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The Mathematical Sciences

Rapid growth in the nature and applications of mathematics means that the Newtonian core — calculus, analysis, and differential equations — is now just one part of a more diverse mathematical landscape. Yet most scientists have explored only this original territory, because that is all that was included in their curriculum in high school, college, and graduate school. With the exception of statistics, an old science widely used across all disciplines that has become largely mathematical during the 20th century, the narrow Newtonian legacy of analysis is the principal connection between practicing scientists and broad mathematical foundations of their disciplines.

The dramatic changes in the mathematical sciences of the last quarter century are largely invisible to those outside the small community of research mathematicians. Today’s mathematical sciences, like yesterday’s Gaul, can be divided into three parts of roughly comparable size: statistical science, core mathematics, and applied mathematics. Each of these three major areas is led (in the United States) by a few thousand active researches and receives approximately $50 million in federal research support annually. Although the boundaries between these parts overlap considerably, each province has an identifiable character paradigm established by Newton: data, deduction, and observation.

Core mathematics investigates properties of number and space, ideas rooted in antiquity. Its tools are abstraction and deduction; its edifices include functions, equations, operators, and infinite-dimensional space. Within core mathematics are found the traditional subjects of number theory, algebra, geometry, analysis, and topology. After a half-century of explosive specialized growth, core mathematics is experiencing a renaissance of renewed integrity based on the unexpected but welcome discovery of deep links among its various components.



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  8. Перевод слова mathematicsMathematics — математика Перевод слова Applied mathematics — прикладная математика computing mathematics — вычислительная математика pure mathematics — чистая математика He’s weak in Mathematics. Он слаб в математике. His only interest was Mathematics. Единственным его увлечением была математика. He could never master Mathematics. Он никогда не мог справиться с математикой....
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  10. Перевод слова coreCore — центр, ядро; основной, центральный Перевод слова The core of an apple — сердцевина яблока the core of a subject — суть дела in the core of the city — в самом сердце города That woman is rotten to the Core! Эта женщина прогнила насквозь! He singled out technology as the Core of the ... Читать далее...
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  29. My School — Моя школа (4)Our school is a fine four-storeyed building. There are many classrooms and specialized rooms for studying different subjects in it. The pupils study Mathematics, Physics, Chemistry, Russian, English, History, Geography and Biology in specialized rooms. Chemistry, Physics and Biology are taught in well-equipped science rooms. There is equipment for laboratory experiments there. At the lessons ... Читать далее...
  30. StarsLife cycle of a star Stars begin as clouds of dust and hydrogen, called nebulas. When they get hot enough they start burning hydrogen and produce energy. This process, called fusion, can last billions of years. When a star runs out of hydrogen the fusion process stops and it starts cooling down. Most stars become ... Читать далее...
  31. Education in the USAAmericans place a high value on education. Universal access to quality education has been one of the nation’s historic goals. Americas first college, Harward was founded in 1636. In 1865 education was becoming available to all. The peculiar feature of American education is the absence of national administration. Each of the 50 states controls and ... Читать далее...
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  33. Mikhail Lomonosov — Михаил ЛомоносовMikhail Lomonosov Mikhail Lomonosov was born in 1711 in Archangelsk province. His father was a fisher and young Mikhail liked to help him. He always strove for knowledge and liked reading books. As he was 19 years old, he decided to study in Moscow. He went there on foot. In Moscow he entered the Slavic ... Читать далее...
  34. Is It Science that Does Us Good or Does it Bring Disaster?В топике Достижения науки – нам во благо или во вред? рассматриваются достижения науки и техники, их влияние на окружающую среду, с одной стороны и улучшение условий жизни человека, с другой стороны. Все-таки, наука сделала очень много для прогресса, и мы уже не можем представить нашу жизнь без привычных удобств, и в этом – большая ... Читать далее...
  35. Перевод слова researchResearch — изучение, исследование, изучать Перевод слова Detailed research — подробное исследование environmental research — исследование окружающей среды a scientific research establishment — научно-исследовательское учреждение This book has been very well Researched. Эта книга была очень хорошо изучена. He did some Research via computer. Он провел небольшое исследование при помощи компьютера. His Researches have been ... Читать далее...
  36. ComputersТопик Компьютеры рассказывает историю компьютеров – потомков простого арифмометра, изобретенного профессором Чарльзом Бэббиджем в 1812 году. В наше время компьютеры используются повсеместно: индивидуальными пользователями, учеными, врачами-практиками, для обучения школьников основам информатики и вычислительной техники. Каждый выпускник школы должен уметь пользоваться компьютером, это важно для дальнейшей успешной карьеры. Если современный компьютер работает быстрее и точнее, чем ... Читать далее...
  37. René Descartes BiographyPhilosopher and mathematician René Descartes is regarded as the father of modern philosophy for defining a starting point for existence, «I think; therefore I am.» Synopsis René Descartes was born on March 31, 1596, in La Haye en Touraine, France. He was extensively educated, first at a Jesuit college at age 8, then earning a ... Читать далее...
  38. Weather and climateClimate is the weather a certain place has over a long period of time. Climate has a very important influence on plants, animals and humans and is different in different parts of the world. Some scientists think that the world is becomming hotter. If you compare Moscow winter and summer temperatures at the beginning of ... Читать далее...
  39. School Life — Школьная жизнь (2)Its very important to have good classmates because we spend a lot of time together. There are 28 pupils in our class — 15 boys and 13 girls. They come to our school from different parts of the city because our class is specialized in physics and mathematics. We do a lot also in chemistry, ... Читать далее...
  40. Exams: my negative experience — Экзамены: мой отрицательный опытIt`s been more that 2 years since I had my final exams, but the memories of them are disturbingly fresh. Though I was top of the class I can`t say that I didn`t have any problems with my finals. So I`d like to tell you mostly about my negative experience. My worst exam nightmare was ... Читать далее...

The Mathematical Sciences