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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
     › Resources for undergrads

    Bridge course

    1. Countable and uncountable sets
    2. Proof techniques
    3. Relations
    4. Functions (bridge course)
    5. Other resources
    This may help you index:
    • Bridge course playlist by Adam Panagos

    Textbooks

    • Precalculus
      by David H. Collingwood, K. David Prince, and Matthew M. Conroy
      PDF