Introduction to Database Management System - Formula Sheet

Database Structural and Syntax Formulas

While relational database management is heavily conceptual, several syntax templates and mathematical relationships govern database interactions, key properties, and data integrity.

1. Relational Model Cardinality Formula

The relation mappings (M to N) between entity sets are mathematically defined as:

• One-to-One (1:1): 0 or 1 instance of Entity A is associated with 0 or 1 instance of Entity B, and vice versa.
• One-to-Many (1:N): For 1 instance of Entity A, there exist 0, 1, or many instances of Entity B, but for 1 instance of B, there exists at most 1 instance of A.
• Many-to-Many (M:N): Multiple instances of Entity A map to multiple instances of Entity B, and vice versa.

2. SQL Command Templates (Syntax Formulas)

These structured query templates act as mathematical functions to define and manipulate data sets:

• Database Creation Function:
  CREATE DATABASE database_name;
  Where database_name represents the unique identifier of the target database space.
• Record Insertion Function:
  INSERT INTO table_name (col_1, col_2) VALUES (val_1, val_2);
  Where table_name is the relation, col represents attributes, and val represents attribute values.
• Aggregate Grouping Formula:
  SELECT grouping_column, SUM(aggregate_column) FROM table_name GROUP BY grouping_column;
  Where SUM is the aggregate addition function over the grouped attribute elements.

3. Credit Card Number Structure Parity Formula

The 16-digit structure printed on payment cards follows a strict partitioning formula for validation:

• Digit 1: Major Industry Identifier (MII) code.
• Digits 1 to 6: Issuer Identification Number (IIN) / Bank Identification Number (BIN).
• Digits 7 to 15: Individual customer account number.
• Digit 16: Check digit (calculated via Luhn's modulo 10 algorithm for error detection).