Proof by Strong Induction (full lecture)

Рет қаралды 33,024

Dr. Valerie Hower

3 жыл бұрын

Mathematical Reasoning. Textbook: Book of Proof by Richard Hammack (section 10.2) www.people.vcu.edu/~rhammack/...

Пікірлер: 93

@MagicalMidgetPete 2 жыл бұрын

I’ve been in two discrete math focused and algorithm analysis courses, I’ve been a TA for one of those courses as well, and not once have i ever seen such a clear explanation of why we do what we do for both weak and strong induction, and how to replicate this consistently and clearly. And you clearly care about your students understanding too!

@DrValerieHower 2 жыл бұрын

Wow. Thank you so much for your kind words. I really appreciate the feedback.

@yashpatel1460 2 жыл бұрын

wish I had you as my prof which is passionate and on point rather than the current one who has 0 interest in what students are understanding.

@emberlynnguyen3458 Жыл бұрын

I love the enormous enthusiasm you put into the videos

@DrValerieHower Жыл бұрын

You are welcome! I really appreciate the feedback. And thanks so much for the kind words.

@ashikacharya 7 ай бұрын

There are very few teachers who make us realize that mathematics can be fun and interesting. You are one of them. Keep up the good work.

@DrValerieHower 7 ай бұрын

Wow thank you!! I appreciate your kind words. :)

@user-uc1ne8ch6s Жыл бұрын

I have been searching for strong induction courses on KZfaq for a couple of days. No other course can explain this particular concept more clearly than this one.

@DrValerieHower Жыл бұрын

Wow thank you for the kind words! I really appreciate your comment.

@jaclynhilton616 3 ай бұрын

You are the type of professor I wish to be in my future 🥰 straight forward and as clear as possible! I have to work really hard but when I finally understand something I’m golden and because of this I think I’m better at explaining where people might have trouble which you do a great job of! I also appreciate you writing out these proofs! Most professors are lazy and short hand everything which can lead to confusion. Thank you so much Dr! You are amazing!

@DrValerieHower 3 ай бұрын

You are welcome. Thanks for the comment and best wishes with your future goals. :)

@umangmehta9319 6 ай бұрын

Usually I just watch videos and move on after grabbing things I want, but this was too helpful that I couldn't resist commenting! GREAT WORK!! Thank you so much for this! This is my first comment ever on any video , all credits to your brilliance

@DrValerieHower 6 ай бұрын

Wow! You are welcome. Thank you so much for the kind words :)

@mameahmed3758 28 күн бұрын

Thanks for ur support ❤

@gaurangruparelia2384 2 жыл бұрын

Love the energy and the clear explanations- thanks!

@DrValerieHower 2 жыл бұрын

You are welcome! Thank you so much for your kind words. I appreciate the feedback :)

@Harshitkumar-bc4vp Жыл бұрын

Your smile ..feels me that how easy is math.... awesome lecture.... Love from India.❤️

@DrValerieHower Жыл бұрын

Thank you!!

@souravsamant 2 жыл бұрын

Beautifully explained... I have a test tomorrow morning and you saved me... Thank you very much... And keep smiling 😊😊😊

@DrValerieHower 2 жыл бұрын

Thank you so much for your kind words. I appreciate the feedback!

@axelwong4633 Жыл бұрын

Love the passion and honestly one of the best explanations I've come across among all other videos

@DrValerieHower Жыл бұрын

Thank you so so much! I appreciate the feedback :)

@Taanish1176 3 ай бұрын

One of the most helpful videos on Strong induction out on YT

@DrValerieHower 3 ай бұрын

Wow thank you so much!!

@100solarmass 5 ай бұрын

Best Lecture on YT regarding Strong Induction

@DrValerieHower 5 ай бұрын

Wow thank you so so much!!

@devrim7720 Жыл бұрын

Loved your energy and the way of teaching!

@DrValerieHower Жыл бұрын

Thank you so much! I appreciate your kind words.

@Rakesh-gv5cn 3 ай бұрын

Great Lecture! Thank you

@DrValerieHower 3 ай бұрын

You are welcome! thanks so much for the feedback :)

@small_creeper 8 ай бұрын

Thank you so much for this video!!! I'm currently preparing for math proof test, and the questions provided in the video were clear and intersting! Thank you!!

@DrValerieHower 8 ай бұрын

You are welcome!! i appreciate the feedback :)

@pavanajsridhar939 2 жыл бұрын

Thank you for the content. It was really helpful and you explained it thoroughly.

@DrValerieHower 2 жыл бұрын

You are welcome. I appreciate the feedback :)

@Anon2310_ 4 ай бұрын

best video iˋve encounter, thanks!

@DrValerieHower 4 ай бұрын

Wow, thank you so much! And you are welcome :)

@machineo12887 3 ай бұрын

Thank you so much, strong induction finally clicked for me!

@DrValerieHower 3 ай бұрын

You are welcome! this is so wonderful to hear. thanks for the comment :)

@venkatsrikanth2942 3 ай бұрын

This was great! THANKS A LOT!! :)

@DrValerieHower 3 ай бұрын

You are welcome!! Thanks for the comment :)

@tonyisgone7900 7 ай бұрын

Amazing lecture, I always watch this video to review strong induction!

@DrValerieHower 7 ай бұрын

Thank you so much!!!!

@rick2690 Жыл бұрын

Love the way you teach. ❤

@DrValerieHower Жыл бұрын

Thank you! I appreciate the feedback.

@x0tek 2 ай бұрын

extremely well made!

@DrValerieHower 2 ай бұрын

Thank you so much.

@ucercem 2 жыл бұрын

Superb teaching skills! Thank you

@DrValerieHower 2 жыл бұрын

You are welcome! Thank you for the comment and kind words.

@MmTriplem 10 ай бұрын

I love you. Thank you for your effort!

@DrValerieHower 10 ай бұрын

You are welcome! Thanks for the comment :)

@collectionofcells8656 3 жыл бұрын

Amazing video, ty!

@DrValerieHower 3 жыл бұрын

My pleasure! Thanks for the feedback.

@tugrageler5248 8 ай бұрын

Hi doctor. I just meet you recently. And After I watch your video I said Why did not I found it before :D Haha whatever I find you. I just have one rewiew about the lesson. your 2 number's written as a 'a' When I saw the question I thoght that was a 'a' when you start the solve the question Than I noticed that it was not a 'a' I do not know did the other people consider about that think but I just wanted write. And except for all of this the lecture was very clear and also it was clear to you love your job to do

@DrValerieHower 8 ай бұрын

Thank you for your comment. I appreciate the feedback. I do not believe I have errors in this video, but my apologies if something is unclear.

@worku-bb5qz1mf8k 7 ай бұрын

I appreciate you 🙏🙏 in addition to this, please share Ethiopian University freshman courses .(general physics, mathematics, logic and critical thinking, anthropology and Introduction to emerging technology.

@christinajoseph3853 Жыл бұрын

for some reason my professor didn't explain how the inductive step is different for mathematical and strong inductions, this made my life easier. Thank you!

@DrValerieHower Жыл бұрын

You are welcome! I appreciate the feedback.

@henryyang3460 Жыл бұрын

Thank you Prof!

@DrValerieHower Жыл бұрын

You are welcome!

@muhdhaziq2422 2 жыл бұрын

Thank you Dr, u helped me a alot

@DrValerieHower 2 жыл бұрын

You are welcome. I am glad this was helpful and appreciate your feedback.

@user-lx6vp7bb8t 2 жыл бұрын

nice video ,topic simplify very esay👍👍👍👍

@DrValerieHower 2 жыл бұрын

Thank you so much for your feedback.

@dzbro1194 Жыл бұрын

What is the difference between strong and weak induction?

@nobody6150 2 жыл бұрын

i was worried about my test . but it your smile which has given a motivation to study more thanks ..😃😃

@DrValerieHower 2 жыл бұрын

Great! I am happy to hear. Thank you for the feedback!

@amornchotsingh3977 3 жыл бұрын

Hi Dr.Valerie. For the last problem, I didn't understand the reasoning about where k-2 came from.

@DrValerieHower 3 жыл бұрын

I think inductively, and I have stamps of 3-cent value and 5-cent value. If I want to make (k+1) cents in an inductive way, I can take postage made for (k-2) cents and then add one 3-cent stamp. This would give (k-2)+3=k+1 total cents. This is "3 steps back" and why I check 3 cases in my basis step. Does this help?

@sameerauf1193 2 жыл бұрын

@@DrValerieHower so more generally, what is the trick to find the (k-2) for inductive step in other problems?

@rachadelmoutaouaffiq5019 Жыл бұрын

Tysm !

@DrValerieHower Жыл бұрын

You are welcome!

@osama_statimath Жыл бұрын

Thank you 🙏

@DrValerieHower Жыл бұрын

You are welcome! Thanks for the comment. :)

@mustafauyghur162 Жыл бұрын

you the best

@DrValerieHower Жыл бұрын

Thank you!

@millenium2003 2 жыл бұрын

You are the GOAT. Run for office, I'll vote for you

@DrValerieHower 2 жыл бұрын

:) I appreciate the feedback. Thanks!

@nsh4658 Жыл бұрын

What does S(n ) mean? Please explain.

@sanjayutchula7849 6 ай бұрын

Was very confused with the stamps problem you blowed up all the contents at once

@naruhina123456789100 8 ай бұрын

17:55 Why is k >=2 when n>=3, doesn't that make 1

@DrValerieHower 7 ай бұрын

I'm not sure where you are getting that statement. I assume k>=2 in order to have k+1>=3. This is needed in the inductive step. Thank you.

@IMadeOfClay 5 ай бұрын

Thank you for the super video Dr. Forgive me but why is one allowed to assume all the steps from k(1) all the way to k(n) are true? This is the only part of strong induction I don't understand. I have scoured KZfaq and the internet for an explanation but cannot find one. Every source I have come across just states you can assume it but I haven't found an explanation as to why. I'm sure it's something obvious that is eluding me :(

@Matt-zn8om 4 ай бұрын

Yeah I have the same question too

@DrValerieHower 4 ай бұрын

So we have to be careful with our wording here. Technically we do not assume k(1) up to k(n). We want to prove an implication. that means: *IF* k(1) to k(n) are true *THEN* k(n+1) is true. now. you are correct as we prove the implication (inductive step) we start off suppose/assume k(1) to k(n) are true and show that with this assumption k(n+1) is true. this is how we prove an implication (due to logic/truth tables). Ok now to your question. One can prove that strong induction is equivalent to (regular) induction. These are both equivalent to well ordering principle of natural numbers. There are many references in textbooks showing the equivalence of different types of induction. hope this helps.

@Matt-zn8om 4 ай бұрын

@@DrValerieHower thank you! How do we know when to use strong induction bs just regular induction? Should strong induction always be used when recursive sequences are involved??

@DrValerieHower 4 ай бұрын

I always tell students that you don't need to make a decision in advance. Just try working with the inductive step. If you realize you can prove for k+1 using only the statement holding for n=k. then (regular) induction is just fine. and then you have one 1 case to check in your basis step. However if you realize you need the statement to hold for some value(s) of n that are less than k to prove for k+1 then this will be strong induction. You will also need to determine how many cases to check in your basis step.

@dzbro1194 Жыл бұрын

Is this not a weak induction?

@dzbro1194 Жыл бұрын

Never mind, I didnt finish the video when I said this.

@DrValerieHower Жыл бұрын

Correct I started with one more example of induction (weak) before moving into strong induction.