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The title page of Elements of Algebra. Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler around 1765 in German. It was first published in Russian as "Universal Arithmetic" (Универсальная арифметика), two volumes appearing in 1768-9 [1] and in 1770 was printed from the original text.
Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols , variables, and set elements .
Wood was born in Holcombe, Bury where his father ran an evening school and taught his son the elements of arithmetic and algebra. From Bury Grammar School he proceeded to St John's College, Cambridge in 1778, graduating as senior wrangler in 1782. [2]
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether. [36] Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: [14] group theory; field theory
The square root of 2 is algebraic over Q, since it is the root of the polynomial g(x) = x 2 − 2 whose coefficients are rational.; Pi is transcendental over Q but algebraic over the field of real numbers R: it is the root of g(x) = x − π, whose coefficients (1 and − π) are both real, but not of any polynomial with only rational coefficients.
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Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [4] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...