The Math Needed for Computer Science (Part 2) | Number Theory and Cryptography

[@zachstar]

Hey guys, since this I made a more updated video on number theory and how it's used in cryptography. Mathematics of Cryptography: kzbin.info/www/bejne/q3_dkoComNqHg5I

[@Basaisehi843]

MajorPrep Man you are super dope ! 🤟

[@Minskpotato]

Hey Zach Star! Could you make a video about Russian/Egyptian multiplication? I found it really interesting but I don't understand how it works. Just want to know the math behind it.

[@sethdon1100]

The most efficient algorithm for factoring integers is Shor’s algorithm. Just a heads up

[@PaulWarren-dt1ms]

Congrats on deciding on a physics PATH I concur 😮

[@randompotato258]

this dude explain GCF better than all the math teachers i've ever had in a really simple and mind friendly way

[@ZaraUTech]

Like really true!!! Maybe maths teachers just make things to complex cause they ain't really had real live experience using it..

[@nigeldupaigel]

Thank you, this made me fully decide to pursue a degree in physics.

[@epicm999]

lol

[@Anskurshaikh]

same here, this math scares me. I'll rather do multivariable Calc and Diff eqns than this.

[@highEntropyGhoul]

You'll still need to do a pretty good amount of calculus

[@anandsuralkar2947]

Lol

[@martinkunev]

If you go into e.g. particle physics, you'll need abstract algebra, in particular group theory. In a way abstract algebra is a generalization of number theory.

[@ratmgant]

CS is looking more and more up my alley. Thanks for these videos sir, you're a blessing.

[@hunggarchristian]

this is why i switched from Mechanical engineering to Computer Science this semester man. I'm enjoying it much more

[@ratmgant]

Justin Wiggins sweet

[@AlphaFoxDelta]

Jean Descole I've got a degree in and am working on another in CompSci, it's the way to go

[@ratmgant]

Andrew Davis What's your other degree?

[@AlphaFoxDelta]

Jean Descole Simulation and Game Developement, it got my foot in the door too. Audio/Video editing, 3D Modeling and Animation, using software like photoshop, Maya, 3D Max etc Or Unreal Engine for level design

[@nk361]

I would love if you did a series on math in computer science, you explain things very well even if they may take longer or bigger jumps. I can write code pretty well, but math can always stop me in my tracks when just written in large or long formulas or with special symbols. When you explain these problems it's more of the logic behind them which I could easily write in code.

[@johnadams4486]

Dude, look what you have done ! You scared them away

[@lakinnisova459]

Eventually the will stumble upon math needed for programming.

[@IZACHARYRIFEI]

I'm a computational mathematics with a computer science specialization and I love this channel so much! If every teacher could express these concepts like this everyone would love math.

[@ianyoung5857]

I just started a PhD program this semester, and my eyes glazed over when we started talking about this (IS background, CE program). You've done a great job explaining it. Thanks for making these videos.

[@chisangamumba2961]

What is CE?

[@MatthewSchellenberg]

I wish I had known this in high school. I was so intimidated that I didn't even find out that the math was actually right up my alley.

[@pvic6959]

never late to start!

[@MatthewSchellenberg]

@@pvic6959 ok where do I start?

[@pvic6959]

@@MatthewSchellenberg these videos are definitely a good start. I really cant help but I have a computer science bachelors degree (class of 2019) I had a TA in his 50s who was getting a masters in computer science without a CS background. It was really cool actually But to answer your question the best I can: these types of videos can help you get you started, text books, and if you have money to spare you can probably find some online classes/certifications. If you're more into the programming than the math/theory side, there are a TON of tutorials and projects you can learn from on youtube! Unfortunately this is the best I can do but I hope it helps

[@MatthewSchellenberg]

@@pvic6959 Thank you very much!

[@MatthewSchellenberg]

@@pvic6959 I had an 800 on my math SAT when I was 16, but for some reason CS intimidated me at the time.

[@pastafarian3758]

I understood gcf for the first time after learning it in 9th grade almost 25 years later. Great stuff mate. Cheers.

[@davidjohnston4240]

Number theory is the thing that has most impinged on my computer science career. Implementing error correction, cryptography and a host of related things call for Galois fields. When you have that hammer, all nails start to look like extensions of GF(2).

[@jstnofficial]

In just 2 vids men youve earned a sub thanks a lot

[@zachstar]

Thanks man!

[@soccerball7828]

;)

[@bozeiky]

The way you broke down those concepts really made me feel like im overcomplicating everything. It's so simple when YOU do it.

[@saisaske1]

Great definition of computer science given by a professor that "computer science is an art of abstraction" . It is clearly demonstrated in your both videos. Thankyou

[@milindbebarta2226]

I love this. Make a new series where you go more in-depth. You're very good at explaining these topics. I'm sure it'll be a hit.

[@artie8561]

Your explanation is one of the best! Thank you for bringing back the joy of mathematics to me who is not a mathematics major in university!

[@kikiz0r730]

You're amazing, man! Don't stop doing these videos, I love them ! :D

[@masonpiatt2798]

I love these videos Keep it up

[@zachstar]

Thank you!

[@emadahmed5739]

this year i am joining cs and man i think i will love it after this video

[@reverenddick8562]

I feel like you just saved me 2 years of struggle with your simplicity.

[@RRatedT]

Man I love and enjoy your videos so much, you make it sound so cool and interesting.

[@Ninjabdul]

that last example blew my mind, prime numbers OP

[@danieljohnkirby9412]

Wow I really wish this video was out when I was in high school.

[@JThompson_VI]

I have never love hated something so much.

[@speedyguy8]

Also note that according to the distribution property 24n+40m = 8(3n+5m)

[@DoubleRBlaxican]

I remember my high-school taking me to a class at my local college where they talked about Cryptography and they went over the same things you did here. I wish I could have gone to college to learn this but I guess your video will do.

[@chairjacker]

Wow i wish all math was made this fun. Keep up the good videos! As Charlie Day says, I'm learning a lot!!

[@johannmichael3894]

This is a good video. Has a bare-bones description of the relation between number theory and cryptography.

[@TheTariqibnziyad]

man you're the man

[@kailashbtw9103]

Great simple explanations with great examples

[@amessman]

I watched Part 1 and 2... +1 subscriber, these explanations are super helpful! Keep up the good work!

[@mohamodsadi656]

This videos are making me crave more math videos from you...😁 Thanks for making them... I hope u'd do some elaborate work on math for Comp sci... 🤗

[@shayorshayorshayor]

To the people thinking “this math is up my alley”, you guys are in for a surprise. Calculus 1,2,3 and differential is actually less harder than discrete math. Just an FYI

[@frederickhofmann843]

This series has been really valuable to me thanks

[@spencerallbritton9459]

Awesome videos man, love your content.

[@SevenDeMagnus]

Very cool, Mathematics rule science, including computer science.

[@the_allucinator]

3:23 Yes, with 6 pcs of 7cm ruler and 9 pcs of 5cm ruler. To think that there's a simpler answer, yet I got this.

[@MAYONNAISEMOOSE]

I have never understood cryptography this vividly!

[@hiteshkumain]

I love and Enjoy You're Videos sir , With Accuracy & Clarity Really Amazing .

[@rajadey4072]

Thank you for these videos!

[@daniellam1257]

This is very helpful for my discrete math final, thanks :)

[@quinn9240]

The hardest class for most cs majors is the cs math class that goes through this and much more.

[@ricchburglar]

Thanks OG Zach

[@SevenDeMagnus]

The ruler puzzle is like the Die Hard water puzzle:-)

[@kumand8259]

Wow that was so cool.! I want more videos like this. Thank you

[@abdoutanta]

Great video, thank you so much.

[@alwaysincentivestrumpethic6689]

Great video

[@TokyoXtreme]

OK, this is epic 😎

[@treyebillups8602]

TokyoXtreme BEN SHAPIRO DESTROYS LIBTARDS WITH SUPERIOR FACTS AND LOGIC

[@bpark10001]

Can you do a video on use if numbers in CAD files? This causes vexing problems, such as calculate a path that is "X" distance from a set of other elements (lines and arcs) on the workspace. This is used to calculate toolpaths (given a cutter radius) to outline a shape formed from lines and arcs. The difficulty is no matter how the precision of the math, computer numbers lack the "property of density" decisions such as whether 2 lines are connected, or whether their intersection point is distinct of identical to one endpoint. How does one write such an algorithm? (I can tell you that expensive software "screws up" this, sometimes generating toolpaths that cut up the piece, others that generate "digital debris" that bogs down the machine!) There has to be a better way! (Comment about software: unlike other engineering, where one can "reverse engineer" a design, it is not practical to do so in software. How does one learn from others?)

[@cad3175]

..just some advice or personal preference which may be common, the white background with black text is much harder in the eye than black background with a lighter coloured font, the blue wavelengths in White led produced light is a health hazard so less White is better in general, 3blue1brown's videos are very easy on the eye as they generally have dark backgrounds, just an idea to incorporate if you're open to suggestions, thanks for your interesting topics

[@toad4966]

That math actually looks fun

[@joelkronqvist6089]

To that ruler problem: isn't it enough of proof that we can measure 3 cm and 2 cm and have unlimited rulers, and can like that measure 1 cm and repeat that 1 cm infinitely?

[@gokulanandaadhikari8680]

You are doing an amazing work man.thanks a lot💕

[@cuddy90210]

Thank you.

[@blzahz7633]

I like these videos, keep them up.

[@VENOM-tx6gp]

2:42 Small?? Seems average to me It might have a great personality 🙂

[@aaryan3461]

7:09 . DARN SMART!

[@SirLuke007]

My gfs dad said he wasn’t great with science and math so he chose CS I see why, I like the fractal concepts

[@davidfarah]

Thank you!

[@chazzman4553]

Great stuff. Thanks!

[@deniscandido4116]

REALLY GREAT CONTENT! Thanks a lot.

[@darcash1738]

A genius and a comedian 😎

[@SilBu3n0]

great theme and both parts! used the opportunity to try to grasp any potential relation between that and finite element method, as well as generative design. anybody?

[@husniaezz2922]

Thanks alot, it was really exciting

[@edattacks]

that's pretty cool

[@mista623]

can he blink?

[@ThalesPo]

now make a part 3 video with the 90% that was too advanced.

[@dusandragovic09srb]

Well done!

[@BlackJar72]

There is an error in your proof with the rulers -- or actually with your statement of the problem: If you lay about four 5 cm ruler on one line and two 7 cm rulers on the other you get a gap of 6 cm; if you then add a 5 cm ruler to line two you get 1 cm. The error appears to be that you had extra rule (that only rulers of the same length can be in a given row), but did not state that assumption. Thus you produced a valid proof of a different set of conditions, but not of the conditions initially stated.

[@antongole5596]

There in no error in his proof. His proof shows that the lengths that can be measured with a 5cm ruler and a 7cm ruler can be any integer (1, 2, 3....n..). So a 6cm gap and a 1cm gap can both be produced with his method, therefore there is no errors in his proof.

[@poopcatapult2623]

Anton Gole you might want to read his comment again.

[@leandrog2785]

He fucked up the metaphor with rulers, but what he actually meant was a linear combination of 2 integers.

[@yadhukrishna.t.r7753]

Pls make a video for chemical engineers😁.

[@chakri620]

Zach..ur superb..

[@lmao6]

Advent of coders will thank you

[@swim3936]

“Number theory is just the study of integers” man, i wish…

[@arshdeepsinghheer8198]

Thanksss

[@neoTriny]

congratulations on Getting 1 million sub 😁😚

[@thomaskember4628]

Alright it possibly to factorise a number if it is an integer. What about a complex number whose real component and imaging component are integers? Is it possible to factorise it? And if it is, are these factors prime numbers? In other words, do prime complex numbers exist?

[@nicolaschataing1457]

Yes : en.wikipedia.org/wiki/Gaussian_integer

[@syedsanaullah9026]

great simple stuff...shukran

[@roadstack1111]

16 calendars of poetry

[@MelordJenkins]

WHY DO I UNDERSTAND ALL OF THIS!!!???!! THE ALPHA SETH IS COMMUNICATING WITH ME!!!

[@garvagarwal4005]

What about linear algebra? It's like the core of CS

[@FarCough145]

1:20 I know how to do this one, the ol proof by calculator

[@jameszenos4045]

Very interesting 👌

[@SohilShah_Melodyman]

very informative...thanks!

[@gontsekganyago4079]

Now this is what I'm talking about....typa sh*t I like

[@soham7226]

Well I'm really passionate in solving problems of maths Is cryptography right for me as a career option

[@carloscuevas8268]

Cryptography is not a career, is part of Computer Science

[@nrlombardi]

@@carloscuevas8268 Cryptography actually stems from mathematics. It is now considered a branch of mathematics and computer science because of the evolution of the field. The father of computer science was a mathematician. Alan Turing.

[@erichuddleston4611]

You can actually become a cryptographer, but you need a graduate degree and / or experience. I would recommended studying computer science and taking cryptography class. That's what I did. Bachelor's of science in computer science with concentration in cyber security. Planning to work in security automation pr cloud security and studying to become cryptographer later.

[@erichuddleston4611]

Computer science is definitely worth it if your interested in cryptography and related topics. I took a class on cryptography and a class on cryptocurrencies. Already getting job interviews. Cs Is definitely worth it.

[@ayushsarkar2305]

Love u bro u inspired me to take cs

[@trevor_idiot]

I wasn't really paying attention to how small the rulers are but, okay

[@bata3258]

zach the star himself?

[@anjaninator]

“Lets say we have an infinite amount of rulers”

[@alnasraltair8948]

yeah but we can't afford 5 cents real ruler full of numbers and cute little faces

[@burntt999]

@@alnasraltair8948 hahaha lets just have a garage sale and buy something useful

[@notyourbusiness2672]

5 cm is not small!

[@sen8078]

that is NOT what she said

[@shaifurrahaman6271]

Could you suggest books or any course to learn number theory?

[@firstdbzmaker]

The textbook used in my Number theory course is Elementary Number Theory by David Burton

[@christianalbertjahns2577]

Discrete Mathematics by Rosen is a pretty good book too but that book also contains other fields from dis. math like mathematical logic, graph theory, relation theory, set theory, and many more.

[@simranray4564]

You earned a SUB, Congratulations!

[@kevinstreeter6943]

As someone with a BS in math, I wish I had taken discreet math.

[@ericcheung8790]

6:56 Encrypted Message divided by Secret Key is the "Hello" appended 79 at the end (the another prime), but how to recover plain text (HELLO)?

[@motoph6942]

Thats why from python begginer exercisies computing prime numbers?... In my mind what the hell do i need prime numbers for?? Now i understand and im very intrested.. Thanks for your help...

[@Dablid77]

Thanks

[@3gysuduyw]

спасибо видео было очень полезным вы мне очень помогли :ru:

[@Lionheartgrudge]

How do you start learning number theory? I have studied Electrical Engineering, which is probably less math intensive than a CS degree. I find myself liking to code nowadays, so I think learning mathematics would help me train my brain better. Any help for dummies would be appreciated.

[@zachjones6944]

Symbolic Logic will help you reason. It is the basis for computer language.

[@GoToMan]

Nope, I believe EE is more math-intensive than a CS degree, and this is coming from someone who has studied math their entire life.

[@jameszenos4045]

I could have done this problem 3:37 using just one pair of rulers How? See. We have already measured 2cm. So with a pen mark that point. Now shift the 5cm ruler to the other end of 7cm ruler so this way I'm getting 2cm from right side. Mark that too. And tadda! we get 3cm in between those two demarcations

[@omarshakir8727]

Nice

[@soccerball7828]

Lol why you using pen? You have nothing but 2 rulers

[@98073]

you want a medal or something?

[@puny1503]

For everyone wanting to pursue a cs degree, u don’t take this maths, nor the maths he talked about in the first video. This is optional if u wanna do a minor in maths degree, i’m a computer science student myself, all we take is discrete structures, probability and statistics and calculus.