### MATH 2420

This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at http://www.gpc.edu/programs/Common-Course-Outlines.
Credit Hours   3
Course Title   Discrete Mathematics
Prerequisite(s)   MATH 1113 or MATH 1433 with a "C" or better
Corequisite(s)   None Specified
Catalog Description
This course introduces the concepts of finite mathematical structures. Topics
include set theory, logic, proof techniques, functions and relations, graphs,
trees, and combinatorics.

Expected Educational Results
As a result of completing this course, the student will be able to do the following:
1. Use critical thinking skills to solve problems by modeling the problem as an
instance of the finite mathematical structures studied in the course;
2. Demonstrate understanding of the concept of a finite mathematical structure
based on experience with various examples of mathematical structures,
especially those with application to computer science;
3. Construct and understand proofs based on direct or indirect reasoning,
mathematical induction, or the pigeonhole principle;
4. Apply the basic operations for sets, namely, union, intersection, complement,
and subset formation;
5. Construct, interpret, and evaluate logical statements involving and, or,
negation, and implication;
6. Describe similarities and differences in the mathematical structures of sets
and logical statements in terms of properties for the basic operations in each;
7. Classify a relation as one-to-one, onto, or functional;
8. Determine if a relation is an equivalence relation, a partial order, a permutation,
or a tree;
9. Given a finite relation, construct its incidence matrix, graph/digraph, and inverse;
10. Compose two sets given as ordered pairs, incidence matrices, or graphs;
11. Determine if a partial order is a Boolean algebra;
12. Represent a Boolean function as a circuit;
13. Traverse a tree in preorder, inorder, or postorder;
14. Describe the language of a phrase structure grammar;
15. Classify a grammar as Type 0, 1, 2 (context-free), or 3 (regular);
16. Represent a context-free or regular grammar with syntax diagrams or in BNF notation.

General Education Outcomes
I.      This course addresses the general education outcome relating to communication by providing
A. Students develop their listening skills through lecture and through group problem solving.
the instructions for text exercises, problems on tests, or on projects. Reading
mathematics text requires recognizing symbolic notation as well as analyzing problems
written in prose.
C. Students develop their writing skills through the use of problems that require written
explanations of concepts.
II.     This course addresses the general education outcome of demonstrating effective individual
and group problem-solving and critical-thinking skills as follows:
A. Students must apply mathematical concepts previously mastered to new problems and situations.
B. In applications, students must analyze problems and describe problems through pictures,
diagrams, or graphs, then determine the appropriate strategy for solving the problem.
III.    This course addresses the general education outcome of using mathematical concepts to
interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problem-solving skills including applications of
finite mathematical structures, functions and relations, graphs, combinatorics and logic.
B. Students must write functions to describe real-world situations and interpret information
from both the function (relation) rule and the graph of the function (relation).
C. Students must solve problems in combinatorics, graph theory and logic that often arise in
modeling numerical relationships.

Course Content
1.      Sets and Logic
2.      Proof Techniques
3.      Relations and Functions
4.      Combinatorics
5.      Graphs and Trees

ENTRY LEVEL COMPETENCIES
Upon entering this course the student should be able to do the following:
1.      Analyze problems using critical thinking skills.
2.      Use algebraic symbols to make a meaningful statements.
3.      Identify a function.
4.      Compose two functions.
5.      State the domain and range of a function.
6.      Sketch and identify a one-to-one function and its inverse.
7.      Find the inverse of a linear function.

Assessment of Outcome Objectives
Exams, assignments, and a final exam prepared by individual instructors will be used

II.     DEPARTMENTAL ASSESSMENT
This course will be assessed every five years. The assessment instrument will consist
of a set of free response questions that will be included as a portion of the final
exam for all students taking the course.

A committee appointed by the Executive Committee of the Mathematics Academic Group