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Logic is the grammar of mathematics. You can have brilliant mathematical intuition, but without logical precision, you can't communicate your ideas or verify they're correct. I walk you through propositions,…
Fermat was convinced he'd found an infinite source of primes. He was wrong. His formula n^2 + n + 41 produces primes for the first 40 values, then fails spectacularly.…
This logic puzzle about three children and two friends is one of my favorites. It looks simple. Then you realize you're missing something. I've used it to teach logical reasoning…
Math majors need communities, not just textbooks. I've found six social networks specifically designed for mathematics enthusiasts. These platforms let you discuss proofs, share problems, collaborate on research, and connect…
Before college, I multiplied numbers the boring way. Then I discovered Vedic multiplication in a Hindi magazine called 'Bhaskar Bhoomi.' It felt like magic. I'll teach you the crisscross method…
Russian Peasant Multiplication is an ancient technique that multiplies any two numbers using only doubling and halving. No multiplication tables needed. I explain the method step by step, prove why…
Think you're good at mental math? Try this quick test. Start with 1000, add 40, add another 1000, add 30, add 1000 again, then add 20. What's your answer? Most…
Pursuit problems are some of the most elegant challenges in classical mechanics. A fox chases a rabbit, both moving at constant speed. What path does the fox follow? I present…
Weierstrass shocked the mathematical world in 1872 by constructing a function that's continuous everywhere but differentiable nowhere. Not at a few points. At no points whatsoever. I walk through the…
Memory isn't fixed. You can train it. I've compiled ten practical methods to improve how you retain and recall information: from simple repetition and spaced practice to visualization techniques and…
I've spent years collecting free calculus textbooks. Not scanned copies with missing pages. Real textbooks that professors and universities have made freely available online. This curated list covers single-variable calculus,…
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts. He showed how to build the real numbers rigorously from…
