MA3025 Logic and Discrete Mathematics II

Provides a rigorous foundation in logic and elementary discrete mathematics to students of mathematics and computer science. Topics from logic include modeling English propositions, propositional calculus, quantification, and elementary predicate calculus. Additional mathematical topics include elements of set theory, mathematical induction, relations and functions, and elements of number theory.

Prerequisite

MA2025 (preferable) or MA1025

Lecture Hours

4

Lab Hours

1

Course Learning Outcomes

After successfully completing this course, you will be able to:

• Represent mathematical statements using propositional and predicate logic. Establish basic results using direct proof, contraposition, and contradiction.
• Define and apply the process of mathematical induction. Identify and carry out strong induction when necessary. Demonstrate basic proficiency with the use of structural induction.
• Confidently use of basic counting techniques such as permutations, combinations, and the pigeonhole principle.
• Describe primality, divisibility, greatest common divisor, and least common multiple. Perform modular arithmetic and solve congruencies.
• State and apply Pascal’s formula and the binomial theorem. Be able to manipulate binomial coefficients and derive mathematical identities.
• Explain the inclusion-exclusion principle. Recognize when its use is necessary, and correctly apply the principle to counting problems.
• Define relation properties and equivalence relations. Analyze, compare, and apply relations to describe properties between sets.
• Identify graph terminology. Employ graphs as models. Define and identify Euler and Hamiltonian paths within graphs. Demonstrate proficiency in identifying and using graph isomorphisms and colorings.