*Algebra* is a branch of mathematics that deals with properties of operations and the structures these operations are defined on. *Elementary Algebra* that follows the study of arithmetic is mostly occupied with operations on sets of whole and rational numbers and solving first and second order equations. What puts elementary algebra a step ahead of elementary arithmetic is a systematic use of letters to denote generic numbers.

Mastering of elementary algebra which is often hailed as a necessary preparatory step for the study of Calculus, is as often an insurmountable block in many a career. However, the symbolism that is first introduced in elementary algebra permeates all of mathematics. This symbolism is the alphabet of the mathematical language.

The word "algebra" is a shortened misspelled transliteration of an Arabic title *al-jebr w'al-muqabalah* (circa 825) by the Persian mathematician known as al-Khowarismi. The *al-jebr* part means "reunion of broken parts", the second part *al-muqabalah* translates as "to place in front of, to balance, to oppose, to set equal." Together they describe symbol manipulations common in algebra: combining like terms, moving a term to the other side of an equation, etc.

In its English usage in the 14^{th} century, *algeber* meant "bone-setting," close to its original meaning. By the 16^{th} century, the form *algebra* appeared in its mathematical meaning. Robert Recorde (c. 1510-1558), the inventor of the symbol "=" of equality, was the first to use the term in this sense. He, however, still spelled it as *algeber*. The misspellers proved to be more numerous, and the current spelling *algebra* took roots.

Thus the original meaning of *algebra* refers to what we today call *elementary algebra* which is mostly occupied with solving simple equations. More generally, the term *algebra* encompasses nowadays many other fields of mathematics: geometric algebra, abstract algebra, boolean algebra, σ-algebra, to name a few.

## Topics in Algebra

- Cubic Formula
- Apparent Paradoxes And Related Wonders
- Cubic In Ars Magna
- How to Remove the Quadratic Term
- Cubic Polynomial In The Angle Trisection
- Tartaglia-Cardano Derivation
- Euler Derivation
- Product of Four Consecutive Integers
- Sum without Adding
- Transform Matrix
- Lagrange Identity
- Cauchy Inequality
- Inequality from Math Magazine 2009
- Sums of Power Series
- Sums of Successive Squares
- Long Up Short Down
- A Telescoping Series
- Cossali's Identity
- Carmichael's Identity
- Sophie Germain's Identity
- 3 Jugs Problem
- Inequality for a Series of Square Roots
- Rational Solution of x^y = y^x
- Vandermonde Determinant
- Divisibility of Prod-Dif and the Vandermonde Determinant
- Solving an Equation with Inverse Function
- Identities with Triangular Numbers
- 1=2 via Continued Fractions
- Viète's Formulas
- Problems in Factorials
- Extrema of x^3+y^3+z^3-xyz on the unit sphere