I don't recall having a teacher that explained why something happened in math so I find this video really helpful. Until 9th grade, I didn't know why in algebra when you do something to one side of an equation, you do the same thing to the other (25 = 3x + 35) because my math teacher never explained it to me.
These videos are lifesavers honestly. I dont know if my professor is just lazy or what but she quite literally does not teach us. She assigns readings, assignments, and that is it. At this point, I feel like I deserve a teaching credential considering how I taught MYSELF, no thanks to my professor.
@@DrTrefor Trivial question Mr Alive but what is that glass voodoo magic cage? You're standing opposite us and writing every single word from our perspective. I know you're a genius but I suspect tech has something to do with it (yes, I have seen a few others use it, though not on TH-cam so much), I would appreciate a heads-up as to what it's called. I tried to look it up but only found smartboards and they absolutely don't do this.
After passing 10th standard, I never really done maths. Now in computer science I had discrete maths , and I was self studying for maths then I found this tutorial and believe me I'm really loving maths and I am thinking why didn't I found math interesting before. I really thank you from bottom of my heart. thank you so much sir. Tannu Shrama
Hi sir, I'd like to ask if the structure of the course is based on the book "Discrete mathematics with applications" by Susanna Epp, because i noticed a lot of similarities, like the order of topics, and the brilliant example of a function being a machine which takes an input and gives an output. I'd also like to thank you for the amazing learning opportunity you are giving to many people like me who can only self-study these things online, without you it would be very difficult to understand these concepts. Many thanks, Federico
I think, he meant that for every input in your domain, there will be the same logic (square number). So, output is always predictable. If the function takes the same input 10 times in a row, it will give the same output always.
Dr. Bazett, what type of camera and software are you using? I’m beginning my math Masters this fall and would like to make similar videos! Thank you. I love your work!
Thanks for the amazing video. I have a question about the term “random function”. I was thinking about this as you spoke on the two properties of a function (i.e., it needs to do something to an input and the same output should always map to the same output). When I think of people saying “P(x) is a random function”, then to me it sounds like we cannot verify if the same input maps to the same output, which would imply that we can’t call it a function. Would it be more correct to say that the input is random (i.e., we cannot deterministically predict the input) as opposed to calling a function “a random function”? To use your analogy of the machine that spits something out, would it be more correct to say that the machine (function) isn’t random, but instead we don’t know what we’re putting into the machine? I hope my question makes sense :p
Not a mathematician, more of a computer science person, but I would say yes it is a function for most pseudo-random generators. In the programming world at least, the random function is magic, because you usually call it like this: random() and somehow even without any inputs, you will always get an output! However, the reality is that there is a hidden internal input value that it uses to calculate the next value (for pseudo-random functions at least). If you are using a pseudo-random function, then it uses some internal seed value as the input. Based on the seed value it calculates the next value, then stores that calculated value to calculate the third value, etc. Thus, if you know the seed or current value, then you can always predict the output as the output is deterministic. In this case, you could argue that it is a function if you treat the seed as the input and pretend it's sort of a "pausable" function, where you can resume it each time you want a new output. Since pseudo-random generators are deterministic, random(seedValue=3) might always give you the value 7. If you know the algorithm, you could fully determine the codomain and range of the random function. That being said, there are some "true" random functions like quantum random generators. Since these are inherently non-deterministic and don't operate on hidden inputs/seed values (as far as we know at least), then those cannot be considered as functions. It could be possible that you get the same output given the exact same physical conditions (the input) due to the nature of quantum randomness. In this case, since one input can have many output values, this is not really a function. In either case, calling it a random function or truly random is just a matter of convenience. For the most part, true randomness won't change anything compared to pseudo-randomness, but if it does, in that case, yes, you'd call a pseudo-random function a random function but designate a quantum number generator as a true random input.
Could you please explain the case for sqrt(x) or a circle. these equations do not follow verticle line rule. So are they not funtions? Thanks in advance :)
A function by definition maps values from argument x into one output y. The square root of 4 can be -2 and 2, so violtes function definition, in math sense. Abs(sort(x)) is a fine function though.
I don't recall having a teacher that explained why something happened in math so I find this video really helpful. Until 9th grade, I didn't know why in algebra when you do something to one side of an equation, you do the same thing to the other (25 = 3x + 35) because my math teacher never explained it to me.
I found you in 2020...I am lucky to be quarantined at home and watch these
These videos are lifesavers honestly. I dont know if my professor is just lazy or what but she quite literally does not teach us. She assigns readings, assignments, and that is it. At this point, I feel like I deserve a teaching credential considering how I taught MYSELF, no thanks to my professor.
I hope you escape from that glass cage one day. Blink twice if we need to call the police.
@@DrTrefor Trivial question Mr Alive but what is that glass voodoo magic cage? You're standing opposite us and writing every single word from our perspective. I know you're a genius but I suspect tech has something to do with it (yes, I have seen a few others use it, though not on TH-cam so much), I would appreciate a heads-up as to what it's called. I tried to look it up but only found smartboards and they absolutely don't do this.
@@ccuny1 I would imagine that he simply uses a mirror effect to correct the perspective as the original image would be backwards
@@ccuny1 there is a special camera that will turn the image into backwards
What a great explaination...... really we need this type of Teachers ....
After passing 10th standard, I never really done maths. Now in computer science I had discrete maths , and I was self studying for maths then I found this tutorial and believe me I'm really loving maths and I am thinking why didn't I found math interesting before. I really thank you from bottom of my heart. thank you so much sir.
Tannu Shrama
SAME LIFE
The fact that He is writing backward is so distracting that I didn't even realize I am already watching the 7th video
Muhammad Umair He is righting in proper direction & fliping the video mate.
@@ShanilkaRajapaksha found a sri Lankan glad to see u mate!
@@inovexa4039 hell yeah dude! 🙌🏽 I follow lot of videos by Trefor! This man saved my semester hahaB
@@ShanilkaRajapaksha from which university are u bro!
I had the same issue. I paid more attention to HOW he was rather than WHAT he was writing. LOL
What an inspiring teaching series! Thank you! I also want to know where I can find practice problems.
I saw the textbook you recommended. Thank you, Dr. Bazett!
Math is easy ! Dating is what is a bummer !
I Enjoyed math Because of you sir😊
Hi sir, I'd like to ask if the structure of the course is based on the book "Discrete mathematics with applications" by Susanna Epp, because i noticed a lot of similarities, like the order of topics, and the brilliant example of a function being a machine which takes an input and gives an output. I'd also like to thank you for the amazing learning opportunity you are giving to many people like me who can only self-study these things online, without you it would be very difficult to understand these concepts.
Many thanks, Federico
discrete maths and application by susanna epp is good book for practice?
please, add transaltion on videos .i cant understand this playlist
Great explanation of a function. Very clear.
Mi the only one not attending any University but still watching
I was looking at your hand OMG !! You are awesome 🙏🤩
pls how do I get the full video for functions?
Is this particular lecture a part of a playlist?
Domain - possible inputs.
Range - possible outputs.
Only one output for any Domain input. Am I correct?
Yep!
I think, he meant that for every input in your domain, there will be the same logic (square number). So, output is always predictable. If the function takes the same input 10 times in a row, it will give the same output always.
if there are two possible inputs then the output is one, for example -2 and +2 x^2 is 4.
is that a function still.?
Dr. Bazett, what type of camera and software are you using? I’m beginning my math Masters this fall and would like to make similar videos! Thank you. I love your work!
Thanks for the amazing video. I have a question about the term “random function”. I was thinking about this as you spoke on the two properties of a function (i.e., it needs to do something to an input and the same output should always map to the same output). When I think of people saying “P(x) is a random function”, then to me it sounds like we cannot verify if the same input maps to the same output, which would imply that we can’t call it a function. Would it be more correct to say that the input is random (i.e., we cannot deterministically predict the input) as opposed to calling a function “a random function”? To use your analogy of the machine that spits something out, would it be more correct to say that the machine (function) isn’t random, but instead we don’t know what we’re putting into the machine? I hope my question makes sense :p
Not a mathematician, more of a computer science person, but I would say yes it is a function for most pseudo-random generators. In the programming world at least, the random function is magic, because you usually call it like this: random() and somehow even without any inputs, you will always get an output! However, the reality is that there is a hidden internal input value that it uses to calculate the next value (for pseudo-random functions at least).
If you are using a pseudo-random function, then it uses some internal seed value as the input. Based on the seed value it calculates the next value, then stores that calculated value to calculate the third value, etc. Thus, if you know the seed or current value, then you can always predict the output as the output is deterministic. In this case, you could argue that it is a function if you treat the seed as the input and pretend it's sort of a "pausable" function, where you can resume it each time you want a new output. Since pseudo-random generators are deterministic, random(seedValue=3) might always give you the value 7. If you know the algorithm, you could fully determine the codomain and range of the random function.
That being said, there are some "true" random functions like quantum random generators. Since these are inherently non-deterministic and don't operate on hidden inputs/seed values (as far as we know at least), then those cannot be considered as functions. It could be possible that you get the same output given the exact same physical conditions (the input) due to the nature of quantum randomness. In this case, since one input can have many output values, this is not really a function.
In either case, calling it a random function or truly random is just a matter of convenience. For the most part, true randomness won't change anything compared to pseudo-randomness, but if it does, in that case, yes, you'd call a pseudo-random function a random function but designate a quantum number generator as a true random input.
how to find shortest distance
how about sqrt(4) it is two corresponding output -2 and 2
sqrt() gives the positive square root only by definition. For example,
x² = 4
x = +- sqrt(4) = +-2
thank you sir.....
Sir one question
From which book I practice questions
I like open discrete math by levin, it's free!
Thanks, great video. I'm just so curious, are you writing backwards??
I was wondering the same since I started watching this tutorials
0:35 Just wanna know how to draw that perfect parabola... with right hand...
Could you please explain the case for sqrt(x) or a circle.
these equations do not follow verticle line rule. So are they not funtions?
Thanks in advance :)
A function by definition maps values from argument x into one output y. The square root of 4 can be -2 and 2, so violtes function definition, in math sense. Abs(sort(x)) is a fine function though.
I've never been taught anything about functions and single line test. I feel like I'm missing videos or just classes, in general.
Thank youuu
2 sets with 1-1 correspondence - sounds better and is more correct than input-output analogy which too simplistic to be truth
Then the function of a circle ? Isn't a real function?
That's why it's called the equation of a circle, as opposed to a function
If you want a function that gives a circle then make your domain 0 to 2pi and go for polar coordinates:
f(angle) = radius
Three years late!
naw
·mahn·kla·chr?
Your function can't square an apple or a dog. Lame. Was looking forward to that.
i wish!
you can, but it will output Motts, and meat, respectively.