Creating RDBMS Calculations

When you create a calculation in an RDBMS, you use a code to inform the system which mathematical operation you want it to perform. Here is a list of the common symbols and the operations they represent.

Eight operations were originally defined for relational databases and they form the core of modern database operations. The following list describes those original operations:

1. Selection: This selects some or all of the records in a table. For example, you might want to select .
   Select drink from fridge where drink = "juice";
2. Projection: This drops columns from a table (or selection).
3. Union: This combines tables with similar columns and removes duplicates. For example, suppose you have another table named FormerCompetitors that contains data for people who participated in previous years competitions. Some of these people are competing this year and some are not. You could use the union operator to build a list of everyone in either table. (Note that the operation would remove duplicates, but for these tables you would still get the same person several times with different events.)
4. Intersection: This finds the records that are the same in two tables. The intersection of the FormerCompetitors and Competitors tables would list those few who competed in previous years and who survived to compete again this year (the slow learners).
5. Difference: This selects the records in one table that are not in a second table. For example, the difference between FormerCompetitors and Competitors would give you a list of those who competed in previous years but who are not competing this year (so you can email them and ask them what the problem is).
6. Cartesian Product: This creates a new table containing every record in a first table combined with every record in a second table. For example, if one table contains values 1, 2, 3 and a second table contains values A, B, C, then their Cartesian product contains the values 1/A, 1/B, 1/C, 2/A, 2/B, 2/C, 3/A, 3/B, and 3/C.
7. Join: This is similar to a Cartesian product except records in one table are paired only with those in the second table if they meet some condition. For example, you might join the Competitors records with the NextOfKin records where a Competitors record's NextOfKin value matches the NextOfKin record's Name value. In this example, that gives you a list of the competitors together with their corresponding next of kin data.
8. Divide: This operation is the opposite of the Cartesian product. It uses one table to partition the records in another table. It finds all of the field values in one table that are associated with every value in another table. For example, if the first table contains the values 1/A, 1/B, 1/C, 2/A, 2/B, 2/C, 3/A, 3/B, and 3/C and a second table contains the values 1, 2, 3, then the first divided by the second gives A, B, C.

Question: What are some of the applications for mathematical calculations which can be performed within a database?
Mathematical calculations are a common task in many database applications. Here are some of the applications for mathematical calculations that can be performed within a database:

1. Financial Analysis: Many financial applications rely on complex mathematical calculations such as interest calculations, amortization schedules, and portfolio analysis. These calculations can be performed within a database to provide fast and accurate results.
2. Statistical Analysis: Databases can be used to store large amounts of data for statistical analysis. Mathematical calculations such as mean, median, mode, and standard deviation can be performed within the database to provide insights into trends and patterns in the data.
3. Data Mining: Data mining is the process of discovering patterns in large datasets. Mathematical calculations such as clustering, classification, and association rule mining can be performed within a database to help identify patterns and relationships in the data.
4. Scientific Research: Databases can be used to store scientific data such as experimental results and simulation data. Mathematical calculations such as regression analysis and Monte Carlo simulations can be performed within the database to analyze the data and test hypotheses.
5. Manufacturing and Quality Control: Databases can be used to store data related to manufacturing processes and quality control. Mathematical calculations such as process capability analysis and control charting can be performed within the database to monitor and improve the manufacturing process.

Mathematical calculations performed within a database can provide fast and accurate results, help identify patterns and trends in data, and support scientific research, financial analysis, manufacturing, and quality control.