Discrete Mathematics

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Provider

YouTube
Pricing

Free Video
Languages

English
Effort

17 hours 11 minutes
Sessions

Self-Paced
Level

Beginner

Found in

Master discrete mathematical structures through this comprehensive 17-hour course covering fundamental concepts from basic logic to advanced lattice theory. Begin with propositional logic, exploring logical operators, truth tables, tautologies, and rules of inference before advancing to first-order logic with predicates, quantifiers, and nested quantifications. Dive deep into set theory fundamentals including set operations, power sets, Cartesian products, and set identities with extensive problem-solving practice. Explore relations in detail, covering types of relations, composition operations, closure properties, and Warshall's algorithm for finding transitive closures. Study equivalence relations, equivalence classes, partitions, and congruence modulo operations with practical applications. Investigate partial orderings, Hasse diagrams, and poset properties including minimal/maximal elements, bounds, and lattice structures. Progress through semilattices, complete lattices, complemented lattices, and distributive lattices with GATE exam problem solutions throughout. Conclude with introductions to functions, counting principles, and permutations & combinations. No prerequisites required as the course builds from foundational concepts with numerous solved examples, puzzles, and competitive exam problems to reinforce learning.

Syllabus

Introduction to Discrete Mathematics
Motivation & Introduction to Propositional Logic
Propositional Logic, Propositional Variables & Compound Propositions
Logical Operators − Negation, Conjunction & Disjunction
Logical Operators − Exclusive OR
Logical Operators − Implication (Part 1)
Logical Operators − Implication (Part 2)
Logical Operators − Implication (Part 3)
Converse, Contrapositive and Inverse
Logical Operators − Biconditional Operator
Propositional Logic − Precedence of Logical Operators
Translating Sentences into Logical Expressions
Propositional Logic − Puzzle 1
Propositional Logic − Puzzle 2
Propositional Logic (Solved Problem 1)
Tautology, Contradiction, Contingency & Satisfiability
Propositional Logic − Logical Equivalences
Propositional Logic (Solved Problem 2)
Propositional Logic (Solved Problem 3)
Propositional Logic (Solved Problem 4)
Propositional Logic (Solved Problem 5)
Propositional Logic (Solved Problem 6)
Propositional Logic (Solved Problem 7)
Rules of Inference - Basic Terminology
Rules of Inference - Definition & Types of Inference Rules
Arguments Building Using Rules of Inference (Part 1)
Arguments Building Using Rules of Inference (Part 2)
Checking The Validity of An Argument (Shortcut Method)
Rules of Inference in Propositional Logic (Solved Problem 1)
Rules of Inference in Propositional Logic (Solved Problem 2)
The Limitation of Propositional Logic
Introduction to First Order Logic
Finding The Truth Values of Predicates (Examples)
Quantifiers
Universal Quantifiers
Universal Quantifiers - Counter Examples
Expressing Quantifications in English
Existential Quantifiers
Existential Quantifiers - Examples
Quantifiers with Restricted Domain
Logical Equivalences Involving Predicates & Quantifiers (Part 1)
Logical Equivalences Involving Predicates & Quantifiers (Part 2)
Negating the Quantified Expressions (Part 1)
Negating the Quantified Expressions (Part 2)
Negating the Quantified Expressions (Examples)
Translating English Sentences to Logical Expressions
First Order Logic (Solved Problems) - Part 1
First Order Logic (Solved Problems) - Part 2
First Order Logic (Solved Problems) - Part 3
First Order Logic (Solved Problems) - Part 4
First Order Logic (Solved Problems) - Part 5
Introduction to Nested Quantifiers
Nested Quantifiers (Solved Example 1)
Nested Quantifiers (Solved Example 2)
Nested Quantifiers (Solved Example 3)
Nested Quantifiers (Translating English Statements) - Example 1
Nested Quantifiers (Translating English Statements) - Example 2
Nested Quantifiers (Translating English Statements) - Example 3
Nested Quantifiers (Translating English Statements) - Example 4
Nested Quantifiers (Translating English Statements) - Example 5
Negating the Nested Quantifiers
Negating the Nested Quantifiers (Example 2)
Negating the Nested Quantifiers (Example 3)
The Resolution Principle (Preliminaries)
The Resolution Principle (Proof of Theorem)
The Resolution Principle (Proving if an Argument is Valid)
The Resolution Principle (Solved Problems)
Fallacies
Rules of Inference for Quantified Statements (Part 1)
Rules of Inference for Quantified Statements (Part 2)
Universal Modus Ponens Rule
Universal Modus Tollens Rule
Set Theory (Basics of Sets)
Set Representation
Inclusion and Equality
Inclusion vs. Membership
Inclusion vs. Membership (Solved Problem)
Types of Sets - Universal, Null, and Singleton
Null Set (Solved Problem)
Non-Empty Set (Important Theorem)
Power Set
Power Set (Solved Problems)
Power Set (GATE Problem 1)
Power Set (GATE Problem 2)
Cardinality of Sets
Cartesian Product
Cartesian Product (Solved Problems)
Set Operations (Intersection & Union with Venn Diagram)
Set Difference and Set Complement
Set Operations (Solved Problems)
Set Identities (Part 1)
Set Identities (Part 2)
Set Identities (Part 3)
Set Operations (Solved Problem 1)
Set Operations (Solved Problem 2)
Symmetric Difference
Set Operations (GATE Problems)
Set Operations (GATE and TIFR Problem)
Introduction to Relations
Types of Relations (Part 1)
Types of Relations (Part 2)
Types of Relations (Solved Problem)
Types of Relations (GATE Problems) - Set 1
Types of Relations (GATE Problems) - Set 2
Operations on Relations
Composition of Relations
Composition of Relation with Itself
Representation of Relations
Closure of Relations – Part 1
Closure of Relations – Part 2
Closure of Relations (Solved Problems) - Set 1
Warshall's Algorithm (Finding the Transitive Closure)
Closure of Relations (Solved Problems) - Set 2
Closure of Relations - GATE Problem
Equivalence Relation
Equivalence Relation (Solved Problems)
Equivalence Relation (GATE Problems) - Set 1
Equivalence Relation (GATE Problems) - Set 2
Equivalence Relation (GATE Problem)
Equivalence Classes
Congruence Modulo m
Modulus of Negative Numbers
Equivalence Classes and Partitions
Equivalence Classes and Partitions (Solved Problems)
Introduction to Partial Ordering
Partial Orderings (Solved Problems) - Set 1
Partial Orderings (Solved Problems) - Set 2
Hasse Diagram
Hasse Diagram (Solved Problems) - Set 1
Hasse Diagram (Solved Problems) - Set 2
Poset (Minimal and Maximal Elements)
Poset (Least and Greatest Elements)
Poset (Lower and Upper Bounds)
Poset (Least Upper Bound and Greatest Lower Bound)
Hasse Diagram (Solved Problems) - Set 3
Symbols for Partial Order
Meet Semilattice
Join Semilattice
Lattice
Lattice (GATE Problems) - Set 1
Complete and Bounded Lattice
Lattice (Complement of an Element)
Lattice (GATE Problems) - Set 2
Complemented Lattice
Distributive Lattice
Functions | Chapter-7 | Discrete Mathematics | nesoacademy.org
Counting | Chapter-8 | Discrete Mathematics | nesoacademy.org
Permutations & Combinations | Chapter-9 | Discrete Mathematics | nesoacademy.org

Taught by

Neso Academy

Reviews

4.8 rating, based on 21 Class Central reviews

Start your review of Discrete Mathematics

Md. Mehedi Hasan 251-35-322 @mehedi4488

This Discrete Mathematics course has been an invaluable asset to my computer science studies. It effectively simplified complex topics like Graph Theory, Logic, and Set Theory, which are crucial for understanding algorithms. The structured approach significantly enhanced my analytical thinking and problem-solving skills. I highly recommend this course to anyone looking to build a rock-solid foundation in technical and mathematical reasoning.
Arvin Yefat Orin 251-35-571

The Discrete Mathematics course by Neso Academy is a solid choice for students who want a clear and structured introduction to the subject. The explanations are simple, direct, and easy to follow, which makes it especially helpful for beginners who…

The Discrete Mathematics course by Neso Academy is a solid choice for students who want a clear and structured introduction to the subject. The explanations are simple, direct, and easy to follow, which makes it especially helpful for beginners who often struggle with abstract topics like logic, set theory, relations, and graph theory.

One of the strongest points of the course is how well concepts are broken down into small, manageable parts. Instead of overwhelming the learner with heavy theory, the instructor builds ideas step by step, often using examples that make the concepts more intuitive. Topics like mathematical induction, recurrence relations, and combinatorics are explained in a way that reduces confusion and helps in exam preparation.

Another advantage is the consistency of the video format. The visuals and pacing remain steady throughout the course, which helps maintain focus. It’s also freely accessible on YouTube, making it a very good resource for students who don’t want to invest in paid courses.

However, the course is more exam-oriented than application-oriented. While it covers theory well, it doesn’t go very deep into problem-solving variations or advanced difficulty levels that some university exams might require. So, students may still need to practice additional problems from textbooks or question banks.

Overall, Neso Academy’s Discrete Mathematics course is an excellent foundation resource. It’s best suited for beginners and students preparing for exams who need clear explanations and structured learning, but it should ideally be supplemented with extra practice for full mastery.
Wakilur Rahman Fuad 251-35-097

The Discrete Mathematics course provides a strong foundation in mathematical reasoning and problem-solving techniques essential for computer science and related fields. The syllabus covers key topics such as logic and proofs, set theory, functions a…

The Discrete Mathematics course provides a strong foundation in mathematical reasoning and problem-solving techniques essential for computer science and related fields. The syllabus covers key topics such as logic and proofs, set theory, functions and relations, combinatorics, graph theory, and basic number theory. These topics help develop analytical thinking and precise formulation of problems.
One of the strengths of the course is its focus on formal reasoning and proof strategies, which enhances logical clarity and strengthens understanding of algorithms and data structures. Classroom lectures were structured, with clear explanations of abstract concepts and useful examples that connected theory with practical computing applications.
The instructor was knowledgeable and supportive, encouraging student participation and providing timely feedback on assignments. Weekly homework and quizzes helped reinforce learning and ensured regular practice, although some students may find the workload challenging if they don't review concepts consistently.
Overall, Discrete Mathematics is a rigorous but rewarding course. It deepens mathematical understanding and builds critical skills that are directly applicable to further study in computer science. Students who actively engage with the material will find it highly beneficial for academic and professional growth.
Md. Rousin

Neso Academy’s Discrete Mathematics course on YouTube is a highly popular and beginner-friendly resource for students studying computer science and engineering. The instructor explains topics such as sets, logic, relations, functions, combinatorics,…

Neso Academy’s Discrete Mathematics course on YouTube is a highly popular and beginner-friendly resource for students studying computer science and engineering. The instructor explains topics such as sets, logic, relations, functions, combinatorics, and graph theory in a clear, step-by-step manner. One of its biggest strengths is simplicity—complex concepts are broken down in an easy-to-understand way, making it ideal for self-learners. The course is completely free and follows a structured sequence, which helps in exam preparation. However, it is mostly lecture-based and lacks interactive exercises or quizzes. Some advanced topics may also require additional references like textbooks or practice problems. Overall, it is an excellent foundation-building resource, but students should supplement it with problem-solving practice to fully master discrete mathematics and improve application skills for exams and real-world use.
Nabid Zaman 251-35-159

This is best course ever!I recently completed a course in discrete mathematics, and it was a very valuable learning experience. The course helped me understand fundamental concepts such as logic, set theory, relations, functions, and graph theory. It improved my problem-solving and analytical thinking skills, which are essential for computer science. The topics were challenging at times, but they became interesting with practice. I especially enjoyed learning about algorithms and mathematical reasoning. Overall, this course built a strong foundation for advanced studies in programming and data structures. I feel more confident now in tackling complex problems and applying mathematical concepts in real-world computing scenarios.
Miraj Hassan

very goood helpful for acadennic ourpose.This piece offers a clear and engaging exploration of its subject, balancing depth with accessibility. The ideas are presented logically, making it easy for readers to follow along without feeling overwhelmed. Strong examples help reinforce key points, while the tone remains consistent and approachable throughout. However, a bit more critical analysis or contrasting viewpoints could have added greater depth. The structure is well-organized, though a slightly more impactful conclusion would leave a stronger lasting impression. Overall, it is an informative and well-crafted work that effectively communicates its message while maintaining reader interest from beginning to end.
Lisan Mahmud 251-35-600

This course is an excellent introduction to discrete mathematics. The instructor breaks down complex topics like logic, sets, relations, graph theory, and proofs into clear, manageable segments. Each video is concise and focused, making it easy to follow along without feeling overwhelmed. The worked examples are particularly helpful for understanding how to apply theoretical concepts. While the course lacks interactive quizzes or assignments, the quality of explanations more than makes up for it. Perfect for CS students or anyone preparing for exams like GATE. Highly recommended for self-learners who prefer structured, no-nonsense teaching.

rating 5 star
Sazid Nahian Oyan

This course provides a clear and beginner-friendly introduction to discrete mathematics. The instructor, Jaspreet Singh, explains core concepts like logic, sets, relations, and functions in a simple and structured way. The lessons are easy to follow, making it suitable for students with little to no prior knowledge. Visual explanations and examples help in understanding abstract topics. However, the course lacks interactive exercises and assessments, which could improve learning. Overall, it is a great resource for building foundational knowledge in discrete mathematics, especially for self-learners looking for a free and accessible introduction to the subject.
Md. Ridwanul Islam

This course is an excellent introduction to discrete mathematics. The instructor breaks down complex topics like logic, sets, relations, graph theory, and proofs into clear, manageable segments. Each video is concise and focused, making it easy to follow along without feeling overwhelmed. The worked examples are particularly helpful for understanding how to apply theoretical concepts. While the course lacks interactive quizzes or assignments, the quality of explanations more than makes up for it. Perfect for CS students or anyone preparing for exams like GATE. Highly recommended for self-learners who prefer structured, no-nonsense teaching.
Oishi Gain 251-35-558

I learned discrete math and it was a good experience. At first, it was a bit difficult to understand the concepts. But slowly, I started to understand topics like sets, predicates, and quantifiers. The examples helped me a lot to learn better. It improved my thinking and problem-solving skills. Sometimes I felt confused, but with practice, it became easier. Now I feel more confident in this subject. Discrete math is important for computer science, so I think it is useful to learn. Overall, it was a helpful and interesting learning experience for me.
Sadman Habij Saim

This is hands down one of the best resources for Discrete Mathematics on YouTube. The lessons are concise, easy to follow, and cover all the essential topics in depth. Whether you are a beginner or looking for a quick revision before finals, Neso Academy has you covered. The problem-solving examples provided after each theory section are particularly helpful for building confidence.
Tohidul Hasan Khan

This Discrete Mathematics course has been an invaluable asset to my computer science studies. It effectively simplified complex topics like Graph Theory, Logic, and Set Theory, which are crucial for understanding algorithms. The structured approach significantly enhanced my analytical thinking and problem-solving skills. I highly recommend this course to anyone looking to build a rock-solid foundation in technical and mathematical reasoning.
Syed Asadur Rahman 251-35-516

Completing the Discrete Mathematics course has greatly strengthened my logical thinking and problem-solving skills. I learned key topics like logic, set theory, combinatorics, and graph theory, which are essential for computer science. Although some concepts were challenging, consistent practice helped me improve. Overall, this course provided a strong foundation for understanding algorithms and advanced computing concepts.
Neloy Saha

I recently completed a Discrete Mathematics course, and it was a highly valuable experience. The course strengthened my logical thinking and problem-solving skills. Topics like graphs, logic, and combinatorics were explained clearly. It built a strong foundation for computer science and programming, making complex concepts easier to understand and apply.
MD. Mahmudul Hasan 251-35-112

This discrete mathematics online course is well-structured and easy to follow. The explanations of topics like graphs, logic, and algorithms are clear, and the practice problems help reinforce understanding. It’s very helpful for building a strong foundation.
Md. Abdullah Al Mamun 251-35-503

This course is a total win! It makes complex logic feel like solving a fun puzzle rather than a chore. Clear, engaging, and genuinely rewarding—I’m finally speaking the language of math!
MD. Akash Hossen 251-35-277

This is a Great course. I Have learned so many things from this course.
This is a Great course. I Have learned so many things from this course.
RIFAT HASAN

Ver good course. Discrete math builds logic, sets, graphs, and proofs skills essential for computing and problem solving now!!
Md. Tanjilur Rahman Maruf

Outstanding. I think this is the very good course. It help us to learn many important topic. This is very important to us.it help to learn very hard topic.
S.M. Mehedi Hasan 252-35-375

very good class for a begginer they dropped almost every topic i learned a lot from this course .hope they keep making these free videos.