Algebra was first studied thousands of years ago by the ancient Egyptians and Babylonians. For most of its history, people studied and developed algebra for enjoyment and intellectual challenge. In the last couple of centuries, algebra has been used extensively in the development of science, engineering medicine, and other fields.
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Algebra exists to find solutions
Islamic algebra is the same as regular algebra. just like Arabic numerals is the same as 1 2 3. why is algebra important today? there is no difference between these questions.
Algebra was not an important invention to Islam as a religion. It was an important invention in mathematics that was discovered by a Muslim (Al-Khwarizmi). Algebra is important in mathematics because it establishes the ability to perform mathematical operations even if some or all of the quantities are unknown.
Geometry is like a block from Algebra 1 to Algebra 2 and it contributes by teaching you the basics of the things you will learn in Algebra 2.
No but it is important. And so is spelling!