COURSE NUMBER AND TITLE: MATH 2030 Logic and Set Theory

CREDIT HOURS: 3

CATALOG DESCRIPTION: A course meant to serve as a transition to advanced courses in mathematics. Topics covered include logical connectives, the algebra of propositions, quantification, and basic properties of sets, relations, and orders.

PREREQUISITE(S): MATH 1220 (grade of C or better) or MATH 2011 (grade of C or better)

SUGGESTED TEXT(S): A Transition to Higher Mathematics, by Smith, Eggen, and St. Andre

COURSE OUTLINE:

1. Basic first-order logic and proof methods
   • Logical connectives
   • Conditional and biconditional statements
   • Quantifiers
   • Proof techniques (direct proof, proof by contradiction, proof by contrapositive)
2. Sets
   • Operations on sets
   • The power set of a set
   • Families of sets
   • The well-ordering principle and proof by induction
3. Relations and functions
   • Cartesian products of sets
   • Relations on a set
   • Special properties of relations (symmetry, reflexivity, antisymmetry, transitivity)
   • Equivalence relations and partitions of a set
   • Orderings of a set (partial orders, linear orders, and well orders)
   • Functions
   • The notions of one-to-one and onto
   • The image and inverse image of a set under a function
4. Cardinal numbers and infinite sets
   • The cardinality of a set
   • Countable versus uncountable sets
   • The axiom of choice
5. Optional topics (time permitting)
   • Structures in Abstract Algebra
   • Ordered field properties of the real numbers