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Dave's Math Channel
United States
เข้าร่วมเมื่อ 25 ก.พ. 2023
Fuzzy Logic
In this video, I give a brief explanation of fuzzy logic, a very useful generalization of classical logic, AKA Boolean algebra, as well as some of the way it is used.
มุมมอง: 73
วีดีโอ
The Liar Paradox
มุมมอง 49วันที่ผ่านมา
In this video, I discuss the liar paradox, also known as the Epimenides paradox, as well as some closely related paradoxes and some possible resolutions.
How Math Can Help You Invest
มุมมอง 63วันที่ผ่านมา
In this video, I describe how some basic math knowledge has helped me become a successful investor, and I think it could help you as well.
The Berry Paradox
มุมมอง 5614 วันที่ผ่านมา
In this video, I describe and resolve the Berry Paradox, one of many logical paradoxes resulting from self-reference.
Polling
มุมมอง 10821 วันที่ผ่านมา
In this video, I explain how poll results are calculated for simple random samples, and how to interpret the results.
Multiperfect Numbers
มุมมอง 59หลายเดือนก่อน
In this video I define and describe multiperfect numbers (also known as multiply perfect numbers, or MPNs), which are a natural extension of perfect numbers.
Applications II, Lesson 6: The Newton-Raphson Method
มุมมอง 128หลายเดือนก่อน
In this sixth video in my subseries on applications of first-year calculus, I discuss and explain the Newton-Raphson method, a powerful method for estimating roots of differentiable functions, and give three examples.
Growing Up as a Math Prodigy
มุมมอง 175หลายเดือนก่อน
This is not a math video, but an autobiographical video about some of my life experiences growing up as a math prodigy.
How to Be a Human Scientific Calculator
มุมมอง 250หลายเดือนก่อน
In this video, I show how one can use known Taylor series of various scientific functions, such as exponential, logarithmic, and trigonometric functions, to come up with some amazingly precise estimates of their values for arbitrary arguments.
How to Compute Square Roots in Your Head
มุมมอง 8Kหลายเดือนก่อน
In this video, I explain how to use Heron's method to mentally calculate very precise estimates of arbitrary square roots!
How to Multiply Two 2-Digit Numbers In Your Head
มุมมอง 637หลายเดือนก่อน
In this first video in my new series on how to be a human calculator, I explain a trick I learned at age 12 for how to compute two 2-digit numbers in my head! It's not easy, but if you're so determined, you could probably do this yourself in a couple years!
Applications II, Lesson 5: Euler's Formula
มุมมอง 5282 หลายเดือนก่อน
In this final video of my series on first-year calculus, I state and derive Euler's formula, one of the most important formulas in mathematics, as well as Euler's identity as a special case.
Applications II, Lesson 4: Taylor Series
มุมมอง 1852 หลายเดือนก่อน
In this video, I discuss Taylor series, including what they are and why they are important. I also present five useful examples of Taylor series and derive the forms of three of them.
Maximal Prime Gaps
มุมมอง 3052 หลายเดือนก่อน
In this video I define maximal prime gaps and show data on the known ones as well as some conjectured upper bounds on their sizes.
Famous Unsolved Math Problems
มุมมอง 3612 หลายเดือนก่อน
In this video I briefly discuss some of the most interesting currently unsolved math problems.
Applications II, Lesson 3: Exponential Growth and Decay
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Applications II, Lesson 3: Exponential Growth and Decay
Applications II, Lesson 2: Falling Bodies II
มุมมอง 1752 หลายเดือนก่อน
Applications II, Lesson 2: Falling Bodies II
Applications II, Lesson 1: Falling Bodies
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Applications II, Lesson 1: Falling Bodies
Integration, Lesson 11: Partial Fractions II
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Integration, Lesson 11: Partial Fractions II
Integration, Lesson 10, Partial Fractions I
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Integration, Lesson 10, Partial Fractions I
Perfect, Amicable, and Sociable Numbers
มุมมอง 752 หลายเดือนก่อน
Perfect, Amicable, and Sociable Numbers
Integration, Lesson 9: A Few More Elementary Integrals
มุมมอง 752 หลายเดือนก่อน
Integration, Lesson 9: A Few More Elementary Integrals
Integration, Lesson 8: Integration by Parts
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Integration, Lesson 8: Integration by Parts
Integration, Lesson 7: Trigonometric Substitution
มุมมอง 363 หลายเดือนก่อน
Integration, Lesson 7: Trigonometric Substitution
Integration, Lesson 5 Integrals of Elementary Functions
มุมมอง 563 หลายเดือนก่อน
Integration, Lesson 5 Integrals of Elementary Functions
Why would I need to do that? I have a calculator.
Yes, and why would you ever use a map since you have GPS?
But what does ELO stands for?
Elo is not an acronym, it's the name of the mathematician who came up with the system.
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
Why is this man so underrated!?
I'd say most mathematicians are highly underrated. How many are you familiar with? Most Americans are only familiar with perhaps one, mainly the Unabomber.
To be honest dave, my idol is the great mathematician Ramanujan i love his work but im still a young one do you have any social media like instagram? I want to prepare for the math olympiads maybe you can teach me? :D
Flashback to my school days!
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
You can't say that investing have positive EV. yes, in long term stock goes up, but when you trade a lot, commissions will take a lot of part of your earnings. Instead of picking 10 companies randomly its much better to just buy ETF - which buys all companies from SP500 or even some all world etf
I don't think I said that investing always has a positive EV, just that it usually does, especially in the long run. However, you're right that it makes a lot more sense to invest in ETFs than to pick stocks at random - I've just never done it myself.
Example 3 has 2 mistakes. First if all 6.5+ 7.07 is not 12.57 but 13.57. Also When you divide 12.57 by 2 its actually 6.285 not 6.785. Is this video trolling or what?
I already pointed out this mistake in the comments section. In any case, the end result of my calculation is correct.
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
AMAZING❤❤❤
Thanks!
@davesmathchannel-ts2ik your welcome!
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
I really like the you multiply the denominator by your test number then use the remainder.
Enjoyable
Thank you!
When I calculate 49*32 I do 50*32=1600 (half of 32 times 100). Then I subtract 32 because 49 is 1 less than 50. I also check that the results ends with an 8 because the final figures 9*2=18 ends with an 8. And a sanity check of the magnitude of the result. When doing mental calculation I only care about the digit sequence, the magnitude or decimal place I do at the end. Several ways to do it, of course. What's efficient depends of what one has trained on. Making those confused neuron connect in a useful way. Numerical mysticism of course says nothing about anything real or about maths. But a sort of it can be helpful for memorization. When I see 49 I see 7, 1, 2 and 100. (What?) Because 7*7 = 100/2 - 2/100. That's what makes 7 so easy to use in mental calculation! It is extremely closely related with 2. √2 = 1.4142135 which is the digit sequence of 7*2, 7*2 again 7*3 and 7*5. 1/7=0.142857 repeated. Again multiples of 7, with a 7 instead of a 6 at the end. It has to do with 142857 having the divisors 9=(10-1), 11, 111 and 13. Those ones mean that it is all about simple shifting and addition. And 13 as a seed. Just like 1/13 = 0.076923 repeated with the divisor 13 exchanged for 7 and the 9, 11, 111 in common. If one shifts the digit sequence of 1/7 := 142857 three steps left and add them, one gets 999999. Same with the digit sequence of 1/13 := 076923. 14+28+57=99 and 142+857=999. Like 07+69+23=99 and 076+923=999. 9*11*111=10989. What if one multiplies it with 9 again instead of with 7 or 13? Oops, 98901, all the figures turned kinda backwards! The miracle of "hyperones" like 11, 111, 101, 9=10-1, 99=100-1 and so on.
The last digit is a good sanity check I should have mentioned.
0:26 babylonian method?
As far as I know, the Babylonian method is just another name for Heron's method.
Holy shit I can’t listen to this guy 😂😂😂😂🤣🤣
sqrt(a^2+b)=a sqrt(1+b/a^2)~a(1+b/(2a^2))=a+b/(2a) If a^2 < n < (a+1)^2, set b=n-a^2. If b>a set b-n=(a+1)^2 and use a+1 instead of a.
This is the Taylor series method, which isn't quite as precise as Heron's method, but still quite good. Thanks for sharing.
I was taught the "9's trick" in elementary school. It's cool but basic arithmetic is one of the very few subjects where rote memorization is the right tool. I wish I could look at 72 and see the 9 and the 8 in there instantly. I can kind of teach myself that as an adult but I often have to check (8+2=10) after I say the answer.
I'm glad you appreciate casting out nines, or the 9's trick if you prefer. However, I disagree that rote memorization is the way to learn math! Although a few things need to first be memorized, such as the multiplication table, the beauty of math is that every result can also be proven or derives, so memorization is ultimately unnecessary, and in fact discouraged in general.
That's awesome. I would love to make a video about the general number field sieve with you sometime.
That would be great, except I never implemented it myself and in fact, although I understand the general idea of the method, I don't completely understand it, so perhaps you know more about it than I do. If so, perhaps you can teach it to me. Once you do, I'd be happy to collaborate with you on a video!
That's cool, but it bugs me how many comments this one is getting compared to your other videos. This TH-cam algorithm seems to reward cheap superficial performance. It's good to have fun, but you are better than this David. This is the world's problem not yours.
I don't understand TH-cam's algorithm either. But I know that shorts in general get many more views that full videos, which is probably the main reason this one is so popular.
In the version of the story I heard, Büttner gave the class the assignment so he would have some time to work on art. That didn't work out for the teacher but I'm still curious what the he was drawing that day.
Interesting! It seems you know more about it than I do!
Nevermind, you got it right. I just rewatched the video and at 0:52 you said "twenty-three cents". It just looked like you wrote down ".22" on the whiteboard. TH-cam has some menu options overlayed on the output that mess with the presentation.
I keep getting 24 cents for the pennies on day 31 not 22. Maybe Microsoft Excel has some rounding/underflow issues. I should get out a better tool. Oh wait, I see my mistake. The last number is the total paid for the entire month rather than day 31. Still, wouldn't the change be 23 cents then? Yeah, I just summed the collum, it's 1073741823 pennies. I think the kid is getting underpaid.
Let’s see: “Four-billion, nine-hundred twenty-four million, nine-hundred sixty-four thousand, two-hundred ninety-six”: 104 “One-hundred four”: 16 “Sixteen”: 7 “Seven”: 5 “Five”: 4 “Four”: 4 Well, that checks out. There may be other loops around weirdly named numbers like “one-googol”. I’m not really sure what the rules are for English number words. Overall, I’m pretty sure you are right about “four” being the only one.
I'm still thinking about whether the name of the integer just before one-googol (10^100 -1) could have more than one-googol characters. I mean I could only count up to a number around nine-hundred ninety-nine quintillion. (If I have enough time.) So that would get us to 10^21 -1. That's not very close to our target and we would have to make up rules to get there. English can be relatively compact and assuming we are sensible about the rules we make up, I think we could do this without causing an information density related black hole on Earth.
Does a "billion-million-gazillion billion trillion" count as a number word? A number like that would probably easier to test than one-googol.
I'm pretty sure that every word you start with will converge to 4 with this procedure. (You don't need to start with the name of a number.) 4 is what is known as a fixed point, an important concept in math, in case you're interested.
I love your video. If we specified the parameters in terms of the thickness of a nickel instead of meters how tall would your building be?
If a and b were gaussian prime complex numbers rather than normal coprime integers would the proof still work?
you look like richard dawkins
Very good!
Thanks! I do my best!
I messed up a bit near the beginning. There are a lot more multiperfect numbers of orders 4, 5, and 6 than shown, as I explain later.
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
OK, my question is can we have a procedure to calculate cubic roots and the other upper roots ?
Great question! I can make another video on that if you like.
To find the n-th root of a, we solve the equation y^n = a by Newton-Raphson,. So we find the roots of f(x) = x^n -a = 0. If x is a guess, then a better approximation should be x - f(x)/f'(x). That gives us x - (x^n - a)/( nx^(n-1) ) which simplifies to ( (n-1)x - a/x^(n-1) ) / n. For example, to find the cube root of a, we use n=3 giving the formula for successive approximations as ( 2x + a/x^2 ) / 3.
If a^m < n < (a+1)^n set b=n-a^m. Then (n^{1/m))=(a^m+b)^{1/m)=a(1+b/a^m)^(1/m)~a(1+b/(ma^m))=a+b/(ma^{m-1)). Modify if n closer to (a+1)^m.
I guess Newton method is converging faster. A naive approach would be to say a approximates cube root of X so a^3~=X If we divide by a^2 then a~=X/a^2 Consider if a<x^1/3 then X/(a^2)>x^(1/3) so considering the 2 terms margins of the interval the solution is inside We can take aritmetic mean to approximate new a a(n+1)=1/2(an+X/(an^2)) But I would say the Newton approximation method will converge faster
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
One iteration accurate to within 0.001 in the first example !
Yes, I know - pretty remarkable I'd say! As I said, this is quite a powerful method!
Silly me, I forgot to give the formula: Product of (oddprimes -2) / (oddprimes-1) . For example, if you pick 11, the value is 135/480. The result is the probability of relative twin prime pairs amid relative primes (both relative to all primes up to and including 11) . By my reasoning, this formula should be really accurate and very precise, but I don't know where to turn to verify this, or even if this is common knowledge. Any feedback would be appreciated. MetaAI tells me that the correct mathematical notation for the formula is: ∏[(p-2)/(p-1)] p∈{3, 5, ..., P}, where P is an odd prime According to MetaAI, the lines in the graph seem to cross just past the 10^8th prime where my formula seems to converge to 0.355.
What are you trying to calculate here?
@@davesmathchannel-ts2ik It's the asymptotic density of twin prime pairs among all primes. While Hardy-Littlewood calculate the density of twin primes LESS than a given number, I'm calculating the density of twin relative prime PAIRS GREATER than the given number. Our formulas are very similar, and while mine seems to be converging to 0.355, theirs converges to 0.330 (looking at pairs should be half of 0.660).
@@davesmathchannel-ts2ik Never mind for now, I just spotted a mistake in the formula. The graph is correct, but not the formula I thought represented the graph. I'll post the correction to the formula as soon as I figure it out. To be clear, the algorithm producing the graph is the correct one, not the formula.
@@adanieltorres OK, thank you for clarifying. I believe the number you're trying to calculate is equal to half of the twin prime constant, denoted as Π₂. Here's a link: mathworld.wolfram.com/TwinPrimesConstant.html
@@adanieltorres This is probably unnecessary since as I mentioned, the formula for the constant you're trying to calculate, namely half the twin prime constant, is already known. I find it rather strange that no one has yet proven that there are infinitely many twin primes, and yet we have a very precise asymptotic formula for estimating their density! Unfortunately, it's very difficult in general to prove conjectures regarding the densities of various types of primes or prime-related sequences, even though we have very good heuristics.
In coding a prime generator, I came up with a way to calculate, at the end of each iteration, the proportion of Relative Twin Primes to Relative Primes. I looked for similar calculations out there but I couldn't find any ( I hadn't searched TH-cam, which is how I just found your video). I had found that there is something called the First Hardy-Littlewood Conjecture (FHLC) which estimates the number of Twin Primes *less than or equal to* a number, which is similar to what I have, but I calculate the number of *relative* Twin Primes *greater than* a number. Then I found the Prime Counting Function (PCF) but its estimates of Primes are also *less than or equal to* a number, not calculating *relative* Primes *greater than* a number. Regardless, I divided the FHLC estimate by the PCF estimate for the smallest 125 primes starting with the prime 5, and I compared it to my calculated proportions of Relative Twin Primes to Relative Primes for the same list of prime numbers. Here's a link an image of the graph drive.google.com/file/d/1jR5KGQyVSaaPUs9PCWZUsmVFFGNsNr14/view?usp=sharing If you're interested, I'd love to chat about it.
Great video. Thanks v much
You're quite welcome! Hopefully you too can be a human square root calculator, but if not, don't worry because most people can't, and in any case, there probably isn't much practical use for this skill other than showing off at parties.
@@davesmathchannel-ts2ik I'm impressed with the precision of this method and I find it quite elegant too. It's quite easy to understand why it works too. (I like to try to understand how stuff works. It's more satisfying, I think). I had a look at doing it by hand on other vids, but it seems a bit messy. I like the Heron's/(Dave's) method better. :) I tried cube roots and 4 roots along the same lines as Heron's method. Seemed to work a bit but errors were bigger. Thanks
@@zalida100 I'm glad you found this method interesting and useful, and I agree with you. If you want to estimate higher roots or other scientific functions, you could either use a more general form of the Newton-Raphson method, which I'll probably make a follow-up video on soon, or Taylor series, which I discuss in another recent video you might want to watch.
There is mature content in this video.
Your story makes me feel less alone when finishing high school and incredibly worried about my future. Thank you for sharing your knowledge.
I'm glad I could help! I think it's important for like-minded people to get together and share stories and experiences so that we know we're not alone and that together, perhaps we can make a difference.
For those interested, I've completed two online math courses on Udemy. Please check them out! Games and Puzzles: www.udemy.com/course/games-and-puzzles/ PI: www.udemy.com/course/pi-hiwvu/
In addition to my online math school, I'm offering online tutoring via Skype in math or physics for anyone who's interested. I charge $30 an hour, for which we can arrange payment through Zelle. If you're interested, please respond.
1:02 This method is way older than that, it's Babylonian!
Thanks for the info - I wasn't aware of this! Unfortunately, in math, as with pretty much everything else, results often get named after the wrong person.
There is no proof that Heron's method was known to ancient Babylonia.
1:12 Newton-Raphson method
I think you mean the Newton-Raphson method, which I believe I do mention.
@@davesmathchannel-ts2ik thank you for the correction
@@TimV-t8x No worries!
@@TimV-t8x No worries!