RECURRENCE RELATIONS - DISCRETE MATHEMATICS

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  • Опубліковано 6 жов 2024
  • Leanr about recurrence relations and how to write them out formally.
    #DiscreteMath #Mathematics #RecurrenceRelations
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    In this video we introduce recurrence relations, specifically looking at geometric progressions and arithmetic progressions.
    Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

КОМЕНТАРІ • 193

  • @thejo6331
    @thejo6331 8 років тому +430

    My data structures professor jumped into recurrence relations without explaining them, ignoring the fact that discrete math isn't a prerequisite course. Your explanation is A+, thanks so much!

    • @AliMalik-yt5ex
      @AliMalik-yt5ex 5 років тому +41

      In my university, you cannot take data structures class without having passed discrete mathematics.

    • @pmz558
      @pmz558 4 роки тому +2

      @@AliMalik-yt5ex what uni is it?

    • @AynChat
      @AynChat 4 роки тому +2

      hmm,looks like our uni have much alike

    • @jimmyli34
      @jimmyli34 4 роки тому +10

      @@AliMalik-yt5ex I took data structures last semester, and just now taking discrete mathematics. So mine is the opposite I guess

    • @MateusKaterp
      @MateusKaterp 2 роки тому +3

      bruh the exact same thing happened to me lol

  • @kyrieirving4206
    @kyrieirving4206 7 років тому +383

    College class is joke, have to look for great videos on youtube like this one anyway

  • @jrgenbrve3990
    @jrgenbrve3990 7 років тому +109

    Why did i go to lectures the whole semester when i can spend 15 min watching this video and understand everything... Great work!

  • @astyanax905
    @astyanax905 8 років тому +209

    Wow, honestly this is the most clear I've ever seen this. good job, it actually makes sense to me

    • @Trevtutor
      @Trevtutor  8 років тому +8

      +astyanax905 Thank you!

  • @gehenna151
    @gehenna151 5 років тому +36

    Missed the lecture on this topic last week with the midterm fast approaching, and you explained this better than my textbook ever could. 10/10

    • @yungzed
      @yungzed Рік тому

      whatd u finish with

  • @newleafoverit
    @newleafoverit 3 роки тому +9

    omg that at the end, this guy cares about us more than he cares about the views
    10/10

  • @clkinder1
    @clkinder1 7 років тому +7

    Currently, I can't understand anything in my Discrete Mathematics class, but these videos are an extremely good resource.

  • @shivanshsingh8173
    @shivanshsingh8173 3 роки тому +6

    My teacher taught me this in class 12 and I forgot it until recently I was required to use it in discreet mathematics, this video was a perfect revision covering all topics and I can solve any questions again from this topic. Thanks 😊

  • @LionHeartSamy
    @LionHeartSamy 7 років тому +29

    Thanks a lot! Just want to point out a small error though; at 11:50, a(n) should be equal to the sum of 2i from i=1 to n, instead of 2n from i=1 to n (since that'd just be 2n^2)

    • @pchat138
      @pchat138 7 років тому +1

      This was confusing me as well. Thanks, I get it now

    • @xinliangwei8865
      @xinliangwei8865 5 років тому

      I found this error too.

    • @mokoepa
      @mokoepa 3 роки тому

      I came here for this to see if I was the only one who saw it... besides.. he mentioned earlier that it's the some of i's, i ranging from 1 to n

  • @ProtonChicken
    @ProtonChicken 5 років тому +5

    Love the KhanAcademy style video. My Algorithms professor jumped right into recurrence relations with no logical order or structure to the lecture so this really helped me.

    • @AynChat
      @AynChat 4 роки тому

      well, they sure did well themself but failed to teaches.

  • @brecoldyls
    @brecoldyls 6 років тому +7

    That was pretty helpful, and the proof at the end was nice. I’ve always used that sum but never knew the proof

  • @multibrainhacker
    @multibrainhacker 7 років тому +2

    Dear Tutor!
    I am Student of BS math, believe me that your conveying method is marvelous.
    i feel honored in my fellows Specially when i give examples of Fibonacci numbers to explain recur.relation........
    Keep it up...... Stay Blessed.

  • @snydex5064
    @snydex5064 3 роки тому +3

    one hour before discrete mathematics
    youtube history: *full of discrete maths tutorial*

  • @ushachandankar
    @ushachandankar Рік тому +1

    THANK YOU VERY MUCH SIR ITS ABOUT TO BOUNCE OFF MY HEAD AND FOUND THIS👍❤️

  • @alvinkatojr
    @alvinkatojr 4 роки тому +1

    This is how mathematics should be taught! Brilliant!

  • @ChenukaGamage
    @ChenukaGamage 3 роки тому

    Thank you so much man, if it weren't for you, I wouldn't have been able to get through my finals.

  • @msrtrini
    @msrtrini 8 років тому +3

    Dude Thank you so much , saved me before my exam .

  • @xaravox
    @xaravox 5 років тому +1

    Videos like this are honestly a godsend. Thank you so much!

  • @braydenchan138
    @braydenchan138 2 роки тому +1

    Thank you, Tutor Trev!

  • @swasthikadev
    @swasthikadev 5 років тому +18

    12:19 isnt it summation Ki

  • @陳翰儒-d5m
    @陳翰儒-d5m 3 роки тому

    Thanks man, you are saving my midterm test!!!

  • @tgg3249
    @tgg3249 Рік тому +1

    Great video, great instructor.

  • @cerealmurderer_nr
    @cerealmurderer_nr 8 років тому +35

    with mid-terms being 2 days away and me not really understanding what my DM professor has taught, your videos helps a lot, A LOT. subbed

  • @mbalazs3544
    @mbalazs3544 8 років тому +1

    you get my like just by being able to explain to me what this is.....and I honestly beloved before your video I will never be capable to understand this thx man.

  • @jon_tradez
    @jon_tradez 3 роки тому

    my discrete maths teacher has a PhD in my maths but shitty in teaching. your amazing trev

  • @JamesBrodski
    @JamesBrodski Рік тому +1

    Thank you so much! Great video.

  • @pjcamiam
    @pjcamiam 5 років тому +2

    The sum in 11:57 from i = 1 to n of n is NOT n(n+1)/2.
    This formula only works if you’re taking the sum of i, which is changing, whereas n is a constant with respect to i. Thus you can factor out the 2n like any constant and you’d really be taking the sum from i = 1 to n of 1, with the sum being multiplied by 2n after it is solved.

  • @farisdurrani
    @farisdurrani 3 роки тому

    Thank you! Your explanations is so helpful for my combinatorics class!

  • @mochabean4325
    @mochabean4325 2 роки тому

    Thank you, my math textbook to a long and bad spoken approach to teaching this concept, this was better explained!

  • @TheHiguy333
    @TheHiguy333 2 роки тому +7

    I have an exam in an hour. Anyone else?

  • @ayushmansrivastava3349
    @ayushmansrivastava3349 8 років тому +1

    Excellent video , crystall clear concepts.....

  • @Elantry
    @Elantry 5 років тому +1

    These videos are seriously good! Wish I'd found them sooner.

  • @whiterice6663
    @whiterice6663 4 роки тому

    1 week until my G12 exams, you have saved me! Thank you from Papua New Guinea :)

    • @duckynatalie
      @duckynatalie 4 роки тому +3

      Image studying for an exam a week in advance... Its 12:45 am right now for me... and my exam is at 8:25 am... oof lol

    • @armin5767
      @armin5767 3 роки тому

      @@duckynatalie and you were reading comments lmao

    • @duckynatalie
      @duckynatalie 3 роки тому

      @@armin5767 yep.

  • @commenting000
    @commenting000 4 роки тому +1

    Hello, Trevor. I wasn't sure about your generalized formula for the segment in 11:23. I ended up trying to find a general formula and I found that An = Ao + (k * (n+1/2)) works as well. If you could clear up this misconception, that would be very helpful.

  • @bartubozkurt7312
    @bartubozkurt7312 3 роки тому

    this is fairly clear expression thank you

  • @musficamurshidopshori2512
    @musficamurshidopshori2512 6 років тому

    Thank you so much for the discrete math tutorial!

  • @hghlndr2
    @hghlndr2 4 роки тому

    good explanation to initial conditions

  • @lalith_kumar_akhila2411
    @lalith_kumar_akhila2411 2 роки тому

    thanks for great explanation

  • @adiletbaimyrzauulu6589
    @adiletbaimyrzauulu6589 Рік тому

    you helped me to get my degree sir

  • @hubbankhan3309
    @hubbankhan3309 3 роки тому

    13 minute into this video and i had the aha moment!! thankyou so much trevtutor((((((:

  • @glitchyplaysstuff1233
    @glitchyplaysstuff1233 2 роки тому

    helped me last minute back in highschool

  • @patientson
    @patientson 6 місяців тому +1

    Lol. As long as it will help to compute excellent algorithm and write excellent programs, I will share it quickly to friends asap

  • @gatos4840
    @gatos4840 7 років тому

    Keep up the good work! Clear explanations that helped me a lot!

  • @DannyPhantumm
    @DannyPhantumm 3 роки тому

    The f's you drew at 0:57 were beautiful.

  • @quirkyquester
    @quirkyquester 6 років тому +1

    you are amazing! Thank you!

  • @Noellexafael
    @Noellexafael 5 років тому +1

    Ok I understand and all but I still can't do my teacher exercises 😐, this is definitely hard but thanks for the video ❤️

  • @palashingle861
    @palashingle861 8 років тому

    Find the solution to the recurrence relation an =6an-1 +11an-2 -6an-3 with a0=2, a1=5 and a2=15.

  • @RajeshKamboj
    @RajeshKamboj 9 років тому +1

    Thank you so much sir.

  • @alphaneracar7063
    @alphaneracar7063 5 років тому +1

    I didn't quite understand the given equation at 11:45, in which you claim that a.n is equal to zero plus the sum as i goes from 1 to n of 2n. I think it should be 2i instead of 2n.

  • @bubblesgrappling736
    @bubblesgrappling736 4 роки тому +1

    the term "recurrence relation" does it descirve the kind of notation that you are using the describe datastructures here?

  • @mikays3580
    @mikays3580 2 роки тому

    Hello, sir! Thank you for your thorough explanation. I would just like to ask if a recurrence relation of a sequence is unique?

  • @deepaskaria7410
    @deepaskaria7410 Рік тому +1

    Thanks

  • @Kamnuma
    @Kamnuma 7 років тому

    Thank you so much! This video was helpful!

  • @majdhaythem1462
    @majdhaythem1462 6 років тому +4

    the best video ever on youtube !!

  • @buntagkendrick887
    @buntagkendrick887 Рік тому +1

    thank you man

  • @FatihAlmutawakkil
    @FatihAlmutawakkil 6 років тому

    I LOVE THIS CHANNEL!!!!! GOOD WORKKKKKKKKKK!!!!!!!

  • @momen_ai
    @momen_ai 3 роки тому

    for the example y you have explained: (0, 2,6,12,20,30,42..): can be written like:
    an = a(n-1) + 2 * a right?

  • @simpleepic
    @simpleepic 2 роки тому

    You believe of not my discrete mathematics professor exactly has your slides in his lectures.

  • @AynChat
    @AynChat 4 роки тому

    well,that was mind blowing

  • @mickey46911
    @mickey46911 8 років тому +3

    +TheTrevTutor
    All your videos are awesome and it helps me out tremendously.

  • @harshvirtomar6552
    @harshvirtomar6552 6 років тому +1

    You are awesome!!!

  • @josephmwanza5086
    @josephmwanza5086 3 роки тому

    well explained

  • @skullcrusade3436
    @skullcrusade3436 29 днів тому

    8:29, the moment everything exploded into my face. I was following along and then KABOOM sigma summation shit and now I'm scared. THank you fro the hlepufl ivode

  • @raziel44
    @raziel44 9 років тому

    Love your videos. Got a question though. Do any of your videos talk about or are you planning on talking about the Fermat Theorem?
    I had this assignment the other day where you had to prove that "2 to the power of 69 + 3 to the power of 69 can be divided by 7". Or something like that.

    • @Trevtutor
      @Trevtutor  9 років тому

      =(eGO)=™Raziel44 I don't have anything planned for Fermat's Theorem quite yet, sorry.

  • @juloguadalquiver3727
    @juloguadalquiver3727 3 роки тому +1

    I honestly say I didnt get it. You didnt explain specifically in 2:47 how to expand it and how 2an-1 actually works to find following sequence

  • @siyiroancreint
    @siyiroancreint 4 місяці тому +1

    Helps decipher the Wiki page, which says all this with 0 explanation. Thanks

  • @sj00100
    @sj00100 Рік тому

    If a(n) = n, so a(n) = n(a(n) - a(n-1)), solving this give formula for sum of frst n natural numbers.

  • @sefaalperis7366
    @sefaalperis7366 7 років тому

    Very good video but I think you made a mistake while writing the formula at 12:15 the k should be in front of the sum symbol and in the sum symbol there should be only i.

  • @piotrjaga6929
    @piotrjaga6929 2 роки тому

    thank you

  • @catherinezhang8334
    @catherinezhang8334 5 років тому

    good video! great explanations!

  • @Selim_Hasan_Raj
    @Selim_Hasan_Raj 3 роки тому

    can you make a video on variation please?

  • @yvanbrunel9734
    @yvanbrunel9734 5 місяців тому

    I know this is old, but I'm trying to understand please:
    At 12:04 you said it would be 2((n)(n+1))/2
    But that would be right if it was a summation of from i=1 to n of i, right?
    Here we are doing a summation from i=1 to n of n, so shouldn't it have been = n^2?
    Thanks

  • @sukkuvaishnavi9387
    @sukkuvaishnavi9387 4 роки тому

    Sir can u explain again geometric progression

  • @bradleyshepard
    @bradleyshepard 8 років тому

    Trev- could you suggest an inexpensive basic text that addresses generating functions at the undergraduate level??

  • @wolfhart8269
    @wolfhart8269 6 років тому

    So with all those formulas. Which is the real formula for recurrence relation?

  • @crowlsyung
    @crowlsyung 6 років тому

    Awesome video! What software do you use to record these videos??

  • @winwin4393
    @winwin4393 Рік тому +3

    Maybe I am stupid ! I don't get anything ☺️☺️☺️☺️

  • @sietzevandervinne4208
    @sietzevandervinne4208 2 роки тому

    thanks strijder

  • @user-dj9iu2et3r
    @user-dj9iu2et3r 2 роки тому

    Before the proof at the end... why did he use k as the variable in the summation when the index variable is i? shouldn't they match?

  • @Justinhoou
    @Justinhoou 8 років тому

    Hi do you have a video on backtracking method? Thanks!

  • @k.alipardhan6957
    @k.alipardhan6957 6 років тому

    for the 10:00 mins mark, why isnt it something like:
    2*i + X_(n-1). were i is the index, and X_(n-1) is the element before.
    did i just think of the recursive solution?

  • @reynardryanda245
    @reynardryanda245 5 років тому +2

    YOU'RE A GOD

  • @SURaviKumarChavali
    @SURaviKumarChavali 3 роки тому

    what is the digital board you used to write. please tell.. thanks in advance

  • @yujiabing8820
    @yujiabing8820 6 років тому

    so clear/ thx

  • @taneja_unchained
    @taneja_unchained 7 років тому

    Which software and device has been used to create this videos, i also want to create some videos of electronics subjects which i want to teach. Please share it :)

  • @AhamedKabeer-wn1jb
    @AhamedKabeer-wn1jb 5 років тому

    Superb...

  • @gcs4558
    @gcs4558 4 роки тому

    which software are you using for this lecture

  • @khadijahflowers9024
    @khadijahflowers9024 6 років тому

    So far, I've only learned about the Master Theorem for solving a recurrence relation which is super helpful and memorable after a few examples. But that is a formula used for recursive algorithms (from what I've seen). Is there another way to measure the time function will take to finished rather than just eye balling it?
    en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)

  • @martinkunev9911
    @martinkunev9911 3 роки тому

    10:30 your notation is confusing. k is not a number, it's a function of n (which we can call k_n). Then at 11:12 the summand is not k, it's k_i.

  • @سبحانالله-ك2ذ
    @سبحانالله-ك2ذ 3 роки тому

    Solve the recurrence relation:
    𝑎𝑛 = 8𝑎𝑛−1 − 21𝑎𝑛−2 + 18𝑎𝑛−3, 𝑎0 = 5, 𝑎1 = 2, 𝑎2 = 13
    ?

  • @sextolife
    @sextolife 9 років тому

    Hello sir,can you please let me know the derivation of Genaral solution of the RR having root with multiplicity >=2

  • @jaideepshekhar4621
    @jaideepshekhar4621 5 років тому +1

    7:18 But WHY are we adding all the terms?

    • @onenicenero1494
      @onenicenero1494 5 років тому

      So most of the terms cancel out and we have only necessary part left. Simplification

  • @denizbabacan3835
    @denizbabacan3835 6 років тому +3

    2+2 is 4 -1=3 quick maths :D

  • @ioannismarkoulakis4978
    @ioannismarkoulakis4978 7 років тому

    is this the same as recursive ranks?

  • @joylox
    @joylox 7 років тому

    I'm doing stuff like this in discrete 1, but only solving them and giving the first few terms. This gets really confusing.

  • @nishithamathew6289
    @nishithamathew6289 7 років тому

    useful video

  • @semirumutkurt6635
    @semirumutkurt6635 7 років тому +5

    you made me remove my ad blocker

  • @JJScene
    @JJScene 2 роки тому

    7:32 You don't explain why you're adding them up, or how on earth a1 - a0 + a2 - a1 is equal to a1 - a1.

  • @debjitkhaskel7879
    @debjitkhaskel7879 5 років тому

    Does recurence relations has only one form

  • @walasker6017
    @walasker6017 4 роки тому

    what type of sequence is the one on 9:18 ?