A difficult Putnam question with an elegant solution.
This video was sponsored by Brilliant: https://brilliant.org/3b1b
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/putnam-thanks
Home page: https://www.3blue1brown.com/

Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/

These videos exist thanks to Patreon:
https://www.patreon.com/3blue1brown

A different write-up of this solution:
http://lsusmath.rickmabry.org/....psisson/putnam/putna

1992 Putnam with this problem:
http://kskedlaya.org/putnam-archive/1992.pdf

A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! The solution for that problem, by the way, was written by Calvin Lin, a friend of mine who works at Brilliant. Small world!
http://kskedlaya.org/putnam-archive/2005.pdf
http://kskedlaya.org/putnam-archive/2005s.pdf

------------------
Animations largely made using manim, a scrappy open source python library. https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcam....p.com/album/the-musi

Stream the music on Spotify:
https://open.spotify.com/album..../1dVyjwS8FBqXhRunaG5

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Alfred Emery Maths and English Tutor in Worthing, Brighton, West Sussex

this video helps in writing lap (coursework). please like and subscribe.

This video provides a brief introduction to how our 1:1 Digital Learning Program has grown and changed over the past few years. We are an internationally recognised Apple Distinguished School, and are leaders in using digital technologies for innovative teaching and learning.

The following video was created by the 2021 Westosha Central National Honor Society at the request of Mrs. Keller of Brighton Elementary. If you are teacher with a video request, please submit video requests to http://coop.nhsfalcons.com.

To download this video, go to http://coop-drive.nhsfalcons.com

#nhscoopbrighton #nhscoop2020 #secondgrade

The math behind cryptocurrencies.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/btc-thanks
This video was also funded with help from Protocol Labs: https://protocol.ai/join/

Some people have asked if this channel accepts contributions in cryptocurrency form. As a matter of fact, it does:
http://3b1b.co/crypto
ENS: 3b1b.eth

2^256 video: https://youtu.be/S9JGmA5_unY

Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat

Here are a few other resources I'd recommend:

Original Bitcoin paper: https://bitcoin.org/bitcoin.pdf

Block explorer: https://blockexplorer.com/

Blog post by Michael Nielsen: https://goo.gl/BW1RV3
(This is particularly good for understanding the details of what transactions look like, which is something this video did not cover)

Video by CuriousInventor: https://youtu.be/Lx9zgZCMqXE

Video by Anders Brownworth: https://youtu.be/_160oMzblY8

Ethereum white paper: https://goo.gl/XXZddT

Timestamps:

0:00 - Introduction
2:25 - Ledgers and digital signatures
7:21 - The ledger is the currency
10:06 - Decentralization
12:26 - Cryptographic hash functions
14:38 - Proof of work and blockchains
19:42 - Double spending
21:41 - Block times, halvenings, and transaction fees
24:40 - Thanks

------------------
Animations are largely made using manim, a scrappy open-source python library. https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcam....p.com/album/the-musi

Stream the music on Spotify:
https://open.spotify.com/album..../1dVyjwS8FBqXhRunaG5

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Professional Learning
-------------------------------
Professional development to teaching is what position is to real estate. Teachers use the Federal Government's Australian Professional Standards for Teachers to benchmark their skills
and the State Government's Teaching for Effective Learning (TfEL) document to organise appropriate pedagogies to deliver curriculum to students.

Teachers at Brighton Secondary School participate in a variety of teams all working to improve teachers' practice, which in turn improves outcomes for students.

Teachers are in Faculty teams linked to subject areas, as well as in Teacher Learning Communities organised around the Australian Cross Curriculum Priorities (Engaging with Asia, Aboriginal and Torres Strait Islander Histories and Cultures, Sustainability) and the Australian Capabilities (Literacy, Numeracy, Social and Personal, Critical and Creative Thinking, Ethical Behaviour, Cultural Understanding, Information and Communication Technology). Staff teams meet to advance their knowledge.

At Brighton Secondary School staff professional development is augmented by the professional learning period on Tuesdays from 2.30 to 4.30pm.

We ground our instructional methods in the three R's: Rigor, Relevance and Relationships. Watch this video to learn more about how we apply these methods in our classrooms and how they seek to challenge students and promote a love of learning.

http://infinitymathtutoring.com 734-301-0352-GED tutoring in Brighton MI-With Infinity Math Tutoring, you will have a Math Professional on your doorstep. We tailor our math instruction to your individual needs, around your unique schedule! Tutoring is on a one-on-one basis, with the same tutor.

Convenience: We provide services in your home, at your school, in the library, wherever you want us to tutor, we’ll be there. We work around your busy schedule.

Quality: One-on-one tutoring is simply the best. We give your student the individualized attention they need with a tailored education plan that fits his or her needs.

Affordable: Infinity Math Tutoring offers the best rates around. Other companies charge above our rates and don’t offer the personalized, one-on-one, in-home attention you deserve. Contact us to find out how surprisingly affordable tutoring can be.

Special Needs: Infinity Math Tutoring understands the classroom challenges students with learning disabilities face on a daily basis. We will find the right tutor and right plan for each child. We work with parents, resource and special education teachers to compliment existing strategies and plans with our one-on-one tutoring.

We are a Michigan based companies services the following cities and surrounding areas: Belleville, Canton, Novi Northville, Plymouth, Livonia, Romulus, Westland, Inkster, Wayne, Redford. Contact us today to schedule a FREE consultation at 734-301-0352.

Enjoy these videos? Consider sharing one or two.
Help fund future projects: https://www.patreon.com/3blue1brown
Special thanks to these supporters: http://3b1b.co/nn2-thanks
Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks

This video was supported by Amplify Partners.
For any early-stage ML startup founders, Amplify Partners would love to hear from you via 3blue1brown@amplifypartners.com

To learn more, I highly recommend the book by Michael Nielsen
http://neuralnetworksanddeeplearning.com/
The book walks through the code behind the example in these videos, which you can find here:
https://github.com/mnielsen/ne....ural-networks-and-de

MNIST database:
http://yann.lecun.com/exdb/mnist/

Also check out Chris Olah's blog:
http://colah.github.io/
His post on Neural networks and topology is particular beautiful, but honestly all of the stuff there is great.

And if you like that, you'll *love* the publications at distill:
https://distill.pub/

For more videos, Welch Labs also has some great series on machine learning:
https://youtu.be/i8D90DkCLhI
https://youtu.be/bxe2T-V8XRs

"But I've already voraciously consumed Nielsen's, Olah's and Welch's works", I hear you say. Well well, look at you then. That being the case, I might recommend that you continue on with the book "Deep Learning" by Goodfellow, Bengio, and Courville.

Thanks to Lisha Li (@lishali88) for her contributions at the end, and for letting me pick her brain so much about the material. Here are the articles she referenced at the end:
https://arxiv.org/abs/1611.03530
https://arxiv.org/abs/1706.05394
https://arxiv.org/abs/1412.0233

Music by Vincent Rubinetti:
https://vincerubinetti.bandcam....p.com/album/the-musi

-------------------
Video timeline
0:00 - Introduction
0:30 - Recap
1:49 - Using training data
3:01 - Cost functions
6:55 - Gradient descent
11:18 - More on gradient vectors
12:19 - Gradient descent recap
13:01 - Analyzing the network
16:37 - Learning more
17:38 - Lisha Li interview
19:58 - Closing thoughts
------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Try The Athletic for FREE for 30 days: https://theathletic.com/tifofootball

Brentford have already shown the Premier League that they will be tough opponents. The fact that they run their club differently to most others has been widely reported.

But what do they do differently? How have they adapted the “Moneyball” theory? What other staff departments have they introduced?

Written by Alex Stewart, illustrated by Alice Devine.

Follow Tifo Football:
Twitter: https://twitter.com/TifoFootball_
Facebook: http://facebook.com/TifoFootball
Instagram: http://instagram.com/TifoFootball_

Listen to the Tifo Football podcast:
The Athletic UK: http://bit.ly/TifoPodChannel
Apple Podcasts: http://bit.ly/TifoFootPod
Spotify: https://open.spotify.com/show/....06QIGhqK31Qw1UvfHzRI

Watch more Tifo Football: Tactics Explained: https://youtube.com/playlist?list=PLWYJXDKS21OE39KTymISkCrgCckZh2_sD&playnext=1
Finances & Laws: https://youtube.com/playlist?list=PLWYJXDKS21OEcOCEjYX59zfcGYrCXFMR2&playnext=1
Tifo Football Podcast: https://youtube.com/playlist?list=PLWYJXDKS21OHj085qILmy-O2-yZqFIcuM&playnext=1
Most Recent Videos: https://youtube.com/playlist?list=PLWYJXDKS21OGSHqQmRnREA6J11Tadn1zC&playnext
1 Popular Videos: https://youtube.com/playlist?list=PLWYJXDKS21OF841IcGORTXynu2l67jpeE&playnext=1

About Tifo Football:
Tifo loves football. We create In-depth tactical, historical and geopolitical breakdowns of the beautiful game.

We know there’s an appetite for thoughtful, intelligent content. For stuff that makes the complicated simple.

We provide analysis on the Premier League, Champions League, La Liga, Serie A, Bundesliga, World Cup and more.

Our podcasts interview some of the game’s leading figures. And our editorial covers football with depth and insight.

Founded in 2017 and became a part of The Athletic in 2020. For business inquiries, reach out to tifo@theathletic.com.

Music sourced from epidemicsound.com
Additional footage sourced from freestockfootagearchive.com

#Brentford #Moneyball #Transfers

Get more lessons like this at http://www.MathTutorDVD.com

In this lesson, you will learn an introduction to physics and the important concepts and terms associated with physics 1 at the high school, college, or university level.

We will review Newton's laws of motion, projectile motion, force, energy (potential and kinetic energy), gravitation, momentum, collisions and more.

The inspirational John Cooper talking about his experience on the Mathematics SKE (Subject Knowledge Enhancement) Course at the University of Brighton during our Pecha Kucha afternoon in February 2011.

What might it feel like to invent calculus?
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/lessons/essence-of-calculus#thanks

In this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.

------------------

These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcam....p.com/album/the-musi

Stream the music on Spotify:
https://open.spotify.com/album..../1dVyjwS8FBqXhRunaG5

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

English Football League game between Leicester City and Brighton & Hove.
African players Daka and Mwepu from Zambia scoring goals and penalties.

2:2 draw (Mwepu scores for Brighton)
2/4 goals for each side
Equivalent fraction simplifies to
1/2

4:2 penalties (Daka scores for Leicester, Mwepu misses)
Simplifies to ratio of 2:1 Leicester penalties to Brighton penalties

6/8 penalties converted/scored
Simplifies to 3/4 equivalent fraction

Also ratio of 6:2 penalties scored to missed
Simplifies to 3:1

Thanks for watching!
Please like, subscribe and share
And watch the Lego and Shapes maths playlists for more videos!

please contact via twitter / X or email if you want to suggest or request more videos

So, Wolfpack, we know you’re all stuck at home
Tryna’ do school while you’re sitting alone
You got packets, and books, that you might never read
But us teachers, we got you, we know what you need

We put lessons and work up online every day
To make sure that the stuff that you learned doesn’t stray
And we get that you might be confused how to stay
On top of it all so we’re here to convey

The best thing for you is your work’s in one place
Just log onto Clever, your online workspace
Start on Cuse homepage and library you click
And on the left side there is Clever, you pick

It brings up a box and you click on log in
It should look familiar, this a place that you been
Now put in your login and classes will load
It’s really that simple, there’s no special code

Your teachers have pages with lots of fun work
You’ll be wishin’ your mama gave you more housework
Make sure you login every morning to check
To see the new work that is next on the deck

You have work to be doing in class every day
So schedule your time to ensure you can play
If you ever need help, just give us a shout
We’ll show you what Wolfpack is really about

We’ve got worksheets we can put at the foot of your door
If your WiFi ain’t working, that’s what we’re here for
We have breakfast and lunch we can get to you too
At Brighton, we’re family, we’ll help you get through

Now some teachers weave and some teachers bop
We’re learning just how to teach from closed shop
We have LearnZillion, Castle, Canvas, myOn
And hundreds of others like Academy of Khan

We can use these cool sites or upload our own
But that doesn’t mean we can do this alone
We need kids to be workin’ and puttin’ in time
Corona ain’t makin us stop on a dime

We’ll keep grindin and learnin some more every day
From math class to art class and of course ELA
All of our teachers are sittin’ at home
Laptops on laps and eyes on our phones

Waitin and lookin to hear from you all
Cuz everything is closed so you aint at the mall
So put down the TikToks and dubsmash for now
We’ll give you some time for a break and some chow

But put in the effort and dig down real deep
Give us some work hours and then you can sleep
It’s crazy how fast things can change in a day
So work hard, play hard and this break we will slay


Make a checklist or schedule to keep right on track
So when we back in class our heads won’t be whack
Take snack breaks and brain breaks whenever you need
But don’t log off for long or you’ll never succeed

Take time for your family and go for a walk
But stay 10 feet away from the peeps on the block
We miss you already, but came up with a plan
To keep us together throughout this long span

We got facebook and twitter and now a TikTok
To send you reminders and so we can talk
About info and Brighton and important things
And to show you we’re cooler than all you kids think

We know that you miss us as much as we do
So call us or text us and let us know too
Spread the word to your friends about our Brighton news
Let’s make Brighton’s Youtube get all Cuse’s views!

http://infinitymathtutoring.com -Private math tutor in Brighton 734-301-0352 With Infinity Math Tutoring, you will have a Math Professional on your doorstep. We tailor our math instruction to your individual needs, around your unique schedule! Tutoring is on a one-on-one basis, with the same tutor.

Convenience: We provide services in your home, at your school, in the library, wherever you want us to tutor, we’ll be there. We work around your busy schedule.

Quality: One-on-one tutoring is simply the best. We give your student the individualized attention they need with a tailored education plan that fits his or her needs.

Affordable: Infinity Math Tutoring offers the best rates around. Other companies charge above our rates and don’t offer the personalized, one-on-one, in-home attention you deserve. Contact us to find out how surprisingly affordable tutoring can be.

Special Needs: Infinity Math Tutoring understands the classroom challenges students with learning disabilities face on a daily basis. We will find the right tutor and right plan for each child. We work with parents, resource and special education teachers to compliment existing strategies and plans with our one-on-one tutoring.

We are a Michigan based companies services the following cities and surrounding areas: Belleville, Canton, Novi Northville, Plymouth, Livonia, Romulus, Westland, Inkster, Wayne, Redford. Contact us today to schedule a FREE consultation at 734-301-0352.