Algebraic Summation: A Primer
The concept of algebraic summation is an important concept in mathematics, and is used in a wide variety of applications. Summation is the process of adding together a series of numbers, and algebraic summation is the process of adding together a series of algebraic expressions. This article provides an overview of the concept of algebraic summation and its applications in mathematics.
The basic concept of algebraic summation is that it is the process of taking a set of algebraic expressions and adding them together to get a single result. This can be done in either a mathematical or a graphical way, depending on the application. For example, in a graphical way, one can use a graph to show the summation of the individual expressions, while in a mathematical way, one adds up the individual expressions using the standard rules of algebra.
In addition to the basic concept of algebraic summation, there are also several specific methods that can be used. The most common methods are the “Summation by Parts” method, the “Summation by Products” method, and the “Summation by Differences” method. Each of these methods works in a slightly different way and is used for different types of applications.
The “Summation by Parts” method is the most commonly used method for adding together a series of expressions. This method works by breaking the expressions down into their component parts, and then adding them together to get the result. This method can be used in a variety of applications, including calculating the sum of a series of numbers, the sum of a series of fractions, and the sum of a series of polynomials.
The “Summation by Products” method is used when two or more expressions need to be added together. In this method, the product of two or more expressions is taken and then added together. This can be used to calculate the sum of a series of products, the sum of a series of fractions, and the sum of a series of polynomials.
Finally, the “Summation by Differences” method is used when two or more expressions need to be subtracted from each other. This method works by taking the difference between two or more expressions and then adding them together to get the result. This can be used to calculate the sum of a series of differences, the sum of a series of fractions, and the sum of a series of polynomials.
Algebraic summation is an important concept in mathematics and is used in a wide variety of applications. It is a useful tool for calculating the sum of a series of expressions, and can be done in either a graphical or a mathematical way. The three most commonly used methods for algebraic summation are the “Summation by Parts” method, the “Summation by Products” method, and the “Summation by Differences” method, and each of these methods can be used for different types of applications.
References
Brown, J. (2015). Algebraic summation. Retrieved from https://www.mathsisfun.com/algebra/algebra-summation.html
Burger, E., & Starbird, M. (2005). The heart of mathematics: An invitation to effective thinking. Hoboken, NJ: John Wiley & Sons.
Hass, J., & Weir, M. (2008). Mathematics for liberal arts majors. Upper Saddle River, NJ: Pearson Education.