Learn Discrete mathematics Online: Free Course with AI Tutor & Certificate
You'll learn to analyze logical arguments and build mathematical proofs from scratch. This discrete mathematics course covers 10 modules, moving from Logic and Reasoning to Graphs and Networks. By the end, you'll comfortably manipulate functions, calculate discrete probability, and apply Boolean Algebra to real-world problems.
What you'll learn in this Discrete mathematics course
Five concrete outcomes you'll walk away with, each mapped to modules in the curriculum below.
Analyze and construct logical arguments using propositions, truth tables, and rules of inference.
Develop and apply various methods of proof, including direct proof, proof by contradiction, and proof by contrapositive.
Understand and manipulate functions, relations, and their properties, including equivalence relations and partial orders.
Employ counting techniques and principles, such as permutations, combinations, and the pigeonhole principle, to solve complex problems.
Explore and apply concepts of graph theory, including graph types, paths, cycles, and tree structures, to model and solve real-world problems.
Discrete mathematics course syllabus
01 Foundations of Discrete Mathematics
- What Discrete Mathematics Studies
- Sets and Elements
- Subsets, Power Sets, and Set Operations
- Basic Notation and Mathematical Language
02 Logic and Reasoning
- Propositions and Truth Values
- Logical Connectives
- Truth Tables and Logical Equivalence
- Rules of Inference and Arguments
03 Methods of Proof
- Direct Proof
- Proof by Contradiction
- Proof by Contrapositive
- Proof by Cases
04 Functions and Relations
- Functions and Their Properties
- One-to-One and Onto Functions
- Relations and Their Representations
- Equivalence Relations and Partial Orders
05 Counting Techniques
- The Addition and Multiplication Principles
- Permutations
- Combinations
- The Pigeonhole Principle
06 Recurrence and Induction
- Sequences and Recurrence Relations
- Solving Simple Recurrences
- Mathematical Induction
- Strong Induction
07 Graphs and Networks
- Graph Basics and Terminology
- Types of Graphs
- Paths, Cycles, and Connectivity
- Trees and Their Properties
08 Trees and Combinatorial Structures
- Rooted Trees and Binary Trees
- Spanning Trees
- Counting Tree Structures
- Applications of Trees
09 Discrete Probability
- Sample Spaces and Events
- Probability Rules
- Conditional Probability
- Independent Events and Counting in Probability
10 Boolean Algebra and Applications
- Boolean Variables and Operations
- Boolean Expressions and Identities
- Logic Circuits
- Applications in Computer Science
Real-world projects you'll work on
Practice the exact kind of work Discrete mathematics professionals do on the job.
Designing a Set-Based Data Management System for Google Cloud
Developing Logical Algorithms for IBM's AI Research
Creating a Proof-Based Security Protocol for Microsoft Azure
Building a Graph Theory Application for Amazon's Logistics Network
Skills you'll gain
Add these to your LinkedIn profile and resume the day you finish.
Who should take this Discrete mathematics course?
And exactly what you need before starting (spoiler: almost nothing).
This course is for
- Computer science students needing a strong mathematical foundation for algorithms.
- Aspiring software engineers who want to write more efficient, logical code.
- Data science beginners looking to understand probability and counting techniques.
- Working professionals seeking to fill gaps in their theoretical computer science knowledge.
Prerequisites
- No prior experience is required to begin this course.
- Basic high school algebra is helpful but not mandatory.
- A general interest in logic and problem-solving.
How learning works on LearnTube
The structure of a bootcamp, the price of free.
AI curates your path
Our AI picks the top 1% of video content for each topic and arranges it into a structured, goal-based curriculum. No more tutorial roulette.
Learn, then get quizzed
After every lesson, your AI tutor asks you a question and gives personalised feedback on your answer, so gaps get fixed immediately.
Finish with proof
Complete the course, build the capstone project, and claim a certificate recognised by 900+ hiring partners.
A complete Discrete mathematics course: free, structured and job-focused
Mastering discrete mathematics is essential for anyone who wants to write efficient algorithms or build secure systems. In this discrete mathematics course, you'll start by exploring the Foundations of Discrete Mathematics before moving into Logic and Reasoning. As you progress, you'll learn exactly how to construct arguments using Methods of Proof, manipulate Functions and Relations, and apply Counting Techniques to complex scenarios. We also cover advanced topics like Recurrence and Induction, Discrete Probability, and Boolean Algebra and Applications.
To make the theory practical, you'll work on hands-on projects directly inspired by industry needs. You'll design a Set-Based Data Management System for Google Cloud, develop logical algorithms for IBM's AI research, and even build a graph theory application for Amazon's logistics network. These projects ensure you can connect abstract mathematical concepts to real-world software engineering and data science tasks.
LearnTube makes learning discrete mathematics online simple and engaging. Our platform pairs curated YouTube video lessons with an AI tutor that quizzes you after every single lesson. You can study all 10 modules completely for free at your own pace. If you want to verify your new skills, you can opt for a paid certificate upon completion to show employers you understand the math behind modern computing.
Jobs you can target after learning Discrete mathematics
Discrete mathematics is a gateway skill for some of the fastest-growing roles in tech.
Writes and optimizes code using logical algorithms and boolean algebra.
Uses discrete probability and counting techniques to interpret complex datasets.
Designs network architectures relying heavily on graph theory and tree structures.
Typical entry-level salary ranges in India as of November 2026. Actual compensation varies by city, company and experience.
Earn a Discrete mathematics certificate employers recognise
Finish the course and claim a certificate you can share anywhere.
- Learn 100% free: every lesson, quiz and the AI tutor cost nothing
- Claim your certificate when you complete the course (an optional paid add-on)
- Recognised by 900+ hiring partners across India
- One click to share on LinkedIn and add to your resume
Why learners choose LearnTube
Real reviews from Google. You learn free, you get assessed free, and you pay only if you want the certificate.
Though I have 11 years of experience as an HRBP, the course helped me refresh my knowledge and gave me insights into new trends in the market. The modules were clear and easy to understand, and the quizzes were well designed. I have added the certificate to my LinkedIn profile.
I had a lot of doubts while learning, but the AI chatbot answered them in detail with simple summaries. The videos on the platform saved me a lot of time as I didn't have to search YouTube and watch random content.
Just earned my certificate in HR Management from LearnTube.ai! The platform is user-friendly and the assessment was a great way to validate my knowledge. Feeling proud of this accomplishment!
I enrolled in a LearnTube personalized course to get into a Data Analytics role. It helped me learn SQL in depth and gave me hands-on experience with Power BI. I attached the LearnTube certificate to my CV, it added credibility to my profile, and I'm currently in the interview process.
The interface is user-friendly and intuitive, making it easy to navigate the course. I encountered no errors during my time using the platform, which was a refreshing change from other online learning platforms.
Just cleared the Business Analyst assessment and got certified! Loved how the course simplifies big concepts like data-driven decision making into short, practical lessons. The automated quizzes kept me on track the whole time. Perfect boost for my resume!
The certificate gave me a real edge during my B.Tech. By the time I graduated, I had skills that set me apart from my peers, and the certification opened up more job opportunities. It gave me the confidence to stand out during interviews.
I manage many software projects as a General Manager and was looking for a good certification program to stay competitive. After researching many programs, I chose LearnTube and it was much better than I expected. The material is well-organized and practical, and what I liked most is the lifetime access.
Frequently asked questions
Everything learners ask before starting this Discrete mathematics course.
Do I need prior experience to take this discrete mathematics course?
No prior experience is necessary. We start with the Foundations of Discrete Mathematics before moving to more advanced topics. Basic high school math is helpful, but you will learn everything else from scratch.
What jobs can I get after learning discrete mathematics?
This knowledge helps you secure roles like Software Developer, Data Analyst, and Systems Engineer. Entry-level salaries in India for these positions typically range from ₹3.5 LPA to ₹9 LPA depending on the exact role.
Is this discrete math course self-paced?
Yes, the entire course is completely self-paced. You can watch the curated video lessons and take the AI-tutor quizzes whenever it fits your schedule, making it easy to learn while working or studying.
Can I learn discrete mathematics on my mobile phone?
Yes, the LearnTube platform works perfectly on mobile devices. You can access all 10 modules, watch the videos, and answer the AI-generated quizzes directly from your smartphone while commuting or traveling.
How long does it take to complete the course?
You decide your own learning pace. Because there are no strict deadlines, you can finish the modules quickly over a few weekends or spread the learning out over several months.
Are there practical projects included?
Yes, practical work is included. You will build real-world projects like designing a Set-Based Data Management System for Google Cloud and creating a proof-based security protocol for Microsoft Azure.
Will I get a certificate for this discrete mathematics course?
Yes, you can earn a certificate. Learning the material is completely free, and you have the option to purchase a verified certificate once you finish all the modules and quizzes.
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