MATH 131 Fundamentals of Mathematics I

Symbolic logic. Set theory. Cartesian product. Relations. Functions. Injective, surjective and bijective functions. Composition of functions. More about relations: Equivalence relations. Equivalence classes and partitions. Quotient set. Order relations: partial order, total order, well ordering. Mathematical Induction and recursive definitions of functions. Axiom of choice and its equivalents.