Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Probability & Data Analysis 🔹 Introduction You’ve seen the normal distribution — the classic bell curve representing continuous random variables.You’ve used it to find probabilities given Z-scores. But what if you know the probability and need to find the Z-score or […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Algebra | Functions & Graphs 🔹 What Is a Function? A function is a rule that assigns to every input (x-value) exactly one output (y-value).In notation: y=f(x)y = f(x)y=f(x) The graph of a function is the set of all points (x,y)(x, y)(x,y) that […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Probability & Data Analysis 🔹 Introduction In statistics, most real-world measurements — like test scores, heights, or manufacturing errors — follow a bell-shaped pattern.That pattern is known as the Normal Distribution. The normal distribution is the backbone of statistical inference — […]

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 […]