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    • ▾Bridge course
      • •Countable and uncountable sets
      • ▸Proof techniques
        • •Example of a nonconstructive proof
        • •Direct proof
        • •Disproof by counterexample
        • •Proof by cases
        • •Proving properties of absolute value
        • •Proof by contrapositive
        • •Proof by contradiction
        • •Proof by induction
        • •Proof by strong induction
        • •Proving de Moivre's theorem
        • •Visual proof
        • •Challenge
      • ▸Relations
        • •Equivalence relations
        • •Intersection of equivalence relations
        • •Representing relations using matrices
        • ▸Combining relations
          • •Composition of relations
        • •Inverse of composite relation
        • •Representing relations using digraphs
        • •Properties of relations
        • •Proving equivalence relations
        • •What is a relation?
        • •Finding the inverse of a relation on a finite set
      • ▸Functions (bridge course)
        • ▸Injective, surjective, and bijective
          • •Intro
          • •Is it bijective? (infinite domain)
          • •Is it injective?
          • ▸Is it surjective?
            • •Proof: Composite of surjections is surjection
          • •Proving properties of injective, surjective, and bijective functions
     › Bridge course

    Other resources

    YouTube videos

    • 3433The Traveler and the Strange Staircase (Screencast 4.1.1)
      GVSUmath
    • 3434Affine ciphers (Screencast 7.4.4)
      GVSUmath
    • 3435Extended Principle of Mathematical Induction: Example from computational geometry (Screencast 4.2.2)
      GVSUmath
    • 3436Function example: Counting primes (Screencast 6.1.4)
      GVSUmath
    • 3437Equivalence relations (Screencast 7.2.2)
      GVSUmath
    • 3440Functions: Terminology (Screencast 6.1.2)
      GVSUmath
    • 3455The Division Algorithm and Integer Congruence (Screencast 3.5.3)
      GVSUmath
    • 3457Negating quantified statements (Screencast 2.4.2)
      GVSUmath
    • 3458Application to Cryptography (Screencast 3.5.4)
      GVSUmath
    • 3461Conditional statements (Screencast 1.1.3)
      GVSUmath
      • More YouTube videos...

    Webpages

    • 128How To Write Proofs