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The William Lowell Putnam Mathematical Competition 1985–2000

This book is the third collection of William Lowell Putnam Mathematical Competition problems and solutions, following [PutnamI] and [PutnamII]. As the subtitle indicates, the goals of our volume differ somewhat from those of the earlier volumes. Many grand ideas of mathematics are best first understood through simple problems, with the inessential details stripped away. When developing new theory, research mathematicians often turn to toy† problems as a means of getting a foothold. For this reason, Putnam problems and solutions should be considered not in isolation, but instead in the context of important mathematical themes. Many of the best problems contain kernels of sophisticated ideas, or are connected to some of the most important research done today. We have tried to emphasize the organic nature of mathematics, by highlighting the connections of problems and solutions to other problems, to the curriculum, and to more advanced topics. A quick glance at the index will make clear the wide range of powerful ideas connected to these problems. For example, Putnam problems connect to the Generalized Riemann Hypothesis (1988B1) and the Weil Conjectures (1991B5 and 1998B6).

Ҳар хил шўрланган тупроқлар шароитида ғўзанинг районлаштирилган “Бухоро-102” навини ўғитлашнинг ҳосилдорликка таъсири

Қорақалпоғистон Республикаси Амударё туманининг суғориладиган гидроморф тупроқлари шароитида турли даражада (шўрланмаган, кучсиз ва ўртача) шўрланишга мойил ерларида “Бухоро-102” ғўза навини маъдан ўғитларнинг N-160, P-100, K-70; N-190, P-130, K-90 ва N-220, P-160, K-110 кг/га меъёрларини таъсирини ўсиши, ривожланиши, ҳосилдорликка таъсирини ва унинг мелиоратив ҳолатига қай даражада таъсир этишини аниқлашдан иборат бўлиб ЎзПИТИ маълумотларидан фойдаланилган.

Mathematical Olympiad Challenges

Working mathematicians often tell us that results in the field are achieved after long experience and a deep familiarity with mathematical objects, that progress is made slowly and collectively, and that flashes of inspiration are mere punctuation in periods of sustained effort. The Olympiad environment, in contrast, demands a relatively brief period of intense concentration, asks for quick insights on specific occasions, and requires a concentrated but isolated effort. Yet we have found that participants in mathematics Olympiads have often gone on to become first-class mathematicians or scientists and have attached great significance to their early Olympiad experiences.

Истиқлол ва истиқбол

Китобда Самарқанд туманининг қисқача тарихи меҳнаткаш ва фидойи халқининг мустақилликдан кейинги йигирма йил давомида қўлга киритган ютуқлари туман аҳолисининг иқтисодий-ижтимоий манавий марифий ҳаёти турли соҳа мутахассислари томонидан ёзилган лавҳаларда ёритилган. Туман шоирлари ижодидан намуналар ҳам ушбу китобдан жой олган.

Сўз қўллаш санъати

Нотиқлик санъатига бағишланган бу иш фақат тилшуносларгагина эмас, барча касб эгаларига, аввало муаллимларга мўлжалланади. Ушбу рисола ёшидан, касбидан қатъий назар, ҳар бир ўзбек фуқаросининг севимли китобчасига айланса, ўзимизнц бахтли ҳис этамиз. Бу соҳадаги деярли дастлабки уриниш бўлиб, унда камчилик ва нуқсонлар учраши табиий. Китобхонларнинг тагслиф, танқид ва мулоҳазаларини мамнуният билан қабул этамиз.

Mathematical Handbook of Formulas and Tables

This handbook supplies a collection of mathematical formulas and tables which will be valuable to students and research workers in the fields of mathematics, physics, engineering, and other sciences. Care has been taken to include only those formulas and tables which are most likely to be needed in practice, rather than highly specialized results which are rarely used. It is a “user-friendly” handbook with material mostly rooted in university mathematics and scientific courses. In fact, the first edition can already be found in many libraries and offices, and it most likely has moved with the owners from office to office since their college times. Thus, this handbook has survived the test of time (while most other college texts have been thrown away). This new edition maintains the same spirit as the second edition, with the following changes. First of all, we have deleted some out-of-date tables which can now be easily obtained from a simple calculator, and we have deleted some rarely used formulas. The main change is that sections on Probability and Random Variables have been expanded with new material. These sections appear in both the physical and social sciences, including education.

Анализ формирования качества семян пшеницы

Селекционеры и семеноводы совместно начали внедрять местные сорта пшеницы селектированные в почвенно- климатических условиях вилоятов. Но они во многом еще не соответствуют к внутренним и внешним стандартным требованиям.

ТАРИХИ ФАРҒОНА

Ҳамдимиз ул зоти вожиб ул-вужудғаким, мавжудоту махлуқотларини «кун» ибораси илан вужудға чиқоруб, холиқ ул-халқ вас-само ва сониъ ул-кавокиб вал-ҳаво ул зоти пок ақдас эконин зул-уқулларга аён ва ошкора этиб, алар маишати ва фойдасиға анвоъи фавокиҳот ва ниъамотларни курраи арзда халқ этиб, муждаи «халақа лакум ма фил-арзи жамиъан» 1 оятин юборди. Ва дуруди номаъдуд ўтмиш анбиёи изомларинаким, барчалари ҳодиййи умам ва набиййи муҳтарамдурлар. Алал-хусус салавоту салом набиййуно саллоллоҳу алайҳи васаллам ҳазратларинаким, шофиъи жами умам ўлуб, «лав лока ламо холақтул-афлок» 2 муждасига ноил ўлуб, «ва-ласавфа юътика роббука фатарзо»3 ояти каримаси ҳақларида нозил ўлмишдур. Ва дуруди номаъдуд чаҳор ёри изом ва хулафойи киромларинаким, миллати ислом учун сидқу эҳсон ва базли жон этмишлар

Mathematical Formula handbook

This Mathematical Formaulae handbook has been prepared in response to a request from the Physics Consultative Committee, with the hope that it will be useful to those studying physics. It is to some extent modelled on a similar document issued by the Department of Engineering, but obviously reflects the particular interests of physicists. There was discussion as to whether it should also include physical formulae such as Maxwell’s equations, etc., but a decision was taken against this, partly on the grounds that the book would become unduly bulky, but mainly because, in its present form, clean copies can be made available to candidates in exams. There has been wide consultation among the staff about the contents of this document, but inevitably some users will seek in vain for a formula they feel strongly should be included. Please send suggestions for amendments to the Secretary of the Teaching Committee, and they will be considered for incorporation in the next edition. The Secretary will also be grateful to be informed of any (equally inevitable) errors which are found.

Янги Оберег, мивали-агро ва фитофакс стимуляторларининг пахта ҳосилдорлигига таъсири

Стимуляторлар билан чигитга ишлов берилганда уларни униб чиқишини тезлаштириб, ниҳолларни касалликларга чидамлилигини ошириб, ғўзани ўсиши ва ривожланишини яхшилайди, ҳосилнинг эрта пишиб етилишига ёрдам беради.

Mathcad: математический практикум для экономистов и инженеров

Пособие представляет собой сборник заданий по стандартному курсу высшей математики для экономических и некоторых инженерных специальностей. Задания включают постановку задачи, краткое описание математического метода решения, анализ результатов вычислений. Примеры содержат все необходимые рекомендации по работе с математической моделью и пакетом. Для студентов экономических инженерных вузов, преподавателей математики, научных работников, пользователей компьютеров, применяющих математические методы в практической работе.

Волшебный мир звуков и слов.

В пособии представлены методические разработки логопедических знаний, в основе которых-комплексно-игровой метод, сказочные сюжеты и лексические темы.

Касб-ҳунар коллежи ўқувчилари шахсида спорт ўйинлари орқали ўз-ўзини назорат қилишнинг диагностикаси

Битирув малакавий иши психологияда етарлича ўрганилмаган психик феноменлардан бири – ўз-ўзини назорат қилиш муаммосига бағишланади. Унда ўз-ўзини назорат қилишнинг тарихий ўрганилиши, илмий психологияда ва айниқса спорт фаолиятига боғлаб ўрганилганлик ҳолатига қаратилган илмий изланишлар таҳлили акс этган.

Вязание крючком от А до Я

Вязание крючком – это увлекательное и модное хобби. Оно не только поможет отвлечься от будничных забот, но и в полной мере раскроет ваш творческий потенциал. Научиться вязать легко! Моток пряжи, крючок, этот наглядный самоучитель - и вы освоите основные техники вязания крючком от А до Я. Пошаговые инструкции описывают каждое движение вязальщицы при выполнении цепочки из воздушных петель, столбиков с накидом и без, при вывязывании узоров, сборке и украшении готового изделия. Шаг за шагом, навык за навыком – и ваша первая модель готова!

Math Wonders

Let me begin by saying that I agree completely with Russell’s statement, which I first read some years ago. However, I had independently arrived at the same conviction decades earlier when, as a 10- or 12-year-old, I first learned of the existence of the Platonic solids (these are perfectly symmetric three-dimensional figures, called polyhedra, where all faces, edges, and angles are the same—there are five such). I had been reading a book on recreational mathematics, which contained not only pictures of the five Platonic solids, but patterns that made possible the easy construction of these polyhedra. These pictures made a profound impression on me; I could not rest until I had constructed cardboard models of all five. This was my introduction to mathematics. The Platonic solids are, in fact, sublimely beautiful (as Russell would say) and, at the same time, the symmetries they embody have important implications for mathematics with consequences for both geometry and algebra. In a very real sense, then, they may be regarded as providing a connecting link between geometry and algebra. Although I cannot possibly claim to have understood the full significance of this relationship some 7 decades ago, I believe it fair to say that this initial encounter inspired my subsequent 70-year love affair with mathematics.

2000 эксклюзивных узоров для вязания

Эта книга представляет собой уникальную коллекцию узоров, особенно модных в 2006 году. Она будет интересна не только опытным, но и начинающим вязальщицам. Представленные здесь узоры можно использовать для вязания джемперов, свитеров, пальто, кофт, костюмов, летних и зимних комплектов и так далее. Простые схемы и техники, собранные в конце книги, даже не нуждаются в описании. Всего лишь глядя на рисунок, вы легко повторите узор. Надеемся, что, используя наш удивительный сборник элегантных и модных узоров, вы всегда, в любой сезон года, будете выглядеть женственно и привлекательно. И, конечно же, не только вы, ведь узоры в этой книге прекрасно подойдут к мужским и детским вязаным моделям.