How many CS students are watching these vids?

good luck to all CS students watchin this. LET'S GET THIS DEGREE AND CLAIM THE BAG!

2:50 format 4:05 first example 8:57 first example solution 9:05 second example 12:44 second example solution

I swear if you were my teacher for every math course I wouldn't have to force myself to go, and I'd actually want to show up to class. I don't understand why but it's hysterical how well you teach this xD

Here is the ladder example from a textbook: "Suppose that we have an infinite ladder, as shown in Figure 1, and we want to know whether we can reach every step on this ladder.We know two things: 1. We can reach the first rung of the ladder. 2. If we can reach a particular rung of the ladder, then we can reach the next rung. Can we conclude that we can reach every rung? By (1), we know that we can reach the first rung of the ladder. Moreover, because we can reach the first rung, by (2), we can also reach the second rung; it is the next rung after the first rung. Applying (2) again, because we can reach the second rung, we can also reach the third rung. Continuing in this way, we can show that we can reach the fourth rung, the fifth rung, and so on. For example, after 100 uses of (2), we know that we can reach the 101st rung. But can we conclude that we are able to reach every rung of this infinite ladder? The answer is yes, something we can verify using an important proof technique called mathematical induction. That is, we can show that P(n) is true for every positive integer n, where P(n) is the statement that we can reach the nth rung of the ladder."

6:57 should read (k(k+1) + 2(k+1))/2 which will give you (k^2 + 3k + 2)/2, then you factor that into (k+1)(k+2)/2

I got stuck on something pretty stupid here: I saw ((k+1)[(k+1)+1]) simplify into ((k+1)[k+2]) and couldn't understand why, because for some reason I was reading the [(k+1)+1] part as [(k+1)1]. I know it's stupid, but because it's not factoring: [(k+1)+1] = (k+1+1) = (k+2). Not sure if anyone got stuck on this same thing, but there you go.

Million thanks and virtual hugs! Your videos saved me from my dicrete mathematics couse in Spanish (my native language Finnish) which I'm taking in my exchange year in Peru;) I would have failed it for sure without your help. Thanks thanks thanks. Keep up the good work!

I took discrete math years ago and this video helped sooo much! You are the man!

In step 3 I found it easier to factor out a k+1 in the left side, which leaves you with (k+1) * (k/2) + 1 Then it is convenient to convert 1 = 2/2, when you simplify (k+1) * (k/2 + 2/2) you get (k+1) * (k + 2)/2 ..... and that is exactly the same as the right side of the equality. Hope I could help at least one poor soul taking this course XD good luck :)

Love your videos thank you so much.. I took a mandatory intro discrete course for CS... We covered video 1-28 in two weeks. Were on the third week and started graph theory and i'm so behind. Thanks so much for the informative videos, they're the only thing keeping me alive. (7 week courses)

I feel that's the way people really want to teach you to learn. My teacher always ignore most of the explanation and assume student knows it from the start, and start all of his proofs.

Thanks. Watching the previous videos in this series along with Hammack's Book of Proof sets the stage for intuitively understanding Proof by Induction. MIT's OCW Math for CS on the other hand jumped into it with very little background and so was far less clear.

This guy needs to be inducted into the hall of fame for math instructors

5:25 Sorry, I got a little lost at where (K+2) came from. At this stage, on the right side of the equation (K(K+1)), is it that both K's are replaced with K+1, making it so that its (K+1)((K+1)+1) = (K+1)(K+2)?

Thank you so much for this, my teacher is a joke and this video just saved me about 3 hours of headaches.

I think I wanna marry you no homo that ladder analogy was godly. Our prof only splatters examples to us and never really explained anything about the logic behind the induction solution (the proving of k+1) this has taught me more than our 90 minute session. Godspeed to you trev.

Thank you, video was really helpful and everything was explained really clearly!

Thank you. I am studying for my cset, this helped out alot.

You better explain the subject in first 2 minutes than my discrete math professor does in 2 x 1,5h lectures

I totally understand NOTHING !! i hate this chapter...

Thank you! Thank you SO MUCH!

This is a very good video. Thank you.

I've never heard induction explained like this, thanks.

thank you so much for this video. studying for finals I was struggling on proving summations via mathematical induction, and I had no idea how to find what it is that I was trying to prove, since our professor seemed to skim over the inductive hypothesis portion, and this video greatly helped. so thank you for this, keep it up.

Thanks a lot man. That really helped me out.

I'm taking a math class in highschool as a junior and this is one topic that is difficult for me😭 the way my teacher explained it wasn't the best thank you!

Thank you very much. I really love your videos. You are the best)))

I think this finally made the principle click for me. Also thank you for addressing the circular reasoning argument. That's something I always struggled with.

I might survive discrete math yet thanks to you!

Your videos are the best! Watching this b4 exams tomorrow

That's the most important part. Is for something to hold forever... *cries in math*

thank u very much!!! wish me luck on my exams 😊😊

Thank you.Your videos are the best

I have a problem here prof n^4 < 4^n, for n> 4, would you help me with this one?

Good work. Thanks

Thank you!

Hello, thanks for the lesson. From the first example, where you initially made a mistake. I did not catch your explanation on where the 2 you later added came from. Thanks

simply amazing keep on the great work!!!

how did you get the (k+2) in the second step ???

Hmm weird we never do it with n

thanks for the help

I have so many of them 1) how do I prove log 6 base(4) is irrational 2) how do I prove using well ordering principle: n

Do you have any videos on strong induction and recursion?

that was so useful!

Thank you for this video. But can you explain strong induction please. Thank you.

can someone please explain the factoring technique that was used? Every single video that does this proof (I've watched 4) doesn't explain where I can find more information on this, they just assume I've memorized every single little thing in algebra that I did 4 years ago.

haaah 12:14 "Ass."

well explained sir

Thanks soooo much!

this video really helped me. thank you so much

I loveee your handwriting!!! 💕💕💕

amazing explenation

best teacher!

what program did you use?

Great video

This video is on my syllabus

how do you know what to choose for your base case for any given problem? what is the strategy for choosing the base case?

Whats the bar ontop?

It would be better if you took recurrence relations as an example for the "Induction Proof". Anyway gold content!

Thank you.

Bro i aint gonna lie, i didn’t study at all throughout this sem😭😭😭 rewatching all your videos two nights before my finals , really helping doooooooooo

How do you simply it at 6:18

Thank you kind sir

really cool! Discrete math is the coolest thing ever! specifically the proofs. It really helps us to understand the world with mathematical perspective.

well understood

Why should I use this in practice? Maybe to prove my algorithm holds true to any random value?

thanks bro

Man I love discrete math it’s so damn interesting

Pls can you make another video explaining the last proof you just explained in this video???

Hey can you add Strong mathematical induction ??

High quality video

I have a discrete math exam today so can someone please tell me how at 7:36 he went from k(k+1)/2 +(k+1) for the left hand side to k(k+1)+*2*(k+1)/2?? where did that 2(k+1) come from? am I missing something? Shouldn't it be just (k+1)?

don't you think here k

The other video is here: kzfaq.info/get/bejne/nNhkpqWEl66Xmmg.html

Can someone explain to me why we do +2(k + 1) around the 7:30 mark. I'm not great with algebra

Gud day. pls, I wnt to no what topics I need to no before I can learn mathematical induction. Thanks

At 7:30 you change it to 2(K+1) why is that?

Hi Trev, where did K+2 come from? This has been troubling me since my discrete class the other day. (k(k+1)(k+1))/2 = ((k+1)(k+2))/2; unless I am getting my math wrong I don't see how this is? I just really need to know where the number is coming from for me to understand.

why do we assume n

So with the ladder analogy what happens if your chosen k is the last step on the ladder would it therefore not have a k+1?

Great video. It's probably worth noting that this is a demonstration of strong induction, as opposed to regular induction; where during the induction hyp. you assume that your statement P(n) holds for some arbitrary k, then show it's also true for k+1.

I think you made a mistake isn't k(k+1)/2 + (k+1) the same as (k(k+1)+2*(k+1))/2? Not just plopping the k+1 on the top of the fraction? Edit: You fixed your error like 10s after I paused whoops

u said you put in k+1 for k at 5:36, but wouldn't that end of being (K+1)(K+1)? Why is one of them K+2?

Isnt it strong induction?

what if the first step is false..i mean the basis???

I LOVE YOU!

I have a hard time understanding why we had k+1 on the left hand side. Could someone explain that to me?

Hello, PLease help with the following problem Prove (using direct proof) that, for all integers a and b, if a 𝑚𝑜𝑑 4 = 3 and b 𝑚𝑜𝑑 4 = 2, Then ab 𝑚𝑜𝑑 4 = 2.

Where did the k+2 come from in the first example though?

on 7:31 mark why did he multiply 2(k+1)? i thought how he had it before was fine?

where did the (k+1)(k+2) come from?

5:22 I saw you add k+1 on the left side but there is still a k there. I mean that k should be replaced by k+1, then why there are even two k there?

why did you use N

7:58 I like your stroke order heheh

I feel 'proof by induction' is a circular argument -- how can we 'assume' what we have set out to prove? What lends legitimacy to this assumption? What's the proof that proof by induction is a valid method of proof?

Thati's great

Pls help me solve this one its been giving me a headache Prove by mathematical induction that n(n+1)(n+5) is a multiple of 3 for all n is an element of natural numbers(n€N)

It would help if instead of making mistakes, continuing, realizing the mistake and then erasing a couple things, you just re-recorded the part. It really messes with understanding when you continue with incorrect work. For example, around the 5-8 minute mark, you changed the (k*(k+1))/2 multiple times, so the steps didn't make much sense

How do you write on your computer? With a mouse? I'm only curious because if you're using a mouse your handwriting is amazing.