The field of computer science summarised. Learn more at this video's sponsor https://brilliant.org/dos

Computer science is the subject that studies what computers can do and investigates the best ways you can solve the problems of the world with them. It is a huge field overlapping pure mathematics, engineering and many other scientific disciplines. In this video I summarise as much of the subject as I can and show how the areas are related to each other.

#computer #science #DomainOfScience

You can buy this poster here:
North America: https://store.dftba.com/produc....ts/map-of-computer-s
Everywhere else: https://www.redbubble.com/people/dominicwalliman/works/27929629-map-of-computer-science?p=poster&finish=semi_gloss&size=small
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Get all my other posters here: https://www.redbubble.com/people/dominicwalliman

A couple of notes on this video:
1. Some people have commented that I should have included computer security alongside hacking, and I completely agree, that was an oversight on my part. Apologies to all the computer security professionals, and thanks for all the hard work!
2. I also failed to mention interpreters alongside compilers in the complier section. Again, I’m kicking myself because of course this is an important concept for people to hear about. Also the layers of languages being compiled to other languages is overly convoluted, in practice it is more simple than this. I guess I should have picked one simple example.
3. NP-complete problems are possible to solve, they just become very difficult to solve very quickly as they get bigger. When I said NP-complete and then "impossible to solve", I meant that the large NP-complete problems that industry is interested in solving were thought to be practically impossible to solve.

And free downloadable versions of this and the other posters here. If you want to print them out for educational purposes please do! https://www.flickr.com/photos/95869671@N08/

Thanks so much to my supporters on Patreon. If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience

I also write a series of children’s science books call Professor Astro Cat, these links are to the publisher, but they are available in all good bookshops around the world in 18 languages and counting:
Frontiers of Space (age 7+): http://nobrow.net/shop/profess....or-astro-cats-fronti
Atomic Adventure (age 7+): http://nobrow.net/shop/profess....or-astro-cats-atomic
Intergalactic Activity Book (age 7+): http://nobrow.net/shop/profess....or-astro-cats-interg
Solar System Book (age 3+, available in UK now, and rest of world in spring 2018): http://nobrow.net/shop/profess....or-astro-cats-solar-
Solar System App: http://www.minilabstudios.com/....apps/professor-astro
And the new Professor Astro Cat App: https://itunes.apple.com/us/ap....p/galactic-genius-wi

Find me on twitter, Instagram, and my website:
http://dominicwalliman.com
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Explore Vermeer's masterpiece "Girl with a Pearl Earring" up close, and see how it's different (and not) from a high-res 3D print of the painting. We visit the Mauritshuis in The Hague and learn what happens when conservation scientists study the painting with today's most advanced technology.

This project was made possible by Google Arts & Culture. For more info go to https://artsandculture.google.com/project/vermeer.

The Girl in the Spotlight research project is a Mauritshuis initiative, with a team of internationally recognised specialists working within the collaborative framework of the Netherlands Institute for Conservation, Art and Science (NCIS).

To support our channel, visit: http://www.patreon.com/artassignment.

Thanks to our Grandmasters of the Arts Vincent Apa and Indianapolis Homes Realty, and all of our patrons, especially Bronze Bond, Patrick Hanna, M12 Studio, Jane Quale, and Constance Urist.

Subscribe for new episodes of The Art Assignment every other Thursday!

--
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Discover how to create AI prompts that deliver exactly what you need as a school psychologist, special education teacher, or school-based professional. In this video, we explain why some prompts don’t work and share actionable tips to help you generate clear and specific instructions. Learn how to save time, maintain control, and make AI a dependable tool in your daily tasks. Whether you’re new to AI or looking to improve your skills, this guide will help you use AI effectively in your educational environment.

Try Sophia Today: www.schoolpsych.ai

Connect with Us:
@schoolpsychai across all platforms.

Remember to engage with us by liking, sharing, and subscribing. Sophia and the team appreciate your support!

This audio podcast was generated using Notebook LM.

Education Week Top School Jobs virtual career fairs are designed to help you find teaching jobs and other jobs in K-12 education. They provide an opportunity to chat 1:1 with recruiters from schools and districts around the country that are actively hiring, as well as critical insights to inform your job search..
_________________
Want more stories about schools across the nation, including the latest news, analysis, and unique perspectives on education issues? Visit www.edweek.org.

About Education Week:
Education Week is America’s most trusted source of independent K-12 education news, analysis, and opinion. Our comprehensive coverage of education policy takes the form of articles, photography, and video journalism.

Published by the nonprofit organization Editorial Projects in Education, Education Week has been providing award-winning coverage of the field for over 35 years.

Follow Education Week:
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To license video footage from Editorial Projects in Education, please contact Education Week Library at rh.eprints@educationweek.org

Another separable differential equation example.

Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/modeling-with-differential-equations/v/particular-solution-given-initial-conditions-for-population?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations

Missed the previous lesson?
https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations

Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Equations channel:: https://www.youtube.com/channe....l/UCxSQHGkaDv8UKXE0T
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

Google just quietly dropped a massive upgrade to the Gemini App! The default image generator has officially been replaced by "Nano Banana 2" (officially known as the Gemini 3 Flash Image model), and the new features are incredible.

In this video, I’ll walk you through exactly what has changed and show you how to use the new capabilities to upskill your workflow and create stunning AI images faster than ever. We'll cover complex prompt understanding, the brand new visual Style Picker, how to generate perfectly legible text inside your images, and even how to use advanced multi-image composition for style transfers and storyboarding!

Read the official Google announcement here: https://blog.google/innovation....-and-ai/technology/a

⏱️ Video Chapters:
0:00 - The New Default AI Image Generator
0:26 - What is Nano Banana 2 (Gemini 3 Flash Image)?
0:48 - How to Use the New Visual Style Picker
1:47 - Demo 1: Complex Text-to-Image
2:24 - Demo 2: Generating Flawless, Legible Text
3:15 - Demo 3: Advanced Editing (Image + Text)
4:06 - Demo 4: Multi-Image Composition & Style Transfer
4:31 - Demo 5: Subject consistency. storyboarding
5:51 - Demo 6: Make a YouTube thumbnail
6:38 - Don't Panic: How to Still Access the "Pro" Model

This video is about: Divide 4 digit numbers by 2 digit numbers. Subscribe to our YouTube channel to watch more Math lectures. Practice tests and free video lectures for Physics, Chemistry, Biology, Math’s, Computer Science, English & more subjects are also available at Sabaq.pk. So, subscribe to Sabaq.pk/Sabaq Foundation now and get high marks in your exams.

About Us:

Sabaq.pk or Sabaq Foundation is a non-profit trust providing free online video lectures for students from classes K - 14 for all education boards of Pakistan including FBISE, Sindh Board, KP Board, Baluchistan Board as well as for Cambridge. We have a team of qualified teachers working their best to create easy to understand videos for students providing 14,000 + free lectures for subjects including Physics, Chemistry, Mathematics, Biology, English, General Science, Computer Science, General Math, Statistics and Accounting. Sabaq.pk also provides study material for MCAT and ECAT in the form of video lectures.

GET CONNECTED WITH US:

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• LinkedIn: https://www.linkedin.com/company/sabaq-foundation/
• Contact #: 051-2356303 (10:00 AM To 6:00 PM)

CLASSES WE COVER AT SABAQ.PK / SABAQ FOUNDATION:

1. KG
2. Class 1
3. Class 2
4. Class 3
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6. Class 5
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10. Class 9
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13. Class 12
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16. MCAT
17. ECAT
18. CSS

BOARDS WE COVER AT SABAQ.PK / SABAQ FOUNDATION:

1. FBISE
2. Sindh Board
3. KP Board
4. Balochistan Board
5. Cambridge

STUDY MATERIAL WE OFFER AT SABAQ.PK / SABAQ FOUNDATION:

1. Physics Lectures
2. Chemistry Lectures
3. Mathematics Lectures
4. Biology Lectures
5. English Lectures
6. General Science Lectures
7. Computer Science Lectures
8. General Math Lectures
9. Accounting Lectures
10. Statistics Lectures
11. Advance Accounting Lectures
12. Cost Accounting Lectures
13. Practice Tests
14. Physics Practical
15. Chemistry Practical #Sabaqpk #sabaqfoundation #freevideolectures

Subscribe to my education channel.
https://www.youtube.com/mrgohbr​

This video introduces Chapter 1 Part 1 Citizenship to the Secondary 3 Express and Normal (Academic) students who are studying Social Studies for the Singapore 2016 new syllabus. This topic is usually taught in Secondary 3 where students learn about 4 different ways to become Singapore citizens.

The video is divided into 5 sections.
0:00 Introduction
1:04 Descent
1:24 Country of Birth
1:32 Marriage
2:13 Naturalization/ Registration

You can view the following slides below.
https://www.slideshare.net/goh....bangrui/social-studi

Thank you and like and pass it on if it helps you.

Credit to owner: -

This site may contain copyrighted material the use of which has not always been specifically authorized by the copyright owner. We are making such material available in an effort to advance our understanding of environmental, political, human rights, economic, democracy, scientific, and social justice issues, etc. we believe this constitutes a ‘fair use’ of any such copyrighted material as provided for in section 107 of the US Copyright Law.
In accordance with Title 17 U.S.C. Section 107, the material on this site is distributed without profit.

COPYRIGHT DISCLAIMER:-

Copyright Disclaimer under section 107 of the Copyright Act of 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research. Fair use is a use permitted by copyright statute that might otherwise be infringing.”

PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateOKAY
↓ More info and sources below ↓

Come see me on Molly’s channel! https://youtu.be/MOmRQb7h5lw
SUBSCRIBE so you don’t miss a video! ►► http://bit.ly/iotbs_sub

I met Molly Burke a few months ago. She’s awesome. I absolutely love what she’s done on YouTube to bring awareness to living with disability, and turning it into ability. And her guide dog Gallop is awesome too! When Molly and I first met, we started talking about how she navigates the world, because I’m a nerd and I always steer the conversation toward science. I was not prepared for what she told me. She said she uses echolocation! Molly’s brain has adapted to listen to sounds in her environment in ways that most of us sighted people can’t even imagine. I went to meet her in LA and brought a special surprise, to see if my brain could learn what hers has.
#echolocation #blind

For audio descriptions, go to Settings - Audio Track - English Descriptive.

Special thanks to Brian Bushway, Daniel Kish, Molly Burke and Gallop!
Learn more about Brian Bushway and echolocation at https://visioneers.org

Descriptive Audio & Captions provided by The Described and Captioned Media Program

References: https://sites.google.com/view/....echolcation-molly-bu

-----------

FOLLOW US for more curiosity:

Twitter
http://www.twitter.com/DrJoeHanson
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This video gives you 4 practice problems for adding mixed numbers that you can work on your own, and then compare your answers against mine.

🔴 Subscribe for more free YouTube tips: https://www.youtube.com/c/ImprovedMath

🔴 Share this video with a friend: https://youtu.be/z8-iScMK_A0

✅ For business inquiries contact me at improvedmath@gmail.com

✅ Let's connect:

https://www.youtube.com/c/ImprovedMath

https://www.tiktok.com/@improvedmath1?

https://www.pinterest.com/improvedmath/


Improved math is a channel created to provide additional instruction on essential math concepts. I’m passionate about math and I know first-hand how important math concepts are in the real world.

Teachers, parents, guardians, homeschoolers, and students can use these videos to help reinforce math skills. These math videos are designed to help teach yourself math or provide self-study math tools to assist when additional instruction is needed. Teaching math and learning math has changed the way many students learn in this virtual environment and during the pandemic. Having on-demand math videos can provide math tutoring needed when children are not able to get help from their teachers after school hours or when trying to do math at home.

The library of math tutorials that I create can also be used as supplemental instructional material for homeschool math. Each full-length video comes with a subsequent knowledge check or math practice problems which serve as a virtual math topic worksheet to test your understanding of each skill. These videos can be paused to work out the problems on your own, then unpaused to check your answers. All of these videos can be found under the Knowledge Check playlist.

I also have a library of shorter videos (less than 1 minute in length - shorts) that are quick math tips and tricks on basic math topics. Some of these short math help videos include problems that you can work on yourself and submit your answers in the comments. They are all listed under my Math Tips and Tricks playlist.

Improved math is creating more videos every day to cover topics from 4th grade, 5th grade, 6th grade, and 7th-grade math. The videos focus on fractions, basic math operations, geometry, and ratios but more topics are being added all the time. If there is a specific topic you would like to see covered, drop me a comment in one of my videos and let me know!

Free math help videos will be posted every Thursday and Friday. For additional math resources, check out my math help website at improvedmath.com where I post math worksheets and answers along with additional context on math basics.


Thanks for watching my channel.

#addingmixednumbers
#fractionhelp
#mathhelpvideos
#homeschoolmath
#selfstudymath
#teachyourselfmath
#mixedfractions

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Please SUBSCRIBE to our channel, LIKE, and SHARE to encourage us to share more useful and interesting knowledge.
請訂閱我們的頻道、點讚、分享，鼓勵我們分享更多有用又有趣的知識。
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Welcome to watch our videos
歡迎觀看我們所創作的的其他影片
1）Basic Conversation 會話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

2) Grammar 語法
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

3）English Speaking
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

4）Funny Jokes 笑話
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

5）Vocabulary 詞彙
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

6）English Idioms 英語成語
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

7）Revision Exercise 重温練習
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

8）Fun Games 趣遊戲味
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

9） Tongue Twister 繞口令
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

10）Writing a composition 作文
https://www.youtube.com/playli....st?list=PLPoPxSDq_eP

-----------------------------------------------------------------------------------
Please SUBSCRIBE to our channel, LIKE, and SHARE to encourage us to share more useful and interesting knowledge.
請訂閱我們的頻道、點讚、分享，鼓勵我們分享更多有用又有趣的知識。
-----------------------------------------------------------------------------------
Daily revision 3_simple present/past tense_BGM info
Candy by Sakura Girl | https://soundcloud.com/sakuragirl_official
Music promoted by https://www.chosic.com/free-music/all/
Creative Commons CC BY 3.0
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Descubre cómo crear miniaturas de YouTube con IA de forma totalmente gratuita y en segundos. En este tutorial paso a paso, te enseño a programar tu propio "Gem" en Gemini, apoyado por la investigación de NotebookLM, para diseñar miniaturas virales.

Si eres creador de contenido, sabes que el CTR (Click Through Rate) es la métrica más importante; sin una buena imagen, el algoritmo no recomendará tus vídeos. Por eso, hoy te muestro cómo dejar de pagar a diseñadores y usar la inteligencia artificial semántica de 2026 para crear miniaturas profesionales, con alto contraste y usando tus propias fotos.
🚀 Beneficios de este método:

• Crea imágenes de alta retención usando tu propio rostro y expresiones.
• Ahorra cientos de horas de edición compleja en Photoshop.
• Incrementa tus impresiones, clics y, en consecuencia, dispara tus suscriptores.

00:00 Hook: El problema de las miniaturas caras (Y la solución IA)
00:41 Paso 1: Usar NotebookLM como tu cerebro estratega
01:20 El Prompt maestro para investigar miniaturas virales
02:39 ⚠️ Una advertencia rápida e importante
03:13 Creando el informe estructurado paso a paso
04:43 Paso 2: Configurando tu "Gem" personalizado en Gemini
06:36 El truco experto: Extensión Kortex (Descarga el informe rápido)
06:57 Entrenando a la IA con el informe y TUS fotos
07:56 Prueba de fuego: Generando una miniatura en vivo
08:48 Análisis: ¿Por qué esta miniatura tiene un CTR brutal?
09:38 Modificando elementos específicos con un solo clic
10:33 Final: Tu nuevo flujo de trabajo (CTA Estratégico)

👇 ENLACES Y RECURSOS UTILIZADOS:
[El prompt completo y los recursos los tienes en el PRIMER COMENTARIO FIJADO]

🚀 Extensión kortex para NotebookLM— Descuento 10% (DAVID10): https://chromewebstore.google.....com/detail/kortex-no

🔔 Si quieres seguir dominando el algoritmo de YouTube y las herramientas de IA, ¡suscríbete y activa la campanita! Suscríbete al futuro aquí:https://www.youtube.com/@NextG....en_IA_YT?sub_confirm

🗣️ ¡Hablemos! ¿Cuánto tiempo tardas actualmente en diseñar una miniatura? ¿Has probado ya a crear Gems personalizados para tu canal? ¡Te leo en los comentarios!

EMAIL COLABORACIONES:
📩 nextgeniahub@gmail.com
📩 hammer31_73@gmail.com

#MiniaturasConIA #NotebookLM #GeminiIAi #ia

Herzlich Willkommen zurück! In diesem Video zeige ich dir die Spaltenstatisitken für deine Tabellen in Google Sheets.

Leo Office Tutorials - Docs - Sheets - Slides - Word - Excel - PowerPoint - Apps Script

Artikel zum Video: https://leoofficetutorials.com/sheets/452

Kapitelmarken
0:00 Begrüßung & Intro
0:25 Spaltenstatistik
6:25 Fazit & Schluss

Hat dir das Video gefallen? Zeige es mir mit einem Like!

TWITTER: https://twitter.com/LeoTutorials
INSTAGRAM: https://instagram.com/leo_officetutorials
TIKTOK: https://www.tiktok.com/@leoofficetutorials
LINKEDIN: https://bit.ly/3EdhzEZ
FACEBOOK: https://bit.ly/3Ecqw1t

Abonnieren nicht vergessen ;)

Hast du Fragen? Ab damit in die Kommentare!

Meine Playlist!
Alle Tutorials: https://bit.ly/3bxPVUm
Google Docs: https://bit.ly/2wJq9h1
Google Sheets: https://bit.ly/2vP3gbo
Apps Script: https://bit.ly/3wcRDV8
Google Slides: https://bit.ly/2Jvq6IB
Word Online: https://bit.ly/3aqGB4c
Excel Online: https://bit.ly/3bw0xD6
Power Point Online: https://bit.ly/2KIs6Ry
Word: https://bit.ly/3408AFP

Meine YouTube Shorts: https://bit.ly/3dZgRAv

Word Online: https://www.office.com/launch/word
Excel Online: https://www.office.com/launch/excel
PowerPoint Online: https://www.office.com/launch/powerpoint

Google Docs: https://docs.google.com
Google Sheets: https://sheets.google.com
Google Slides: https://slides.google.com

Für Vorschläge oder Videowünsche schreibt mir bitte auf Instagram.

Intro Musik: Cat Shat in the Box - josh pan
https://www.youtube.com/c/joshpan89

Endcard Musik: JPB & MYRNE - Feels Right (ft. Yung Fusion)
https://www.youtube.com/watch?v=dXYFK-jEr8Y

Kanal: https://youtube.com/Leoofficetutorials

#sheets #googlesheets #tutorial

Best of 2021 with Steve and Maggie. Another year is nearly behind us. Can you remember all the adventures of Steve and Maggie in 2021? Let's remember some of them but first let´s start with a fully new video. What do you think, will shrinked Steve win the board game and get out of the game plan? And do you remember how Maggie tried to get Steve to eat healthily? Then there are some Halloween stories and songs. Are you scared? Steve and Maggie really love playgrounds, so they have visited a lots of them. And there is much more! So let's jump into this huge English compilation for children with Steve and Maggie. HAVE FUN and learn English! Speak and Learn with Steve and Maggie!
--------------------
VISIT: https://SteveAndMaggie.com
.
INSTAGRAM: https://instagram.com/SteveAndMaggieOfficial
FACEBOOK: https://facebook.com/SteveAndMaggie
.
SHOP:
SpreadShirt: https://shop.spreadshirt.co.uk/SteveAndMaggie
Teespring: https://teespring.com/stores/steve-and-maggie-1
.
APPS FOR KIDS:
https://app.steveandmaggie.com/
.
ENGLISH TEACHING MATERIALS for kids: https://wowenglish.com
.
SHOUTOUTS and personalised messages via: https://cameo.com/steveandmaggieofficial
.
SONGS FOR KIDS:
iTunes: https://itun.es/gb/i_oMcb
Spotify: https://spoti.fi/2hlcWya
.
Support us and receive a personalised birthday message for your child from Steve.
Patreon: https://patreon.com/steveandmaggie
--------------------
Produced by © Wattsenglish Ltd. ©
https://wattsenglish.com/

This video is brought to you by Aloud. Learn more about the video translation tool that’s breaking the language barrier: https://aloud.area120.google.com/?utm_source=youtube&utm_medium=creator&utm_campaign=kg

The Kings and Generals animated historical documentary series on the ancient civilizations continues with a video on the evolution of the Indo-European Languages, as we give a summary of how this language family formed and how the languages belonging to each are still connected to each other:

Arabia Before Islam: Religion, Society, Culture: https://youtu.be/07OsSSt0ytc
Vandals: https://youtu.be/-IpbeEW6I9Y
How Rome Conquered Greece: https://youtu.be/v5q1rerf-qw
Did the Trojan War Really Happen: https://youtu.be/12eHJL2yRtk
Demosthenes: https://youtu.be/ABS1iepXG0U
Ancient Greek Politics and Diplomacy: https://youtu.be/MVnp4NilDLI
Pyrrhic Wars: https://youtu.be/2QBA6ZPmj3Q
Ancient Macedonia before Alexander the Great and Philip II: https://youtu.be/FXX1FVYysjQ
Diplomatic Genius of Philip of Macedon: https://youtu.be/yVTrkESkuTw
Etruscans: https://youtu.be/FkySjRwUteE
Bosporan Kingdom: https://youtu.be/ltikjXUiAC4
Ancient Greek State in Bactria: https://youtu.be/IQATsepKoLE
The Greco-Chinese War Over the Heavenly Horses: https://youtu.be/g6Rphg_lwwM
Ancient Greek Kingdom in India: https://youtu.be/ZxJk4KHZxi8
Ghaznavids: https://youtu.be/yJ91rv0xdWM
Huns: https://youtu.be/bFpQjWtpHcM
White Huns: https://youtu.be/JJWddbCUZLQ
Gokturks: https://youtu.be/BChpoa_IuQs

Yuezhi: https://youtu.be/2KdM6AlyLUY
Seljuks: https://youtu.be/P79ECnISamo

Support us on Patreon: http://www.patreon.com/KingsandGenerals or Paypal: http://paypal.me/kingsandgenerals or by joining the youtube membership: https://www.youtube.com/channe....l/UCMmaBzfCCwZ2KqaBJ We are grateful to our patrons and sponsors, who made this video possible: https://docs.google.com/docume....nt/d/1ooKPbpq0z8ciEj

The video was made by Arb Paninken, while the script was developed by Georgi Kolev. This video was narrated by Officially Devin (https://www.youtube.com/channe....l/UCU0-VII-V376zFxiR & https://www.youtube.com/channe....l/UC79s7EdN9uXX77-Ly

✔ Merch store ► https://teespring.com/stores/kingsandgenerals
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#Documentary #DubbedWithAloud #Civilization

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/e/scaling_vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/linear-algebra-vector-examples?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/adding-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Learn the letter V with Ollo the Elephant from Khan Academy Kids!

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