Iam 48 --ooh--long time to understand things!!!despite a degree in Agric.and MSc.in Agric Economics , A MSc.in Informatics, yet u r the first ever Professional--found in the mist--- tutuor who could tell me simply best ever words on functions.Pls something on use of boolean algebra or automata if u can. Thanks alot...
@khalifamak123 That's a different request! Automata? Do you want explanations outside of computer science? I guess I think of those subjects as having countless practical applications, but "practical" means programming. I am, however, not a computer scientist.
this is great video and totally agree with you one this a lot of people i talk to dont like maths because tehy think alegbra has no use and they lose interest when they reach things they see no use for in their everyday lives so this is a brilliant idea but then why learn to rationalize the denominator it isnt really used because the other from is still correct so people can argue why does this matter
@MathMikie Of course my conclusion is that they shouldn't. Don't rationalize the denomintor. It's an algebraic trick that actually turns out to be useful for finding the multiplicative inverse of a comple number, but I'm comfortable with showing that trick to the people who need it. And it will not be difficult for them.
I'm all for getting rid of useless, antiquated tricks.
@andreasox23, Thanks! Glad you like them. I see you are subscribed to ViHart. Very wise. George Hart is terrific too, but I don't even know if he's on youtube. Beautiful math.
For grass problems use a scythe :) It does not mater if it is long or wet actually the better the longer the grass is. Sorry for my redneck observation. These vids really have a great deal of info on how to present a problem to people and how to make them think. Thanks for sharing
@VikingNightmare Yeah, but that would take ten times as long. And I'd have blisters when I was finished. I prefer to be able to think about math while I'm mowing.
i'm in my final year of university majoring in math and i'm tutoring some teens as well. I try to figure out ways to explain concepts to them in a way they would understand and i must say you make it look so easy, i just love the way you explain things. i wish you were my teacher and can't wait for your next videos
i'm in my final year of university majoring in math and i'm tutoring some teens as well. I try to figure out ways to explain concepts to them in a way they would understand and i must say you make it look so easy, i just love the way you explain things. i wish you were my teacher and can't wait for your next videos
@ninjaprincess87, I'm glad you like them. I hope you are just starting a life long journey of helping people understand math. We sure need more people doing it.
You say that "function" is suppose to make sense to students, are they suppose to be born with this knowledge? I heard you describe how you could take some concrete situations an create a correspondence between them and numbers, and you showed a rule that might be used to describe a function, but I never really saw/heard you say what a function is. I'm thinkin you probably know since you teach college algebra, but I'm not sure. How bout a precise mathematical definition? no hand waving.
You can find the precise definition in written words in the info to the right of the video. You need to cllck on "more info" to see it, I believe.
To be really precise, however, we need to discuss the definition of "relationship." Really, the definiton (if you want it at this level of detail) of a function from set A to set B is a subset of AxB such that for each element a of A there is an element of AxB with first term a. That is there exists a b in B such that (a,b) is in the function.
For the audience I have in mind for these videos, I find that such a definition is much more of a hindrance to understanding than a help. That's why I focus on how the concept of function is one that is very intuitive and should make common sense to people. The precise definition is intended to have only clear, unambiguous terms and loses some of the intuitive nature when you first see it.
So is this the way you teach? Is instantiation of the definitions of , AXB... then relation.... then function are these your first primary objectives when teaching functions? Why was there none of this in the video?
No, as I said I would not teach it that way for the audience I have in mind for this video. Nor do I teach it that way for my College Algebra classes. I do teach it that way for my intro math major class. The precision needed to do mathematical proofs is wonderful (my favorite) but is not needed for most people. I consider it a hindrance to their learning. The word "relationship" is clear enough for mathematical modelling.
No. "Everyone that is tan, plays tennis" is a proposition (a logical statement which is either true or false). That is a false statement.
I could make a function though...T=f(t) where T is how tan you are, and t is how long you have been in the sun. I'm not sure what the units of T would be. How does one quantify how tan someone is? By shade?
One of my math teachers mentioned a use for rationalizing denominators. If you try to estimate 5/sqrt(2) in your head you may run into difficulties. Even if you estimate sqrt(2) as 1.41, who knows what 5/1.41 is? 5/sqrt(2)=5sqrt(2)/2, so your left trying to find 5*1.41/2. I can do that in my head, 5*1.41/2=7.05/2=3.525. My teacher also said that computers can more efficiently compute expressions with rationalized denominators, which can be important for computer programing, or something....
Yes, that's exactly the reason why people still do it. Or, it's historically the reason why it was done, and we still do it because that was what was done. But is there really a point to that still?
I hadn't really thought about the point about the efficiency in computing. That's cool, but is a topic that could easily be taught in and advanced computer science class where it would actually be useful.
It's just an anachronism today that gets in the way of true understanding.
Maybe you could weight the grass that could probably account for both height and wetness and be easier to measure. Say just mow a square meter and weight the cuttings then use that to calculate.
Also sharpen your mower blades and you won't have that problem so much.
So you're saying that the length of time really is just a function of one quantity, weight of the grass. That's an interesting theory. I don't think it jibes with my impression. The water's surface tension is the problem, not the added weight. It sticks to the blades and clogs up the path for dispelling the grass. But we could certainly test our mathematical models to see which predicts better.
Iam 48 --ooh--long time to understand things!!!despite a degree in Agric.and MSc.in Agric Economics , A MSc.in Informatics, yet u r the first ever Professional--found in the mist--- tutuor who could tell me simply best ever words on functions.Pls something on use of boolean algebra or automata if u can. Thanks alot...
khalifamak123 9 months ago
@khalifamak123 That's a different request! Automata? Do you want explanations outside of computer science? I guess I think of those subjects as having countless practical applications, but "practical" means programming. I am, however, not a computer scientist.
jamesblackburnlynch 9 months ago
this is great video and totally agree with you one this a lot of people i talk to dont like maths because tehy think alegbra has no use and they lose interest when they reach things they see no use for in their everyday lives so this is a brilliant idea but then why learn to rationalize the denominator it isnt really used because the other from is still correct so people can argue why does this matter
MathMikie 11 months ago
@MathMikie Of course my conclusion is that they shouldn't. Don't rationalize the denomintor. It's an algebraic trick that actually turns out to be useful for finding the multiplicative inverse of a comple number, but I'm comfortable with showing that trick to the people who need it. And it will not be difficult for them.
I'm all for getting rid of useless, antiquated tricks.
jamesblackburnlynch 11 months ago
I love your videos...
andreasox23 1 year ago
@andreasox23, Thanks! Glad you like them. I see you are subscribed to ViHart. Very wise. George Hart is terrific too, but I don't even know if he's on youtube. Beautiful math.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch yeah her videos are awesome, her daddy taught her well! his sculptures are beautiful.
andreasox23 1 year ago
For grass problems use a scythe :) It does not mater if it is long or wet actually the better the longer the grass is. Sorry for my redneck observation. These vids really have a great deal of info on how to present a problem to people and how to make them think. Thanks for sharing
VikingNightmare 1 year ago
@VikingNightmare Yeah, but that would take ten times as long. And I'd have blisters when I was finished. I prefer to be able to think about math while I'm mowing.
jamesblackburnlynch 1 year ago
A talking glossy-board, help!
PythonandCat 1 year ago
you should add one more var, the area of grass :))
good job.
Greetings from Poland (here math edu is too unlogical)
samorajp 1 year ago
GEE...i love ur explaination~~well done~~
jninlove 1 year ago
This has been flagged as spam show
i'm in my final year of university majoring in math and i'm tutoring some teens as well. I try to figure out ways to explain concepts to them in a way they would understand and i must say you make it look so easy, i just love the way you explain things. i wish you were my teacher and can't wait for your next videos
ninjaprincess87 1 year ago
i'm in my final year of university majoring in math and i'm tutoring some teens as well. I try to figure out ways to explain concepts to them in a way they would understand and i must say you make it look so easy, i just love the way you explain things. i wish you were my teacher and can't wait for your next videos
ninjaprincess87 1 year ago
@ninjaprincess87, I'm glad you like them. I hope you are just starting a life long journey of helping people understand math. We sure need more people doing it.
jamesblackburnlynch 1 year ago
Have to agree, rationalizing the denominator is pretty much useless.
Griever0510 2 years ago
You say that "function" is suppose to make sense to students, are they suppose to be born with this knowledge? I heard you describe how you could take some concrete situations an create a correspondence between them and numbers, and you showed a rule that might be used to describe a function, but I never really saw/heard you say what a function is. I'm thinkin you probably know since you teach college algebra, but I'm not sure. How bout a precise mathematical definition? no hand waving.
teachless 2 years ago
You can find the precise definition in written words in the info to the right of the video. You need to cllck on "more info" to see it, I believe.
To be really precise, however, we need to discuss the definition of "relationship." Really, the definiton (if you want it at this level of detail) of a function from set A to set B is a subset of AxB such that for each element a of A there is an element of AxB with first term a. That is there exists a b in B such that (a,b) is in the function.
jamesblackburnlynch 2 years ago
For the audience I have in mind for these videos, I find that such a definition is much more of a hindrance to understanding than a help. That's why I focus on how the concept of function is one that is very intuitive and should make common sense to people. The precise definition is intended to have only clear, unambiguous terms and loses some of the intuitive nature when you first see it.
jamesblackburnlynch 2 years ago
And, of course, I mean there is a UNIQUE b in B such that (a,b) is in the function.
jamesblackburnlynch 2 years ago
So is this the way you teach? Is instantiation of the definitions of , AXB... then relation.... then function are these your first primary objectives when teaching functions? Why was there none of this in the video?
teachless 2 years ago
No, as I said I would not teach it that way for the audience I have in mind for this video. Nor do I teach it that way for my College Algebra classes. I do teach it that way for my intro math major class. The precision needed to do mathematical proofs is wonderful (my favorite) but is not needed for most people. I consider it a hindrance to their learning. The word "relationship" is clear enough for mathematical modelling.
jamesblackburnlynch 2 years ago
so everyone that is tan play tennis? is that function?
sassa07 2 years ago
No. "Everyone that is tan, plays tennis" is a proposition (a logical statement which is either true or false). That is a false statement.
I could make a function though...T=f(t) where T is how tan you are, and t is how long you have been in the sun. I'm not sure what the units of T would be. How does one quantify how tan someone is? By shade?
jamesblackburnlynch 2 years ago
One of my math teachers mentioned a use for rationalizing denominators. If you try to estimate 5/sqrt(2) in your head you may run into difficulties. Even if you estimate sqrt(2) as 1.41, who knows what 5/1.41 is? 5/sqrt(2)=5sqrt(2)/2, so your left trying to find 5*1.41/2. I can do that in my head, 5*1.41/2=7.05/2=3.525. My teacher also said that computers can more efficiently compute expressions with rationalized denominators, which can be important for computer programing, or something....
Desrathedemon 2 years ago
Yes, that's exactly the reason why people still do it. Or, it's historically the reason why it was done, and we still do it because that was what was done. But is there really a point to that still?
I hadn't really thought about the point about the efficiency in computing. That's cool, but is a topic that could easily be taught in and advanced computer science class where it would actually be useful.
It's just an anachronism today that gets in the way of true understanding.
jamesblackburnlynch 2 years ago
I'm with JBL on this one, rationalizing a denominator is very, very impotent. LOL
no kiddin
teachless 2 years ago
Maybe you could weight the grass that could probably account for both height and wetness and be easier to measure. Say just mow a square meter and weight the cuttings then use that to calculate.
Also sharpen your mower blades and you won't have that problem so much.
ArchNME 2 years ago
So you're saying that the length of time really is just a function of one quantity, weight of the grass. That's an interesting theory. I don't think it jibes with my impression. The water's surface tension is the problem, not the added weight. It sticks to the blades and clogs up the path for dispelling the grass. But we could certainly test our mathematical models to see which predicts better.
My mower is brand new. No luck.
jamesblackburnlynch 2 years ago
Ohhhh math.
:)
MrBook8 2 years ago
Is there a tune that goes with that? Oooooooooooo math!
jamesblackburnlynch 2 years ago
There is, sort of.
/watch?v=bxAYHOWxGi8
By the way, I found a great way to apply integrals to one of my pastimes. Maybe I'll post a video about it sometime. ;)
ahypnos 2 years ago
I was thinking of this one:
watch?v=vXwfA5a-I3U&feature=PlayList&p=6B7B8A5ACECDC431&index=0
What is the pastime? Maybe I can guess the application.
jamesblackburnlynch 2 years ago