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MIT professor kills a trick that used to take students twenty minutes, and replaces it with one move: stop thinking in real numbers.
he calls it "complexifying the integral." sounds fancy, isn't.
his example: integrate e^x times cosine x. the textbook way needs integration by parts, twice, in the same direction, then a comparison trick that barely anyone remembers under pressure.
his way: treat cosine x as the real part of a complex exponential. integrate the exponential, that takes seconds. then peel off the real part at the end.
this is Arthur Mattuck, MIT 18.03. it's the same move quants use on oscillating cash flows, interest rate models, anything with a sine or cosine buried inside an exponential.
nobody grinds through integration by parts on a trading floor. they push the problem into the complex plane and let the algebra do the work.
his own line on it: this is the moment you actually have to know how to divide complex numbers, not just recognize them. that's what separates the students who fake their way through from the ones who really get it.
no textbook, no calculator, just a chalkboard and one shift in how you look at the problem. that shift alone saves more time than any formula sheet ever will.
THIS IS F**KING DANGEROUS
FOUND AN AI RED TEAM THAT NEEDS ZERO HUMAN INPUT
PentAGI. Scanner โ> Exploiter โ> Reporter โ> three agents, working as a swarm, sharing results in real time.
One does recon, another finds and runs the actual exploits, a third writes the professional vulnerability report at the end.
FULLY AUTONOMOUS โ> plans its own steps, executes through terminal, browser, and code editor, monitors its own progress.
Runs entirely inside sandboxed Docker, integrated with 20+ real security tools (Nmap, Metasploit, SQLmap, and more).
It has over 22k STARS on GitHub
MIT licensed, self hostable โ> free if you run it on local models, cloud LLM costs only if you plug in OpenAI or Claude.
The tradeoff nobody skips past: this drops the cost of serious security testing for companies who couldn't afford it before and puts the same capability in everyone's hands.
Cybersecurity is genuinely becoming AI vs AI.
Authorized security testing only. Using this on systems you don't own is illegal.
REPO BELOW
IIT Madras professor S. Lakshmi Bala walks a full quantum mechanics class through the two-level atom, and she does it for free.
Western physics departments charge over $2,000 per credit for a graduate course in quantum mechanics. This entire course has been free since the early 2000s, but someone is trying to hide it.
In this lecture she has already moved past abstract vector spaces into a real physical system, the same two-level atom model that shows up later in laser physics and quantum computing.
No login wall. No certificate fee to just watch. One professor, one blackboard, one camera that never stopped rolling for over 40 lectures.
Physics departments built million dollar tuition systems around gatekeeping exactly this material. IIT Madras just recorded it and gave it away through NPTEL, a program that now hosts over 3,200 free courses.
โช $0 to watch, no account required
โช Filmed lecture hall style since the early 2000s
โช Same physics that underlies quantum computing today
๐Just don't lose it and find a way to save the lecture, because other paid institutions don't want you to have access to it for free.