1. Dr. Kritesh Kumar Gupta
Assistant Professor
Amrita School of Artificial Intelligence,
Amrita Vishwa Vidyapeetham, Coimbatore, India
22nd Aug 2023
Bootcamp (Week 2)
Introduction: Discrete Mathematics
3. Discrete Mathematics
3
Discrete mathematics is part of mathematics devoted to the study of discrete (as
opposed to continuous) objects.
Calculus deals with continuous objects and is not part of discrete mathematics.
Examples of discrete objects: integers, distinct paths to travel from point A to
point B on a map along a road network, ways to pick a winning set of numbers in a
lottery.
A course in discrete mathematics lays a foundation of several courses
corresponding to computer science, such as compiler design, databases, computer
security, automata theory etc.
5. Relevance: Why study Discrete Mathematics?
Design efficient and secure computer systems.
•How did
Google
managed to
build a fast
search engine?
What is the
foundation of
internet
security?
algorithms, data structures,
database, parallel
computing, distributed
systems, cryptography,
computer networks…
Logic, number theory, counting, graph theory….. 5
6. Unit-1
6
How do computers think?
Logic Proofs
Artificial Intelligence, algorithms, data structures
How do computers process?
•Combinations, Permutations, Binomial theorem
• Counting by mapping, pigeonhole principle
• Recursions
8. Unit-3
8
cryptography, coding theory, and advanced algorithm design
Number Theory
• Number sequence
• (Extended) Euclidean algorithm
• Prime number, modular arithmetic, Chinese remainder theorem
• Cryptography, RSA protocol
9. Familiarity with various concepts in logic and proof techniques.
Objectives of the Course
9
Understanding of the concepts of various types of relations, partial ordering
and equivalence relations.
Understanding of the concepts of generating functions and apply to solve the
recurrence relations.
Familiarity with basic results in number theory and understand it applications in
information security.
