What exactly is e? Exploring e in 5 Levels of Complexity

Рет қаралды 53,055

Күн бұрын

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What is e? Let's explore the number e in 5 levels of complexity, ranging from compound interest, to representing e in calculus, to simulating e with probability.
This video was sponsored by Brilliant.
00:00 Introduction
00:12 Level 1: Compound Interest
02:30 Level 2: Probability
03:38 Level 3: Calculus
05:43 Sponsor Message
07:00 Level 4: Pascal's Triangle
09:17 Level 5: Simulating e

Пікірлер: 95

@DrSeanGroathouse 17 күн бұрын

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/DrSean . You’ll also get 20% off an annual premium subscription.

@mohammadmorshed4684 16 күн бұрын

This man explains math in such an intuitive way and his videos are rlly high quality, but he only has 15k subs. Actually underrated fr

@ExtraTrstl 16 күн бұрын

For real. This is some of the most accessible and coherent explanations. Dude is one of the best teachers I’ve ever had.

@2kchallengewith4video 16 күн бұрын

A very underrated math channel for sure

@Tristanlj-555 16 күн бұрын

One of the rare times “underrated” is used correctly:)

@westongunningham7151 15 күн бұрын

I'd just like to say I followed him before 5k

@AdityaPutatunda 15 күн бұрын

Agreed! The same way your comment needs some vowels

@AntoNqnt 14 күн бұрын

I have a presentation for an important exam in literally 2 days that is exactly about the number e, as well as the exponential function; and a video such as this one truly is appreciated edit : i went crazy with it tysm

@linuxp00 12 күн бұрын

My favorite representation is the Taylor's Series, because it relates e with sine, cosine, i, pi, sinh, cosh and hyperreal calculus. Also, as an infinite series you're mind blown when you see that it's derivative is really itself!

@user-jm9tf3uw1p 14 күн бұрын

e is the most insane number I have ever seen. I started learning it yesterday and I was shocked when I realized how versatile e is. For example the derivative of e^x is e^x and e^((x^h-1)/h)=x as h approaches zero

@Simpson17866 12 күн бұрын

You can approximate e to 18 trillion trillion decimal places using the digits 1-9 once each :D (1 + 9 ^ (-4^ (7*6)) ) ^ (3^2^85)

@SeanRaleigh 16 күн бұрын

Both levels 4 and 5 are mind-blowing. Well done!

@Unchained_Alice 5 сағат бұрын

The probability one was always my favourite. I worked it out myself without first knowing a long time ago so it is special to me. Plus probability theory is up there with my favourite fields in maths.

@bemusedindian8571 13 күн бұрын

Level 5 was mind blowing. Never heard this before.

@DrSeanGroathouse 11 күн бұрын

I'm glad you liked it! It's probably my favorite

@S-payanage 16 күн бұрын

A letter duh

@nahuelsotomayor32 5 күн бұрын

Literally just e, why make it harder

@kavehtehrani 16 күн бұрын

I'm a math graduate and I find your videos to be educational even to me! Keep up the good work the quality is top notch my friend!

@DrSeanGroathouse 11 күн бұрын

Thanks so much, I'm glad to hear that!

@hamedajab2483 16 күн бұрын

Quality is absolutely crazy

@DanielC618 16 күн бұрын

Great job! By far the best explanation I found 👏👏👏let's get that KZfaq algorithm going, this channel needs way more exposure!

@Fire_Axus 15 күн бұрын

@NicholasAngelidis1 16 күн бұрын

another great video!

@randyzeitman1354 14 күн бұрын

Superb. Far away, the best explanation of e.

@randyzeitman1354 9 күн бұрын

e is far more important than pi. Pi explains how many straight segments make up a circle. e explains how those circles integrate into reality itself.

@SobTim-eu3xu 16 күн бұрын

Great video, I love it❤

@eliteteamkiller319 13 күн бұрын

I love this channel so much.

@DrSeanGroathouse 11 күн бұрын

Thanks so much! I'm glad you like it

@DingleTwit 16 күн бұрын

The derivative part of level 3 made me literally put down my book and go “whoa” when I read it. That’s the version that finally made e click for me.

@kashemvai5025 4 күн бұрын

great channel and great video

@jaymethodus3421 14 күн бұрын

E as I use it: Exact; Equivalent; Expression (energy), e^i for 'computational cost' but the most [E]vil way I use it, as to denote exponential constant values, for scaling of base 3/4 calculation expressions into self-similar real-number ratios of irrational "digits" being operated on logarithmically.

@AndrewDangerously 14 күн бұрын

Can you explain this at level 1 and 2?

@jaymethodus3421 13 күн бұрын

@@AndrewDangerously It would require an exponential amount of text. Do you describe that 'amount' of that text using units derived from paragraphs? from words? from characters? From sentences? Pixel on/ off rate? The various electrical circuitry quantitues, taking their own exponential functions into account of this unknown value exponent? See, 0,1, and 2, are not real. 3 is where the real value baseline begins, as far as the instructional code for reality. 012 is a *continuum constant* that acts as a function instructing relative operational order of value exchange between real quantities. Dimensions aren't real. Yet trigonometry is extremely correlative to the deep-scaling of that very concept. Idk what to call my theory yet, but seems to be very well supported by every stone I turn over in my expansive search.

@jaymethodus3421 13 күн бұрын

@@AndrewDangerously Uhh. I tried... So 1^2 is 1. Terrence Howard really screwed me on this shit ngl lol.... but he's crazy. And I'm both/neither. He is onto something deeply irreducible about the discrepencies of '1', '0', and 2; to the exponent of the discrepancies from using -=X/ as our 4 highest order "math operations". 1 is actually an irreducible scale unit that represents an infinitely irreducible and unique value composed of higher and lower order integral values as they are ALL, mutually calculated. In %base10linear: 1=sqrt(-2)

@jaymethodus3421 13 күн бұрын

@@AndrewDangerously How's that for level 1 and 2? Pun intended lol

@jaymethodus3421 13 күн бұрын

Terrence has glimpses and he's high EQ, he knows what he saw, and he just runs with it. But he has no idea wtf he's talking about it what it actually means, or when and where to actually appy it without sounding like a snake oil salesman.

@moonwatcher2001 9 күн бұрын

Excellent, interesting and amene!!!

@Neodynium.the_permanent_magnet 16 күн бұрын

Yeah, baby, yeah!

@andrealves6545 16 күн бұрын

The last one took me by surprise ahah

@geraltofrivia9424 7 күн бұрын

Great content

@Fractured_Scholar 10 күн бұрын

Care to do a Level 6 for Rotors?

@jeremyi4693 16 күн бұрын

In high school calculus, our teacher taught us a mnemonic device for the approximate value of e. Think of a picture of Andrew Jackson in a square frame with a diagonal line from one corner to the other corner. Andrew Jackson served 2 terms, he was the 7th president, he was first elected in 1828, because he had 2 terms, we use 1828 twice. And the angles in the frame are 45-90-45. So, 2.718281828459045

@bsbrawl1653 16 күн бұрын

😮 cool

@ianbennett2443 16 күн бұрын

unfortunately, i know more about integrals than i do us history

@andyghkfilm2287 14 күн бұрын

Agh but what if I don’t know what Andrew Jackson looks like??

@jeremyi4693 13 күн бұрын

@andyghkfilm2287 think of a square with the name Andrew Jackson written in it.

@carultch 10 күн бұрын

@@andyghkfilm2287 He's on the most common printed bank note of US currency. He's Mr $20 Bill.

@m_c_8656 Күн бұрын

Word!

@guglielmotranchina249 10 күн бұрын

McLovin's smart doppelganger

@Skellborn 16 күн бұрын

I'm sorry, i dont get the Limit at 5:30: e^x lim((e^h-e^0)/h) is 0/0 for h-> 0. Meaning you have to do l'hospital. But dir this you have to differentiate e^x and you start all over again. How do you know it's 1? By stating it 1min earlier?

@joelganesh8920 16 күн бұрын

As stated in the video, the limit is the definition of the derivative of e^x at x=0, which was already assumed to be 1.

@sachavalette1437 10 күн бұрын

exp is the reciprocal function of ln so its derivative is 1/f’(f^-1(x)) = 1/(1/exp(x)) = exp(x). This is how to prove it.

@yawninglion 13 күн бұрын

I was expecting the final level to be some circles in the complex plane.

@infinityleleveling 14 күн бұрын

There are more ways to intuitively think about e. My favorite is the “e is the image of 1 by the exponential function” approach. But for that to really make sense, you would have to really understand what we mean by the exponential function and its many definitions. The exponential function can be defined as the inverse of the natural logarithm, but I find this definition to be superior: the only function whose derivative is equal to itself and is 1 at 0.

@orologioimpazzito 16 күн бұрын

Why you look like Sheldon´s brother 😀

@carultch 10 күн бұрын

He doesn't look anything like Georgie.

@orologioimpazzito 10 күн бұрын

@@carultch 😪

@ElGnomistico 11 күн бұрын

*E*

@gaigor 15 күн бұрын

@CallOfCutie69 6 күн бұрын

$@fractodacto$

@fractodacto 16 күн бұрын

cool

@RobertoCarlos-tn1iq 13 күн бұрын

a medical doctor and a mathematician! congrats!

@rikisanity6045 16 күн бұрын

Engineers: e=pi=3

@willie333b 15 күн бұрын

👀

@delta9990 16 күн бұрын

e > π calculus > geometry i will die on this hill

@sebas31415 16 күн бұрын

What about Calc 3 and 4 which touches on geometry (as in proof of area, surface area, and volume formulae)

@danmiltenberger5616 16 күн бұрын

2.718 is not > than 3.14.........

@unicorn3232 16 күн бұрын

@@sebas31415 that is barely geometry tbh, and that's actually fun

@Cow.cool. 16 күн бұрын

Abstract linear algebra > calculus any day

@hydropage2855 16 күн бұрын

@@sebas31415I’ve definitely seen you before somewhere else. Another gd player

@Fire_Axus 15 күн бұрын

why sponsor this video?

@JJW410 14 күн бұрын

So he can earn money?

@Lolwutdesu9000 16 күн бұрын

Nice video but at 5:40 you skipped why the limit simply equals 1. You can't just wave your hands and make it so as the limit tends to 0/0.

@joelganesh8920 16 күн бұрын

As stated in the video, the limit is the definition of the derivative of e^x at x=0, which was already assumed to be 1.

@S-payanage 16 күн бұрын

Otters 🦦

@assassinraider442 16 күн бұрын

@carultch 10 күн бұрын

Integral z^2 dz From 1 to the cube root of 3 Times the cosine Of 3 pi over 9 Is the log of the cube root of e