Mathematics — Book Reviews

"In six far ranging chapters, Elran takes us on a journey from ciphers, to ancient puzzles, through mathematical poetry and art. With secret messages and mystery challenges, there's plenty to keep a curious mind busy, novice and expert alike — at heart this is a book of fun things to think about and do. It is also an accessible, richly detailed, cross-cultural, and up-to-date sourcebook showing off the roots of our subject (and will remain a valued reference in my own library).

In short, a compendium of stimulating mathematical gems for the home or classroom.""

"This is an amazing textbook about the generalizations in convergence theory, which we see in analysis or general topology courses. Those who study lattice theory will also benefit from the book.

In conclusion, this book goes well beyond what we typically see in first-year graduate level course textbooks. Since the book has a strong flavor of point-set topology and analysis, completion of these courses is ideal before reading it. Students who have been exposed to these subjects will especially appreciate the material presented here."

"This excellent two-volume monograph is a must for anyone interested in Continuous Optimization... It is a very intense lecture, containing a dense material with many explanations and references... written in an accessible manner for the targeted audience of PhD students, researchers, and practitioners.

All in one, I am convinced that this book will become soon a solid and highly cited reference for everyone interested in Variational Analysis"

"The book discusses recently obtained results on the Gibbs measures of the q-state Potts model... It is proved that there are [q/2] critical temperatures and shown how this 2q - 1 translation-invariant splitting Gibbs measures distribute with respect to these critical temperatures."

*Note that the review is brief and to the point, and does not contain overly effusive praise. However, it does highlight the book's discussion of recent results and its proofs of certain key concepts, suggesting that the reviewer found the book to be a useful contribution to the field.

"This is a well-written and quite helpful book... The book will definitely be of some interest and importance for the people who work in these presented subjects as well as for the beginners who start their scientific carrier by working in these directions of the algebra."

"The book under review combines abstract harmonic analysis with applied topics of spectral analysis and approximation by orthogonal expansions.

For those who search for a new setting in harmonic analysis (for some as a starting point), this book presents enough material and ideas to be absorbed in"

"The chapter titles provide a clearer picture of the contents... McIntyre envisages an audience of “scientifically-minded readers and especially young scientists” and aims for a presentation “that avoids equations and technical jargon."

"The presentation is compact and clear. There is a large number of well-chosen explicit examples all explained in detail. The book will be useful for advanced undergraduate students, also for graduate students."

"The book provides a comprehensive introduction to parallel algorithms and especially to the techniques for efficient parallelization. It carefully leads the reader into the field of design and analysis of parallel algorithms, without requiring previous knowledge of parallel computing or computational mathematics.

The nine chapters of the book are organized using an innovative vision. The reader can appreciate the high number of exercises and their detailed solutions."

"The author Tuvi Etzion has done a good job in producing a textbook which provides a learner friendly introduction to “Perfect codes and related structures”. The book will certainly be a welcome contribution to anyone studying perfect codes. Due to its presentation and good organization, it definitely provides good material for graduate students and research scholars."

"This monograph contains some of the recent achievements in Bloch-type periodic functions and their applications to evolution equations."

"This book represents lecture notes on the qualitative theory of ODEs and an introduction to the dynamical systems theory.

The book is full of various examples. Each chapter contains quite a lot of exercises (of varying degrees of complexity) designed for independent solution."

"In this book, the authors consider new properties of Hardy operators in the last decade. The book gives sharp bounds for the n-dimensional (fractional) Hardy operators, dual Hardy operators, m-linear Hardy operators, and Hardy operators on product spaces."

"The book is easy to read and self-contained with bibliography for each chapter."

"A prominent feature of the book is its role as a unified and accessible reference, consolidating dispersed results from various disciplines into a single comprehensive resource... In summary, this book is an important contribution to the literature on the mathematics of tomography techniques based on single-scattered particles, providing a combination of theoretical insights and practical applications that will appeal to a wide range of readers."

"I couldn't put down this delightful book. It's an absolutely marvelous tour of millennia of mathematics, full of tidbits that were new to me."

"Chris Budd conveys the power and wonder of mathematics in stories ?and, having gained your interest, explains the underlying mathematics. Discover how, during a boring sermon, Galileo observed the predictability of the swing of a pendulum, later explained by the mathematics of Newton. Mathematical models are relatively easy to develop for physical systems where the underlying equations are understood, and are also now being used in biological and social sciences. This was vital during the COVID-19 pandemic. Chris explains how models can describe population behaviour and also spells out their limitations. He uses analogies, quotes, and stories to enliven a complex topic. Look out for the glass of whisky and the warning 'don't eat the menu'."

"This book presents a very nice invitation to the new theory of modular and automorphic forms, presented in a concise form. It might be a useful opus for a rather wide readership interested in this subject, both experts and novices."

"The book is very interesting, and it is suitable for a wide class of readers, from hobbyists to professors. This book is well written and very attractive indeed."

"Multiple examples and detailed line-by-line derivations which allows easy tracing and understanding the line of reasoning"

"This book provides an excellent introduction to the important topic of secret sharing schemes and leads the reader into the field of contemporary research that these classical methods triggered."

"The book covers well-trodden and secure ground."

"The collection covers linear and nonlinear operators, continuity, compactness, and differentiability, variational methods, monotone operators, and fixed point theory. These topics belong to the standard analysis programme of every serious Math Department"

"The book illustrates several trends and perspectives for this field and contains numerous applications. It is oriented to interested researchers in modern algebra and its applications."

"Topics covered include numbers, arithmetic, analytic geometry, calculus, complex numbers, probability, and infinite series. These topics stick more closely to the high school and university curriculum than typical recreational math books; and the examples are almost all accessible to a reader with a high school background. This is consistent with the author's stated intention of writing a book to demonstrate to the skeptical why one should love mathematics."

"The technical tools used in the book are comparatively simple, therefore the book is quite accessible and useful for study by graduate students, teachers, practitioners and all interested persons. The material of the book is very modern and successfully combines interesting theoretical results and statistical inference."

"This book on nonabelian cohomology in the differentiable setting adds an original and coherent overall viewpoint to the theory of higher stacks that originated in the classical works of Grothendieck and Giraud and has seen a recent expansion in many directions. Viewed here through a lens of higher Lie theory, topics such as higher differential Chern characters constitute important new structures in differential homotopy, cohomotopy, and the K-theory of motives. Applications to physics are a central motivation for the study of higher Bianchi identities, leading the authors to find natural new differential forms of interest."

"The book under review is a welcome addition to this scant literature, aiming to introduce Einstein's theory, as well as the needed differential geometry, in a fully rigorous manner … It can be used as a textbook for a course on either differential geometry or general relativity (or both) for undergraduate or beginning graduate mathematics or physics students, and is also well suited for autonomous study … This book is a valuable addition to the general relativity literature for mathematicians, and one which I highly recommend."

"The chapters are clearly organized. Each chapter comprises many original results where precise proofs alternate with intuitive comments, and terminates by some notes which outline the evolution of ideas. Christer Kiselman's book attempts to juxtapose three branches of image processing which are usually not considered as a whole. That is a remarkable achievement. As regards mathematical morphology, another merit of the text is to present increasing operators in a new light, and to thoroughly develop this original point of view."

"This is a user-friendly book and this reader thoroughly enjoyed following the author's path. Some brief biographical snippets throughout the text both give some historical perspective and add to the enjoyment. As befits lecture notes, there are numerous exercises, of varying degrees of difficulty (without solutions included). Much of this would be suitable for self-study. Those intending to specialize will appreciate the flags to more advanced topics or perspectives, and should be inspired to delve further. To summarize, these lecture notes are a valuable resource." See full review

"I use tensors in computer vision and ML/AI (see my books on amazon.com) and for years I had to deal with deciphering various definitions of tensors on my own. Professor Hongyu Guo's book is the first to unify many different and often confusing definitions of tensors, as well as presenting their properties in the context of machine learning, but also in mechanics, electrodynamics and general relativity. I highly recommend it to both mathematicians and physicists but above all to a wide group of practitioners. I really enjoy reading it!"

"This well-written book provides important information on a timely topic, Compton tomography, in a very readable form. The author focuses on models for Compton tomography that are generalized Radon transforms on broken rays (V-s or stars) in the plane or cones in space. The reader will come away with a solid understanding of the applications and physical background, along with the mathematical models and the properties of the associated generalized Radon transforms."

"This book fully covers the curriculum of elementary schools in the countries of Central Europe – even if the author adapted it, as he himself states, to the curricula of the USA, England, Australia, Singapore, and other non-European countries. (The fact that the curricula of elementary schools in most countries are similar is of course a positive message; I mention it in this context just because this book is a very useful companion not only in the countries Abramovich mentions, but certainly also in the above mentioned countries of Central Europe (I can confirm it, because my more than 40 years experiences in teaching mathematics for prospective mathematics teachers at elementary schools in the Czech Republic, Slovakia, Poland, Hungary, Austria, Germany) and certainly also in other countries.)..."

"Following an exposition of systems and control theory foundations, Motion Control presents the author's work with medical collaborators on human gait problems; this includes a presentation of their virtual reality feedback device for gait stabilization, in particular for those suffering from Parkinson's Disease. Motion Control joins the author's preceding monograph, The Subcritical Brain, to make a valuable contribution to the scientific and clinical area of human cybernetics."

"The book under review offers from its initial chapter 1 (Euclidean Space), to the last chapter 21 (The Dirichlet and Neumann problems), a well-founded selection of Goursat's encyclopedia, were one can find the excellent mathematical taste of the author. I believe that because of the choice of topics and the clarity of the exposition, this text will be of great help for students who have a background in Linear Algebra and Calculus of one variable, and who are interested in getting a degree in Physics or Mathematics." See full review

"This book is an essential contribution to the reform in thinking needed to face the complexity of our troubled times and the uncertainties of our future."

"This is a richly detailed and fascinating account by one of the most influential mathematicians of our time, of the people he has known, the mathematics he has enjoyed, and the challenges he has encountered."

"The book is essential if one wishes to initiate research in the field of fractional rheology. The topic is quite promisimg and this book is a useful tool for taking the first step. In my opinion, it is well written and is very readable, with many technical details."

"Science by Simulation is a personal and altruistic call to science teachers to bring more mathematical modelling into their science lessons. This interesting and impressive book contains a dozen examples of how mathematical modelling can be applied to mostly physics-related situations, such as fluid dynamics or the movement of double pendulums …"

"This book will certainly be a welcome contribution to anyone studying dichotomies or functional differential equations, mainly because of its core meaning, but also due to its presentation and good organization. It definitively provides good material for seminars and elective courses."

"The book was developed over many years from class notes for a set theory course at the University of Florida, which has been taught to advanced undergraduates as well as beginning graduate students. It gives a solid introduction to axiomatic set theory and presents several interesting applications."

"It covers all the essentials in an exposition which is clear and precise but not compendious beyond comprehension. The book contains a wealth of exercises with a wide (and by-and-large discernible) range of difficulty. There are short but useful appendixes on pushouts and pullbacks and the snake lemma and Baer's criterion."

"I am a mathematician with an interest in the history of mathematics and of mathematicians. As such, I loved this book. It is a fascinating tour of the life and work of Norbert Wiener. It is a book written for someone who knows a reasonable amount of mathematics and has an interest in Wiener's life and his times. In short, it is a book written especially for me. But I do hope and expect that others will also delight in this book."

"This book is addressed first of all to beginners, but starting with students of senior courses and graduate students and can also be of interest both for theorists and persons involved in applied aspects of science. It is highly recommended to scientists interested in such directions as theory of optimization and control, calculus of variations, nonsmooth and convex analysis, theory of differential equations, theory of games, and mathematical economics."

"The book is clearly written and rich of examples, all of them presented with many details. Thanks to a large bibliography, the whole research work done on Lie systems so far is offered to the reader."

"For the second edition, the author considerably updates several results to record and explain some new and significant developments of the past 20 years. For example, the new Chapter 7, 'Extension of Cartan's theorem and Schmidt's subspace theorem', includes the recent results of the author and P Vojta for establishing the second main theorem and subspace theorem for general divisors on projective varieties … These updates will be valuable and helpful for researchers in related areas.”

"The strength of this excellent textbook is that it overviews the broad field of deterministic and stochastic operations research in a clear, easy to follow way with a rich collection of examples, applications and exercises (many of them with solutions).

The book is well-written, provides a comprehensive review of the subject and is interesting for a quite number of disciplines. It is also useful for self-study and gives a good ground for further, more advanced studies. Any curious student will love this book. I highly recommend this book"

"The main goal of this book is to provide a unified approach for proving strong laws of probability theory, among them the strong law of large numbers. To show the universality of the theory developed, the author provides corollaries that include all the strong laws listed."

"Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or engineering undergraduates. The student who is prepared to work through the book will get a good grounding in basic techniques and gain a feel for the possible behaviours of standard equations. He will also be given some indication of the usefulness and potential complexity of discrete systems in modern science and engineering."

"Hösel et al. should be thanked and congratulated for putting together such a full and mathematically deep discussion, particularly concerning the evolution of cooperation and how we might go about thinking about the topic in microbes … I highly recommend this publication; it belongs on the desk of every serious student of microbial evolution, ecology, or population genetics."

"The book provides a comprehensive review of the DRM approach to data fusion. It is well written and easy to follow, although the technical details are not trivial. The authors did an excellent job in making a concise introduction of the statistical techniques in data fusion. The book contains several real data … Overall, I found that the book covers an important topic and the DRM is a promising tool in this area. Researchers on data fusion will surely find this book very helpful and I will use this book in studying with my PhD students."

"This book is a welcome, and well-written, addition to the higher categorical literature that is well suited to readers at varying levels of commitment and expertise. Its introduction provides a thorough, if terse, tour of the categorical prerequisites, which in combination with Part I might serve as the text for a graduate course, or for self-study, in higher category theory. Exercises, at varying levels of difficulty, are liberally sprinkled throughout and Appendix C is devoted to providing solutions and hints."

"This delightful book connects mathematical concepts in a dozen areas to magic tricks. Expositions of the mathematics precede description and analysis of the tricks. The expositions are too short for in-depth learning; the intent is to give sophomores a taste of the content and ideas of later mathematics courses. Each chapter features exercises on the mathematics, and students can have fun practicing the tricks."

"Michael Shlesinger has provided a compelling personal and scientific account of a remarkable career a nd at the same time has presented a highly pedagogical and accessible account of many topics related to probability, random walks and complex systems. This would be a valuable book for everyone interested in learning about a personal view of life of a scientist as well as mathematical aspects of random walks and related subjects." [Read Full Review]"

"Carlier's book on Optimization is one of its kind: it provides all the material necessary for beginners while covering at the same time a wide range of lively problems and algorithms in finite or infinite-dimensional spaces, drawing examples from cutting-edge data-driven problems, optimal transport, or from the classical calculus of variations. Its conciseness, sharpness, and insight make it an excellent reference both for students and researchers."

"In this book, the authors teach the art of physical applied mathematics at the advanced undergraduate level. In contrast to traditional mathematics books, formal derivations and theorems are replaced by worked examples with intuitive solutions and approximations, given some familiarity with physics and chemistry. In this way, the book covers an ambitious range of topics, such as vector calculus, differential and integral equations, linear algebra, probability and statistics, functions of complex variables, scaling and dimensional analysis..."

"Remarkable as it may sometimes seem, the world provides us with many good opportunities for clear thought, exploratory thought, evaluative thought. Our ability to do these things is part of what makes us human. 'Critical Thinking' is the somewhat spiky modern term for this essential human feature. Thinking Matters is a very readable, leisurely book (I hate to say textbook) meant to help develop a person's innate talents in critical thinking, largely presented through an immense range of entertaining puzzles of all kinds, generally with their interesting histories attached. It beautifully illustrates, but does not try to solve, the central puzzle of all: why it is so important to us to be puzzled, and why a subsequent self-created aha moment is so satisfying."

"There is no shortage of problem-solving books available, but this one, in several respects, stands out from the crowd. For one thing, it is very clearly and engagingly written, and should be accessible not only to college math majors but also good high school students as well..."

"Much of the work shows the author's own influence and interests. All six parts are well written and give a good ground for further studies to researchers who are interested in this field. The book ends with five appendices based on author's joint works with Professor K Sugahara. This book is a fine piece of work which gives a more deeper and wider look to the theory of zeta-functions"

"This book can be regarded as a mathematical legacy of Professor Snaith. It provides an account of several research projects which the author has pursued for many years … The book can be recommended to mathematicians who want to learn about monomial resolutions or who are looking for a research topic."

"The book is intended for the advanced graduate level students who may find it useful in carrying out modeling and simulation of anomalous diffusion. The book is recommended for the universities and research establishments."

"The rich experience of the authors in teaching analysis (in the broadest sense) transpires on every page and I highly recommend this book to anyone teaching or studying the topics presented … The present one is logically constructed and, by paying great attention to details, provides a valuable resource for teaching material, too. The book is suitable for advanced undergraduate students in mathematics with operator theory, and also as a reference for researchers."

"This book is a nice textbook on modern econometrics. It is essentially based on the author's lecture notes taught at Cornell University and several universities in China … The text provides a clear, understandable introduction to key concepts of econometrics."

"The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.
Summing Up: Recommended. General readers."

"The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended."

"The numerical algorithms presented are written in pseudocode and based on MATLAB, a programming and numeric computing platform widely used in STEM fields. Thus, no formal training in computer science or knowledge of any specific programming language is needed to parse the algorithms. Summing up: Recommended."

"This is definitely an original approach to the Second Law. The main users of the book will be mathematicians with a strong background in Fourier analysis and combinatorics. However, it is also readable for physicists in particular for those who are interested in a rigorous approach to the Second Law. The book is very suitable for advanced student seminars. The writing style of the author is precise and convincing. I enjoyed reading very much."

"There were parts of the history section covering aspects that I've rarely seen before in a popular mathematics text … this is a genuinely useful addition to the popular maths coverage of probability."

"Many interesting facts from the life of Ragnar Norberg and other classics of risk theory can be found in the book presented. The circumstances of the development of this theory are described. The authors of the articles provide an extensive bibliography."

"An extraordinary feature of this book is its gentle style. Even proofs of advanced theorems are organized in such a way that each intermediate step is well-motivated, carries some interest in itself and is easy to understand. It is accessible to anyone with a basic knowledge of proof methods, group theory and, obviously, some general mathematical knowledge … The book is very well suited as a basis for an introductory course to algebra-flavored number theory."

"The material of the book Metric in Measure Spaces is complete and self-contained — almost all needed background is presented, and also most statements are clear and the proofs are written in detail. Hence the book can be of interest not only to mathematicians working in fields related to measure theory, but also to students."

"The book is intended for undergraduate course students. I believe that it will be useful as a source of interesting exercises, examples and counterexamples for teachers and researchers as well. The main value of this volume is the collection of a large number of problems, mostly with their solutions, on a wide variety of topics in functional analysis. I have no hesitation in recommending the book to any mathematics library."

"This booklet provides a very lucid and versatile introduction to the methods of linear partial differential equations. It covers a wealth of very important material in a concise, nevertheless very instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in this area of both classical and contemporary mathematics."

"This handbook provides a self-contained resource, very helpful guidance and excellent teaching supplement in the field of inverse scattering in electromagnetism for use by professional researchers and graduate students. It will take pride of place among lots of excellent books concerning the mathematical theory of the Maxwell equation and scattering theory ... It is written in an accessible language. The first three chapters can be used as a textbook for undergraduate students. The next two chapters are a good introduction for graduate students."

"The presentations gathered in this book offer plenty of ideas and advice for anyone seeking to start a program or affiliate with an existing one. In general, the authors do not compare their programs to those described in other chapters, but readers of the whole volume will identify significant commonalties across the various audiences, processes, obstacles, and outcomes described.
Summing up: Recommended. All readers."

"Being a physicist, the author has followed successfully his wish to present the topics in an intuitive and easy way, as much as possible. Some important statements are given rigorously. In many cases suitable references are indicated for details. The notations, the terms and in general the style are common for researchers and university teachers of courses in physics to graduate students. In fact, these three groups, researchers, teachers and graduate students, form the audience to which the book is addressed."

"The book is well readable — the transition between elementary basic subjects and advanced ones is very smooth and in some sense effortless. The text is attended with large number of examples and 45 exercises (most of them with solutions). In aid of interested reader the book contains very rich bibliography — 317 titles … The book can used as a basis for courses in analytic number theory given to students studying mathematics or more applied subjects."

"This book also provides an introduction to the basic theory of geometrical analysis with a new foundational presentation based on ordinary differential equations techniques, in a unitary and self-contained way."

"The book is an interesting and useful reading for scientists and students in the area of mathematics and statistics."

"This book offers insight and motivation into the major theorems of undergraduate single-variable and multivariable calculus. In this, the text is successful — working from physical principles and complete with many pictures, the text demystifies the 'big theorems' that arise in the calculus sequence. As a result, the text is a worthwhile and engaging read for both undergraduate and graduate students looking to better understand the results that appear at the end of a traditional Calculus 3 course. It would also be recommended to a professor of Calculus 3 who is looking for inquiry-based approaches or thought experiments to use in their course."

"It's not just about the puzzles! Cats and Rats also tells us about their historical and mathematical context, and how mathematicians think when they solve problems. Refreshing, challenging (but not too much so), fun, and unusual."

"The theory presented in this book has found (and still finding) many interesting applications in various branches of ordinary differential equations where nonabsolutely integrable functions or discontinuities occur. Therefore, a material containing basic facts together with more advanced results of Kurzweil-Stieltjes integration is very welcome and highly appreciated."

"The author spreads other research problems and conjectures throughout the text, and the reviewer believes that many who are interested in knots and braids will also find something for them in it."

"The second part is a central discussion about history of board games and chess variations. The content is not about a mathematical analysis of the games but really about the games themselves: pictures of the board and pieces, rules, strategies, variations and interpretations."

"If high education teachers decide to teach the topic of creativity, then this is an excellent textbook for such a course. The book includes also a rich bibliography on creativity. This bibliography can serve researchers who wish to study the field of creativity.

"Generally, the book is rich of ideas and techniques involved. It is a piece of a very good mathematics and you can find many parts inspiring to your own research."

"The book assumes familiarity only with basic classical and complex analysis, and therefore graduate students can easily read it. The book will be a useful tool for those who work on combinatorial identities, enumeration, or special sequences or polynomials."

"The information on the subjects is, generally speaking, up to date. The diptych is highly recommended for an informed start in the field of ODE's and BVP's."

"For the increasing significance of these algebras in physics, the book may be of interest to a wide spectrum of scientists, and serves as a good basis for a graduate (or advanced undergraduate) course."

"... the volume is impressively accessible. The result is a book that is valuable and approachable for biologists at all levels, including those interested in deepening their skills in mathematical modeling and those who seek an overview to aid them in communicating with collaborators in mathematics and statistics. The former group of readers may especially appreciate the first chapter, an introduction to key concepts in probability, and the set of ten assignments provided as an appendix."

"The book is a nice reading. It gives a clear and comprehensive exposition of fine properties of the sample paths of an interesting class of Gaussian and non-Gaussian random fields obtained by the method of wavelet expansions. The book can be recommended to students, researchers, and practitioners who are working in the areas of both theoretical and applied probability and harmonic analysis."

"This research monograph is suitable as a reference book for a practitioner who uses the mixed effects models, and for a researcher who studies these models, as it covers methods, theory and applications on mixed effects models. It can also be treated as a graduate text for a course on mixed effects models and their applications."

"This is an excellent guide book for advanced undergraduate and graduate students to understand the basic concepts of Algebra and its fruitful relation with other branches of Mathematics. I particularly like its pedagogical approach. Each new concept is first introduced through examples commonly appearing in nature, reserving for a later step its abstract introduction, where the potential reader will be able to assimilate it without much effort. I also like the choice of the authors of accompanying the development of the theory with a lot of exercises, the most significant of which appear solved in a final section, and many historical notes that help to put into context the origin of the concepts introduced."

"The reference list is excellent. This is a worthwhile (though 'niche') book that will be attractive to a particular sector of the general reading public interested in mathematical riddles and puzzles. Professional educators might well employ it in integrated learning settings. Summing Up: Recommended. All readers."

"The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer's opinion, this excellent monography will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods."

"This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics."

"The forte of the book is the large quantity of examples ... It is a self-contained book that will be helpful for physicists, as well as for engineers and applied mathematicians."

"The beauty if this book is that it is inherently interdisciplinary, combining foundational, conceptual, and philosophical notions with state-of-the-art engineering and technological applications, including artificial intelligence, big data, and high performance computing ... With the current advent of machine intelligence and the explosion of big data and the corresponding increase in demand for computational power, the author sees the necessity and urgency of constructive proofs and tests of algorithms ... Constructivity, provability, and computability all improve control, security, safety and reliability."

"The book is carefully written and should be useful as a textbook for courses on convex geometry ... Also of interest are the notes after each chapter. More of these would be appreciated by an expert reader. The exercises are a treasure. The book serves its purpose well and can be recommended without reservation."

"For high school AP Stat teachers who want to understand, and should want to understand, probability deeper than what the course curriculum requires, this book would be very helpful."

"Given the reforms in mathematics education, the issue of how teachers develop their knowledge has become a big challenge for practitioners as well as for researchers. While many people believe that teachers teach as they were taught, Prof Fan shows that the phenomenon is much more complex. This book is an important source for students, teachers, teacher educators, school administrators, and policy-makers."

"Guillemin and Haine's goal is to construct a well-documented road map that extends undergraduate understanding of multivariable calculus into the theory of differential forms. Throughout, the authors emphasize connections between differential forms and topology while making connections to single and multivariable calculus via the change of variables formula, vector space duals, physics; classical mechanisms, div, curl, grad, Brouwer's fixed-point theorem, divergence theorem, and Stokes's theorem ... The exercises support, apply and justify the developing road map."

"The presentation proceeds in a logical way, with illustrative examples and some exercises. The authors also point out the relevant R routines that implement some of the procedures discussed in the book. Readers interested in further references will find the detailed bibliography at the end helpful. The book is suitable for an introductory graduate course in nonparametric statistics or for advanced undergraduates. Practitioners of nonparametric statistical methods will also find it a useful reference."

"The book is very well-written by one of the leading figures in the subject. It is self-contained, includes relevant recent advances and is enriched by a large number of examples and illustrations. In addition to the general bibliography, each chapter includes a section of notes, which details the authorship of the main results, and provides useful hints for further readings. Undoubtedly, this edition will be received by researchers with the same success as the first one."

"Heavy-tailed risk modelling plays a central role in modern risk theory; within this perspective, the book provides an excellent guide concerning problems and solutions in risk theory."

"This is a solid mathematical treatment of some topics in the analysis of change-point models. The book is intended for graduate students and scientific researchers using statistics in practice."

"Dr Markin's book serves as a highly valuable tool box for integration. It guided me through the scenarios where a particular technique should be applied and how to apply that technique. I love the organization of the techniques, especially in Chapter 7 Integration of Rational Functions and Chapter 8 Rationalizing Substitutions, a remarkable chapter of the book. The book also provides theorems that explain why the method works, which I found very useful for my Analysis class."

"The title In the Search for Beauty reflects not just a beauty of geometry (and mathematics in general) but also a beauty of creativity, intellectual challenge and intellectual courage. The author, Voldemar Smilga, produced these reflections in a form of dramatical story of the fifth Euclidean postulate. The lively presentation of main characters makes it an interesting reading for everybody."

"This book offers one of the few places where a collection of results from the literature can be found ... The book has an extensive bibliography ... It is very nice to have the compendium of results that is presented here."

"I believe the book will be welcome by amateur, as well as professional, metagrobologists. Many of the puzzles could be used as warm-up exercises to engender creative atmosphere in a math class. I am sure that many a math teacher will agree with this assessment."

"Professor Lima-de-Faria's book is wonderful and a pioneering work."

"This book provides an instructive and fascinating reading for scientists and mountaineers alike. It is written in an informal, witty style — yet the discussion is scientifically sound, without too little or too many details. The reader will learn not only about physics, but also about other subjects such as geology, mathematics and astronomy. Indeed, the author's strong background in theoretical physics adds flavour to the presentation, revealing unexpected connections with topics like quantum mechanics or cosmology..."

"This is an important book at a critical time. The paradox is that while our problems are complex and require long-term solutions our world is increasingly short-term focused. The only solution is to embrace stewardship so that we leave organisations and the world in better shape as a result of our efforts. This book lays out a powerful approach to do so"

"The text is lightly written but, underneath the entertaining gloss of anecdote and personal detail, this is actually an intensely serious and carefully constructed book, aimed at informing the educated public about science in general and nanotechnology in particular. It is attractively produced, with innumerable well-captioned coloured images ... To my mind, Colm Durkan has succeeded in combining the accessible style of the best science journalists with the authority and vision that come from being a successful scientist and an expert in his field."

"This is an essential book for anyone aiming to start a career in solar power or just seeking a deeper understanding. It's also an entertaining read, salted with personal anecdotes and, in places, wry humour. Jenny Chase gives a lively account of how she rose through a precarious startup to become the head of solar analysis at Bloomberg. There is helpful career advice. At its core the book contains detailed analysis of the history, technology, economics, finance, and business practices of the photovoltaics industry and her views on its prospects. The style is relaxed and discursive, and the reader feels privileged to be enjoying a coffee and a friendly chat with someone who is uniquely well informed about this industry so vital for our future."

"This appealing introduction to numerical analysis is unusual in the sense that it is truly introductory. It begins with a lengthy chapter that tells students what numerical analysis is about, what its major components are, and why understanding error is so important ... The authors pace the exposition very carefully ... The variety of exercises in the book is also a strength. There are exercises that test understanding of basic concepts, explorations that ask to students to work hands-on with ideas just presented, and end-of-chapter exercises. This book is definitely worth considering for anyone looking for a good introductory text..."

"The presentation is clear and easy to read. The book is well suited for its target audience and can serve as a good introductory textbook for students of theoretical physics and / or applied mathematics. Even active researchers may find in it a concise, accessible introduction to some advanced topics they are not familiar with."

"This is a truly wonderful book, utterly encyclopedic, deeply scholarly, and fascinating in the many stories it tells, and explaining the perplexing yet authentic development and resilient stream of Chinese Medicine — from its most ancient times, to the present day — an abundance of detail and historic quotations from classical works, and very many examples of how acupuncture, Chinese herbal and rehabilitative medicine have withstood the vicissitudes of famines, epidemics, book-burnings and dynastic wars, over the last 3,000 years or so."

"It is a book purely for the fun of solving puzzles ... The current book will add new problems to the existing ones."

"This is a marvellous book. The diversity of possible puzzles that can be given with these very limited resources, which are basically some paper and scissors, is overwhelming, and the challenges are sometimes very tough. Even the two-star problems may be hard for an untrained puzzler. This is medicine against boredom on long rainy days, but be careful not to get addicted or it may suck up your less empty and sunny days as well."

"There is a nice graduation of the level of the problems in the book. Some problems cover classical uses of the theory and will be very instructive to beginners, some are more refined and require a good knowledge of the theory and a bit of thinking, and some are even more sophisticated and sometimes close to Ayad's research questions. The interested readers will gradually get into the field and the more motivated ones will find some really challenging questions possibly leading to quite advanced research questions. With more than 90 problems on this topic, this is a very nice contribution to the topic, for which only a limited list of standard problems was available in the literature ... This rich book will be helpful to many mathematicians."

"Like its predecessors in this series, the book is an excellent reference for anyone interested in these topics. The authors did not lower the standards with respect to both clarity of the presentation and depth of the material. The reader can sense everywhere in the book the rich experience of the authors in teaching Mathematics, in particular Analysis in the broader sense, and the best proof for this are the fine balance they found between the hard theoretical results and applications, on one hand, and the appropriate examples that illustrate the theoretical results."

"The theory described in this book provides valuable perspective on real-valued Morse theory, and in the case of circle-valued functions it provides a new set of tools that could be quite useful to topological data analysts, just as Novikov's theory has allowed traditional Morse-theoretic ideas to be applied to new settings. Accordingly it should be of considerable interest to researchers and students studying persistent homology or Morse theory."

"Everyone interested in geometric dissections, and this kind of puzzles, either mathematically or recreationally will embrace this publication. But also the readers interested in the history and certainly those who became curious about this mystery man and his manuscript, after reading Frederickson?¡¥s 2006 book, will be fully satisfied with this respectful reproduction eventually made available for a general public."

"Overall, the eleven chapters give a diverse and detailed overview of the complex but fascinating topic of music and mathematics in partnership and how various academics have approached the problem of applying mathematics to music theory. This is a book for teachers interested in taking the teaching of rhythm and meter to a new level and introducing their students to current thinking on the topic in a practical and proven way."

"Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume. With a focus on mathematics and peppered with a scattering of computer science settings, the entries range from lightly humorous to curiously thought-provoking. Each chapter includes sections and sub-sections that illustrate and supplement the point at hand. Most topics are self-contained within each chapter, and a solid high school mathematics background is all that is needed to enjoy the discussions. There certainly is much to enjoy here."

"Krishnaswami Alladi has done a great service to the international academic community by editing the exciting auto-biography of his father, the eminent physicist Alladi Ramakrishnan. This book should be read by all those interested in the birth and growth of Matscience, The Institute of Mathematical Sciences, in Madras, India."

"Abramovich's book is unique in terms of variety... a strength of this book is that it includes many different content areas. This book exemplifies high quality teaching of teachers. It is the epitome of 'practice what you preach,' and would be an excellent resource for pre-service and in-service teachers, as well as graduate students who are studying mathematics teaching from a theoretical perspective."

"The exposition is exceptionally clear, and keeps its audience in mind: in the end, this is 'a book for adults on mathematics for children'. 'Adults' here includes parents as well as teachers; in the author's words, 'Every parent is automatically an educator!' There is considerable merit in including parents in the elementary mathematics conversation; it is a pleasure to see books like Kupferman's that explain elementary math to adults. If our students, in their future role as teachers, can enlist parents as allies, everyone will benefit. These books are one good way to begin addressing that challenge."

"A focus on issues that are important in economic theory or finance is clear throughout the book, and is likely to be a precious guideline for students of economic disciplines. Graduate students in economics and finance will find this book a valuable tool which will provide them with a strong motivation to deepen their knowledge of probability and statistics, leading to a better understanding of economic and financial theory."

"The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate... The book is carefully written, and the relevant literature is provided in the list of references."

"It's well written and is peppered with sections titled, ??exercises and complements'. Clearly the reader needs to take these very seriously. I personally find exercises in category theory and homological algebra very satisfying because of their architecture and their minimalist quality: it's a lot of fun for it all to come down to dancing all over a commutative diagram or two and to draw a lot of arrows. I like the subject a great deal, and I think this is a good book to learn it from."

"Faddeev's selected papers give ample evidence of his contributions at the forefront of physics and mathematics. The breadth, vigor and beauty of Ludwig's permanent accomplishments fully justifies calling him the 'Beethoven of mathematical physics.'" (See Full Review)

"The book is intended to convey to high school students or other interested laypeople some new and interesting things about numbers. It's also a useful book for faculty members to have on their shelves; they may find the book a useful collection of interesting information with which to spice up a lecture."

"This textbook is excellent for learning — or reviewing — methods of solving ODE's and their applications. Most textbooks have a limited number of solutions for exercises; Dr. Deng's book, however, not only provides answers for all problems in an appendix, but also provides the detailed step-by-step ways that one may arrive at those solutions, which is of great value to the student. For the price, you cannot go wrong with this book, even if it is not required for a course you are taking or if you are simply looking for a reference in the future to refresh your knowledge when you need it."

"It manages to give a useful and well-balanced coverage of numerical analysis."

"The authors give many examples, illustrations and exercises to help students digest the theory and they employ use of clear and neat notation throughout. I really appreciate their selection of exercises, since many of the problems develop simple techniques to be used later in the book or make connections of analysis with other parts of mathematics. There are also solutions to all of the exercises in the back of the book. As in the first volume there are some real gems in volume II. A Course in Analysis seems to be full of these little gems where the authors use the material or ask the readers to use the material to obtain results or examples that the reader will certainly see again in another context later in their studies of mathematics. Generally, the quality of exposition in both of the first two volumes is very high. I recommend these books." (See Full Review)

"It is a great book for a first year (US) graduate student. One of the nice features of the book is that the book contains full solutions for all of the problems which make it useful as reference for self-study or qualifying exam prep."

"This is a deep and beautiful monograph in functional analysis, at the interface with mathematical physics."

"The book is essentially self-contained, as the reader interested in copulas from the simulation point of view will find all necessary material in it, including an introduction to copulas if he has never been exposed to them. Both the theoretical and practical frameworks emerge quite clearly from the book. In any case, the rich bibliography contains all the references required for further in-depth analyses of specific issues. I think that the authors did a very good job, filling a gap in the statistical literature and providing a contribution that is going to be particularly helpful to statisticians without a specific background in copulas."

"I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very good book. It's pitched at the right level, it does a lot of serious stuff in preparation for what is coming the students' way in the future, and it does it well."

"This book is a useful reference for faculty members involved in contest preparation or teaching Euclidean geometry at the college level."

"This book is a recollection of her long life and impressive career. Overall it is a delightful self-portrait of a remarkable woman."

"In addition to presenting such a wonderful sweep of deep and beautiful material, it is very strong pedagogically. It's very well written, in an accessible and clear style, the material dealt with is effectively motivated and discussed in a sound and rigorous manner, all the proofs are there, and McLaughlin gives the reader a large number of exercises to do along the way, as he travels these paths. Again, the expressions and formulas that pepper the pages of this book are at first sight daunting, but they do yield to persistent pressure. The language of q-series makes for some beautiful poetry."

"This is likely to be an exciting and challenging book for motivated students, and would be fun to use in the classroom."

"This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access."

"The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ??friendly' aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises."

"The book has plenty of stimulating material and is very suitable for deepening many concepts of differential geometry and relativity in a hands-on manner."

"The collection transcends the traditional institutional division lines (private, public, large, small, research, undergraduate, etc.) and has something to offer for readers in every realm of academia. The collection challenges the reader to think about how to implement and improve undergraduate research experiences, what such experiences mean to students and faculty, and how such experiences can take a permanent place in the modern preparation of undergraduate mathematics and STEM majors. The book is an open invitation to learn about what has worked and what hasn't in the inspiration, and has the potential to ignite initiatives with long-lasting benefits to students and faculty nationwide."

"The basic ideas are very well written, the exposition is clear and the authors give complete proofs of most of the results they present."

"Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors."

"All are every interesting topics treated with a high level of mathematical sophistication. One of the very useful tricks the author repeatedly resorts to is the introduction of one-parameter families of operators interpolating between two operators which appear naturally in the formalism. From this one-parameter family a differential equation for the determinant (or ratio of determinants) or for correlation functions is derived, which can then be solved. This is a very simple, elegant and powerful technique."

Review of the First Edition: "The idea of numerous true-false questions was a particularly good one. The book was written for a student audience ... it should also prove quite valuable to instructors of an introductory topology course, as a readily available source of supplementary homework questions or exam questions."