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