Mathematical Writing

• Follow guidelines for use of symbols.
• Use displays for important formulas and long expressions and calculations.
• Use effective transition phrases to connect the stages of a proof.

Sets

• Define a set by listing its elements or by stating a membership criterion.
• Recognize the common "number universes" N, Z, Q, R, C.
• Determine whether sets are equal.
• Determine when a set is a subset of another. Distinguish between the set membership relation and subset inclusion.
• Perform and use set operations: union, intersection, complement and relative complement.
• Work with indexed collections of sets.
• Recognize disjoint sets; use partitions of sets.
• Form the Cartesian product of sets.

Logic

• Use Truth Tables to determine the truth value of composite statements.
• Use statement connectives "not", "and", "or", "implies" and "if and only if".
• Recognize and use elementary logical equivalences (De Morgan's Laws, Conditional Statements, etc.)
• Determine logical equivalence of statements by using truth tables or by algebraic calculation.
• Use quantifiers symbolically and in English. Form the negation of statements containing quantifiers.
• Identify characterizations.

Proof

• Recognize and construct trivial and vacuous proofs.
• Construct direct proofs.
• Construct proofs using the contrapositive.
• Construct proofs using cases.
• Construct proofs about integers using the Division Algorithm.
• Evaluate purported proofs.

alex at iastate dot edu

Document last modified on Wed Feb 11 2009