Discrete Mathematics – University Level
Notes
Chapter 1: Introduction to Discrete
Mathematics
1.1 What is Discrete Mathematics?
Definition:
Discrete mathematics is the branch of
mathematics that deals with objects that can
take only distinct, separated values, unlike
continuous mathematics which deals with
objects that vary smoothly.
Key Features:
●Deals with finite or countably infinite sets
●Focuses on structures that are separate
and non-continuous
, ●Involves reasoning about logical
statements, sets, functions, and
algorithms
Applications in Real Life & Computer
Science:
Area Application
Comput Algorithm design, data
er structures, network
Science protocols
Cryptogr Encryption, secure
aphy communication
Combina Counting possibilities,
torics optimization problems
Graph Social networks, internet
Theory topology, logistics
Logic Program verification,
database queries
,Automat Language recognition,
a Theory compilers
Examples of Discrete Structures:
1. Integers: 0, 1, 2, 3, …
2. Finite Sets: {apple, banana, cherry}
3. Graphs: Nodes and edges representing
networks
4. Logic Statements: True or False
propositions
5. Combinations & Permutations:
Counting arrangements
1.2 Importance in Computer Science
, Discrete mathematics forms the theoretical
foundation for most computer science
concepts:
1. Algorithm Analysis:
○Complexity analysis (Big O, Big Theta,
Big Omega)
○Correctness proofs using induction
2. Data Structures:
○Trees, graphs, stacks, queues, hash
tables
○Efficient storage and retrieval of data
3. Cryptography & Coding Theory:
○Encryption algorithms, digital signatures
Notes
Chapter 1: Introduction to Discrete
Mathematics
1.1 What is Discrete Mathematics?
Definition:
Discrete mathematics is the branch of
mathematics that deals with objects that can
take only distinct, separated values, unlike
continuous mathematics which deals with
objects that vary smoothly.
Key Features:
●Deals with finite or countably infinite sets
●Focuses on structures that are separate
and non-continuous
, ●Involves reasoning about logical
statements, sets, functions, and
algorithms
Applications in Real Life & Computer
Science:
Area Application
Comput Algorithm design, data
er structures, network
Science protocols
Cryptogr Encryption, secure
aphy communication
Combina Counting possibilities,
torics optimization problems
Graph Social networks, internet
Theory topology, logistics
Logic Program verification,
database queries
,Automat Language recognition,
a Theory compilers
Examples of Discrete Structures:
1. Integers: 0, 1, 2, 3, …
2. Finite Sets: {apple, banana, cherry}
3. Graphs: Nodes and edges representing
networks
4. Logic Statements: True or False
propositions
5. Combinations & Permutations:
Counting arrangements
1.2 Importance in Computer Science
, Discrete mathematics forms the theoretical
foundation for most computer science
concepts:
1. Algorithm Analysis:
○Complexity analysis (Big O, Big Theta,
Big Omega)
○Correctness proofs using induction
2. Data Structures:
○Trees, graphs, stacks, queues, hash
tables
○Efficient storage and retrieval of data
3. Cryptography & Coding Theory:
○Encryption algorithms, digital signatures
