• The course emphasizes        
  • true or false 
  • proofs
  • counterexamples
  • logic
  • justifications
  • true vs. justified
  • precision in statements
  • connections between facts
  • a new attitude 

    an attitude toward mathematics that emphasizes truth, reasoning, and justification
    (as opposed to algorithms for calculation. There is very little calculation in this course.) 


 

Important things you will eventually understand

  • conditional sentences
  • generalizations
  • conjectures
  • counterexamples

    simpler counterexamples are better

  • existence statements
  • quantifiers (for all, there exists)
  • negation
  • logical forms 

    basic logical forms, for example, the contrapositive
    the logical equivalence called “a hypothesis in the conclusion”

  • concept definitions vs. concept images
  • definitions in “sentence-form”
  • prior results
  • proofs have two components, form and prior results

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