Contents. Biography Vladimir Igorevich Arnold was born on 12 June 1937 in,. His father was Igor Vladimirovich Arnold (1900–1948), a mathematician. His mother was Nina Alexandrovna Arnold (1909–1986, Isakovich), an art historian.
When Arnold was thirteen, an uncle who was an engineer told him about and how it could be used to understand some physical phenomena, this contributed to spark his interest for mathematics, and he started to study by himself the mathematical books his father had left to him, which included some works of and. While a student of at and still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby solving. After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then.
He became an academician of the ( since 1991) in 1990. Arnold can be said to have initiated the theory of as a distinct discipline. The on the number of fixed points of and were also a major motivation in the development of. In 1999 he suffered a serious bike accident in Paris, resulting in, and though he regained consciousness after a few weeks, he had amnesia and for some time could not even recognize his own wife at the hospital, but he went on to make a good recovery. Arnold worked at the Steklov Mathematical Institute in and at up until his death.
As of 2006 he was reported to have the highest among Russian scientists, and of 40. To his students and colleagues Arnold was known also for his sense of humour. For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said: “There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer.
In accordance with this principle I shall formulate some problems.” Death Arnold died of on 3 June 2010 in, nine days before his 73rd birthday. His students include, and. He was buried on June 15 in Moscow, at the. In a telegram to Arnold's family, stated: “The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science. Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists. The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man.” Popular mathematical writings Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching and education.
His writings present a fresh, often approach to traditional mathematical topics like, and his many textbooks have proved influential in the development of new areas of mathematics. The standard criticism about Arnold's pedagogy is that his books 'are beautiful treatments of their subjects that are appreciated by experts, but too many details are omitted for students to learn the mathematics required to prove the statements that he so effortlessly justifies.' His defense is that his books are meant to teach the subject to 'those who truly wish to understand it' (Chicone, 2007). Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the school in France—initially had a negative impact on French, and then later on that of other countries as well. Arnold was very interested in the history of mathematics. In an interview, he said he had learned much of what he knew about mathematics through the study of 's book Development of Mathematics in the 19th Century —a book he often recommended to his students.
He liked to study the classics, most notably the works of, and, and many times he reported to have found in their works ideas that had not been explored yet.
Partial Differential Equations![]()
Excellent geometric insight, but occasionally annoying tendency to write 'it is obvious that.' For rather (notationally or logically) tricky parts of proofs.
![]() Ordinary Differential Equations Arnold
There is a fair number of errors, though these usually do not hamper understanding. Certain sections of the text may demand unexpectedly high levels of prior knowledge. In addition, there are some diagrams with crucial explanations (or no explanations at all) that are ambiguous, which can be frustrating to interpret. However, if one sticks Excellent geometric insight, but occasionally annoying tendency to write 'it is obvious that.'
Examples Of Differential Equations
For rather (notationally or logically) tricky parts of proofs. There is a fair number of errors, though these usually do not hamper understanding. Certain sections of the text may demand unexpectedly high levels of prior knowledge. In addition, there are some diagrams with crucial explanations (or no explanations at all) that are ambiguous, which can be frustrating to interpret. However, if one sticks to the reading and works through the problems as best they can, they will benefit substantially from it. It should be mentioned that it is often very difficult to treat proofs formally (partly because Arnold himself often does not give entirely formal proofs for the theorems proven). This therefore encourages an appreciation of the geometric view of ODEs.
“A fresh modern approach to the geometric qualitative theory of ordinary differential equations.suitable for advanced undergraduates and some graduate students. The notions of vector field, phase space, phase flow, and one parameter groups of transformations dominate the entire presentation. The author is acutely aware of the pitfalls of this abstract approach (e.g., putting the reader to sleep) and does a brilliant job of presenting only the most essential ideas with an easily grasped notation, a minimum formalism, and very careful motivation.”— Technometrics. “This college-level textbook treats the subject of ordinary differential equations in an entirely new way. A wealth of topics is presented masterfully, accompanied by many thought-provoking examples, problems, and 259 figures. The author emphasizes the geometrical and intuitive aspects and at the same time familiarizes the student with concepts, such as flows and manifolds and tangent bundles, traditionally not found in textbooks of this level.
The exposition is guided by applications taken mainly from mechanics. One can expect this book to bring new life into this old subject.”— American Scientist.
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