{"title":"Vi Arnold","description":null,"products":[{"product_id":"ordinary-differential-equations-book-vi-arnold-9780262510189","title":"Ordinary Differential Equations","description":"Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49543786987793,"sku":"GOR010172748","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":50098512167185,"sku":"CIN0262510189G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52684904005905,"sku":"NLS9780262510189","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0262510189.jpg?v=1751258951"},{"product_id":"experimental-mathematics-book-vi-arnold-9780821894163","title":"Experimental Mathematics","description":"One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years.  This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments).  Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50628641194257,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50628641620241,"sku":"GOR013034460","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":52948555202833,"sku":"CIN0821894161G","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821894161.jpg?v=1763475524"},{"product_id":"singularities-of-differentiable-maps-volume-1-book-vi-arnold-9780817683399","title":"Singularities of Differentiable Maps, Volume 1","description":"​Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science.  The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.   The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level.  With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51008516489489,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51008519405841,"sku":"NIN9780817683399","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52593841275153,"sku":"NLS9780817683399","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0817683399.jpg?v=1751169808"},{"product_id":"geometrical-methods-in-the-theory-of-ordinary-differential-equations-book-vi-arnold-9780387966496","title":"Geometrical Methods in the Theory of Ordinary Differential Equations","description":"Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, aswell as all users of the theory of differential equations.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52134684131601,"sku":"NLS9780387966496","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":52772113744145,"sku":"CIN0387966498G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387966496.jpg?v=1757544511"},{"product_id":"dynamical-systems-v-book-vi-arnold-9783540653790","title":"Dynamical Systems V","description":"Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to hot topics, such as the characterization of personalities and the difference between a genius and a maniac. Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52143722823953,"sku":"NLS9783540653790","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540653790.jpg?v=1757585699"},{"product_id":"singularities-of-differentiable-maps-book-vi-arnold-9781461295891","title":"Singularities of Differentiable Maps","description":". there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life . A. P. Chekhov. On the road In this book a start is made to the zoology of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144307175697,"sku":"NLS9781461295891","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461295891.jpg?v=1757588306"},{"product_id":"singularities-of-differentiable-maps-book-vi-arnold-9781461284086","title":"Singularities of Differentiable Maps","description":"The present. volume is the second volume of the book Singularities of Differentiable Maps by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled Classification of critical points, caustics and wave fronts, was published by Moscow, Nauka, in 1982. It will be referred to in this text simply as Volume 1. Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52337322197265,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52337322885393,"sku":"NLS9781461284086","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461284086.jpg?v=1758166277"},{"product_id":"singularity-theory-i-book-vi-arnold-9783540637110","title":"Singularity Theory I","description":"This is a compact guide to the principles and main applications of Singularity Theory by one of the world's top research groups. It's ideal for any mathematician or physicist interested in modern mathematical analysis.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52485731549457,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52485732598033,"sku":"NLS9783540637110","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540637110.jpg?v=1759858125"},{"product_id":"geometrical-methods-in-the-theory-of-ordinary-differential-equations-book-vi-arnold-9781461269946","title":"Geometrical Methods in the Theory of Ordinary Differential Equations","description":"Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. 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