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🔱IIT Madras professor V. Balakrishnan walks a full classical physics class through the foundations that connect Newton to quantum mechanics - he does it for free. US universities charge over $3,000 per credit to sit in a room and hear this material. Balakrishnan covers more ground in one semester...

36,029 görüntüleme • 21 gün önce •via X (Twitter)

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An Indian institute of technology filmed a full course on how money actually moves through a banking system and released it for nothing. The course is Economics of Banking and Finance Markets, produced at IIT Kanpur under NPTEL, India's national open courseware programme. It runs in sequence as one continuous argument rather than a set of clips. A green chalkboard, a lapel microphone, a checked shirt, one fixed camera. He opens with the only question that matters at the start. Where does surplus money sit, who needs it, and what stands between them. Then he splits the answer in 2. Direct finance, where the saver reaches the borrower through a market. Indirect finance, where a bank stands in the middle and absorbs the risk instead. Everything after that hangs off the split. Time value of money, risk, information asymmetry, why institutions exist at all, and what regulators are actually regulating. The turn is what he does with information. Banks are not warehouses for money. They exist because one side of every transaction knows things the other side does not, and the whole industry is built on charging for that gap. It matters more now. Every fintech product claims to cut out the middleman, and almost none of them remove the information problem that put him there. Free, in order, subtitled, funded by a public programme. The banking system explained from the first principle, for nothing. Lecture 1. 2 channels. It is in the video.

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A Japanese mathematician published a result in 1944 that nobody understood for twenty years. Today it runs inside every options desk on Wall Street. Goldman pays $400K to quants who can derive it from scratch and explain why classical calculus gives the wrong answer without it. His name is Choongbum Lee. MIT, 18.S096, Topics in Mathematics with Applications in Finance. The course that Wall Street watches. This is lecture 17. It derives Ito's Lemma from scratch. He opens with the problem nobody in classical calculus can solve. Then the foundation. Brownian motion is the limit of a random walk taken to infinity. Each trade pushes a price up or down by a tiny amount. A million trades a day. The limit of that process is Brownian motion. Einstein proved this for pollen particles in 1905. The finance world borrowed the math fifty years later. Then three properties that make no sense until you see them derived. Brownian motion crosses zero infinitely often. It never escapes to infinity. And it is nowhere differentiable - with probability one, every path is continuous but has no slope at any point. That last property is why classical calculus breaks completely. Then quadratic variation. For any smooth function, chop an interval into n pieces, square the increments, sum them - the result goes to zero. For Brownian motion it goes to T. The increments are too wild to vanish. That single fact is why Ito's Lemma has a second term that classical calculus does not. Watch the moment he derives it. Taylor expansion applied to a function of Brownian motion. The first term is what you expect. The second term appears precisely because the squared increment does not vanish. Without it, options pricing gives wrong answers. With it, you have Black-Scholes. A quant I know sends this lecture to junior analysts who cannot explain why their pricing model drifts. Says it fixes in ninety minutes what two years of finance courses left open. Free on YouTube, MIT OpenCourseWare, 18.S096. bookmark this and watch later - the math behind every options desk on Wall Street fits on one blackboard, and this is the lecture that shows you why

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