Together with geometry, analysis, and number theory, algebra is one of the several main branches of mathematics. Elementary algebra is usually part of the curriculum in early high school and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variable, definition of polynomials, along with factorization and determining their roots. However, algebra is much broader than this. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields. Most students at the high school level are being exposed only to elementary algebra—its most basic form. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, -, ×, ÷) occur; in algebra, numbers are often denoted by symbols (such as a, x, y). This is useful because:
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