Discrete Structures for AI
This course introduces the core ideas of discrete mathematics that support reasoning in computing and intelligent systems. Students learn through real scenarios, mathematical representations, proof techniques, combinatorics, graph theory, and selected Python activities. The emphasis is on understanding, problem solving, and connecting mathematical thinking with practical system design.
Course Description
This course develops essential discrete mathematics concepts for students of Artificial Intelligence and computing. It covers logic, proof reasoning, sets, relations, functions, counting, graphs, trees, and related structures through applied examples and problem solving. Selected Python activities are used to reinforce mathematical ideas and connect them with computational thinking.
Course Learning Outcomes
Apply principles of mathematical logic, sets, relations, and functions to solve discrete problems.
Construct and evaluate mathematical proofs using appropriate proof techniques.
Analyze combinatorial structures and apply counting principles to computational problems.
Model and solve problems using graphs, trees, and other discrete structures.
Faculty
Dr. Hira Benish
Associate Professor, Head of Mathematics Department
Riphah International University SahiwalCourse Outline
Course Outline
Official course outline and syllabus.
Lecture Notes
Introduction
Mathematical reasoning and propositional logic.
logic and rules of inference:
Logics, statements, operators
Mathematical reasoning
Methods and proof techniques
Mathematical induction
Method of reasoning
Set Theory
Set theory; functions and mappings.
Relations
This lecture includes relations , types and its excercise with python.
Number Theory
Divisibility, primes, greatest common divisor, Euclidean algorithm
Sequences and series
Arithmetic and geometric patterns
Recurrence relations and recursive functions
Recursion versus iteration; simple growth models
Counting foundations and permutations
Addition/product rules; inclusion–exclusion for two sets; Pigeonhole principle
Counting foundations
Permutations II and combinations
Graph Theory
Elements of graph theory and Euler graphs: vertices/edges, degree, walk/trail/path/cycle, adjacency representations.
Graph Coloring
Elementary planar graphs, graph coloring, and Hamiltonian paths/cycles
Trees and Traversals
Rooted trees and traversals: root, parent/child
Assignments
Quizzes
Case Studies
Additional Resources
Reference Material
Supplementary mathematical learning material.
Useful Links
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