INTERNATIONAL UNIVERSITY OF GRAND-BASSAM
STEM: School of Science, Technology, Engineering and Mathematics
MTH 2300 – DISCRETE MATHEMATICS
Tuesday/Thursday 11:30 AM-12:50 PM – Room 22
Fall 2025
I.
II.
Instructor Information:
A. Name :
B. Phone :
C. Email :
D. Office location :
E. Office hours :
Akossi Aurelie Phd
N/A
akossi.a@iugb.edu.ci
TH 1:00pm-2:30 pm
By appointment
Course information
A. Number of Class Hours per week:
B. Number of Credits:
C. Articulation with Georgia State University:
D. Course Prerequisites:
3h
3
Yes
1.
MATH 1113 or MTH 1303, minimum grade of C
2.
MATH 2211 or MTH 1401, minimum grade of C
or
E.
F.
Computer Skills Prerequisites (CSP):
Course Description:
1, 2, 6
Introduction to discrete structures which are
applicable to computer science. Topics include
number bases, logic, sets, Boolean algebra, and
elementary concepts of graph theory.
III.
Position of the Course in the University Curriculum:
A. Level:
Undergraduate
B. Core Curriculum Group(s):
D,F,G elective [BS Math]
C. Required for majors:
IV.
Institutional Learning Outcomes supported by the Course:€
€
€
€
€
€
€
V.
VI.
Communication (Oral and Written):
Y
Collaboration:
N
Critical Thinking:
Y
Contemporary Issues:
N
Quantitative Skills:
Y
Technology:
N
Problem Solving:
Y
Instructional Goals Alignment: School, subject area and individual course goals
A.
Learn to write a mathematical proof,
B.
Strengthen problem solving skills,
C.
Learn the basic language and problem solving tools of discrete mathematics in order to use these infurther
study (either of computer science or of more advanced topics in discrete mathematics).
Learning Objectives: At the end of the course, students should be able to:
gMTH 2300 Syllabus
Spring 2025
Page 1
A.
Identify logical form, form compound statements using the connectives and, or and not, determine truth
tables of more general compound statements, determine whether two statement forms are logically
equivalent or nonequivalent, apply De Morgan’s laws to form negations of andandor, determine whether a
statement is a tautology or a contradiction, and use logical equivalences to simplify statement forms.
B.
Determine truth tables for compound statements containing conditional and biconditional connectives,
represent if-then as or, and then use this representation to negate an if-then statement, determine the
negation, contrapositive, converse and inverse of a conditional statement, rewrite a conditional statement
as an “only if” statement, and as sufficient and necessary conditions.
C.
Determine whether an argument is valid or invalid, use valid argument forms such as modus ponens,
modus tollens, etc. to do complex deductions, and illustrate a proof by contradiction using the knights and
knaves example.
D.
Give the input/output table for the following gates: OR, ANDandNOT, find a Boolean expression (input/output
table, respectively) of a circuit, find a circuit corresponding to a Boolean circuit (input/output table,
respectively) by finding the disjunctive-normal or sum-of-products form, determine whether two logical
circuits are equivalent, and simplify a combinatorial circuit.
E.
Represent a binary (hexadecimal, octal) number as a decimal number, represent a decimal (hexadecimal,
octal) number in binary notation, represent a binary number in hexadecimal (octal) notation, and add and
subtract binary numbers.
F.
Determine the domain and the truth set of a predicate variable, identify universal and existential
statements, be able to write these statements in formal and informal language, and identify universal
conditional statements, negate universal and existential statements, as well as statements containing both
universal and existential statements.
G. Define an even (odd) integer, prove an existential statement using an example, use a direct proof to prove
universal statements such as “The sum of an even integer and an odd integer is odd”, “If the difference of
any two integers is odd, then so is their sum”, etc., disprove a universal statement by an example, follow the
directions for writing proofs of universal statements, and identify common mistakes in proving statements.
H.
Use direct proofs or counterexamples to prove or disprove statements involving the rational numbers.
I.
Use direct proofs or counterexamples to prove or disprove statements involving the divisibility of integers,
and use the quotient-remainder theorem to illustrate a proof by division into cases.
J.
Use methods of proofs by contradiction and contraposition to prove various statements.
K.
Find the explicit formula for a sequence, and be able to do calculations involving factorial, summation and
product notations.
L.
Be able to prove statements using mathematical induction.
M. Determine whether one set is a subset of another, whether two sets are equal, whether an element is in a
set or not, be able to determine the union, intersection, difference and complement of sets, illustrate sets
using Venn diagrams, determine the Cartesian product of two or more sets, prove set identities, use set
identities to derive new set properties from old set properties, use Venn diagrams to prove set identities,
determine whether sets form a partition of a given set, and determine thepower set of a set.
N.
Determine whether a relationship is a function or not, determine the domain, co-domain, range of a
function, and the inverse image of x, prove or disprove whether a function is one-to-one or not, determine
whether a function is onto or not, determine the inverse of a one-to-one correspondence, determine the
composition of two functions, and show that if two functions are one-to-one (onto) so too is their composition.
O. Determine the arrow diagram of a relation, whether a relation is a function or not, determine the inverse of a
relation, whether a relation is reflexive, symmetric or transitive, determine the transitive closure of a
relation, show that the binary relation induced by a partition is an equivalence relation, and show that the
set of equivalence classes of an equivalence relation on A forms a partition of A.
P.
Identify loops, parallel edges, etc. in a graph, draw the complete graph on n vertices, and the complete
bipartite graph on (m,n) vertices, determine whether a graph is bipartite or not, list all the sub-graphs of a
given graph, determine the degree of a vertex in a graph, prove that the sum of the degrees of the vertices
is equal to twice the number of edges, show that in any graph there is an even number of vertices of odd
degree, apply these results, and determine the complement of a simple graph.
Q. Determine whether a walk is a path, simple path, closed walk, circuit or a simple circuit, determine whether
a graph is connected or not, prove that a graph has an Euler circuit if and only if the graph is connected
and every vertex of the graph has even degree, determine whether a given graph has an Euler circuit and, if
so, indicate one, prove that a graph has an Euler path if and only if the graph is connected and has exactly
gMTH 2300 Syllabus
Spring 2025
Page 2
two vertices of odd degree, determine whether a given graph has an Euler path and, if so, indicate one, and
determine whether a graph has a Hamiltonian circuit and, if so, indicate one.
R.
Determine whether a graph is a tree or not, show that any tree with more than one vertex has two leaves,
show that any tree with n vertices has n-1 edges, show that if G is a connected graph with n vertices and n1 edges, then G is a tree, determine in a rooted tree, the root, level of a given vertex, height of the tree,
children, parent, siblings, ancestors and descendants of a vertex, determine whether a given tree is a
binary or full binary tree, and prove results regarding binary trees.
S.
Apply Kruskal’s algorithm or Prim’s algorithm to determine a minimal spanning tree for a given graph.
VII.
Required Texts
Discrete Mathematics with Applications, 3rd edition by Susanna S. Epp, Brooks/Cole Publishing Company,
1995
VIII.
Additional References / Bibliography
IX.
Course Outline
Week Lecture Topic
1 Logic of Compound Statements
•
Logical Form and Logical Equivalence
•
Conditional Statements
•
Valid and Invalid Arguments
•
Digital Logic Circuits
•
Number Systems & Circuits for Addition
3 Logic of Quantified Statements
•
Predicates
•
Negation of Quantified Statements
•
Multiply Quantified Statements
•
Arguments with Quantified Statements
5 Elementary Number Theory and Methods of Proof
•
Proof and Counterexample
•
Rational Numbers
•
Divisibility
•
Quotient and Remainder
•
Contradiction and Contraposition
7 Sequences and Mathematical Induction
•
Sequences
•
Mathematical Induction
8 Set Theory
•
Basics of Set Theory
•
Set Properties
•
Boolean Algebra
9 Functions
•
Generic Functions
•
One-to-One, Onto and Inverse Functions
•
Pigeonhole Principle
•
Composition of Functions
11 Relations
•
Relations on Sets
•
Reflexivity, Symmetry and Transitivity
•
Equivalence Relations
•
Partial Order Relations
13 Graphs and Trees
•
Graphs
•
Paths and Circuits
•
Trees
•
Spanning Trees
X.
Reading
Chapter 1
1.1
1.2
1.3
1.4
1.5
Chapter 2
2.1
2.2
2.3
2.4
Chapter 3
3.1
3.2
3.3
3.4
3.6
Chapter 4
4.1
4.2
Chapter 5
5.1
5.2
5.3
Chapter 7
7.1
7.2
7.3
7.4
Chapter 10
10.1
10.2
10.3
10.5
Chapter 11
11.1
11.2
11.5
11.6
Methodology Used
gMTH 2300 Syllabus
Spring 2025
Page 3
Lectures will be based on the textbook. Students will have to read parts of the book before lectures, hence, to
help better understanding and participation of students in class. You are responsible for all the material
covered in class, whether or not you attended this class. It is therefore your responsibility to get miss
material from others before the next class
Taking good notes during the class is of significance importance.
XI.
Assessments
A.
Frequency
There will be weekly homework assignments. The purpose of them is to get you to live and breathe the
mathematics that we will be covering. It will be most helpful to regard them as a fun challenge.
B.
Weighting of different assessments
The course grade will be computed as follows: 30% homework, 25% midterm, 40% final, 5% contribution to
group discussions.
This last 5% will be based upon my assessment of the extent of your constructive participation in class
discussions. This is a judgment call that I alone will make.
C.
Types and expectations
There will be one midterm and a final. No programming assignments will be given. Your lowest homework
score might be dropped from the grade computation.
1.
Individual: All tests and assignments will be done on an individual basis. Anyone found cheating and/or
copying, in my opinion, will receive an automatic F for the course.
2.
Quizzes
3.
Exams
4.
In-class Participation
IUGB Grading Scale
Letter Grade Credit
A+
A
AB+
B
BC+
C
CD
F
K
V
W
WF
I
XII.
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
NO
YES
NO
NO
NO
NO
Quality
GradingScale
Points
(In Percentage)
4.30
97-100
4.00
93-96
3.70
90-92
3.30
87-89
3.00
83-86
2.70
80-82
2.30
77-79
2.00
73-76
1.70
70-72
1.00
59.5-69
0.00
<59.5
0.00
Credit by Exam Pass/Fail
0.00
Audit
0.00
Withdrawal
0.00
Failing withdrawal
0.00 Must be made up before the next semester begins
General Policies
Students are expected to follow all published IUGB rules and regulations.
The instructor reserves the right to modify the outline and/or the assignments as deemed necessary to meet
certain needs or situations that will arise during the semester.
Students with Special Needs or Disabilities: Please let the instructor know if you have any special needs and
need specific accommodations.
gMTH 2300 Syllabus
Spring 2025
Page 4
Attendance Policy: Attendance will be taken. I reserve the right to withdraw a student (with a ‘WF’) who has
excessive (≥ 6) absences.
Submission of Assignments: Hidden collaboration will be regarded as cheating.We will be discussing the
homework problems in class on the day that they are due. Therefore, you must hand them in either at the
beginning of class, or email them BEFORE class to me. In the absence of a documented medical or family
emergency, late homeworks will not be accepted.Any queries about the grades should be brought to my
attention within a week after the graded students’ works have been returned to the class.
Make-up Policy: There will be no makeup test. A missed test or exam will result in 0 points. Contact me in
advance in case of a disaster such as illness. An original letter addressed to me on a letterhead paper from a
physician or hospital stating that you could not take the test or exam as scheduled is necessary for me to
consider your case.
Academic Integrity: All work submitted for grading must be the student’s own work. Plagiarism will result in
a score of 0 for the work or dismissal from the course and the Dean will be notified. No copying from another
student’s work, of any class, is allowed. It is the student’s duty to allow no one to copy his or her work. If it is
found that one student copied from another, both papers will be given a score of 0 regardless of who copied
from whom.
Classroom Conduct: All Mobile Phones MUST be turned OFF at the beginning of each class.
Assistance with the Course
gMTH 2300 Syllabus
Spring 2025
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