Normalization is a systematic approach to organizing data in a database to reduce redundancy and improve data integrity. The main goal of normalization is to divide large tables into smaller, more manageable pieces while ensuring that the relationships between the data are preserved. This process involves applying a series of rules, known as normal forms, to the database schema.

• Redundancy: Duplication of data within a database, which can lead to inconsistencies.
• Anomalies: Problems that arise in a database due to redundancy. There are three main types of anomalies:
  • Insertion Anomaly: Difficulty in adding new data due to the absence of other required data.
  • Update Anomaly: Inconsistencies that occur when updating data in multiple places.
  • Deletion Anomaly: Unintended loss of data when deleting other data.

• Definition: A relationship between two attributes, typically between a primary key and a non-key attribute.
• Notation: If attribute B is functionally dependent on attribute A, it is denoted as A → B.
• Example: In a table of employees, if each employee has a unique ID, then the employee's name is functionally dependent on the employee ID (EmployeeID → EmployeeName).

Normalization involves organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. The process is divided into several normal forms:

• First Normal Form (1NF): Ensures that the table is a valid relation (i.e., it contains only atomic values and each column contains values of a single type).
• Second Normal Form (2NF): Achieved when the table is in 1NF and all non-key attributes are fully functionally dependent on the primary key.
• Third Normal Form (3NF): Achieved when the table is in 2NF and all the attributes are functionally dependent only on the primary key.
• Boyce-Codd Normal Form (BCNF): A stricter version of 3NF where every determinant is a candidate key.

• Reduced Data Redundancy: Minimizes duplicate data, saving storage space and reducing the risk of inconsistencies.
• Improved Data Integrity: Ensures that data is accurate and consistent across the database.
• Easier Maintenance: Simplifies the process of updating and maintaining the database.
• Enhanced Query Performance: Optimizes the database structure, which can lead to faster query execution.

Consider a table that stores information about students and the courses they are enrolled in:

• Redundancy: The student name "Alice" is repeated.
• Update Anomaly: If Alice's name changes, it must be updated in multiple rows.
• Insertion Anomaly: Cannot add a new course without assigning it to a student.
• Deletion Anomaly: Deleting a student could remove information about a course.

1. First Normal Form (1NF): Ensure atomicity.

   • The table is already in 1NF as each cell contains only a single value.

2. Second Normal Form (2NF): Remove partial dependencies.

   • Split the table into two tables to separate student and course information.

   Students Table: | StudentID | StudentName | |-----------|-------------| | 1 | Alice | | 2 | Bob |

   Enrollments Table: | StudentID | CourseID | CourseName | Instructor | |-----------|----------|------------|------------| | 1 | 101 | Math | Dr. Smith | | 2 | 102 | Science | Dr. Jones | | 1 | 103 | History | Dr. Brown |

3. Third Normal Form (3NF): Remove transitive dependencies.

   • Further split the Enrollments table to separate course information.

   Courses Table: | CourseID | CourseName | Instructor | |----------|------------|------------| | 101 | Math | Dr. Smith | | 102 | Science | Dr. Jones | | 103 | History | Dr. Brown |

   Enrollments Table: | StudentID | CourseID | |-----------|----------| | 1 | 101 | | 2 | 102 | | 1 | 103 |

Normalization is a crucial process in database design that helps to reduce redundancy and improve data integrity by organizing data into well-structured tables. By understanding and applying the concepts of normal forms, functional dependencies, and the benefits of normalization, you can create efficient and maintainable database schemas.