Discrete Math for Critical Thinking & Problem Solving Skills

Beyond Mathematics—Building the Way You Think

Throughout my journey—from preparing for the IIT entrance exam to studying at IIT and later working as an engineer at NVIDIA, a global leader in AI—I came to appreciate something that extends far beyond mathematics itself.

The greatest value of learning mathematics is not simply solving equations or proving theorems. It is the way mathematics trains your mind to think. Every challenging problem strengthens your ability to analyze, reason logically, recognize patterns, and break complex problems into manageable parts. Over time, these habits become second nature, allowing you to approach technical and real-world challenges with greater clarity, confidence, and precision.

Looking back, I believe that the mathematical foundation I developed during my IIT preparation and education played a significant role in how I approached engineering challenges at NVIDIA. While technical knowledge is essential, it is often critical thinking, logical reasoning, and systematic problem-solving that distinguish exceptional engineers. Those are skills that mathematics quietly develops through years of consistent practice.

That belief is the inspiration behind every course I create.

My goal is not just to teach you Precalculus, Calculus, or Discrete Mathematics through my Udemy courses. My goal is to help you transform the way you think by developing the critical thinking skills that mathematics builds—an asset that will stay with you throughout your career, whether you pursue AI, Machine Learning, Data Science, Computer Science, Engineering, Finance, Research, or any field that rewards logical reasoning, critical thinking, and effective problem-solving.

If you commit to learning mathematics deeply rather than memorizing formulas, you will gain far more than mathematical knowledge. You will develop stronger critical thinking skills, greater confidence in tackling complex challenges, and a disciplined way of thinking that will continue to benefit you throughout your academic and professional journey.

That is the philosophy behind every lesson in this course.

How This Course Is Designed To Make Discrete Math Easier:

Discrete Math is the study of distinct mathematical objects rather than continuously varying quantities. It is not hard because of the concepts; it is hard because of how it is traditionally taught. This course bridges that gap by building an unshakeable discrete mathematical foundation. We break down the absolute essentials of discrete mathematics so that you can conquer them with total confidence, clarity, and zero stress.

Whether you are a Math Student trying to ace your discrete math exam, or an AI or Computer Science Student looking to build a strong discrete math foundation, this course delivers exactly what you need. This course teaches you the core fundamentals of discrete math and helps you master them through carefully explained, step-by-step worked examples and quizzes.

What You Will Master In This Course:

1. Set Theory

• Master Set Basics: Master set definition and understanding.

• Master Set Representation (Roster and Set Builder notations): Master representing sets in roster and set builder forms, for example a set of sweet fruits will be represented in roster form as S={Apple, Mango, Banana} and in set builder form as S = {x | x is a sweet fruit from the given list}

• Master Set Cardinality: Master figuring set cardinality |S| of any given set. Set Cardinality refers to the number of elements in set S, for example if S = {Apple, Mango, Banana}, then |S| = 3

• Master all Types of Sets: Master finite set, infinite set, empty set (Ø), singleton set, equal sets (A = B), equivalent sets (A ~ B), disjoint sets, and overlapping sets.

• Master Subset & Superset: Explore subset (A ⊆ B), proper subset (A ⊂ B), and superset (A ⊇ B)

• Master Special Sets: Understand power set (P (A)) and universal set (U)

• Master all Set Operations: Master union (A ∪ B), intersection (A ∩ B ), set difference (A-B) , and complement (A')

• Master Cartesian Products: Master cartesian/cross products (A × B) of sets step-by-step.

• Master Visual Problem Solving using Venn Diagram: Master representing sets and set operations on venn diagram, and solving complex problems visually using venn diagrams.

2. Relations

• Master Relation Basics: Master relations and their representation.

• Master Domain and Range of a Relation: Master finding the exact domain and range of a relation.

• Master all Types of Relations: Master empty, universal, identity, and inverse relation.

• Master all Properties of Relations: Master reflexive, symmetric, transitive, and equivalence relation.

3. Functions

• Master Function Basics: Master functions and determining whether a given relation qualifies as a function.

• Master Domain, Codomain, and Range of a Function: Master finding exact domain, codomain, and range of a function.

• Master all Types of Functions: Master injective (one-to-one), surjective (onto), and bijective (one-to-one correspondence) function.

• Master Even and Odd Function: Master even and odd function, and determining if a given function is even, odd or neither.

• Master Composite Function: Master function composition and evaluating function composition.

• Master Inverse Function: Master inverse function and finding the inverse function

4. Mathematical Induction

• Master the Principle of Mathematical Induction: Master the core principle of mathematical induction, step-by-step.

• Master Proving Sum of Squares: Master proving the sum of squares of the first n natural numbers using inductive logic.

• Master Proving Progressions: Master proving the sum of Arithmetic Progression (AP) and Geometric Progression (GP).

• Master Proving a Result from Geometry: Master applying mathematical induction in proving a geometric result.

• Master Proving Inequality and Divisibility: Learn applying induction in proving algebraic inequality and divisibility.

• Master Solving a Brain-Teaser: Master solving a brain-teasing real world problem using mathematical induction.

• Master Solving the Towers of Hanoi Puzzle: Master applying induction to the iconic Towers of Hanoi puzzle.

• Master Computer Science Program Correctness Proof: Master applying induction in computer science for program correctness proof.

Who Should Enroll for This Course:

• Math Students looking to master discrete math - set theory, relations, functions, and mathematical induction with clear, step-by-step guidance.

• Aspiring AI, Data Science & Computer Science Engineers looking to build the exact mathematical maturity needed to read advanced research papers and confidently comprehend complex algorithmic structures.

• Software Engineers & Computer Programmers looking to transition from simply writing basic syntax to mastering the deep mathematical logic that drives elite system design.

• Self-Taught Developers & Tech Professionals who skipped a formal university degree and want to rapidly fill the critical gap in their math foundations.

Testimonials From The Current Students:

This is what the current students who are enrolled in this course have to say:

"Excellent course!!! I highly recommend it." - Real Udemy User

"Awesome lectures, they are easy to follow and understand. Thanks for such videos." - Real Udemy User

"Just great!" - Real Udemy User

"Very clear introduction with good definitions and examples." - Real Udemy User

"Helped me finally understand set theory as it was explained better than university lecturers and other online tutorials. Would recommend!" - Real Udemy User

"Very good course. Although I am still completing it, the instructor explains things in detail. I am sure I will have complete satisfaction." - Real Udemy User

"It was good and easy to follow." - Real Udemy User

"The course was very well explained. Later parts were a bit hard, probably not something that is easy to understand at first, but nothing impossible. I humbly recommend this course." - Real Udemy User

"Absolutely amazing. Great instructions!" - Real Udemy User

"So far it is a good match for my interest and experience level." - Real Udemy User

"Excellent." - Real Udemy User

"Very useful." - Real Udemy User

"Amazing, above expectations!" - Real Udemy User

"Simple and crisp, great job." - Real Udemy User

"A well-organized course and an excellent tutor." - Real Udemy User

Take Away More Than Mathematical Knowledge:

This course is designed to help you build more than mathematical knowledge—it is designed to help you build your critical thinking skills.

The mathematical foundation you develop today can continue to strengthen the way you think, solve problems, and approach challenges throughout your academic and professional journey.

Stop memorizing mathematics. Start understanding it. Build the critical thinking and problem solving skills that will benefit you for years to come.