Discrete Mathematics for GATE CSE Exam

Discrete Mathematics plays an important role in the GATE (Graduate Aptitude Test in Engineering) examination, particularly for GATE CSE aspirants aiming for disciplines like Computer Science, Information Technology, and Electronics.

This article provides complete tutorial on Discrete Mathematics for GATE CSE Exam which contains topics in a simplified and easy-to-understand sections.

You can also refer to Discrete Mathematics Previous Year Questions - Topic wise

1. Propositional and First order Logic

• Propositional Logic
• Knowledge Representation in First Order Logic
• Propositional Equivalences
• Predicates and Quantifiers
• Rules of Inference

2. Sets, Relations and Functions

• Set Theory
• Relation and Function
• Recurrence Relations
• Closure of Relations and Warshall's Algorithm
• Representation of Relation in Graphs and Matrices

3. Partial order and Lattices

• Partial Orders and Lattices | Partial Orders and Lattices (Set-2)
• Elements of POSET | Maximal Element, Minimal Element, Lower and Upper Bounds 
• Hasse Diagrams
• Groups and Monoids

4. Graphs

• Graph Theory
• Matching and Coloring
• K-connected Graph and Biconnected Graph

5. Combinatorics

• Principle of Counting
• Principle of Inclusion and Exclusion
• Pigeonhole Principle
• Permutations and Combinations
• Recurrence Relations
• Generating Functions

Official Syllabus of Discrete Mathematics for GATE CSE

Here's the complete syllabus of Discrete Mathematics, as per GATE CSE 2025 official notification:

• Propositional and first order logic.
• Sets, relations, functions, partial orders and lattices.
• Monoids, Groups.
• Graphs: connectivity, matching, colouring.
• Combinatorics: counting, recurrence relations, generating functions

GATE CS/IT Subject-Wise Weightage

The subject-wise weightage for GATE CSE exam, based on the previous year patterns, is listed below:

Tips For Candidates While Preparing for Discrete Mathematics in GATE Exams

Discrete Mathematics is often considered a moderate to challenging subject, as it requires some high level problem solving skills and also the questions often test the ability to apply concepts in unique and unexpected ways, but with the correct approach and strategies, you can easily master the subject.

• Understand the Basics: Before exploring complex topics, ensure you have a strong grasp of basic mathematical concepts such as the Sets, relations and function, Permutation and Combinations, Logic building. A thorough understanding of the basics will make it easier to deal with more advanced topics.
• Solve Previous Year Questions: This is crucial for understanding the type of questions that appear in the GATE exam. It also helps in identifying important topics that are frequently tested.
• Avoid Memorizing the concepts and Theorems: Topics like logic, graph theory, and combinatorics are abstract and require a strong conceptual understanding memorizing the theorems won't be of any help.
• Focus on Application: Understanding how to apply theories in real-world scenarios is critical. Pay special attention to how different theorems can be applied to various types pf problems.
• Revise Regularly: Regular revision is key to ensuring that you remember concepts over the long term. Make a revision timetable and stick to it.

This tutorial provides a complete and simple guide to the core concepts of Discrete Mathematics as per the GATE CSE syllabus. By breaking down each topic and explaining it in simple terms, this tutorial will help you master the subject and excel in your exam.