of 23 results for Books: "Skanavi M.I." Problems in Mathematics for entering universities / Sbornik zadach po matematike dlya postupayushchikh v vuzy. You are given two nested radicals. To denest each of them, we can try to find two numbers u,v∈Q such that. 9+√80=(u+√v)3,9−√80=(u−√v)3. The product. Skanavi, M.I. i dr. Collection of tasks on mathematics for entering univ [n/a] on ruthenpress.info Author interviews, book reviews, editors' picks, and more.
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Skanavi Algebra. Uploaded by George Brown. Copyright: Attribution Non- Commercial (BY-NC). Download as PDF or read online from Scribd. Flag for. All sections of curriculum of elementary mathematics. Various e-books range containing full step by step instructions. ruthenpress.infov, ruthenpress.infov, ruthenpress.infoi. Items similar to Collection of tasks in mathematics for competitive exams, Edited by ruthenpress.infoi. Vintage Soviet mathematics book for university entrants. Math on.
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References The site materials have been prepared using the following literary sources: Text-books: 1. Elementary Geometry. Zaitsev, V. Ryzhkov, M. Elementary Mathematics. Kudryavtsev, B. Brief Course of Higher Mathematics. Venttsel, L. Theory of Probability. Reference books: 1. Reference Book of Elementary Mathematics.
All Course of Mathematics. Tsypkin, G.
Mathematical Formulas. Books of problems: 1. Edited by M. Book of Mathematical Problems for University Entrants. Edited by A. Vahovsky, A. Seller's other items.
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Approximately 1. Your max bid:. Resume bidding , if the page does not update immediately. In the first university years, it was Emmanuel L.
Fabelinskii, now famous for his work in physical optics, who stood at my side. Patashinski Yes. MFTI was a very special place to study, I know no analogies. No expense was spared to hire the best Soviet scientists to be our teachers. The number of students accepted each year grew rapidly over time, but in , the number of famous teachers seemed to be larger than the number of students.
After the five admission exams, a special commission, headed by the Rector, General Petrov, interviewed me in order to decide whether to accept me or not. I was one of only a few people who passed all exams without losing any points, and I had a gold medal from the school and I was a boxing champion of my large Siberian city, and other stuff.
The difficult question was, "Why are you Jewish? PoS What did you answer? Patashinski Oh, I had expected this question. I had the answer from a book I read: "I'm Jewish because my mother is Jewish, my father is Jewish, my cat is Jewish and my dog is Jewish. It wasn't clear after that if they would accept me. My friends decided just to kick out all the windows in the building if I was not accepted. But when the day of acceptance came and I came to the office, the secretary of the committee just waved her hand in a friendly greeting, and my friends went away, probably disappointed.
PoS How long were you in Moscow before you were accepted? Patashinski Abut a month or two. I came, probably, in June, and the acceptance exams in MFTI were scheduled in July or early August, earlier than in other places, to allow those not accepted to try with other universities.
PoS And these exams were physics and mathematics, or? Patashinski For a gold medallist, three exams in mathematics, and two in physics, written and oral; for others, additional exams in chemistry, in Russian language and literature, and probably in history and foreign language. PoS So by that time you knew it was going to be either physics or mathematics, or physics, strictly physics?
Patashinski It was important that it had some engineering flavor. I had chosen the Department of Radio-Physics--my father had had ties to electricity and radio.
PoS What did your father do? Patashinski As I mentioned, my father Zakhar had no rights to normal higher education in USSR, but due to the deficit of educated engineers in the s, he had a job as an electrical engineer, and learned extramurally, which was not forbidden to him.
He got his engineering diploma just before he went into the army, in I was told he was brilliant in math and could do many technical things with his hands. I actually can't remember his image because I was not even five when he went to the army, and he died from wounds in He was a communications officer in a special howitzer regiment.
PoS So in Moscow, what happened when you went to the Institute? What courses did you take? The intensity of learning, especially in the first 4 years was well above what was allowed in other universities. You had to pass a special medical test to prove that you would be able to hold the load. Mathematics was taught at a good university level for applied mathematicians, and experimental physics, and engineering, a lot of lab work, and a lot of other stuff, and Marxist-Leninist philosophy, and a foreign language too.
I chose German, because the language in my family was Yiddish, and my paternal grandmother actually spoke German rather than Yiddish, I don't know why. PoS How many in the class when you started? Patashinski In the freshman class, there were about 30 Radio-Physics students accepted in This went down to about 20 at the end because some would not make it and had to go to other institutions, to Moscow University, the Bauman Institute, or whatever.
PoS That's for the Radio Technology department? About students were accepted to all four departments in PoS For example, in the mathematics course, how many would there be in a math class? In the classroom, how many students would there be? Patashinski The students were free to attend or not attend lectures, except for the mandatory Marxist-Leninist courses, and language classes.
But you had to pass exams and exercise tests. Normally, students were assigned into groups of about ten students for exercise training. This was separate from lectures that were given in a large auditorium for all of us. Our lecturer in mathematical analysis was a famous mathematician, Professor Mark A.
Neimark, a well-known algebraist. At some point, when I attended his supplemental classes in differential equations, he suggested that I become his student and a mathematician. I wanted to become an engineer at that time, I didn't want to become a mathematician. General physics was lectured by Professor Gabriel Gorelik. In , he threw himself under a train, people whispered this was because of disagreement with politics.
The hidden reason for that expulsion was that there was an International Youth Festival in Moscow, and it was seen as good to avoid us contacting foreigners. PoS I'm sorry, why were you sent to Kazakhstan?
Patashinski I, and many of my friends, thought it was a desire to prevent us contacting foreigners. A lot of foreigners were expected to attend the International Youth Festival in Moscow in Those students who tried to somehow avoid going to Kazakhstan were punished severely, in many cases expelled from MFTI. I went to Kazakhstan, and I worked in these fields and it was a pleasure, but when we understood the lies that lay behind keeping us in Kazakhstan for the entire summer instead of doing something else, there was an attempt to protest.
This almost ended up in big troubles for me when we returned to MFTI. I was warned, on time, by friends, and my friends and other students made it impossible for the guy Kudinov who was the party-assigned leader of our group in Kazakhstan, to make public accusations in a meeting of all students. There was actually nothing I could be really accused of, it was only my opinions and my stance, so to say. The time was the Khrushchev "thaw," a more democratic time, and for a short period one got new opportunities to survive.
PoS At what point did you switch over to becoming a physicist? The MFTI engineers were physicists specially taught and trained to generate new ideas and communicate to those who make real things, to hardware specialists, and do this on the fundamental and highest available level of basic science.
The idea in organizing MFTI in was to pick the best students available in the country and train them to lead in competition with the West in military and important industries.
This training included work in labs, in and outside MFTI, well- equipped with anything available in the world. We were permitted the risk to break the devices we were working on. This was, I bet, the best education one can imagine, extremely expensive for the state, but very good for us. In the U. PoS So just for a little bit, what is the kind of mathematics that Neimark would teach you? Patashinski The system of mathematical education was: first to teach us general mathematical ideas and formalisms, beginning with abstract spaces and objects in those spaces.
Definitions, objects and operations in abstract spaces, and then, on this basis, you can easily teach details. Analytical geometry, mathematical analysis, differential equations, Hilbert space, linear operators, groups. Say, if you go to quantum mechanics, that's very important stuff. The only important void, as I now think, in our math education was topology.
Topology was not taught, probably because this was not considered something that you can really use in calculations. PoS Where did you learn complex variables?
Patashinski Once, in a discussion here at Northwestern with my friend John [Ketterson], I started using a few theorems involving complex variables, and John said "Sasha, do you pretend to have in your university a special course in complex variables. The Lavrentiev and Shabad textbook plus some other books. The teacher in my group was Nikolay N. Moiseev, in later years a well-known scientist and Academy member. To pass his exam was not easy because in several hours of examination he tried to find my weak points.
PoS Somehow you're being trained to be some kind of very high-level engineer, but you gravitate towards theoretical physics. Patashinski A natural process plus chance. You work hard in the lab, and then make a test of the facility, and analyze factors limiting the accuracy of the experiment, and show this to your teacher.
Then you hear that "oh, you probably will become a theorist. We had to take a train to go from Dolgoprudnaja, where the Institute is situated, to Moscow. In my first student years, it was a steam engine. Once in this train, I run into a group of students who went to a special interview. Curious, I went with them; after they all had gone through the interview, I was interviewed, too, and accepted.
A year later, I met in the train a student who told me that he was preparing himself for the Landau theoretical minimum exam.
It appeared that there was a way to see Landau and even talk to him. Well, I and two of my friends got the program and the books, did some exercises, and passed the first Landau exam, math In a few years, I passed seven exams of the Landau theoretical minimum out of nine ; the last two exams were waved for me by Landau himself when I became his student.
Landau's theoretical minimum included two math exams, not in proofs and existence conditions, but a test of free and elegant use of any kind of mathematics, including tensors, curved spaces, differential equations, and complex variables. The math-1 included stuff used in mechanics and field theory like ordinary differential equations, the mathmore sophisticated stuff used in quantum mechanics. There were exams in mechanics, field theory including general relativity and cosmology, quanta, statistical mechanics, hydrodynamics, condensed matter, etc.
Not all of them existed at the time I describe, but there were very detailed programs and carefully chosen references. Before you went to take Landau's exam, what was your physics education?
Patashinski MFTI program was my physics education, a lot of physics and mathematics. I had nothing to add.