Discrete/Abstract Mathematics

• Logic & Boolean Algebra
  • Basic Logical Equivalencies and Valid Arguments
  • Proving Logical Equivalencies Using Boolean Algebra
  • Deriving Conclusions Using Valid Arguments
• Basic Proofs
  • Direct Proofs
  • Proofs By Cases
  • Proofs By Contraposition
  • Proofs By Contradiction
• Divisibility Proofs
  • Quotient-Remainder Theorem
• Naive Set Theory
  • Set Properties/Boolean Identities
  • Proving Set Identities Using Boolean Algebra
  • Proofs Involving Sets
    • Basic Operations
    • Indexed Families
    • Power Sets
    • Cartesian Products
• Equivalence Relations and Partitions
• Order In The Reals
  • Infimum and Supremum
  • Density of Rationals and Irrationals
  • Archimedean Property of Real Numbers
• Proofs Involving Functions
  • Well-defined Functions
  • Injectivity, Surjectivity, and Bijectivity
  • Image and Inverse Image
• Modular Arithmetic
• Principle of Mathematical Induction
  • Closed Forms of Summations
    • Special Summations
  • Closed Forms of Recursive Sequences
  • Recursive Identities
  • Divisibility
  • Inequalities
• Binomial Theorem
  • Proof of the Binomial Theorem
  • Binomial Expansions
  • Finding Binomial Coefficients of Specific Terms
  • Putting Combinatorial Sums in Closed Form