Undergraduate Courses

MA 330, Foundations of Mathematics

Course Description and Goals

This is a basic course on the foundations of mathematics, primarily intended for students in mathematics, science, engineering, and philosophy. Topics include

• symbolic logic and the algebra of logical operations, including conjunction, disjunction, negation, implication and equivalence
• methods of proof, including direct proof, counterexamples, and mathematical induction
• sets and the algebra of set operations, including union, intersection, complement, and Cartesian product
• abstract functions
• equivalence relations and their properties
• partial order relations and their properties
• cardinality, including finite sets, countably infinite sets, and uncountable sets

Additional topics may include

• combinations and permutations
• recurrence relations
• construction of number systems (integers, rational numbers, real numbers)

Course goals include

• an improved ability to think abstractly, and in particular, a basic understanding of mathematical structures defined axiomatically
• the ability to construct careful, correct, succinct proofs of simple theorems
• the ability to recognize fallacious arguments and logical flaws
• an improved understanding of the interplay between conjecture, example, counterexample, and proof
• a basic understanding of the central role of sets, functions, and relations in mathematics
• an improved ability to read, write, speak, and think in mathematical terms

Prerequisites

MA 172, Calculus B and one MA course at the 200 level or above

Credit Hours

3 Semester Hours

Grading System

This course is graded A, B, C, D, F. The grade typically depends on a combination of class tests, homework assignments, quizzes, and a comprehensive final exam.