply it to their practical life, and to decision-making on a greater scale. These objectives are met in the various formats and media through which mathematical science communication is brought to the public.The first 13 chapters of the book consist of best-practice examples from the areas of informal math education, museums and exhibitions, and the arts. The final 5 chapters discuss the structural aspects of mathematical science communication and contribute to the basis for its theoretical framework.

Read more less

Book SynopsisThis concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics and computer science majors, it emphasizes applications, offering more than 200 exercises to help students test their grasp of the material and providing answers to selected exercises. 1991 edition.

Read more less

Book SynopsisStatistics for Engineers and Scientists stands out for its clear presentation of applied statistics. The book takes a practical approach to methods of statistical modeling and data analysis that are most often used in scientific work. This edition features a unique approach highlighted by an engaging writing style that explains difficult concepts clearly, along with the use of contemporary real world data sets, to help motivate students and show direct connections to industry and research. While focusing on practical applications of statistics, the text makes extensive use of examples to motivate fundamental concepts and to develop intuition.The new edition of Statistics for Engineers and Scientists is also available in McGraw Hill Connect, featuring SmartBook 2.0, Adaptive Learning Assignments, and more!Table of ContentsChapter 1: Sampling and Descriptive StatisticsChapter 2: ProbabilityChapter 3: Propagation of ErrorChapter 4: Commonly Used DistributionsChapter 5: Confidence IntervalsChapter 6: Hypothesis TestingChapter 7: Correlation and Simple Linear RegressionChapter 8: Multiple RegressionChapter 9: Factorial ExperimentsChapter 10: Statistical Quality Control

Read more less

Book SynopsisTough Test Questions? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's.More than 40 million students have trusted Schaum's Outlines to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you: Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.Table of Contents Schaum's Outline of Advanced Mathematics for Engineers and Scientists 1.Review of Fundamental Concepts 2.Ordinary Differential Equations 3.Linear Differential Equations 4.LaPlace Transforms 5.Vector Analysis 6.Multiple Line and Surface Integrals and Integral Theorems 7.Fourier Series 8.Fourier Integrals 9.Partial Differential Equations 10. Complex Variables and Conformal Mapping 11. Complex Inversion Formula for Laplace Transforms 12. Matrices 13. Calculus of Variations

Read more less

Book SynopsisOver the past decade or so, we have seen a multitude of improvement programmes and projects to improve the safety of patient care in healthcare. However, the full potential of these efforts and especially those that seek to address an entire system has not yet been reached. The current pandemic has made this more evident than ever.We have tended to focus on problems in isolation, one harm at a time, and our efforts have been simplistic and myopic. If we are to save more lives and significantly reduce patient harm, we need to adopt a holistic, systematic approach that extends across cultural, technological, and procedural boundaries. Patient Safety Now is about the fact that it is time to care for everyone impacted by patient safety, how we need to take the time to care for everyone in a meaningful way and how hospitals need to enable staff time to care safely.This book builds on the authorâs two previous books on patient safety. Rethinking Patient Safety Table of ContentsAcknowledgements. About the Author. Introduction. 1 How Did We Get Here? 2 Where Do We Want to Be? 3 How Do We Get There? Conclusion. References. Index.

Read more less

Book SynopsisExam Board: Edexcel, AQA, OCR & WJEC EduqasLevel: GCSE 9-1Subject: Maths FoundationSuitable for the 2025 examsComplete revision and practice to fully prepare for the GCSE grade 9-1 examsRevision that Sticks! Collins GCSE 9-1 Maths Foundation Complete All-in-One Revision and Practice uses a revision method that really works: repeated practice throughout.A revision guide, workbook and practice paper in one book!With clear and concise revision for every topic, plus seven practice opportunities, Collins offers the best revision at the best price.Includes:quick tests as you goend-of-topic practice questionstopic review questions later in the bookmixed practice questions at the end of the bookmore topic-by-topic practice in the workbooka complete exam-style paperfree Q&A flashcards to download onlinefree ebook version

Read more less

Book SynopsisThe perfect introduction to the essential mathematical concepts which all chemistry students need to master. Working from foundational principles, the book builds the student's confidence by leading them through the subject in a steady, progressive way from basic algebra to the mathematics of quantum chemistry. mathematics.Trade ReviewA very useful text to gradually guide students through both the fundamental and more advanced aspects of mathematics specifically relevant for a chemistry undergraduate degree. It is particularly useful in allowing students to test their knowledge of mathematical concepts and processes via self-test exercise and additional problems that are directly relevant to chemistry. * Dr Jon Tandy, Senior Lecturer in Physical Chemistry, London Metropolitan University *This is an outstanding and carefully thought-out introduction to the mathematical toolkit required for students embarking on a chemistry degree programme. * Dr Robert Johnson, Lecturer, School of Chemistry, University College Dublin *Table of ContentsSection A: Core mathematics: algebra, logarithms and trigonometry 1: The display of numbers 2: Algebra I 3: Algebra II 4: Algebra III 5: Algebra IV 6: Algebra V 7: Algebra VI 8: Algebra VII 9: Powers I 10: Powers II 11: Trigonometry 12: Advanced BODMAS Section B: Calculus 13: Differentiation I 14: Differentiation II 15: Differentiation III 16: Differentiation IV 17: Differentiation V 18: Differentiation VI 19: Integration I 20: Integration II 21: Integration III 22: Integration IV Section C: Matrices, vectors and complex numbers 23: Matrices I 24: Matrices II 25: Complex numbers 26: Vectors Section D: Laboratory mathematics 27: Graphs I 28: Graphs II 29: Graphs III 30: Probability I 31: Probability II 32: Statistics I 33: Statistics II 34: Statistics III 35: Statistics IV 36: Dimensional analysis

Read more less

Book SynopsisAstronomy needs statistical methods to interpret data, but statistics is a many-faceted subject that is difficult for non-specialists to access. This handbook helps astronomers analyze the complex data and models of modern astronomy. This second edition has been revised to feature many more examples using Monte Carlo simulations, and now also includes Bayesian inference, Bayes factors and Markov chain Monte Carlo integration. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions and clustering. Exercises at the end of each chapter guide readers through the techniques and tests necessary for most observational investigations. The data tables, solutions to problems, and other resources are available online at www.cambridge.org/9780521732499. Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced undTrade Review"Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced undergraduate and graduate students and professional astronomers." -Mathematical ReviewsTable of Contents1. Decision; 2. Probability; 3. Statistics and expectations; 4. Correlation and association; 5. Hypothesis-testing; 6. Data modelling and parameter-estimation: basics; 7. Data modelling and parameter-estimation: advanced topics; 8. Detection and surveys; 9. Sequential data - 1D statistics; 10. Statistics of large-scale structure; 11. Epilogue: statistics and our Universe; Appendices; References; Index.

Read more less

Book SynopsisMathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students'' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions (''By the Ways'') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, manTrade Review'Schramm's Mathematical Methods and Physical Insights is a very welcome new textbook in the area of pedagogical mathematical physics. The book contains numerous insightful and helpful examples from classical and modern physics, as well as unusual and interesting applications of the presented mathematical concepts within and beyond physics. I find the 'BTW' inserts, and the lively, unpretentious style of the book both exciting and entertaining. The material discussed in Schramm's textbook covers entirely the scope of our three-trimester-long Mathematical Methods offering, and additionally provides useful background material to 'even out' the often inhomogeneous preparation of students in these classes; I will definitely consider adopting this textbook for my next offerings of Mathematical Methods for Physics here at the University of California, Santa Cruz.' Professor Stefano Profumo, University of California, Santa Cruz'As the title suggests, Schramm's book distinguishes itself from traditional mathematical methods texts in its thematic approach that builds from unit to unit, using rich examples from physical systems that elucidate each topic. A must-read for physicists wanting to expand their mathematical toolkit as well as for mathematicians hoping to gain new insights from the physical world.' Professor Jason Detwiler, University of Washington'For students taking physics courses, one of the difficulties is how to apply appropriate mathematical skills in problem solving (e.g., using integration to find the electric field produced by a continuous charge distribution). This book introduces commonly used mathematical skills from the perspective of a physicist. Focusing on the topics in upper-level physics courses, it provides the mathematical skills for solving problems in each topic. The book is easy to read, and the problems at the end of each chapter offer plenty of exercises for students. The book is a valuable resource for undergraduate students taking upper-level physics courses, and instructors teaching such courses. It could also be a useful reference for graduate students.' Professor Hong Lin, Bates College'Physics and engineering students often struggle with mathematics texts that present the material in an abstract fashion, disconnected from practical applications. Schramm's text represents a refreshing and much needed change. Providing context and intuition throughout, with many worked examples, and in engaging prose, it does more than just explain mathematical methods; it infuses them with meaning and relevance.' Dr. Jochen Rau, RheinMain University of Applied Sciences, GermanyTable of ContentsPreface; Part I. Things You Just Gotta' Know: 1. Prelude: symbiosis; 2. Coordinating coordinates; 3. Complex numbers; 4. Index algebra; 5. Brandishing binomials; 6. Infinite series; 7. Interlude: orbits in a central potential; 8. Ten integration techniques and tricks; 9. The Dirac delta function; 10. Coda: statistical mechanics; Part II. The Calculus of Vector Fields: 11. Prelude: visualizing vector fields; 12. grad, div & curl; 13. Interlude: irrotational and incompressible; 14. Integrating scalar & vector fields; 15. The theorems of Gauss & Stokes; 16. Simply connected regions; 17. Coda: mostly Maxwell; Part III. Calculus in the Complex Plane: 18. Prelude: path independence in the complex plane; 19. Series, singularities & branches; 20. Interlude: conformal mapping; 21. The calculus of residues; 22. Coda: analyticity & causality; Part IV. Linear Algebra: 23. Prelude: superposition; 24. Vector space; 25. The inner product; 26. Interlude: rotations; 27. The Eigenvalue problem; 28. Coda: normal modes; Entr'acte: Tensors; 29. Cartesian tensors; 30. Beyond cartesian; Part V. Orthogonal Functions: 31. Prelude: 1 2 3 . . . infinity; 32. Eponymous polynomials; 33. Fourier series; 34. Convergence and completeness; 35. Interlude: beyond the straight & narrow; 36. Fourier transforms; 37. Coda: of time intervals and frequency bands; Part VI. Differential Equations: 38. Prelude: first order first; 39. Second-order ODEs; 40. Interlude: the Sturm-Liouville Eigenvalue problem; 41. Partial differential equations; 42. Green's functions; 43. Coda: quantum scattering; Appendix A. Curvilinear coordinates; Appendix B. Rotations in R3; Appendix C. The Bessel family of functions; References; Index.

Read more less

Book SynopsisThis detailed yet accessible text introduces the advanced mathematical methods at the core of theoretical physics. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering.Trade Review'The recent explosive development of topological quantum matter requires a deep systematic understanding of modern mathematics. Quantum many-body entanglement in topological quantum matter is a new phenomenon that requires new mathematical language to describe. This is a rare book that provides systematic and in-depth coverage of some of the most important mathematical concepts, such as groups, geometry, topology and algebra, among others. Many abstract mathematical notions are explained in an easy, explicit fashion. This is an in-depth, friendly book on modern mathematics. Very timely and highly recommended.' Xiao-Gang Wen, Massachusetts Institute of TechnologyTable of Contents1. Introduction; 2. Group theory; 3. Representation theory of groups; 4. Differentiable manifolds; 5. Riemannian geometry; 6. Semisimple Lie algebras and their unitary representations; Appendix A; References; Index.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisProbability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters'' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.A special feature is the authors'' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbersTable of ContentsPART A BASIC PROBABILITY; PART B FURTHER PROBABILITY

Read more less

Book SynopsisThis substantially revised and expanded new edition of the bestselling textbook, addresses the difficulties that can arise with the mathematics that underpins the study of symmetry, and acknowledges that group theory can be a complex concept for students to grasp.Trade Review"the best introduction to the subject, especially for those whose mathematics is weak." (Chemistry and Industry, 2nd April 2001) ".I recommend this book..." (Education in Chemistry, September 2002)Table of ContentsPreface to the Second Edition vii How to use the Programmes ix Programme 1: Symmetry Elements and Operations 1 Programme 2: Point Groups 22 Programme 3: Non-degenerate Representations 46 Programme 4: Matrices 65 Programme 5: Degenerate Representations 85 Programme 6: Applications to Chemical Bonding 102 Programme 7: Applications to Molecular Vibration 122 Programme 8: Linear Combinations 139 Bibliography 173 Mathematical Data for use with Character Tables 174 Character Tables for Chemically Important Symmetry Groups 176 Index 186

Read more less

Book SynopsisLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading pTrade ReviewThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *Table of Contents1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors

Read more less

Book SynopsisConfusing Textbooks? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.Table of ContentsThe Laplace Transform.The Inverse Laplace Transform.Applications to Differential Equations.Applications to Integral and Difference Equations.Complex Variable Theory.Fourier Series and Integrals.The Complex Inversion Formula.Applications to Boundary-Value Problems.Appendix A: Table of General Properties of Laplace Transforms.Appendix B: Table of Special Laplace Transforms.Appendix C: Table of Special Functions.

Read more less

Book SynopsisFor more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant''s and Herbert Robbins''s classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat''s Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.Trade ReviewCan...be read with great profit by anyone desiring general mathematical literacy. * Mathematics Abstracts *A great book. * Ludwig Otto, Paul Quinn College *A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods. * Albert Einstein *Without doubt, the work will have great influence. It should be in the hands of everyone, professional or otherwise, who is interested in scientific thinking. * The New York Times *A work of extraordinary perfection. * Mathematical Reviews *It contains an excellent selection of material for students who have no desire to develop mathematical skills but who may be willing to look briefly into this field of intellectual activity....For the inquiring student who wishes to know what real mathematics is about, or for the trained engineer or physicist who has some interest in the justification of procedures he uses, it should prove a source of great pleasure and satisfaction. * Journal of Applied Physics *This book is a work of art. * Marston Morse *This is not a book in philosophy; but there are probably few philosophers who can not gain instruction and clarification from it. It succeeds brilliantly in conveying the intellectual excitement of mathematical inquiry and in communicating the essential ideas and methods."Journal of PhilosophyIt is a work of high perfection, whether judged by aesthetic, pedagogical or scientific standards. It is astonishing to what extent What is Mathematics? has succeeded in making clear by means of the simplest examples all the fundamental ideas and methods which we mathematicians consider the life blood of our science. * Herman Weyl *Still a book that all prospective mathematics teachers should read and experience. A rare book that has retained its "freshness" and readability for more than 50 years....Very readable. * Stephen Krulik, Temple University *

Read more less

Book SynopsisProvides a handbook of ecological methods and analytical techniques pertinent to the study of animals, with an emphasis on non-microscopic animals in both terrestrial and aquatic environments.Table of ContentsPreface to Fifth Edition, 2020 Preface to Fourth Edition, 2015 Preface to Third Edition, 1998 1: Introduction to the Study of Animals 2: The Sampling Programme and the Measurement and Description of Dispersion 3: Absolute Population Estimates Using Capture-Recapture Experiments 4: Absolute Population Estimates by Sampling a Unit of Habitat -Air, Plants, Plant Products and Vertebrate Hosts 5: Absolute Population Estimates by Sampling a Unit of Aquatic Habitat 6: Absolute Population Estimates by Sampling a Unit of Soil or Litter Habitat-Extraction Techniques 7: Relative Methods of Population Measurement and the Derivation of Absolute Estimates 8: Estimates of Species Richness and Population Size Based on Signs, Products and Effects 9: Wildlife Population Estimates by Census and Distance Measuring Techniques 10: Observational and Experimental Methods to Estimate Natality, Mortality, Movement and Dispersal 11: The Construction, Description and Analysis of Age-Specific Life-Tables 12: Age-Grouping, Time-Specific Life-Tables and Predictive Population 13: Species Richness, Diversity and Packing 14: The Estimation of Productivity and the Construction of Energy Budgets 15: Techniques for the Study of Long-Term Dynamics-Analysing Time Series 16: Studies at Large Spatial Scales, Citizen Science and the Classification of Habitats

Read more less

Book SynopsisThe Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. Taking a clear, straightforward approach, the book develops ideas in a logical, coherent way, allowing students progressively to build a thorough working understanding of the subject.Topics are organized into three parts: algebra, calculus, differential equations, and expansions in series; vectors, determinants and matrices; and numerical analysis and statistics. The extensive use of examples illustrates every important concept and method in the text, and are used to demonstrate applications of the mathematics in chemistry and several basic concepts in physics. The exercises at the end of each chapter, are an essential element of the development of the subject, and have been designed to give students a working understanding of the material in the text.Online Resources:The online resources feature the following: - Figures from the book in electronic format, ready to download- Full worked solutions to all end of chapter exercisesTrade ReviewReview from previous edition It seems well suited both for its stated purpose and as a "brush-up" book for undergraduates, graduate students, and others. The mathematics are carried out briskly and with very little dressing ... there is much material to cover here and it works well through Steiner's particularly lucid presentation. The notation is standard and clear ... I am impressed with this book, I am sure that it will remain open on my desk and will become well worn in short order. * C. Michael McCallum, University of the Pacific, Journal of Chemical Education, Vol. 74 No. 12 December 1997 *Table of Contents1. Numbers, variables and units ; 2. Algebraic functions ; 3. Transcendental functions ; 4. Differentiation ; 5. Integration ; 6. Methods of integration ; 7. Sequences and series ; 8. Complex numbers ; 9. Functions of several variables ; 10. Functions in 3 dimensions ; 11. First-order differential equations ; 12. Second-order differential equations. Constant coefficients ; 13. Second-order differential equations. Some special functions ; 14. Partial differential equations ; 15. Orthogonal expansions. Fourier analysis ; 16. Vectors ; 17. Determinants ; 18. Matrices and linear transformations ; 19. The matrix eigenvalue problem ; 20. Numerical methods ; 21. Probability and statistics

Read more less

Book SynopsisCore Maths for the Biosciences introduces the range of mathematical concepts that bioscience students need to master during thier studies. Starting from fundamental concepts, it blends clear explanations and biological examples throughout as it equips the reader with the full range of mathematical tools required by biologists today.Trade ReviewExactly the sort of thing that will be helpful in showing those with biological problems how mathematics can be very useful - and that what is really important is maintaining an intuitive understanding between the mathematics - which is essentially no more, but no less, than a way of thinking very precisely - and the actual phenomena they are dealing with...Very fine indeed. * Professor Lord May of Oxford, Department of Zoology, University of Oxford *Fantastic. Easy to understand, interactive, biologically relevant and dictated in a way that seemed as though you are almost having a conversation with the author. * James Sleigh, Student, University of Oxford *Coherent and clear. The best I have seen this kind of material treated. * Stephen Hubbard, University of Dundee *This book is by far the best of its kind, a spectacular diamond in the rough. * Helen Smith, student, University of Salford *The interactive spreadsheets are a work of genius. * Stuart Fisk, student, University of Essex *Table of ContentsPART 1: ARITHMETIC, ALGEBRA & FUNCTIONS; PART 2: CALCULUS AND DIFFERENTIAL EQUATIONS

Read more less

Book SynopsisMathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. It introduces and builds on concepts in a progressive, carefully-layered way, and features over 2000 end of chapter problems, plus additional self-check questions.Trade ReviewReview from previous edition This textbook offers an accessible and comprehensive grounding in many of the mathematical techniques required in the early stages of an engineering or science degree and also for the routine methods needed by first and second year mathematics students. * Engineering Designer March/April 2003 *There are also significant changes in content in the opening chapter, where the foundation material has been expanded usefully. The authors do not attempt to dodge theoretical hurdles. They are careful to explain many of the less intuitive properties of functions and to highlight generalisations without becoming over abstract. * Times Higher Education Supplement, November 2002 *Thoroughly recommended. * Zentralblatt MATH, 993:2002 *Table of ContentsPART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS; PART 2. MATRIX AND VECTOR ALGEBRA; PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS; PART 4. TRANSFORMS AND FOURIER SERIES; PART 5. MULTIVARIABLE CALCULUS; PART 6. DISCRETE MATHEMATICS; PART 7. PROBABILITY AND STATISTICS; PART 8. PROJECTS; SELF-TESTS: SELECTED ANSWERS; ANSWERS TO SELECTED PROBLEMS; APPENDICES; FURTHER READING; INDEX

Read more less

Book SynopsisThere are not many calculus books that are very accessible to students without a strong mathematical background and the large majority of financial derivatives students do not have a strong quantitative background. This book provides a short introduction to the subject with examples of its use in mathematical finance e. g pricing of derivatives.Table of ContentsPreface xiii 1 Brownian Motion 1 1.1 Origins 1 1.2 Brownian Motion Specification 2 1.3 Use of Brownian Motion in Stock Price Dynamics 4 1.4 Construction of Brownian Motion from a Symmetric Random Walk 6 1.5 Covariance of Brownian Motion 12 1.6 Correlated Brownian Motions 14 1.7 Successive Brownian Motion Increments 16 1.7.1 Numerical Illustration 17 1.8 Features of a Brownian Motion Path 19 1.8.1 Simulation of Brownian Motion Paths 19 1.8.2 Slope of Path 20 1.8.3 Non-Differentiability of Brownian Motion Path 21 1.8.4 Measuring Variability 24 1.9 Exercises 26 1.10 Summary 29 2 Martingales 31 2.1 Simple Example 31 2.2 Filtration 32 2.3 Conditional Expectation 33 2.3.1 General Properties 34 2.4 Martingale Description 36 2.4.1 Martingale Construction by Conditioning 36 2.5 Martingale Analysis Steps 37 2.6 Examples of Martingale Analysis 37 2.6.1 Sum of Independent Trials 37 2.6.2 Square of Sum of Independent Trials 38 2.6.3 Product of Independent Identical Trials 39 2.6.4 Random Process B(t) 39 2.6.5 Random Process exp[B(t) – t] 40 2.6.6 Frequently Used Expressions 40 2.7 Process of Independent Increments 41 2.8 Exercises 42 2.9 Summary 42 3 Itō Stochastic Integral 45 3.1 How a Stochastic Integral Arises 45 3.2 Stochastic Integral for Non-Random Step-Functions 47 3.3 Stochastic Integral for Non-Anticipating Random Step-Functions 49 3.4 Extension to Non-Anticipating General Random Integrands 52 3.5 Properties of an Itō Stochastic Integral 57 3.6 Significance of Integrand Position 59 3.7 Itō integral of Non-Random Integrand 61 3.8 Area under a Brownian Motion Path 62 3.9 Exercises 64 3.10 Summary 67 3.11 A Tribute to Kiyosi Itō 68 Acknowledgment 72 4 Itō Calculus 73 4.1 Stochastic Differential Notation 73 4.2 Taylor Expansion in Ordinary Calculus 74 4.3 Itō’s Formula as a Set of Rules 75 4.4 Illustrations of Itō’s Formula 78 4.4.1 Frequent Expressions for Functions of Two Processes 78 4.4.2 Function of Brownian Motion f [B(t)] 80 4.4.3 Function of Time and Brownian Motion f [t, B(t)]82 4.4.4 Finding an Expression for 83 4.4.5 Change of Numeraire 84 4.4.6 Deriving an Expectation via an ODE 85 4.5 Lévy Characterization of Brownian Motion 87 4.6 Combinations of Brownian Motions 89 4.7 Multiple Correlated Brownian Motions 92 4.8 Area under a Brownian Motion Path – Revisited 95 4.9 Justification of Itō’s Formula 96 4.10 Exercises 100 4.11 Summary 101 5 Stochastic Differential Equations 103 5.1 Structure of a Stochastic Differential Equation 103 5.2 Arithmetic Brownian Motion SDE 104 5.3 Geometric Brownian Motion SDE 105 5.4 Ornstein–Uhlenbeck SDE 108 5.5 Mean-Reversion SDE 110 5.6 Mean-Reversion with Square-Root Diffusion SDE 112 5.7 Expected Value of Square-Root Diffusion Process 112 5.8 Coupled SDEs 114 5.9 Checking the Solution of a SDE 115 5.10 General Solution Methods for Linear SDEs 115 5.11 Martingale Representation 120 5.12 Exercises 123 5.13 Summary 124 6 Option Valuation 127 6.1 Partial Differential Equation Method 128 6.2 Martingale Method in One-Period Binomial Framework 130 6.3 Martingale Method in Continuous-Time Framework 135 6.4 Overview of Risk-Neutral Method 138 6.5 Martingale Method Valuation of Some European Options 139 6.5.1 Digital Call 139 6.5.2 Asset-or-Nothing Call 141 6.5.3 Standard European Call 142 6.6 Links between Methods 144 6.6.1 Feynman-Kač Link between PDE Method and Martingale Method 144 6.6.2 Multi-Period Binomial Link to Continuous 146 6.7 Exercise 147 6.8 Summary 148 7 Change of Probability 151 7.1 Change of Discrete Probability Mass 151 7.2 Change of Normal Density 153 7.3 Change of Brownian Motion 154 7.4 Girsanov Transformation 155 7.5 Use in Stock Price Dynamics – Revisited 160 7.6 General Drift Change 162 7.7 Use in Importance Sampling 163 7.8 Use in Deriving Conditional Expectations 167 7.9 Concept of Change of Probability 172 7.9.1 Relationship between Expected Values under Equivalent Probabilities 174 7.10 Exercises 174 7.11 Summary 176 8 Numeraire 179 8.1 Change of Numeraire 179 8.1.1 In Discrete Time 179 8.1.2 In Continuous Time 182 8.2 Forward Price Dynamics 184 8.2.1 Dynamics of Forward Price of a Bond 184 8.2.2 Dynamics of Forward Price of any Traded Asset 185 8.3 Option Valuation under most Suitable Numeraire 187 8.3.1 Exchange Option 187 8.3.2 Option on Bond 188 8.3.3 European Call under Stochastic Interest Rate 188 8.4 Relating Change of Numeraire to Change of Probability 190 8.5 Change of Numeraire for Geometric Brownian Motion 192 8.6 Change of Numeraire in LIBOR Market Model 194 8.7 Application in Credit Risk Modelling 198 8.8 Exercises 200 8.9 Summary 201 Annexes A Annex A: Computations with Brownian Motion 205 A. 1 Moment Generating Function and Moments of Brownian Motion 205 A. 2 Probability of Brownian Motion Position 208 A. 3 Brownian Motion Reflected at the Origin 208 A. 4 First Passage of a Barrier 214 A. 5 Alternative Brownian Motion Specification 216 B Annex B: Ordinary Integration 221 B. 1 Riemann Integral 221 B. 2 Riemann–Stieltjes Integral 226 B. 3 Other Useful Properties 231 B. 4 References 234 C Annex C: Brownian Motion Variability 235 C. 1 Quadratic Variation 235 C. 2 First Variation 238 D Annex D: Norms 239 D. 1 Distance between Points 239 D. 2 Norm of a Function 242 D. 3 Norm of a Random Variable 244 D. 4 Norm of a Random Process 244 D. 5 Reference 246 E Annex E: Convergence Concepts 247 E. 1 Central Limit Theorem 247 E. 2 Mean-Square Convergence 248 E. 3 Almost Sure Convergence 249 E. 4 Convergence in Probability 250 E. 5 Summary 250 Answers to Exercises 253 References 299 Index 303

Read more less

Book SynopsisThis work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.Table of ContentsForest fires, fractal oil fields and diffusion; cluster numbers; cluster structure; finite size scaling and the renormalization group; conductivity and related properties; walks, dynamics and quantum effects; application to thermal phase transitions. Appendices: numerical techniques; dimension dependent approximations.

Read more less

Book SynopsisWritten for senior undergraduates in all disciplines of physical science and engineering, the plain language style of this concise guide to numerical methods concentrates on developing computational skills and avoids potentially intimidating formal mathematical proofs. Including numerous worked examples and exercises, this textbook explains the practical realities of numerical techniques.Table of ContentsPreface; 1. Fitting functions to data; 2. Ordinary differential equations; 3. Two-point boundary conditions; 4. Partial differential equations; 5. Diffusion: parabolic PDEs; 6. Elliptic problems and iterative matrix solution; 7. Fluid dynamics and hyperbolic equations; 8. Boltzmann's equation and its solution; 9. Energy-resolved diffusive transport; 10. Atomistic and particle-in-cell simulation; 11. Monte Carlo techniques; 12. Monte Carlo radiation transport; 13. Next steps; Appendix A. Summary of matrix algebra; Index.

Read more less

Book SynopsisThe two volumes of Maths for Chemists provide an excellent resource for all undergraduate chemistry students but are particularly focussed on the needs of students who may not have studied mathematics beyond GCSE level (or equivalent). The texts are introductory in nature and adopt a sympathetic approach for students who need support and understanding in working with the diverse mathematical tools required in a typical chemistry degree course. The early chapters of Maths for Chemists Volume I: Numbers, Functions and Calculus provide a succinct introduction to the important mathematical skills of algebraic manipulation, trigonometry, numbers, functions, units and the general grammar of maths. Later chapters build on these basic mathematical principles as a foundation for the development of differential and integral calculus. In spite of the introductory nature of this volume, some of the more important mathematical tools required in quantum chemistry are deliberately included, through a gradual introduction to, and development of, the concept of the eigenvalue problem. Ideal for the needs of undergraduate chemistry students, Tutorial Chemistry Texts is a major series consisting of short, single topic or modular texts concentrating on the fundamental areas of chemistry taught in undergraduate science courses. Each book provides a concise account of the basic principles underlying a given subject, embodying an independent-learning philosophy and including worked examples.Trade ReviewA useful addition to the resources available for teaching mathematics to chemists."""... Undergraduates in biochemistry and all branches of chemistry, particularly students with a limited background in maths, will find this book essential. """"""... The importance of mathematics in chemistry can not be under estimated; books aiming to show the many applications of the subject are always very welcome. """The mathematical ability of chemistry undergraduates continues to be an issue for many departments, so this new edition is a timely update to the resources available for both staff and students.Table of ContentsNumbers and Algebra; Functions and Equations: Their Form and Use; Limits; Differentiation; Differentials; Integration; Differential Equations; Subject Index

Read more less

Book SynopsisThe ancient Roman orator Horace (65 B.C.-8 B.C.) wrote, 'Control your mind or it will control you.' In today's society we are faced with more information, and more complex information, than ever. Faced with making decisions, we can feel overwhelmed and helpless. One way to become less helpless — to gain control over our lives — is to gain control over our own thinking. We can feel helpless when faced with this barrage of information, opinions, data, and conflicting arguments if we lack the skills to quickly grasp and critically evaluate them. This book is designed to impart these kinds of skills.Any course in a university should do more than teach information — in nearly every field, 'facts' become obsolete quickly. The goals of Thinking Matters are to help you: The text is punctuated with exercises or 'personal experiments' to challenge and stimulate your curiosity. These exercises may take the form of an inventory to be taken, a puzzle to be solved, or some thoughts to ponder.The first module Thinking Matters: Critical Thinking as Creative Problem Solving introduces the student to all the above topics — logic, probability, argument forms and fallacies, ethical reasoning, algorithms, and computational thinking — through logic puzzles and games and mathematical magic tricks.

Read more less

Book SynopsisAimed at a broad audience of graduate students and researchers in ecology and evolution, this novel creates a persuasive argument that an explicit consideration of history will often lead to a deeper, more nuanced understanding of almost every eco-evolutionary system.

Read more less

Book SynopsisBiomedical scientists are the foundation of modern healthcare, from cancer screening to diagnosing HIV, from blood transfusion for surgery to food poisoning and infection control. Without biomedical scientists, the diagnosis of disease, the evaluation of the effectiveness of treatment, and research into the causes and cures of disease would not be possible.The Fundamentals of Biomedical Science series has been written to reflect the challenges of practicing biomedical science today. It draws together essential basic science with insights into laboratory practice to show how an understanding of the biology of disease is coupled to the analytical approaches that lead to diagnosis. Assuming only a minimum of prior knowledge, the series reviews the full range of disciplines to which a Biomedical Scientist may be exposed - from microbiology to cytopathology to transfusion science. Data Handling and Analysis is the most relevant and useful statistics and data analysis text for biomedical sciTrade ReviewA gem of a find! For once it makes statistics understandable and it also clearly explains research and professional practice. Few books cover this range of topics. It is ideal for students completing research and also introduces student to good clinical practice. The statistical sections are very well explained indeed and simplify complicated concepts in a very readable manner. * Ruth Shiner, University of Wolverhampton *Provides clear explanations of basic statistical and experimental design concepts which are placed into a practical context that is highly relevant for BMS students * Lewis Bingle, University of Sunderland *An easy-to-read book that explains how to use a range of statistical tests that can be applied to data * Amreen Bashir, Aston University *Table of Contents1: Information in biomedical science 2: Handling quantities: mass, volume, and concentration 3: Obtaining and verifying data 4: Presenting data in graphical form 5: Quality, audit, and good laboratory practice 6: Research 1: Setting the scene 7: Research 2: The analysis of modest data sets 8: Research 3: Large data sets 9: Communication

Read more less

Book SynopsisMathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics.

Read more less

Book SynopsisThis richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences.Trade ReviewFrom the reviews: "The 2nd volume of the authors elucidating work highlights a surprisingly broad spectrum of applications in the field of mathematical biology. The sense given to the mathematical texture of thoughts broadens the reader’s insight … . The growing number of specialists in sub-disciplines of mathematical biology will be enjoying the truly concise approach … . It can so be said that the foremost results … might be essential for new interpretations of data … . It is a recommended text for mathematicians … ." (Daniel Gertsch, Bioworld, Issue 2, 2004) From the reviews of the third edition: "This is the second volume of the third edition of Murray’s ‘Mathematical Biology’. … covers a wide variety of problems in pattern formation, each discussed in its biological context. … This volume alone is a large book, with more than 800 pages and a similar number of references. … it is a valuable collection of results from different areas of mathematical biology." (Carlo Laing, New Zealand Mathematical Society Newsletter, Issue 90, April, 2004) "This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences. The multi-layer way of material presentation makes the book useful for different types of reader including graduate-level students, bioscientists … . it is an enjoyable reading and I recommend it to anyone with serious interest in mathematical modelling." (V.V. Fedorov, Short Book Reviews, Vol. 23 (3), 2003) "This second volume of the third edition of Murray’s Mathematical biology focuses on partial differential equations (spatial models) and their application to the biomedical sciences. … Each chapter deals with its particular topic in great detail, usually focusing on one biological example and the associated mathematical model and results. This volume is not an introductory text … making it extremely useful in graduate courses and for reference." (Trachette L. Jackson, Mathematical Reviews, 2004b) "In this second volume … the development towards specific biological configurations and towards a mechanism for understanding morphogenesis represents an important portion of the work. … chapters deal with attractive topics … . There is an extensive index at the end. … very interesting and strongly recommended." (A. Akutowicz, Zentralblatt MATH, Vol. 1006, 2003) "In this volume it becomes clear that compiling the third edition was a ‘labor of love’. The book has a significantly different feel from the original first edition. … my reaction to the third edition was positive. … The historical and biological overviews have much interesting information. … Certainly, the spicy writing will keep students alert … . In summary, I recommend the new and expanded third edition to any serious young student interested in mathematical biology … ." (Leah Edelstein-Keshet, SIAM Review, Vol. 46 (1), 2004) "Mathematical Biology would be eminently suitable as a text for a final year undergraduate or postgraduate course in mathematical biology … . It is also a good source of examples for courses in mathematical methods … . Mathematical Biology provides a good way into the field and a useful reference for those of us already there. It may attract more mathematicians to work in biology by showing them that there is real work to be done." (Peter Saunders, The Mathematical Gazette, Vol. 90 (518), 2006)Table of ContentsMulti-Species Waves and Practical Applications * Spatial Pattern Formation with Reaction Diffusion Systems * Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms * Pattern Formation on Growing Domains: Alligators and Snakes * Bacterial Patterns and Chemotaxis * Mechanical Theory for Generating Pattern and Form in Development * Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies * A Mechanical Theory of Vascular Network Formation * Epidermal Wound Healing * Dermal Wound Healing * Growth and Control of Brain Tumours * Neural Models of Pattern Formation * Geographic Spread and Control of Epidemics * Wolf Territoriality, Wolf-Deer Interaction and Survival

Read more less

Book SynopsisThe Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A.C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Written by a physicist, Statistics is tailored to the needs of physical scientists, containing and explaining all they need to know. It concentrates on parameter estimation, especially the methods of Least Squares and Maximum Likelihood, but other techniques, such as hypothesis testing, Bayesian statistics and non-parametric methods are also included. Intended foTable of ContentsUsing Statistics. Describing the Data. Theoretical Distributions. Errors. Estimation. Least Squares. Probability and Confidence. Taking Decisions. Ranking Methods. Notes for Number Crunchers. Bibliography. Appendices. Index.

Read more less

Book SynopsisThis book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.Trade ReviewReview of the hardback: 'The authors are distinguished researchers who have made fundamental contributions to mathematical fluid dynamics over their careers. The aim of the volume is, in the authors' own words, 'to let physicists and engineers know about existing mathematical tools from which they might benefit [and] … to help mathematicians learn what physical turbulence is about so they can focus their research on problems of interest of physics. …' The monograph is a substantial step toward bringing together physicists' and engineers' theoretical treatments of turbulence with mathematicisns' rigorous analysis of the Navier-Strokes equations and their solutions. In this regard the book is the first of its type. This book is far from elementary, but the authors' efforts to make it accessible on several levels make it a valuable and unique resource for researchers interested in both turbulence theory and mathematical analysis. I hope, as do the authors, that this work will help to establish new and constructive lines of communication between these two communities.' SIAM ReviewTable of ContentsPreface; Acknowledgements; 1. Introduction and overview of turbulence; 2. Elements of the mathematical theory of the Navier–Stokes equations; 3. Finite dimensionality of flows; 4. Stationary statistical solutions of the Navier–Stokes equations, time averages and attractors; 5. Time-dependent statistical solutions of the Navier–Stokes equations and fully developed turbulence; References; Index.

Read more less

Book SynopsisThis book is the first systematic survey of morphometric methods for landmark data. It combines conventional multivariate statistical analysis with themes from plane and solid geometry and from biomathematics to support biological insights into the features of many different organs and organisms.Trade Review"...will certainly be a landmark volume in this difficult but important field of shape analysis." K.V. Mardia, International Statisical Institute Short Book Reviews"The new geometric morphometry, as epitomized in Bookstein's text, is a fully rounded scientific achievement. I recommend this well-written book to all biometricians concerned with the analysis of shape." R.A. Reyment, Biometrics"...specialists working in this field may find the book to be a useful collation of methods for the study of shape." Shumei Guo, Journal of the American Statistical Association"...a serious and wide-ranging effort to systematize morphometrics...Bookstein has done an admirable job in bringing together the tools needed to reach this goal and, consequently, in building his case about the importance of landmarks in morphometrics...will clearly be important in morphometrics for some time." Scott Ferson, The Quarterly Review of Biology"...this is essential reading for quantitative morphologists." Miriam Zelditch, BioScience"Bookstein, through his strong personality and energy, has made the field of morphometrics very visible and has particulary made statisticians aware of the potential of the field for both statistical as well as scientific research...I would like to praise the author for making statisticians aware of the important field of morphometrics and for 'making us think'." Subhash Lele, Journal of the American Statistical AssociationTable of Contents1. Introduction; 2. Preliminaries; 3. Landmarks; 4. Distance measures; 5. Shape coordinates; 6. Principal axes of shape change for triangles; 7. Features of shape comparison; 8. Retrospect and prospect.

Read more less

Book SynopsisA revised edition of the best-selling, most widely used and respected physics calculations book.Table of ContentsBasic ideas; mechanics; matter; oscillations and waves; geometrical optics; heat; electricity and magnetism; atomic and nuclear physics; calculations involving graphs; special topics; further revision questions.

Read more less

Book Synopsis

Read more less

Book SynopsisGraph theory can be applied to ecological questions in many ways, and more insights can be gained by expanding the range of graph theoretical concepts applied to a specific system. But how do you know which methods might be used? And what do you do with the graph once it has been obtained? This book provides a broad introduction to the application of graph theory in different ecological systems, providing practical guidance for researchers in ecology and related fields. Readers are guided through the creation of an appropriate graph for the system being studied, including the application of spatial, spatio-temporal, and more abstract structural process graphs. Simple figures accompany the explanations to add clarity, and a broad range of ecological phenomena from many ecological systems are covered. This is the ideal book for graduate students and researchers looking to apply graph theoretical methods in their work.Table of ContentsPreface; 1. Graphs as structure in the ecological context; 2. Shapes of graphs: trees to triangles; 3. Species interaction networks; 4. Trophic networks: structure, partitioning, and dynamics; 5. Species associations, communities, and graphs of social structure ; 6. Competition: hierarchies and reversals; 7. Mutualism, parasitism, and bipartite graphs; 8. Temporal or time-only graphs; 9. Spatial graphs; 10. Spatio-temporal graphs; 11. Graph structure and system function: graphlet methods; 12. Synthesis and future directions; Visual glossary; References; Index; Appendix.

Read more less

Book SynopsisThis is the first book to provide life scientists with a practical guide to using experimental design and statistics when running animal experiments. The chapters cover a range of design types and analysis techniques employed by practitioners, using non-mathematical terms and drawing on real-life examples.Trade Review'At last, a readable statistics book focusing solely on preclinical experimental designs, data and its analysis that should form part of an in-vivo scientist's personal library. The author's unique insight into the statistical needs of preclinical scientists has allowed them to compile a non-technical guide that can facilitate sound experimental design, meaningful data analysis and appropriate scientific conclusions. I would also encourage all readers to download and explore 'InVivoStat', a powerful software package that both my group and I use on a daily basis.' Darrel J. Pemberton, Janssen Research and Development'This book provides an indispensable reference for any in-vivo scientist. It addresses common pitfalls in animal experiments and provides tangible advice to address sources of bias, thus increasing the robustness of the data. … The text links experimental design and statistical analysis in a practical way, easily accessible without any prior statistical knowledge. The statistical concepts are described in plain English, avoiding overuse of mathematical formulas and illustrated with numerous examples relevant to biomedical scientists. … This book will help scientists improve the design of animal experiments and give them the confidence to use more complex designs, enabling more efficient use of animals and reducing the number of experimental animals needed overall.' Nathalie Percie du Sert, National Centre for the Replacement, Refinement and Reduction of Animals in Research'This book will transform the way biomedical scientists plan their work and interpret their results. Although the subject matter covers complex points, it is easy to read and packed with relevant examples. There are two particularly striking features. First, at no point do the authors resort to mathematical equations as a substitute for explaining the concepts. Secondly, they explain why the choice of experimental design is so important, why the design affects the statistical analysis and how to ensure the choice of the most appropriate statistical test. The final section describes how to use InvivoStat (a software package, assembled by the authors), which enables researchers to put into practice all the points covered in this book. This is an invaluable combination of resources that should be within easy reach of anyone carrying out experiments in the biomedical sciences, especially if their work involves using live animals.' Clare Stanford, University College LondonTable of ContentsPreface; Acknowledgements; 1. Introduction; 2. Statistical concepts; 3. Experimental design; 4. Randomisation; 5. Statistical analysis; 6. Analysis using InVivoStat; 7. Conclusion; Glossary; References; Index.

Read more less

Book Synopsis

Read more less

Book SynopsisThe chapters in this contributed volume showcase current theoretical approaches in the modeling of ocular fluid dynamics in health and disease. By including chapters written by experts from a variety of fields, this volume will help foster a genuinely collaborative spirit between clinical and research scientists. It vividly illustrates the advantages of clinical and experimental methods, data-driven modeling, and physically-based modeling, while also detailing the limitations of each approach. Blood, aqueous humor, vitreous humor, tear film, and cerebrospinal fluid each have a section dedicated to their anatomy and physiology, pathological conditions, imaging techniques, and mathematical modeling. Because each fluid receives a thorough analysis from experts in their respective fields, this volume stands out among the existing ophthalmology literature.Ocular Fluid Dynamics is ideal for current and future graduate students in applied mathematics and ophthalmology who wish to explore the field by investigating open questions, experimental technologies, and mathematical models. It will also be a valuable resource for researchers in mathematics, engineering, physics, computer science, chemistry, ophthalmology, and more.Table of ContentsPart I. Introduction.- Mathematical and physical modeling principles of complex biological systems.- Part II. Blood.- Vascular Anatomy and Physiology of the Eye.- Pathological Consequences of Vascular Hemodynamic Alterations in the Eye.- Measurement of geometrical and functional parameters related to ocular blood flow.- Mathematical modeling of blood flow in the eye.- Part III. Aqueous Humor.- Changes in Parameters of Aqueous Humor Dynamics Throughout Life.- Aqueous Humor Dynamics and its Influence on Glaucoma.- Approaches to Aqueous Humor Outflow Imaging.

Read more less

Book SynopsisStatistics is the science that focuses on drawing conclusions from data, by modeling and analyzing the data using probabilistic models. In 'An Introduction to Mathematical Statistics' the authors describe key concepts from statistics and give a mathematical basis for important statistical methods. Much attention is paid to the sound application of those methods to data. The three main topics in statistics are estimators, tests, and confidence regions. The authors illustrate these in many examples, with a separate chapter on regression models, including linear regression and analysis of variance. They also discuss the optimality of estimators and tests, as well as the selection of the best-fitting model.Each chapter ends with a case study in which the described statistical methods are applied. This book assumes a basic knowledge of probability theory, calculus, and linear algebra.Table of Contents1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1[-]1.1. WhatIsStatistics? . . . . . . . . . . . . . . . . . . . . . 1[-]1.2. StatisticalModels . . . . . . . . . . . . . . . . . . . . . 2[-]Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 12[-]Application: Cox Regression . . . . . . . . . . . . . . . . . 15[-]2. DescriptiveStatistics . . . . . . . . . . . . . . . . . . . . . . 21[-]2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 21[-]2.2. UnivariateSamples . . . . . . . . . . . . . . . . . . . . . 21[-]2.3. Correlation . . . . . . . . . . . . . . . . . . . . . . . . 32[-]2.4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . 38[-]Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 39[-]Application: Benford's Law . . . . . . . . . . . . . . . . . 41[-]3. Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . 45[-]3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 45[-]3.2. MeanSquareError . . . . . . . . . . . . . . . . . . . . . 46[-]3.3. Maximum Likelihood Estimators . . . . . . . . . . . . . . . 54[-]3.4. MethodofMomentsEstimators . . . . . . . . . . . . . . . . 72[-]3.5. BayesEstimators . . . . . . . . . . . . . . . . . . . . . . 75[-]3.6. M-Estimators . . . . . . . . . . . . . . . . . . . . . . . 88[-]3.7. Summary . . . . . . . . . . . . . . . . . . . . . . . . . 93[-]Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 94[-]Application: Twin Studies . . . . . . . . . . . . . . . . . 100[-]4. Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . 105[-]4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 105[-]4.2. Null Hypothesis and Alternative Hypothesis . . . . . . . . . . 105[-]4.3. SampleSizeandCriticalRegion . . . . . . . . . . . . . . 107[-]4.4. Testing with p-Values . . . . . . . . . . . . . . . . . . . 121[-]4.5. StatisticalSignificance . . . . . . . . . . . . . . . . . . 126[-]4.6. SomeStandardTests . . . . . . . . . . . . . . . . . . . 127[-]4.7. Likelihood Ratio Tests . . . . . . . . . . . . . . . . . . 143[-]4.8. ScoreandWaldTests . . . . . . . . . . . . . . . . . . . 150[-]4.9. Multiple Testing . . . . . . . . . . . . . . . . . . . . . 153[-]4.10. Summary . . . . . . . . . . . . . . . . . . . . . . . . 159[-]Exercises . . . . . . . . . . . . . . . . . . . . . . . . 160[-]Application: Shares According to Black-Scholes . . . . . . . . 169[-]5. ConfidenceRegions . . . . . . . . . . . . . . . . . . . . . 174[-]5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 174[-]5.2. Interpretation of a Confidence Region . . . . . . . . . . . . 174[-]5.3. PivotsandNear-Pivots . . . . . . . . . . . . . . . . . . 177[-]5.4. Maximum Likelihood Estimators as Near-Pivots . . . . . . . . 181[-]5.5. ConfidenceRegionsandTests . . . . . . . . . . . . . . . 195[-]5.6. Likelihood Ratio Regions . . . . . . . . . . . . . . . . . 198[-]5.7. BayesianConfidenceRegions . . . . . . . . . . . . . . . . 201[-]5.8. Summary . . . . . . . . . . . . . . . . . . . . . . . . 205[-]Exercises . . . . . . . . . . . . . . . . . . . . . . . . 206[-]Application: The Salk Vaccine . . . . . . . . . . . . . . . 209[-]6. Optimality Theory . . . . . . . . . . . . . . . . . . . . . . 212[-]6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 212[-]6.2. SufficientStatistics . . . . . . . . . . . . . . . . . . . . 212[-]6.3. EstimationTheory . . . . . . . . . . . . . . . . . . . . 219[-]6.4. TestingTheory . . . . . . . . . . . . . . . . . . . . . 231[-]6.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . 245[-]Exercises . . . . . . . . . . . . . . . . . . . . . . . . 246[-]Application: High Water in Limburg . . . . . . . . . . . . . 250[-]7. RegressionModels . . . . . . . . . . . . . . . . . . . . . . 259[-]7.1. Introduction

Read more less

Book SynopsisThis contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.Table of ContentsPart I: Computational Science and Engineering.- Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications.- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods.- Modular time integration of coupled problems in system dynamics.- Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems.- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models.- Challenges in the Simulation of Radio Frequency Circuits.- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics.- From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory.- Part II: Data Analysis and finance.- Topological Data Analysis.- Prediction Models with Functional Data for Variables related with Energy Production.- Quantization Methods for Stochastic Differential Equations.

Read more less

Book SynopsisJourney through the world of abstract mathematics into category theory with popular science author Eugenia Cheng. Featuring humanizing examples and demystification of mathematical thought processes, this book is for fans of How to Bake Pi who want to dig deeper into mathematical concepts and build their mathematical background.Trade Review'This book is an educational tour de force that presents mathematical thinking as a right-brained activity. Most 'left brain/right brain' education-talk is at best a crude metaphor; but by putting the main focus on the process of (mathematical) abstraction, Eugenia Cheng supplies the reader (whatever their 'brain-type') with the mental tools to make that distinction precise and potentially useful. The book takes the reader along in small steps; but make no mistake, this is a major intellectual journey. Starting not with numbers, but everyday experiences, it develops what is regarded as a very advanced branch of abstract mathematics (category theory, though Cheng really uses this as a proxy for mathematical thinking generally). This is not watered-down math; it's the real thing. And it challenges the reader to think-deeply at times. We 'left-brainers' can learn plenty from it too.' Keith Devlin, Stanford University (Emeritus), author of The Joy of Sets'Eugenia Cheng loves mathematics—not the ordinary sort that most people encounter, but the most abstract sort that she calls 'the mathematics of mathematics.' And in this lovely excursion through her abstract world of Category Theory, she aims to give those who are willing to join her a glimpse of that world. The journey will change how they view mathematics. Cheng is a brilliant writer, with prose that feels like poetry. Her contagious enthusiasm makes her the perfect guide.' John Ewing, President, Math for America'Eugenia Cheng's singular contribution is in making abstract mathematics relevant to all through her great ingenuity in developing novel connections between logic and life. Her latest book, The Joy of Abstraction, provides a long awaited fully rigorous yet gentle introduction to the 'mathematics of mathematics,' allowing anyone to experience the joy of learning to think categorically.' Emily Riehl, Johns Hopkins University, author of Category Theory in Context'Archimedes is quoted as having said once: 'Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.' In this fascinating book, Eugenia Cheng approaches the abstract mathematical area of Category Theory with pure love, to reveal its beauty to anybody interested in learning something about contemporary mathematics.' Mario Livio, astrophysicist, author of The Golden Ratio and Brilliant Blunders'Eugenia Cheng's latest book will appeal to a remarkably broad and diverse audience, from non-mathematicians who would like to get a sense of what mathematics is really about, to experienced mathematicians who are not category theorists but would like a basic understanding of category theory. Speaking as one of the latter, I found it a real pleasure to be able to read the book without constantly having to stop and puzzle over the details. I have learnt a lot from it already, including what the famous Yoneda lemma is all about, and I look forward to learning more from it in the future.' Sir Timothy Gowers, Collège de France, Fields Medalist, main editor of The Princeton Companion to Mathematics'At last: a book that makes category theory as simple as it really is. Cheng explains the subject in a clear and friendly way, in detail, not relying on material that only mathematics majors learn. Category theory – indeed, mathematics as a whole – has been waiting for a book like this.' John Baez, University of California, Riverside'Many people speak derisively of category theory as the most abstract area of mathematics, but Eugenia Cheng succeeds in redeeming the word 'abstract'. This book is loquacious, conversational, and inviting. Reading this book convinced me I could teach category theory as an introductory course, and that is a real marvel, since it is a subject most people leave for experts.' Francis Su, Harvey Mudd College, author of Mathematics for Human Flourishing'Finally, a book about category theory that doesn't assume you already know category theory! In this inviting but rigorous introduction to what she calls 'the mathematics of mathematics', Eugenia Cheng brings the subject to us with insight, wit, and a point of view. Her story of finding joy-and advantage-in abstraction will inspire you to find it, too.' Patrick Honner, award-winning high school math teacher, columnist for Quanta Magazine, author of Painless Statistics'This higher category theory is the mathematics of the twenty-first century (at least my corner of it). If you'd like a taste of it, I recommend Dr. Cheng's book. The first half is an accessible and thought-provoking insight into categorical thinking. The second half climbs into the rarified air of theoretic math, but it is worth a read to get a feel for what some parts of modern mathematics look like.' Jonathan Kujawa, 3 Quarks Daily'… a successful addition to the literature that I am sure students will use in the future and I would be happy to recommend.' Constanze Roitzheim, Mathematische SemesterberichteTable of ContentsPrologue; Part I. Building Up to Categories: 1. Categories: the idea; 2. Abstraction; 3. Patterns; 4. Context; 5. Relationships; 6. Formalism; 7. Equivalence relations; 8. Categories: the definition; Interlude: A Tour of Math: 9. Examples we've already seen, secretly; 10. Ordered sets; 11. Small mathematical structures; 12. Sets and functions; 13. Large worlds of mathematical structures; Part II. Doing Category Theory: 14. Isomorphisms; 15. Monics and epics; 16. Universal properties; 17. Duality; 18. Products and coproducts; 19. Pullbacks and pushouts; 20. Functors; 21. Categories of categories; 22. Natural transformations; 23. Yoneda; 24. Higher dimensions; 25. Epilogue: thinking categorically; Appendices: A. Background on alphabets; B. Background on basic logic; C. Background on set theory; D. Background on topological spaces; Glossary; Further reading; Acknowledgements; Index.

Read more less

Book Synopsis

Read more less