Visit  https://brilliant.org/Reducible/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.

Chapters:
00:00 Introducing JPEG and RGB Representation
2:15 Lossy Compression
3:41 What information can we get rid of?
4:36 Introducing YCbCr
6:10 Chroma subsampling/downsampling
8:10 Images represented as signals
9:52 Introducing the Discrete Cosine Transform (DCT)
11:32 Sampling cosine waves
12:43 Playing around with the DCT
17:38 Mathematically defining the DCT
21:02 The Inverse DCT
22:45 The 2D DCT
23:49 Visualizing the 2D DCT
24:35 Introducing Energy Compaction
26:05 Brilliant Sponsorship
27:23 Building an image from the 2D DCT
28:20 Quantization
30:23 Run-length/Huffman Encoding within JPEG
32:56 How JPEG fits into the big picture of data compression

The JPEG algorithm is rather complex and in this video, we break down the core parts of the algorithm, specifically color spaces, YCbCr, chroma subsampling, the discrete cosine transform, quantization, and lossless encoding. The majority of the focus is on the mathematical and signal processing insights that lead to advancements in image compression and the big themes in compression as a whole that we can take away from it. 

Animations created jointly by Nipun Ramakrishnan and Jesús Rascón.

References/Additional Resources:
https://www.red.com/red-101/video-chroma-subsampling - great resource on different types of chroma subsampling

http://weitz.de/dct/ - play around with the DCT

https://www.cse.iitd.ac.in/~pkalra/col783-2017/DCT-History.pdf - paper referenced in video

http://www.ee.ic.ac.uk/hp/staff/dmb/courses/DSPDF/00300_Transforms.pdf - a more rigorous signal processing approach to the DCT

https://www.impulseadventure.com/photo/jpeg-huffman-coding.html - great landing point for learning more about how huffman codes work in the context of JPEG

https://www.youtube.com/watch?v=CPT4FSkFUgs&list=PLpsTn9TA_Q8VMDyOPrDKmSJYt1DLgDZU4&ab_channel=DanielHarding - a great playlist I recommend that dives deep into actually implementing a JPEG decoder

This video wouldn't be possible without the open source library manim created by 3blue1brown and maintained by Manim Community.
The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.11.0) [Computer software]. https://www.manim.community/

Here is link to the repository that contains the code used to generate the animations in this video: https://github.com/nipunramk/Reducible

All music in the video is from Aakash Gandhi

The Unreasonable Effectiveness of JPEG: A Signal Processing Approach

LIVE tutorial on the basics of Painting with Mathematics. Source code/math for the painting here: https://www.shadertoy.com/view/XssSRX
Support this channel: https://www.patreon.com/inigoquilez

More tutorials on maths , art, SDFs and computer graphics: https://iquilezles.org

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The basics of Painting with Maths

Thanks to Dr Rohin Francis of Medlife Crisis and Dr Rishi Desai of Osmosis for their feedback.
More info on GiveDirectly
- https://www.givedirectly.org/
- https://www.givewell.org/charities/give-directly

Interactive COVID-19 simulations from Nicky Case and epidemiologist Marcel Salathé:
- https://ncase.me/covid-19

More on logistic growth
- 3Blue1Brown, also regarding disease spread: https://youtu.be/Kas0tIxDvrg
- Primer, regarding carrying capacity: https://youtu.be/uRTtlpD_U54
- Khan Academy, modeling biology with calculus: https://www.khanacademy.org/math/ap-calculus-bc/bc-differential-equations-new/bc-7-9/v/modeling-population-with-differential-equations

Ways to support Primer
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For discussion and updates
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Streaming myself working on these monstrosities:
- Twitch: https://www.twitch.tv/primerjustin

This video is presented under a Creative Commons Attribution-NonCommercial-ShareAlike License. More at:
https://creativecommons.org/licenses/by-nc-sa/4.0/

Made with Unity
Thanks to Same Van Cise and Sebastian Lague for helping me learn Unity. You can find some of their work here:
- https://vancisesam.com/
- https://www.youtube.com/user/Cercopithecan 

Music by Mathieu Keith. For business inquiries: mathieu.keith@gmail.com

Several other inputs into the graphics are from public domain contributions to blendswap.com

Thanks to supporters on Patreon, especially:
José Hamilton
Noah Healy
Vladimir Duchenchuk
Zachariah Richard Fournier
Jordan Scales
Anders Fjeldvær
Erik Broeders
Ghost Goat
Jérôme Graf
Kairui Wang
Luc Cedric R.
Marcial Abrahantes
Thomas Roggina
Bas Velner
Eric Helps
Leonardo Kluppel
Sean Barker
Tamas Gombkoto
Ben Kamens
Ben Komalo
Josh White
Tudor Lincu
Aymeric Duigou--Majumdar
Charly Cardeño
3blue1brown
abledbody
Alex Beardsley
Alex Garber
Alexander Mahone
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ALoneCoder
Anselm Eickhoff
Ben McGill
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Chris
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DanSoc
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Kataklyst
ketura
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Max Kaye
Michael Jones
Michael Wang
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Nicky Case
Paul Straw
Philippe Panzini
Ramon Leon
Ravi Jayanti
Rikard Eide
Ryan Mahuron
Sam Van Cise
sunny ho
Talon Howitt
Tengou
ThePotatoGuy
Will Robinson
Wyatt Nelson

Epidemic, Endemic, and Eradication Simulations

Painting a cute little flower with mathematical formulas in Google Sheets.
Support this channel by subscribing or on Patreon: https://www.patreon.com/inigoquilez

Google Document with the flower: https://docs.google.com/spreadsheets/d/1zPtl4DpFRb-RANetrK4RrgSH-nuttDo6FdSgNiViKic/edit?usp=sharing
Tutorials on maths , art, SDFs and computer graphics: http://iquilezles.org


Donate: http://paypal.me/inigoquilez
Subscribe: https://www.youtube.com/c/inigoquilez
Support: https://www.patreon.com/inigoquilez
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Soundtrack by Khrome:  https://www.facebook.com/KhromeMusic

Painting with Maths in Google Sheets

Primer Merchandise: https://store.dftba.com/collections/primer
Support Primer on Patreon: https://www.patreon.com/primerlearning

For discussion and updates
- Discord: https://discord.gg/NbruaNW
- Reddit: r/primerlearning
- Twitter: @primerlearning
- Facebook: facebook.com/primerlearning

Streaming myself working on these monstrosities:
- Twitch: https://www.twitch.tv/primerjustin

This video is presented under a Creative Commons Attribution-NonCommercial-ShareAlike License. More at:
https://creativecommons.org/licenses/by-nc-sa/4.0/

Made with Unity
Thanks to Same Van Cise and Sebastian Lague for helping me learn Unity. You can find some of their work here:
https://vancisesam.com/
https://www.youtube.com/user/Cercopithecan 

Music by Mathieu Keith. For business inquiries: mathieu.keith@gmail.com

Several other inputs into the graphics are from public domain contributions to blendswap.com

Thanks to supporters on Patreon, especially:
Zachariah Richard Fournier
Vladimir Duchenchuk
Noah Healy
Jason Han
Jordan Scales
Jacob Maes
Marcial Abrahantes
Luc Cedric R.
Kairui Wang
Feimeng Zheng
Erik Broeders
Tamas Gombkoto
Sean Barker
Leonardo Kluppel
Eric Helps
Bas Velner
Victor Moisescu
Tudor Lincu
Josh White
Ben Komalo
Ben Kamens
Charly Cardeño
Aymeric Duigou--Majumdar
Wyatt Nelson
Will Robinson
Tom
ThePotatoGuy
Tengou
Talon Howitt
Sam Van Cise
Ryan Mahuron
Roy Steves
Rikard Eide
Ramon Leon
potted_penguin
Philippe Panzini
Paul Straw
Niko
Nicky Case
Morgan Baglin-Clarke
Mitchell Douglass
Michael Wang
Michael Jones
Max Kaye
Matthäus Pawelczyk
Martin Obretenov
Lotus
Lee Berman
Krum Valkov
Kevin Holesh
ketura
Jonathan Sterkenburg
Jeff
Jason Prado
Jason Louro
Jacob Luedecke
Garrett F
EndyStar
Elliot Press
Edono Dondolo
DanSoc
Daniel Schramm
Daniel Kjellevold Steinsland
Daniel Giavedoni
Colin Winhall
Christy Serbus
Chris Loftus
Chris
Brian
Ben McGill
Anselm Eickhoff
Andreas Carbel
ALoneCoder
Alexander Mahone
Alex Garber
Alex Beardsley
Alec Burns
3blue1brown

Simulating Foraging Decisions

How to translate, rotate, and scale points in 2D space, using basic algebra and trigonometry.
Part of a larger series teaching game programming and general programming. Visit http://codeschool.org

3D Transformations

Get Your Billy T-Shirt: https://my-store-d2b84c.creator-spring.com/
Discord: https://discord.gg/Ap2sf3sKqg
Instagram: https://www.instagram.com/mrpsolver/

Highschool Vs. University Physics Be Like...

Thanks to supporters on Patreon, especially:
Jordan Scales
Kairui Wang
Eric Helps
Ben Kamens
Ben Komalo
Christy Serbus
Sean Barker
Rikard Eide
Wyatt Nelson
Aurélien Géron
Patrick Foster

Send market signals by supporting Primer on Patreon! 
https://www.patreon.com/primerlearning

For discussion and updates
- Discord: https://discord.gg/NbruaNW
- Reddit: r/primerlearning
- Twitter: @primerlearning
- Facebook: facebook.com/primerlearning

Streaming myself working on these monstrosities:
- Twitch: https://www.twitch.tv/primerjustin

This video is presented under a Creative Commons Attribution-NonCommercial-ShareAlike License. More at:
https://creativecommons.org/licenses/by-nc-sa/4.0/

Made with Blender and python. 
- Github: https://github.com/Helpsypoo/primer

Speaking of attribution:
- The music is "Divider" by Chris Zabriskie, distributed under a CC-BY license via Free Music Archive.
- Several other inputs into the graphics are from public domain contributions to blendswap.com