Symmetry in Physical Laws
Symmetry in physics isn't just about visual balance. It means an operation leaves physical laws unchanged. I explain the deep…
Education
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TeXstudio Review: The Most Complete Free LaTeX Editor in 2026
I first installed TeXStudio in 2012. 'Peaceful' was the word I used to describe it, and that hasn't changed through…
Top 10 ways to dominate your final exams
Your final exams are approaching. Are you ready to score memorable grades? I share ten proven strategies to dominate your…
Macrostates and Microstates and their relations with Thermodynamic Probability
The difference between macrostates and microstates confused me for months in statistical physics. Then a concrete example made everything click.…
How to change Differential Equations into Integral Equations?
Every differential equation can be converted into an integral equation. Just integrate it. Sounds too simple, right? The details matter…
How students’ brains like to be treated during an exam revision
Your brain needs specific treatment during exam revision, and most students get it wrong. I explain how memory formation works,…
Square Integrable Functions, Norms, and the Trial Method
Part II of the integral equations series. Covers L2 spaces, inner products, norms, Schwarz inequality, and solving integral equations by…
Definitions and Types of Integral Equations
Integral equations look intimidating, but they're built from ideas you already know. I explain what integral equations are, their classification…
Exam Strategies That Actually Work: What Cognitive Science Says About Test Performance
Most exam advice is generic: sleep well, eat breakfast, arrive early. Here's what cognitive science actually says works. Retrieval practice…
Complete Elementary Analysis of Ramanujan’s Nested radicals
I wrote this analysis in 2010 at age 17, obsessed with Ramanujan's nested radicals while studying under the INSPIRE-SHE scholarship.…
Hopalong Orbits Visualizer: The Math Behind the Most Beautiful WebGL Experiment
Barry Martin's Hopalong attractor turns three lines of algebra into galaxy-like structures rendered in real-time 3D. Here's the mathematics behind…
Real Sequences: Definitions, Theorems, and Examples
Real sequences form the backbone of real analysis and advanced calculus. I've taught this topic to dozens of students, and…