Applying Concepts Part One
Matrices
In the information technology field, teams use algebra in places where most are unaware. Normal users who use programs do not realize that computer-programming codes rely on mathematics to perform calculations. Calculations like a website calculating the mileage and how much gas a vehicle will use on a trip from AAA auto club is an example of a program using algebra calculations (American Automobile Association, n.d.). Other uses of algebra functions in the IT field or programming is the use of matrices or arrays.
A simple example of the using matrices is in the writing of computer programs such as Java would be for calculating tables. A developer can write a program to calculate a student’s total and average scores for a class.
Students Name Test 1 Test 2 Average Score
Tom 89 93 91
Sue 75 90 82.5
Frank 88 84 86
Average Test score of students = 87.5
In the program, the developer will set up a matrix within the code by declaring the number lines and columns of the matrix (m x n). The program will then ask for input to fill in the matrix (Programming Simplified, 2011), for example:
System.out.println (“Enter the first student’s name :”)
System.out.println (“Enter the first students Test #1 score :”)
After the user inputs the name and test score of the student, the program will then calculate the students score, an example of this code would be: averageScore = test1 * test2
The program will calculate the average score for the first student. After all the students are inputted, the program code would then calculate the total average score from the matrix. This can then be displayed for the user and others to show the scores and average scores for the class. The scientific and research fields leverage tables for data collection, inputting, calculation, and analysis. Programs and the accompanying code simplify the user’s work to calculate data.
Distance Between Two Points
In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to rules and is an effective way of describing the proximity of elements. In most cases, the distance between two points is the same if someone inverts the points, such as point A to point B is equivalent to point B to point A (Weisstein, 2013).
For example, the usual definition of distance between two real numbers x and y is d(x,y) = |x − y|. This definition satisfies the three conditions above, and corresponds to the standard topology of the real line. Distance on a specific set is a definition choice whereas another possible choice is defining: d(x,y) = 0 if x = y, and 1 otherwise. This also defines a metric, but gives a different topology, the "discrete topology"; with the definition that numbers are not close in proximity. In terms of relating to the everyday world, people use math frequently to determine the distance between two points. Motorists use MPH, which is a formula to determine distance by using the speed, and the number of miles left until the vehicle arrives at the destination. This helps to provide the remaining travel time (Weisstein, 2013).
Performing Operations on Functions and Relational Functions
The definition of a relation is any set of ordered pairs. Algebra states this is the set of the first components of the ordered pairs. Algebra calls this the domain of the relation and the set of the second components is the range of the relation. One may defines a function as the correspondence from a first set, known as the domain, to a second set, known as the range, such that each element in the domain corresponds to exactly one element in the range (Blitzer, 2010).
One uses these concepts with databases because the inputs and outputs are pieces of information that a Database Administrator uses to analyze data. Most companies store data in a type of database, which ranges from a Microsoft Access database to an SQL database. These technologies provide the ability to reference or query data quickly and easily. A real life scenario of using relations and functions is in the use of building a database. When designing a database, a database administrator must understand how relations and functions work to design a database that meets the requirements of the organization.
Example: USER_NAME and USER_ID
(Smith, 123), (Jones, 456), (Lopez, 789)
These relations are functions because there is one element that directly corresponds to another element in the range. The relationships are known as one-to-one relationships in databases. Numerous relationships would cause output inaccuracies.