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Student Learning Outcomes

Course Name: A Transition to Advanced Mathematics
Course Number: Math 245
Course Objectives:
  • Students will feel that mathematics is a beneficial part of their education
  • Use techniques such as contradiction and contrapositive to prove statements.
  • Perform set operations using union, intersection, complementation, and DeMorgan's Laws.
  • Write proofs involving the well-ordering principle and mathematical induction.
  • Write proofs pertaining to relations, equivalence relations, partitions, and equivalence classes.
  • Write proofs involving one-to-one functions, onto functions, preimage, and inverse image.
  • Write proofs pertaining to finite sets, countable sets, and uncountable sets. Apply the Bernstein-Schroder Theorem to prove the equivalence between sets.
  • Use the Axiom of Choice to prove statements pertaining to the cardinality of a set. Apply the Axiom of Choice to prove the Comparability Theorem.
  • Use the Heine-Borel Theorem to prove statements involving compact sets.
  • Math students feel they have the resources necessary for their success.
  • Use the Bolzano-Weierstrass Theorem to prove statements involving accumulation points and limit points.