Discrete Structures
MT217
Lecture 01
Course Objectives
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Express statements with the precision of formal logic
Analyze arguments to test their validity
Apply the basic properties and operations related to sets
Apply to sets the basic properties and operations related to
relations and functions
Course Objectives
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Define terms recursively
Prove a formula using mathematical induction
Prove statements using direct and indirect methods
Compute probability of simple and conditional events
Course Objectives
• Identify and use the formulas of combinatorics in different
problems
• Illustrate the basic definitions of graph theory and properties
of graphs
• Relate each major topic in Discrete Mathematics to an
application area in computing
Recommended Books
• Discrete Mathematics with Applications (second edition) by
Susanna S. Epp
• Discrete Mathematics and Its Applications (sixth edition) by
Kenneth H. Rosen
• Discrete Mathematics by Ross and Wright
MAIN TOPICS
1. Logic
2. Sets & Operations on sets
3. Relations & Their Properties
4. Functions
5. Sequences & Series
6. Recurrence Relations
7. Mathematical Induction
8. Loop Invariants
9. Loop Invariants
10. Combinatorics
11. Probability
12. Graphs and Trees
Marks Distribution
Two Sessional Exam 25%
Assignments and Quizzes 25%
Final Exam 50%
Contact
E-mail: zahidabbas@ciitvehari.edu.pk
What is Discrete Mathematics?
• Discrete mathematics is the study of mathematical structures
that are fundamentally discrete rather than continuous. In
contrast to real numbers that have the property of varying
"smoothly", the objects studied in discrete mathematics –
such as integers, graphs, and statements in logic– do not vary
smoothly in this way, but have distinct, separated values.
What is Discrete Mathematics?
• Discrete mathematics focuses on problems that are not over a
continuous domain. For example, is it possible to visit 3 islands
in a river with 6 bridges without crossing any bridge more than
once? That is a discrete math problem (because there are a
finite (fixed, discrete) number of bridges). Or, what is the
smallest number of telephone lines needed to connect 200
cities? The numbers can be large and the logic can be
complex, but these type of problems are different from
finding an optimal value for a function where the domain can
be 3, 3.14, 3.14159, or any real value.
What is Discrete Mathematics?
• Discrete Mathematics concerns processes that consist of a
sequence of individual steps.
Logic
Logic is the study of the principles and methods that
distinguishes between a valid and an invalid argument.
Statement
Examples
TRUTH VALUES of Propositions
Examples
Examples
Not Propositions
Rule
Example
Example
Understanding Statements
Understanding Statements
Compound Statement
Symbolic Representation
Logical Connectives
Examples
Translating from English to
Symbols
Translating from English to
Symbols
Translating from English to
Symbols
Translating from English to
Symbols
Translating from English to
Symbols
Negation (~)
Truth Table
Truth Table for
Conjunction (^)
Truth Table for
Disjunction (ᴠ)
Truth Table for
Summary