MAT422: March 2012 – July 2012

Mathematical Logic & Proving Techniques

Class Schedule

CSB1Af, CSB2Af, CSB3Bf, CSB3Af

  • Tuesday – 1600-1750 – A001
  • Wednesday – 1600-1750 – A001

Contents

  1. Set Theory
    • Sets and Subsets
    • Set Operations
    • Laws of Set Theory
    • Counting and Venn Diagrams
  2. Logic
    • Propositions: primitive, compound, truth values
    • Logical connectives and truth tables; negation, conjunction, disjunction, implication, biconditional
    • Converse, contrapositive, inverse
    • Translating English statements into symbolic form
    • Tautology, contradiction
    • Logical equivalences
    • Laws of logic, principle of duality
    • Logical implication
    • Arguments – validity of arguments by using truth tables and rules of inference, invalidity of arguments by using counterexamples
    • Quantifiers – existential and universal quantifiers, logical connectives and negations, logical equivalences, logical implications
    • Nested Quantifiers
  3. How to do proofs
    • Introduction
    • The Forward – Backward method
    • Definitions and Mathematical Terminology
    • The Construction Method
    • The Choose Method
    • Specialization Method
    • Negations
    • The Contradiction Method
    • The Contrapositive Method
    • Induction Method

Textbooks

  1. Douglas Ralph P. Grimaldi, Discrete and Combinatorial Mathematics,  4th edition, Addison Wesley, 1999.
  2. Daniel Solow, How to Read and Do Proofs, 4th edition. John Wiley & Sons, 2005.
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