Upon successful completion of the course, each student should be able to do the following:

  1. Use statements, variables, and logical connectives to translate between English and formal logic.
  2. Use a truth table to prove the logical equivalence of statements.
  3. Identify conditional statements and their variations.
  4. Identify common argument forms.
  5. Use truth tables to prove the validity of arguments.
  6. Use predicates and quantifiers to translate between English and formal logic.
  7. Use Euler diagrams to prove the validity of arguments with quantifiers.
  8. Construct proofs of mathematical statements - including number theoretic statements - using counter-examples, direct arguments, division into cases, and indirect arguments.
  9. Use mathematical induction to prove propositions over the positive integers.
  10. Exhibit proper use of set notation, abbreviations for common sets, Cartesian products, and ordered n-tuples.
  11. Combine sets using set operations.
  12. List the elements of a power set.
  13. Lists the elements of a cross product.
  14. Draw Venn diagrams that represent set operations and set relations.
  15. Apply concepts of sets or Venn Diagrams to prove the equality or inequality of infinite or finite sets.
  16. Create bijective mappings to prove that two sets do or do not have the same cardinality.
  17. Identify a function's rule, domain, codomain, and range.
  18. Draw and interpret arrow diagrams.
  19. Prove that a function is well-defined, one-to-one, or onto.
  20. Given a binary relation on a set, determine if two elements of the set are related.
  21. Prove that a relation is an equivalence relation and determine its equivalence classes.
  22. Determine if a relation is a partial ordering.
  23. Use the multiplication rule, permutations, combinations, and the pigeonhole principle to count the number of elements in a set.
  24. Apply the Binomial Theorem to counting problems.
  25. Identify the features of a graph using definitions and proper graph terminology.
  26. Prove statements using the Handshake Theorem.
  27. Prove that a graph has an Euler circuit.
  28. Identify a minimum spanning tree.
  29. Define Boolean Algebra.
  30. Apply its concepts to other areas of discrete math.
  31. Apply partial orderings to Boolean algebra.
  32. Give explicit and recursive descriptions of sequences.
  33. Solve recurrence relations.