Branch of mathematics: algebra.

I would like to tell you about one of the oldest branches of mathematics, the algebra.

Algebraic problems and methods, distinguishing it from other branches of mathematics, have been founding gradually from the ancient times. Algebra arose as a result of finding the formula or the uniform method to solving arithmetical tasks of the same type. Usually these methods are the compiling and solving equations. Thus in algebra concrete numbers was replaced by abstract symbols. So algebra consider only operations with abstract elements and properties of the operations; in other word, in modern sense of a term *algebra is the science about algebraic systems*.

Algebra's history:

First algebra's discoveries were made in Ancient China, Ancient Arabic countries, Mesopotamia and the others about 4000 years ago. But algebra became separate branch of mathematics in 9^{th} century, when al-Khwarizmi published his work "The Science of Reduction and Cancellation". Ancient Chinese mathematician used words in algebraic expression, but it was not comfortable, and the progress of algebra was impossible. From 13^{th} to 16^{th} century words in algebraic sentence were replaced by symbols. Earliest mathematicians, who developed algebra before 18^{th} century, were Arabic mathematician al-Khwarizmi, Greek mathematician Diofant (Диофант) (he was solving equations in whole numbers), later Italian mathematician Leonardo Fibonachi (Фибоначчи) (he was solving cubic equations), French mathematician Fransua Viet (Виет) (he finished replacing words by symbols) and others.

In 18^{th} century algebra developed in intimately relation with other branches of math. In that time mathematical analysis - powerful apparatus for solving many problems in different fields of mathematics - arose. And many problems of algebra such as basic algebra's theorem were solved by using methods of mathematical analysis. Algebra in 18^{th }- 19^{th} centuries is called algebra of polynoms. In the beginning of the 19^{th} century Norwegian mathematician Niels Abel (Абель) and French mathematician Evariste Galois (Галуа) proved that equations of fifth and higher degrees are unsolvable in radicals. Later Galois researched equations, which are solvable in radicals, and created groups theory. Thus algebraic science turned out to modern algebra, the science about algebraic systems. Modern algebra includes study of groups, fields, rings, algebras, lattices and a host of other subjects developed from formal, abstract point of view. Algebra is the science of a future. Algebraic discoveries, that were made about three hundred years ago, are applied not in mathematics only now in computer technology. And, I think, modern algebraic discoveries will be applied many years or hundreds years later.

Algebraicians from Omsk:

There are many world-known mathematicians in Omsk. V.N.Remeslennikov (Ремесленников) investigates applications of mathematical logic in algebra: model theory and algorithmic problems in algebra. V.A.Roman'kov's (Романьков) most famous results are about groups of automorphisms of algebraic systems. G.P.Kukin (Кукин) is a specialist in combinatorial and algorithmic algebra, and A.N.Zubkov (Зубков) - in invariant theory. A.N.Grishkov (Гришков) researches Lie algebras (алгебры Ли) and their generalizations. A.G.Mjasnikov (Мясников) and I.V.Ashaev (Ашаев) develop the computability theory. A.S.Shtern (Штерн) investigates representations of Lie algebras and their generalizations. G.V.Krjazhovskikh (Кряжовских) proved some bright theorems about algebras without identities. M.A.Shevelin (Шевелин) is a specialist in the cogomology theory. V.G.Shantarenko (Шантаренко) is studying the theory of algebra's varieties. S.A.Agalakov (Агалаков) proved many theorems about residually finite algebras. G.A.Noskov (Носков) researches algebraic groups.

Algebra is the most essential and beautiful branch of mathematics. It is the most exact science. Nowadays algebraic methods are used in all branches of mathematics. That is why I vary interested in algebra and, I think, I'll be specializing in algebra.