Foundations of Computer Science

Foundations of Computer Science

TOPICS:-

The following list contains the topics to be be covered. Most of the topics, except for functional programming, are covered in the textbook.

• The Logic of Compound Statements
  • Logical form and logical equivalence
  • Conditional statements
  • Valid and invalid arguments
  • Application: Digital logic circuits
• The Logic of Quantified Statements
  • Predicates and quantifiers
  • Arguments with quantified statements
• Proof Methods
  • Direct proofs and counterexamples
  • Contradiction and contraposition
• Mathematical Induction and Recursion
  • Standard mathematical induction
  • Strong mathematical induction
  • Recursive definitions of sequences
• Set Theory
  • Basic definitions and properties
• Functions
  • Basic definitions and properties
  • Composition
  • Cardinality
  • Recursive definitions of functions
  • Functional programming
• Relations
• Basic definitions and properties
• Equivalence relations
• Partial order relations

Lecture Notes

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• Logic of Compound Statements (pdf, 22pp)
• Logical Arguments (pdf, 8pp)
• Logic of Quantified Statements (pdf, 14pp)
• Mathematical Induction (pdf, 19pp)
• Sequences (pdf, 10pp)
• Set Theory (pdf, 23pp)
• Functions (pdf, 25pp)
• Recursion (pdf, 16pp)
• Functional Programming (pdf, 23pp)
• Relations (pdf, 24pp)