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Николаевич обсуждает свое отношение к разделению учеников на способных и менее способных в возрасте 15 лет.","Он считает, что выделение способных учеников для более интенсивной работы и целеустремленности необходимо, но не хочет, чтобы эти школы стали единственными поставщиками будущих ученых."]},"endTime":62,"title":"Отношение к разделению на способных и менее способных","beginTime":0},{"list":{"type":"unordered","items":["Андрей Николаевич говорит, что около половины ученых проявили свои способности и готовность работать в своем направлении в возрасте 15 лет.","Он также отмечает, что в возрасте 18 лет многие ученики теряют свою мечту стать учеными или физиками."]},"endTime":116,"title":"Влияние возраста на выбор профессии","beginTime":62},{"list":{"type":"unordered","items":["Андрей Николаевич рассказывает о том, как они стараются помочь ученикам, которые оказались недостаточно подготовленными, и отправляют их обратно в общеобразовательную школу.","Он также упоминает, что были случаи, когда ученики хотели попасть на биологический факультет или отделение прикладной лингвистики, но это было в порядке применения математики."]},"endTime":160,"title":"Решение о продолжении 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видео обсуждается реактивность и альтернативность в истории, где каждый переход сопровождается хаосом и возникновением диктатуры.","Автор приводит пример революции в Иране 1979 года, где после хаоса и коренной ломки, была установлена исламская республика."]},"endTime":662,"title":"Реактивность и альтернативность в истории","beginTime":388},{"list":{"type":"unordered","items":["Автор упоминает Макиавелли, который описал различные формы государственного устройства и их переход в тиранию или олигархат.","Он также приводит пример Украины, где олигархат установил свою власть, и это привело к хаосу и установлению тирании."]},"endTime":1144,"title":"Макиавелли и его идеи","beginTime":662},{"list":{"type":"unordered","items":["Украинцы в Херсоне пытаются угодить россиянам, но это не мотивирует их выступать за Россию.","Украинское население зомбировано и не включает разум."]},"endTime":4348,"title":"Проблемы в 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для любого целого числа a и простого числа p, a в степени b минус 1 сравнимо с единицей по модулю p.","Доказательство: умножение на a, a в степени 2, a в степени 3 и т.д.","приводит к различным остаткам по модулю p, что доказывает утверждение."]},"endTime":930,"title":"Малая теорема Ферма","beginTime":120},{"list":{"type":"unordered","items":["Определение многочлена с коэффициентами в кольце или поле.","Примеры многочленов: x в степени 2, x в степени 3, x в степени 4 и т.д.","Обсуждение свойств многочленов и их корней.","Вывод: многочлен x в степени n имеет n корней в поле остатков по модулю p."]},"endTime":1101,"title":"Многочлены над конечными полями","beginTime":930},{"list":{"type":"unordered","items":["Утверждается, что если многочлен f(x) делится на x-α, то существует многочлен g(x), такой что f(x) = g(x) (x-α).","Это утверждение верно для любых колец, включая кольца остатков."]},"endTime":4630,"title":"Теорема Безу","beginTime":1101}],"linkTemplate":"/video/http://www.youtube.com/watch?v=CyS4y8iT2Bs&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"cwidth":1920,"cheight":1080,"cratio":1.77777,"dups":["12398109580973502853"]},"7832669239249792576":{"videoId":"7832669239249792576","docid":"33-0-16-Z4DDF89BE9B62EDE2","preview":{"posterSrc":"data:image/png;base64,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видео обсуждается идея доказательства, которая заключается в том, что почти все траектории процесса Гельдерова порядка альфа-бета являются непрерывными.","Это условие выполняется с помощью оценки, которую дает Чебышев."]},"endTime":518,"title":"Идея доказательства","beginTime":413},{"list":{"type":"unordered","items":["План доказательства включает в себя определение процесса на двоично-рациональных временах, затем определение процесса на прочих временах с помощью предельного перехода."]},"endTime":687,"title":"План доказательства","beginTime":518},{"list":{"type":"unordered","items":["Мера Колмогорова определяется по конечномерным распределениям, но она не определена на множестве непрерывных траекторий.","Это приводит к проблеме, что разумные множества траекторий, такие как непрерывные, ограниченные и не отрицательные, оказываются неизмеримыми."]},"endTime":4280,"title":"Применение меры 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которая существует до сих пор."]},"endTime":1253,"title":"Научная деятельность и открытия","beginTime":612},{"list":{"type":"unordered","items":["Упоминается, что Колмогоров предложил аксиоматику, на основе которой развивается теория вероятностей.","Упоминается его вклад в топологию и открытие кольца когологии."]},"endTime":2923,"title":"Андрей Николаевич 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