Pronit nag

Lecture 1 from this semester's "Introduction to Formal Real Analysis" is posted: youtube.com/watch?v=TN51-1… We first go over why "Real Analysis" is even needed (why is "Calculus" insufficiently rigorous), and then the first steps in using Lean. We're following "Real Analysis, The Game", which I'm writing as the semester progresses. Feel free to try your hand at it! adam.math.hhu.de/#/g/AlexKontor… And if you think of an improvement, feel free to submit a PR!

The first day of the dwarvish New year, only if the last moon of autumn and sun are in the sky at the same time

#TolkienArchivist When is Durin's Day? @mellon_heads @MiddleearthMixr @SethMoldenhauer @SamwisetheSwol @Strangeland_Elf @TheMiddleborne @TolkienWorldG @Tolkien_erklart @Tolkien_32Years @Teresa__Martin @LadyGravemaster

@SamwisetheSwol @mellon_heads @MiddleearthMixr @SethMoldenhauer @Strangeland_Elf @TheMiddleborne @TolkienWorldG @Tolkien_erklart @Tolkien_32Years @Teresa__Martin @LadyGravemaster Correct

@Pronitnag @mellon_heads @MiddleearthMixr @SethMoldenhauer @Strangeland_Elf @TheMiddleborne @TolkienWorldG @Tolkien_erklart @Tolkien_32Years @Teresa__Martin @LadyGravemaster Burt Tom and William.

#TolkienArchivist Who were the three trolls the company first ran into? @mellon_heads @MiddleearthMixr @SethMoldenhauer @SamwisetheSwol @Strangeland_Elf @TheMiddleborne @TolkienWorldG @Tolkien_erklart @Tolkien_32Years @Teresa__Martin @LadyGravemaster

Please Lord.

@3RenChengHu @tomrocksmaths He asks a question Student starting at his hand

@tomrocksmaths Honestly, if you're teaching the course, you really shouldn't need a cheat sheet this badly.

Tattoo 75 - Divergence Theorem. One of my favourite results in multivariable calculus allowing you to change between a volume integral and a surface integral depending on which one is easiesr to solve. Part of the 1st year ‘Vector Calculus’ course I teach at Cambridge University.

You'll Never Walk Alone ❤️

10 years ago today, I lived every boy’s dream in a Red shirt. Scoring against Borussia Dortmund in the Europa League at Anfield — the lights, the noise, the Kop roaring as we fought back in one of the greatest European nights this club has ever seen. That goal, that moment, that Liverpool shirt… it’s etched in my soul forever. Still gives me goosebumps. Thank you to every teammate, every fan, and everyone who made that night magic. This one’s for the memories that never fade. ❤️ You’ll Never Walk Alone Good luck tonight LFC. BELIEVE!

10 years ago today 🤩🗓️

Kenny Dalglish: “Liverpool have always been about spirit and belief.” @LFC_RV @LFCMumbai @Nikky_LFC @MightyRed_LFC @LFC

@Nikky_LFC Big deflection thogh

Tie over Sack him at half time and get it over with

Be still

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Real Analysis Lecture 2 is up. youtu.be/U2oCgeVgd9M We went over Newton’s computation of Pi, both because it’s super cool (first and foremost), and also because it’s a quintessential calculation encompassing everything that’s “wrong” with plain old Calculus, needing rigorous justification: - What does it mean for a sequence of real numbers a₀, a₁, a₂, ... to converge? - What does it mean for a series (that is, sequence of partial sums of some sequence) a₀ + a₁ + a₂ + ··· to converge, and can we sum these numbers in any order we like? - What does it mean for a series involving a variable, like a power series a₀ + a₁x + a₂x² + ··· to converge, and if it does, what kind of function does it converge to? - When can we interchange limits with integrals, like integrating term by term, ∫(a₀ + a₁x + a₂x² + ...)dx ··· ?=? ∫ a₀ dx + ∫ a₁x dx + ∫ a₂x² dx + ···? These are all exactly the kinds of questions that Real Analysis answers, but I find most presentations of these vital issues unmotivated. Hopefully the Newton example brings them to life...

In 2019, MIT professor Patrick Winston gave a legendary 1-hour lecture called “How to Speak.” It has 18M+ views for a reason. His frameworks: • Your ideas are like your children • The 5-minute rule for job talks • Why jokes fail at the start 15 lessons on communication:

BREAKING🚨: PETER JACKSON announces NEW Lord of the Rings movie!!! Focusing on Chapters 3-8 of The Fellowship of the Ring!!

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A man with no money and a woman without Beauty sees the world without illusion - Friedrich Nietzsche