Heartland Community College
Master Course Syllabus
Division: Technology
Course Prefix and number: CSCI 115
Course Title: Discrete Structures
DATE PREPARED: July 1, 1999
DATE REVISED:
March 27, 2009
PCS/CIP/ID NO: 11-270101
IAI NO. (if available): CS 915, M1 905
EFFECTIVE DATE OF FIRST CLASS: June 1, 2000
CREDIT HOURS:
4.0
CONTACT HOURS: 4.0
LECTURE HOURS: 4.0
LABORATORY HOURS: 0.0
CATALOG DESCRIPTION:
Prerequisite: MATH 109 or equivalent, with a grade of C or better, or placement. Introduction to
analysis of finite collections and mathematical foundations of sequential machines, computer system
design, data structures and algorithms. Topics include sets and logic, sequences, subscripting and
arrays, number systems, counting, recursion, graph theory, trees, nets, Boolean algebra, automata, and
formal grammars and languages. Formal proofs (including induction) are introduced early in the
course and addressed throughout the course. Connections between the mathematical theory and
corresponding computer science applications are pervasive throughout the course. Computer
programming labs are written in the current language used in the core Computer Science
courses. This course is not intended for a Mathematics major or minor.
TEXTBOOK(S):
Kolman, B., Busby, R., Ross, S., (2004) Discrete Mathematical Structures, 5th Edition., Pearson
Prentice Hall.
RELATIONSHIP TO ACADEMIC DEVELOPMENT PROGRAMS AND
TRANSFERABILITY:
CSCI 115 fulfills 4 of the 3 (AA) or 6(AS) semester hours of credit in Mathematics, and the Math
requirement for the A.A.S. degree in Information Technology. CSCI 115 should transfer as part of
the general education core curriculum described in the Illinois Articulation Initiative to other Illinois
colleges and universities participating in the IAI. However, students should consult an academic
advisor for transfer information regarding particular institutions. Refer to the IAI web page for
information as well as www.itransfer.org.
COURSE OBJECTIVES (Learning Outcomes):
Outcomes
Demonstrate an understanding of
classical problem solving strategies in
varying circumstances.
Demonstrate an understanding of sets,
sequences and matrices and their
corresponding operations.
Solve basic counting and probability
problems, including some involving
combinations and permutations.
Demonstrate understanding of various
methods of proof, including induction.
Solve problems using recursive and
explicit algorithms.
Identify the costs and benefits of
recursion.
Demonstrate an in-depth understanding
of relations. Be able to represent them
in various ways (matrix, ordered pairs,
digraphs).
Apply the concept of growth of
functions to compute and compare the
complexity of simple algorithms.
Apply several classical algorithms
related to applications of Boolean
algebras, trees, and graphs.
Manipulate finite state machines using
different representations.
Demonstrate understanding of the
mathematical theory as it applies to
computer programming applications.
COURSE/LAB OUTLINE:
General Education Range of Assessment
Outcomes
Methods
PS4
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
PS4
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
CO1
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
Assignments
(Homework, labs, and
class discussion) and
exams
CO1
Assignments
(Homework, labs, and
class discussion) and
exams
1. Sets and sequences
2. Matrices and arrays
3. Logic
1. Notation
2. Proofs
4. Counting techniques (including recursion)
5. Relations
1. General relations and their representations
2. Functions (including growth and cryptography)
3. Partially ordered sets, lattices, and Boolean algebras
6. Trees
7. Graph theory
8. Automata theory
METHOD OF EVALUATION (Tests/Exams, Grading System):
Exams and Assignments:
Students will be evaluated by examinations and assignment (homework, labs, and class
discussions).
Assignments
%
44
Exams
38
Comprehensive Final Exam
Total
18
100
Grading Scale:
A
90% - 100%
B
C
D
80% - 89%
70% - 79%
60% - 69%
F
Below 60%
REQUIRED WRITING AND READING:
Students are expected to communicate the results of problem solving symbolically, graphically,
verbally, and narratively. Each section of homework exercises is preceded by required reading from
appropriate resources.