Download MAD 2104

MAD 2104
Discrete Mathematics
MAD 2104 Discrete Mathematics: (3) A.A. Three hours per week. Prerequisite: MAC 1105. This course
meets Area II requirements for both the A.A. General Education Requirements and A.S. General
Education Requirements. A proof-oriented approach to and applications of propositional logic, sets,
functions, relations, combinatorics, graphs and trees.
STUDENT LEARNING OUTCOMES:
The student, at the successful completion of MAD 2104, should be able to:
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Apply the techniques of logic in order to understand and create mathematical proofs.
Apply the concepts of universal and existential quantifiers in order to determine the truth value
of a given propositional function.
Determine the validity of an argument.
Apply the principle of mathematical induction in proofs.
Apply the concepts of set theory to problems that involve set operations, cardinality and
counting techniques.
Determine if a given relation is an equivalence relation.
Determine if integer ‘a’ is congruent to integer ‘b’ modulo ‘m’ and find all the residue classes
mod m.
Apply the concepts of relations and functions to problems involving recursion, sequences and
set equivalence.
Find the following when given a graph: vertices, edges, loops, length of a path, adjacency matrix
and subgraph.
Determine if a graph is connected, a tree, directed or undirected.
Find a minimum spanning tree for a weighted graph.
Determine if a connected graph has an Euler circuit and find such a circuit if one exists.
Date of Original Submission:
Date of Last Revision:
Date of Last Review:
6/4/07
10/14/13