e.bhanuprakash

[𝐇𝐚𝐦𝐳𝐚 | Networking Guy @Hamzaonchain]

HOW TO KNOW IF YOUR PC IS HACKED

[e.bhanuprakash @ebhanuprakash]

@worldoffra35851 16, 81

[e.bhanuprakash @ebhanuprakash]

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[e.bhanuprakash @ebhanuprakash]

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[e.bhanuprakash @ebhanuprakash]

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[e.bhanuprakash @ebhanuprakash]

@GodswillChemist 2.5kg

[Jonny @aiwithjonny]

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[Amit Sharma @AmitSha77280075]

Instead of watching an hour of Netflix, watch this 2 hour hour Stanford lecture will teach you more about how LLMs like ChatGPT and Claude are built than most people working at top AI companies learn in their entire careers.

[Abyzon @Abyzonn]

THE PROFESSOR WHOSE TEXTBOOKS SIT IN OVER 3000 UNIVERSITIES SHOWS IN 30 MINUTES WHY NEWTON'S METHOD HAS SURVIVED 400 YEARS UNCHANGED - AND WHY FOLLOWING A STRAIGHT LINE IS ALMOST ALWAYS GOOD ENOUGH

This is Gilbert Strang, MIT, a lecture on linear approximation and Newton's method. He opens with one sentence - both ideas come from the same place. Delta f over delta x. In one case you know x and want f. In the other case you know f and want x. The formula is the same. The insight is the same. Follow the tangent line instead of the curve.

First example - the square root of 9.06. You cannot compute it exactly in your head. But you know the square root of 9 is exactly 3, and you know the slope of the square root function at 9 is 1/6. Go across 0.06 on the tangent line, go up 0.01, and the answer is 3.01. The error is in the fourth decimal place.

Then Newton's method for the same problem. Set up the equation x squared minus 9.06 equals zero. Start at x equals 3. The function value there is minus 0.06. The slope is 6. Newton's formula gives a correction of 0.01. New guess: 3.01. Square it: 9.0601. The error is 0.0001 - way out in the fourth decimal place.

Then the second iteration of Newton's method. Start at 3.01. The error is 0.0001. The slope is 6.02. The correction is tiny beyond what you can compute in your head. Square the new x and the error has moved to somewhere around the eighth decimal place. Each step of Newton's method roughly doubles the number of correct decimal digits.

Watch the moment he connects linear approximation to Taylor series. The linear approximation of e to the x around zero is 1 plus x. The full Taylor series is 1 plus x plus x squared over 2 plus x cubed over 6 and so on. Linear approximation is just Taylor series stopped after the first two terms. Everything after that is the error of following the straight line instead of the curve.

A numerical methods engineer I know shows this lecture to every new hire before they implement any root-finding algorithm. Said it was the first time Newton's method felt like something you would naturally invent rather than something you memorize.

Free on YouTube, MIT OpenCourseWare, Gilbert Strang at a chalkboard.

bookmark this and watch later - after this lecture every equation you cannot solve exactly will feel like an invitation to follow a tangent line

[e.bhanuprakash @ebhanuprakash]

@0xLuciferCore 16

[e.bhanuprakash @ebhanuprakash]

@son1imkan 130

[e.bhanuprakash @ebhanuprakash]

@son1imkan 50.

[e.bhanuprakash @ebhanuprakash]

@Siya_22100 2100

[anand mahindra @anandmahindra]

Couldn’t believe my eyes when I saw this news.

Of course, India is a global force in shooting, but most of our success has come in rifle & pistol events.

Trap and skeet have always been much tougher to crack, demanding a very different ecosystem of ranges, coaching and competition.

That’s what makes Neeru Dhanda’s victory so special.

To win an ISSF World Cup gold in trap is one thing. To do it at Lonato, which is one of the sport’s most iconic venues and a place every shotgun shooter reveres, is another.

Clay target shooting has long been a European stronghold and is a discipline many Americans proudly regard as their own. Which is why Neeru’s gold feels like such a breakthrough.

Congratulations, Neeru. May this be the first of many more podiums. 🇮🇳

[E R R o R @SaEr0r]

🤐

[anand mahindra @anandmahindra]

Winning against the Chinese. In China.

At the Asian Relay Championships.

Srabani, Sudeshna, Sneha & Tamanna in the 4x100 relay.

Power. Speed. Grace. Commitment.

But above all, teamwork.

This clip has it all.

I’m watching it on loop.

More of this please. 🇮🇳

[Craft Gallery @5min__crafts]

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[This Account Makes You Happy @FeelYouHappy]

She going to think her dad has magic powers😅So perfect 👏

[folie à deux @folieadeeux]

Mıknatıs kullanarak bedava elektrik üretmişler.

[狗鷲イヌワシChapter II @emoemo78354888]

ワンちゃんたちが守る❣️🤗😱😘