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…
Education
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Examination Strategies: 12 Tactics That Lift Scores 10-30% (Cognitive Science Edition)
Most exam prep advice is folk wisdom. Here are 12 tactics with cognitive-science evidence: spaced repetition, retrieval practice, sleep timing,…
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…
Tunnel through the Earth
Drop a ball through a tunnel drilled straight through Earth. It won't fall forever. It'll oscillate back and forth, popping…
Euler’s (Prime to) Prime Generating Equation
Euler discovered a simple formula that generates 40 consecutive prime numbers: n squared plus n plus 41. Plug in 0…
Statistical Physics: Ensembles
Ensembles in statistical physics are collections of macroscopically identical but essentially independent systems. I explain the three main types: microcanonical,…
Analysis of Meteorological Data of Pantnagar Weather Station
This paper presents a statistical analysis of 20 years of meteorological data from the Pantnagar weather station in Uttarakhand, India.…
Introduction to Object Oriented Ontology
Object Oriented Ontology (OOO) challenges the idea that humans are the center of philosophical inquiry. It argues that objects exist…
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I…
The Area of a Disk
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know…