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

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

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

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 […]

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 […]

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 […]

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 […]

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 […]

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, […]

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 […]