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Mathematics is more than just numbers—it is the language of logic, problem-solving, and STEM excellence. For ambitious students in Singapore, excelling in math opens doors to top local and international universities, scholarships, and competitive STEM programs. As an IIT Guwahati and Indian Statistical Institute alumnus, published author, and passionate educator with 6+ years of global […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor & Author)Published: October 2025Category: Education | IB Mathematics | Global STEM Preparation 🔹 Introduction The International Baccalaureate (IB) is more than a qualification — it’s a framework for thinking globally and reasoning deeply. At Math By Rishabh, we are redefining IB Mathematics learning by offering […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Probability & Inference 🔹 Introduction In real-world statistics, we often estimate population parameters using sample data. But what if the population standard deviation (σ) is unknown — which is almost always the case? That’s where the Student’s t-distribution comes in. The […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Algebra | Graphs & Functions 🔹 What Are Function Transformations? A transformation of a function changes its shape, position, or orientation on a graph — without altering its fundamental nature. Every transformation can be understood as a modification of the base function f(x)f(x)f(x). […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Algebra, Trigonometry & Geometry 🔹 Introduction What if exponentials, trigonometry, and complex numbers were all part of the same language? They are.And the key that connects them is the most elegant equation in mathematics: eiθ=cos⁡θ+isin⁡θ\boxed{e^{i\theta} = \cos\theta + i\sin\theta}eiθ=cosθ+isinθ​ This […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Calculus | Applications of Integration 🔹 What Is Definite Integration? Definite integration calculates the exact numerical value of an integral between two limits — representing the total accumulation or net area under a curve between two points. If f(x)f(x)f(x) is a continuous function […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Geometry & Algebra 🔹 Introduction Every complex number can be represented algebraically as z=x+iyz = x + iyz=x+iy.But there’s a more powerful way to express it — using length and angle instead of x and y. This is called the […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Algebra Meets Geometry 🔹 Introduction Complex numbers are more than just algebraic expressions — they represent points in a plane.This geometric representation is called the Argand Diagram. The Argand plane lets us see complex numbers — turning abstract algebra into […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Calculus | Integration Techniques 🔹 What Is Integration by Substitution? Integration by Substitution is the reverse process of the chain rule in differentiation. It’s used when the integral contains a composite function — something inside something else — and a direct integration approach […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Trigonometry & Geometry 🔹 Introduction Complex numbers are not just algebraic curiosities — they form a geometric system where algebra, trigonometry, and exponential functions meet beautifully. One result stands above the rest in uniting them: De Moivre’s Theorem. It transforms […]