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Basics of Olympiad Inequalities

The aim of this note is to acquaint students, who want to participate in mathematical Olympiads, to Olympiad level inequalities from the basics. Inequalities are used in all fields of mathematics. They have some very interesting properties and numerous applications. Inequalities are often hard to solve, and it is not always possible to find a nice solution. But it is worth approaching an inequality rather than solving it. Most inequalities need to be transformed into a suitable form by algebraic means before applying some theorem. This is what makes the problem rather difficult. Throughout this little note you will find different ways and approaches to solve an inequality. Most of the problems are recent and thus need a fruitful combination of wisely applied techniques. It took me around two years to complete this; although I didn’t work on it for some months during this period. I have tried to demonstrate how one can use the classical inequalities through different examples that show different ways of applying them. After almost each section there are some exercise problems for the reader to get his/her hands dirty! And at the end of each chapter some harder problems are given for those looking for challenges. Some additional exercises are given at the end of the book for the reader to practice his/her skills. Solutions to some selected problems are given in the last chapter to present different strategies and techniques of solving inequality problems. In conclusion, I have tried to explain that inequalities can be overcome through practice and more practice.

Geometry and Topology

Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the M¨obius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups, having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. While the book requires minimal prerequisites, it provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics.

Энг чиройли исмлар ва уларнинг маънолари

Фарзанд дунёга келгач, унга чиройли ва туғри исм қўйиш ота- онанинг энг муҳим вазифаларидан ҳисобланади. Дарҳақиқат, инсоннинг исми унинг келажак тақдирига ҳам дахлдордир.

BIOLOGY IS TECHNOLOGY The Promise, Peril, and New Business of Engineering Life

This bookis the sum of more than a decade of discussions, research, and travel. The effort was made possible only through the generosity and patience of friends, colleagues, and family.

Handbuch Politische Ökologie

Wirklich, ich lebe in finsteren Zeiten!« – so beginnt Bertold Brechts Gedicht »An die Nachgeborenen«, das 1939 veröffentlicht wurde. Mit den »finsteren Zeiten« verweist Brecht auf die Zeit des Nationalsozialismus. Seine Kritik richtet sich dabei an all jene, die die »Untaten« des Nationalsozialismus verschweigen, indem sie »arglose« Wörter verwenden und belanglose Gespräche führen.

Red Hat Enterprise Linux 7

The System Administrator's Guide documents relevant information regarding the deployment, configuration, and administration of Red Hat Enterprise Linux 7. It is oriented towards system administrators with a basic understanding of the system. To expand your expertise, you might also be interested in the Red Hat System Administration I (RH124), Red Hat System Administration II (RH134), Red Hat System Administration III (RH254), or RHCSA Rapid Track (RH199)training courses. If you want to use Red Hat Enterprise Linux 7 with the Linux Containers functionality, see Product Documentation for Red Hat Enterprise Linux Atomic Host. For an overview of general Linux Containers concept and their current capabilities implemented in Red Hat Enterprise Linux 7, see Overview of Containers in Red Hat Systems. The topics related to containers management and administration are described in the Red Hat Enterprise Linux Atomic Host 7 Managing Containers guide.

Realm of ALGEBRA

ALGEBRA IS just a variety of arithmetic. Does that startle you? Do you find it hard to believe? Perhaps so, because the way most of us go through our schooling, arithmetic seems an "easy" subject taught in the lower grades, and algebra is a "hard" subject taught in the higher grades. What's more, arithmetic deals with good, honest numbers, while algebra seems to be made up of all sorts of confusing x's and y's. But I still say there's practically no difference between them and I will try to prove that to you. Let's begin by saying that if you had six apples and I gave you five more apples, you would have eleven apples. If you had six books and I gave you five more books, you would have eleven books. If you had six dandelions and I gave you five more dandelions, you would have eleven dandelions.

Problems in Mathematical Analysis II

This is the second volume of a planned series of books of problems in mathematical analysis. The book deals with real functions of one real variable, except for Section 1.7 where functions in metric spaces are discussed. Like the first volume, Problems in Mathematical Analysis I. Real Numbers, Sequences and Series, the book is divided into two parts. The first part is a collection of exercises and problems, and the second contains their solutions. Although often various solutions of a given problem are possible, we present here only one. Moreover, problems are divided into sections according to the methods of their solutions. For example, if a problem is in the section Convex Functions it means that in its solution properties of convex functions are used. While each section begins with relatively simple exercises, one can still find quite challenging problems, some of which are actually theorems. Although the book is intended mainly for mathematics students, it covers material that can be incorporated by teachers into their lectures or be used for seminar discussions. For example, following Steven Roman (Amer. Math. Monthly, 87 (1980), pp. 805-809), we present a proof of the well known Faà di Bruno formula for the nth derivative of the composition of two functions. Applications of this formula to real analytic functions given in Chapter 3 are mainly borrowed from the book A Primer of Real Analytic Functions by Steven G. Krantz and Harold R. Parks. In fact, we found this book so stimulating that we could not resist borrowing a few theorems from it. We

Problems in Mathematical Analysis I

This book is an enlarged and revised English edition of a Polish version published in 1996 by the Publishing House of Maria Curie-Skłodowska University in Lublin, Poland. It is the first volume of a planned series of books of problems in mathematical analysis. The second volume, already published in Polish, is under translation into English. The series is mainly intended for students who take courses in basic principles of analysis. The choice and arrangement of the material make it suitable for self-study, and instructors may find it useful as an aid in organizing tutorials and seminars. This volume covers three topics: real numbers, sequences, and series. It does not contain problems concerning metric and topological spaces, which we intend to present in subsequent volumes. The book is divided into two parts. The first part is a collection of exercises and problems, and the second contains their solutions. Complete solutions are given in most cases. Where no difficulties could be expected or when an analogous problem has already been solved, only a hint or simply an answer is given. Very often various solutions of a given problem are possible; we present here only one, hoping students themselves will find others.

Дилларда Ватан мадҳи

Мазкур тўплам кенг китобхонлар учун мўлжалланган бўлиб, ундан Ватан мадҳи алоҳида эътироф билан баён этилган. Тўплам кенг китобхонлар оммасига мўлжалланган.

Автомобил йўлларидаги сув ўтказувчи иншоотларни лойихалашда сув ва сел тошқинларининг тавсифларини хисоблаш

Хисоблашлар муайян мисолларда кўриб чиқилган ва уларни бажариш тартиби келтирилиб лойихалаш норматив қийматлари кўрсатиб ўтилган.

Beyond the square crochet motifs: 144 circles, hexagons, triangles, squares, and other unexpected shapes

Move beyond granny squares and get ready for crocheted circles, triangles, hexagons, and stars. Edie Eckman opens up the door to crocheting creativity with more than 140 motifs of every shape and size. Embellish your clothing, linens, housewares, and bags with colorful patterns as you put odd yarn leftovers to good use. Step-by-step instructions and color photographs provide the building blocks to limitless possibilities.

Ватанни семоқ иймондандир

Рисола кенг китобхонлар учун мўлжалланган бўлиб, ундан таълим-тарбия, тарғибот-ташвиқот, Ватан улуғлиги тўғрисида маълумотлар берилган.

Суғоришнинг бақлажон ҳосилдорлиги, сифатига таъсири ва унинг иқтисодий самарадорлиги

Битирув ишини бажаришдан асосий мақсад бақлажон махсулотини кўпайтириш ва уни иқтисодий самарадорлигини оширишдан иборат. Бақлажон етиштириш технологиясини ўрганиш, хосилдорлигини ошириш, ўсимликни экиш муддатлари, усуллари ва уни парваришлаш суғориш, ўғитлаш ва қатор ораларига ишлов бериш хамда касаллик ва зараркунандаларга қарши курашиш чораларини белгилаш вазифалари хисобланади. Шу билан бирга бақлажон етиштиришнинг иқтисодий самарасини аниқлаш яъни таннархини пасайтириш ва рентабеллик даражасини ошириш чоралари асосий вазифалардан бири хисобланади.

Чигитни пуштага экишнинг пахта ҳосилдорлигига таъсири

Олиб борилган ҳисобларига қараганда, ғўзани пушталарда ўстириш қўлланилаётган агротехник тадбирларнинг самарадорлигини ошириш, ҳар центнер пахта етиштириш учун сарфланадиган харажатларни камайтиришга имконият беради. Янги нав ва технологияларни ишлаб чиқаришга кириб келиши бу соҳада изланишлар олиб боришни талаб этади. Давлат аттестацияси комиссияси эътиборига ҳавола этилаётган ушбу битирув малакавий ишининг долзарблиги ҳам ана шунда деб ҳисобланади. Шундан келиб чиқиб битирув малакавий ишининг мақсад ва вазифалари белгилаб олинди.

Ўзбекистоннинг мустақил тараққиёти ва мафкуравий жараёнлар

Ушбу рисолада мустақилликни мустаҳкамлаш вазифалари миллий истиқлол ғоясининг зарурати ва унинг шаклланиш жараёнидаги ўзига хос жиҳатлар, юртдошларимиз қалби ва онгини эгаллашга қаратилган мафкуравий тажовузлар, уларга қарши кураш, ғоявий бўшлиққа йўл қўймасллик, янгича эътиқод каби масалалар акс эттирилган. Рисола кенг китобхонлар оммасига мўлжалланган.