🧭 Scalar Product & Vector Projections — Geometry Meets Algebra
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Vectors | Geometry in Space 🔹 Introduction Vectors describe direction and magnitude — but to analyze how two vectors relate, we need tools like the scalar (dot) product and vector projection. These concepts reveal: Scalar product measures “alignment”; projection measures “influence.” ⚡️ 1️⃣ […]
🔍 Chi-Square Test — Understanding Independence, Association & Goodness of Fit
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Hypothesis Testing 🔹 What Is the Chi-Square Test? The Chi-Square Test (χ² Test) is a statistical method used to test whether observed data fits an expected distribution or whether two categorical variables are related. It’s one of the simplest and most […]
📈 Why the Standard Normal Distribution Is So Important
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Probability & Statistics 🔹 Introduction Almost every statistical table, test, or formula you’ve seen — Z-scores, confidence intervals, hypothesis testing, or control charts — comes back to one elegant concept:the Standard Normal Distribution. It’s not just a special case of the normal curve […]
🧮 Binomial Theorem for Fractions & Negative Integers — Beyond the Basics
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Algebra | Binomial Expansion | Advanced Topics 🔹 Introduction The Binomial Theorem is one of the most powerful results in algebra — it expands expressions of the form (1+x)n(1 + x)^n(1+x)n for any exponent nnn. Most students learn it for positive integers like […]
🎲 Conditional Probability — Explained with Venn & Tree Diagrams
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Probability | Statistics & Logic 🔹 Introduction Conditional probability tells us how likely an event is, given that another event has already occurred. It’s one of the most powerful tools in probability — and one of the most misunderstood. Conditional probability connects what […]
🎯 Expected Value and Variance — Understanding Expectation in Probability
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Probability & Statistics 🔹 Introduction In probability, every random event carries uncertainty — but we can still measure what happens on average. That’s what expected value (or expectation) tells us. Expected Value = the “center of gravity” of a random variable’s distribution. Similarly, […]
🌐 Domain, Range & Asymptotes — Understanding Function Behavior Deeply
Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Algebra | Functions & Graph Analysis 🔹 Why This Matters Every function tells a story — but to understand it fully, we must know: Together, these three concepts give the complete picture of any function’s behavior — algebraically and geometrically. 🧭 1️⃣ Domain […]
🎯 Inverse Normal Calculations — Finding Z-Scores and Probabilities
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 […]
📈 Graph of a Function — The Visual Language of Mathematics
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 […]
📈 Normal Distribution and Confidence Intervals — Foundations of Statistical Inference
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 — […]