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.
Course Materials
The text is Introduction to Advanced Mathematics second edition, by William Barnier and Norman Feldman, published by Prentice Hall, 1990.
Spring 2008