Topics for Comprehensive Exam in Mat 637

Logic:
Implications, Quantifiers, Negations, Converse and Contrapositive

Induction:
Simple induction proofs

Number Theory:
Prime Numbers, Greatest Common Divisor and Least Common Multiple, Euclidean Algorithm and Chinese Remainder Theorem

Combinatorics:
Definitions and simple examples for Permutations and Combinations, Pigeonhole Principle


Topics for Comprehensive Exam in Mat 604

Axioms for Counting Numbers
Induction and basic properties of Counting Numbers

Rational Numbers
Definition and basic properties

Place Value Representation
Base n representation of counting numbers and rationals, addition

Farey numbers and Continued fractions: real numbers