MATH 3000 – Learning Outcomes
Title: Bridge to Higher Mathematics
After successfully completing Math 3000, a student should be able to:
- Develop a truth table for a logical expression
- Express the negation of a logic statement
- Correctly decide if two statements are logically equivalent
- Express the converse, inverse and contrapositive of a logic statement
- Express universally and existentially quantified statements, and their negations
- Understand the definition of a set
- Correctly express the union, intersection and complement of sets
- Do a direct proof
- Correctly decide if a given proof is valid
- Do a proof by contrapositive, contradiction or exhaustion
- Understand indexed families of sets, their unions, intersections and complements
- Do a proof using mathematical induction: the statement to be proved may be an equality or an inequality
- Correctly decide if a given relation is an equivalence relation
- Correctly determine the equivalence classes of an equivalence relation
- Understand the division algorithm and its implications in divisibility problems
- Correctly express the power set of a given set, and its cardinality
- Correctly decide if a function is one-to-one, onto, or has an inverse
- Correctly formulate the composition of two functions
- Correctly decide if a set is finite, countable or uncountable
- Correctly use the epsilon definition of greatest lower bound and least upper bound in proofs
- Correctly apply the concepts of open and closed sets to proofs
- Correctly apply the concepts of limit points, deleted neighborhoods and closure to Proofs
- Correctly decide if a sequence is monotone and/or bounded
- Prove that a sequence converges to a limit, using the definition of convergence
- Correctly decide if a function is bounded or monotone