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3. RELATIONAL DATABASE THEORY

Part 3 of this book explains the mathematical and theoretical foundations of relational database technology. The diagram below shows the strong dependencies between chapters. The first three chapters need to be read in order; however, chapter 3.3 on database normalization should be accessible for students who have a strong foundation in relational databases through the lens of SQL (Part 1 of the text) even without the preceding chapters on the relational model. Readers of chapter 3.4 will benefit from some exposure to SQL as well, although that is not a prerequisite.

Chapter dependency graph for Part 3

• 3.1. The relational model of the database
  • 3.1.1. Model basics
    • 3.1.1.1. Sets
    • 3.1.1.2. Relations
    • 3.1.1.3. Tuples
    • 3.1.1.4. Attributes
    • 3.1.1.5. Schemas
  • 3.1.2. Uniqueness and permutations
  • 3.1.3. Constraints
    • 3.1.3.1. Keys and primary keys
    • 3.1.3.2. Foreign keys
    • 3.1.3.3. Consistency
  • 3.1.4. Modification operations
  • 3.1.5. NULL
    • 3.1.5.1. Three-valued logic
    • 3.1.5.2. Constraints and NULL
  • 3.1.6. Self-check exercises
• 3.2. Relational algebra
  • 3.2.1. Unary operations
    • 3.2.1.1. Selection
    • 3.2.1.2. Projection
    • 3.2.1.3. Renaming
  • 3.2.2. Cross products and joins
    • 3.2.2.1. Cross product
    • 3.2.2.2. Join
    • 3.2.2.3. Theta-join and equijoin
    • 3.2.2.4. Natural join
  • 3.2.3. Set operations
  • 3.2.4. Division
  • 3.2.5. Queries
    • 3.2.5.1. Operation sequences
    • 3.2.5.2. Expression trees
• 3.3. Normalization
  • 3.3.1. Introduction
    • 3.3.1.1. Modification anomalies
    • 3.3.1.2. Example solution
  • 3.3.2. Normal forms
  • 3.3.3. Keys and superkeys
  • 3.3.4. Functional dependencies
    • 3.3.4.1. Types of functional dependency
    • 3.3.4.2. Inference rules
    • 3.3.4.3. Closure
  • 3.3.5. Second, third, and Boyce-Codd normal forms
    • 3.3.5.1. Second normal form
    • 3.3.5.2. Third normal form
    • 3.3.5.3. Boyce-Codd normal form
  • 3.3.6. Decomposition
    • 3.3.6.1. Decomposition algorithm
    • 3.3.6.2. Worked example
    • 3.3.6.3. Decomposition properties
  • 3.3.7. Multivalued dependencies and fourth normal form
  • 3.3.8. Trade-offs
  • 3.3.9. Normalization in database design
• 3.4. Differences between SQL and the relational model
  • 3.4.1. Relations as sets
  • 3.4.2. Tuples and attributes
  • 3.4.3. Logical confusions

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