Isn't Calculus just about the greatest thing ever?

[Sarg338]

[Sarg338]

[THABEAST721]

We are finally getting into actual calculus in my multivariable calc class. We just touched limits of functions of more than one variable, and it's pretty interesting. Hopefully it doesn't lose its appeal due to being incredibly difficult though.
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[THABEAST721]

We are finally getting into actual calculus in my multivariable calc class. We just touched limits of functions of more than one variable, and it's pretty interesting. Hopefully it doesn't lose its appeal due to being incredibly difficult though.
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[bclare]

[bclare]

[THABEAST721]

Yeah visualizing really helps a lot. I impressed my teacher by solving a problem of finding the line that goes through a certain point and is perpendicular to a given line in 3-space with a clever solution he didn't think of. I'm not trying to brag or anything, but I just thought that was really freakin' sweet. I feel like I have the vectors and visualization down, so I guess I will have some fun in this class.
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[THABEAST721]

Yeah visualizing really helps a lot. I impressed my teacher by solving a problem of finding the line that goes through a certain point and is perpendicular to a given line in 3-space with a clever solution he didn't think of. I'm not trying to brag or anything, but I just thought that was really freakin' sweet. I feel like I have the vectors and visualization down, so I guess I will have some fun in this class.
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[THABEAST721]

Would it be possible for anyone to explain this solution to me? I don't really understand what they are talking about.





With a binary operation being something like addition, subtraction, multiplication, division, modulo, or something custom. If someone could give me an explanation that would be great. Maybe you could explain it if the only 4 operations were addition, subtraction, multiplication, and division, and extend it to a more general sense or something like that?
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[THABEAST721]

Would it be possible for anyone to explain this solution to me? I don't really understand what they are talking about.





With a binary operation being something like addition, subtraction, multiplication, division, modulo, or something custom. If someone could give me an explanation that would be great. Maybe you could explain it if the only 4 operations were addition, subtraction, multiplication, and division, and extend it to a more general sense or something like that?
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[bclare]

A binary operation is a mapping from S x S to S (where x here means cross)

I'm going to call my operation *, because my keyboard doesn't have a button for (plus sign inside a circle)

We're implicitly only concerned with closed operations, where a*b = x and as long as a and b are in S, so is the product/sum/whatever x.

This is equivalent to saying (a,b)-> x, the ordered pair (a,b) maps to x.

This is very general, so we aren't assuming that * is symmetric/commutative.

Basically what is being said is that however big the set S is, we can make a *-table that'll be n rows by n columns, for n^2 total entries. Each of those entries could be any of the elements from n. (n^2) choices to make, n options each, so it's n^(n^2).


Here's a small example. Say we take the set S = {0,1}. Standard addition isn't even a binary operation on this set (1+1=2 is not in S) but multiplication is, and it looks like this

(assume this is a table with rows and columns both labeled 0 and then 1)

0 0
0 1

But I could define another operation on S like this

a*b = 1 for all a,b in S

1 1
1 1

or another operation

a*b = 0 for all a,b in S

0 0
0 0

Or I could give operations which don't even have a single general rule, just a direction for each particular case:

0*0 = 0
0*1 = 1
1*0 = 0
1*1 = 1

0 1
0 1


Etc. I hope it's clear that there are 2^4 possible tables that can be made here, and the general case is just with n not necessarily equal to 2


edit note: We're also talking about distinct operations of course.
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[bclare]

A binary operation is a mapping from S x S to S (where x here means cross)

I'm going to call my operation *, because my keyboard doesn't have a button for (plus sign inside a circle)

We're implicitly only concerned with closed operations, where a*b = x and as long as a and b are in S, so is the product/sum/whatever x.

This is equivalent to saying (a,b)-> x, the ordered pair (a,b) maps to x.

This is very general, so we aren't assuming that * is symmetric/commutative.

Basically what is being said is that however big the set S is, we can make a *-table that'll be n rows by n columns, for n^2 total entries. Each of those entries could be any of the elements from n. (n^2) choices to make, n options each, so it's n^(n^2).


Here's a small example. Say we take the set S = {0,1}. Standard addition isn't even a binary operation on this set (1+1=2 is not in S) but multiplication is, and it looks like this

(assume this is a table with rows and columns both labeled 0 and then 1)

0 0
0 1

But I could define another operation on S like this

a*b = 1 for all a,b in S

1 1
1 1

or another operation

a*b = 0 for all a,b in S

0 0
0 0

Or I could give operations which don't even have a single general rule, just a direction for each particular case:

0*0 = 0
0*1 = 1
1*0 = 0
1*1 = 1

0 1
0 1


Etc. I hope it's clear that there are 2^4 possible tables that can be made here, and the general case is just with n not necessarily equal to 2


edit note: We're also talking about distinct operations of course.
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[slfan68]

So I'm in Math 122 here at my University, which is basically Calculus I and is also a M Tu W Th F course. However, I have quite possibly the worst teacher ever to teach at all. I took Calculus in high school last year, so I have a pretty good idea of how things work. However, she does not explain things like theorems at all. She writes them on the board and then proceeds to just working out problems. AND THEN, when she's working out problems on the board, she will, multiple times per class, make very stupid mistakes yet she continues to work the problems. Sometimes we catch her mistakes as soon as she makes them, but often if she makes a mistake on something she is just teaching us, there's no way we can know that she's making a mistake. AND THEN (it gets more cool), on tests we are given some of the most ridiculous problems she can think of. Problems that, instead of testing that we know the Calculus concepts, instead end up testing how well we can do extensive amounts of Algebra. And we aren't allowed to use calculators of any kind. The combination of ridiculous problems with an incapable teacher make this the biggest joke of a class I've ever seen. However, I need to somehow pull my grade up to at least a B, or I'm going to risk losing my scholarship. So frustrating

EDIT: I forgot to mention the teacher is on academic probation from the University for having consistently terrible pass/fail rates in her classes. Just one more thing to make me love college -.-
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[slfan68]

So I'm in Math 122 here at my University, which is basically Calculus I and is also a M Tu W Th F course. However, I have quite possibly the worst teacher ever to teach at all. I took Calculus in high school last year, so I have a pretty good idea of how things work. However, she does not explain things like theorems at all. She writes them on the board and then proceeds to just working out problems. AND THEN, when she's working out problems on the board, she will, multiple times per class, make very stupid mistakes yet she continues to work the problems. Sometimes we catch her mistakes as soon as she makes them, but often if she makes a mistake on something she is just teaching us, there's no way we can know that she's making a mistake. AND THEN (it gets more cool), on tests we are given some of the most ridiculous problems she can think of. Problems that, instead of testing that we know the Calculus concepts, instead end up testing how well we can do extensive amounts of Algebra. And we aren't allowed to use calculators of any kind. The combination of ridiculous problems with an incapable teacher make this the biggest joke of a class I've ever seen. However, I need to somehow pull my grade up to at least a B, or I'm going to risk losing my scholarship. So frustrating

EDIT: I forgot to mention the teacher is on academic probation from the University for having consistently terrible pass/fail rates in her classes. Just one more thing to make me love college -.-
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[THABEAST721]

Ok I think I understand it a bit better now. I will be relearning this stuff next semester in an actual math class, so I will probably understand it a lot better then. Learning math in a computer science class just doesn't achieve much. We are getting into combinatorics, but the teacher doesn't really teach anything; we are just expected to already know a lot about them, and apply them to algorithms. Right now, the math class I am taking (other than calculus) is an intro to mathematics class, and we have just finished learning the basics of sets. So this stupid discrete math course for computer science is ahead of that class, and the teacher is not all that great; he's one of those guys who hates teaching but works at the university for a good opportunity for research.

But anyway, I think I understand it better now, so thanks for that.
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[THABEAST721]

Ok I think I understand it a bit better now. I will be relearning this stuff next semester in an actual math class, so I will probably understand it a lot better then. Learning math in a computer science class just doesn't achieve much. We are getting into combinatorics, but the teacher doesn't really teach anything; we are just expected to already know a lot about them, and apply them to algorithms. Right now, the math class I am taking (other than calculus) is an intro to mathematics class, and we have just finished learning the basics of sets. So this stupid discrete math course for computer science is ahead of that class, and the teacher is not all that great; he's one of those guys who hates teaching but works at the university for a good opportunity for research.

But anyway, I think I understand it better now, so thanks for that.
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[GlassDragon]

Combinatorics and set theory are common introductory topics in math but they can be intuitively very difficult. You have to watch out for ordered vs. unordered sets as well as with/without replacement. Overall one of the most irritating "easy" math topics.
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[GlassDragon]

Combinatorics and set theory are common introductory topics in math but they can be intuitively very difficult. You have to watch out for ordered vs. unordered sets as well as with/without replacement. Overall one of the most irritating "easy" math topics.
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[bclare]

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[Brockbfball1563]

I can't be the only one who like's Calc but absolutely DESPISES linear algebra. Seriously, anything where I have to deal with vectors just makes me want to quit everything.
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[Brockbfball1563]

I can't be the only one who like's Calc but absolutely DESPISES linear algebra. Seriously, anything where I have to deal with vectors just makes me want to quit everything.
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[Sixen]

[Sixen]

[conlan22]

[conlan22]

[bclare]

I didn't pay much attention in linear algebra when I took it, but I like it a lot more now. Calculus is kinda boring honestly, it's too methodical, you can get all the right answers without really understanding what you're doing. Linear algebra you actually have to understand what's going on; of course that means it's even more of a pain if you have a crappy teacher.
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[bclare]

I didn't pay much attention in linear algebra when I took it, but I like it a lot more now. Calculus is kinda boring honestly, it's too methodical, you can get all the right answers without really understanding what you're doing. Linear algebra you actually have to understand what's going on; of course that means it's even more of a pain if you have a crappy teacher.
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[-Sparks-]

I REALLY like math. Always liked it my whole life, I'll never forget my 770 score on the Math SAT's (missed one question... FFFFFFFFFFFFFUUUUUUUUUUUUUUUUUUUUUU...)

But how do I deal with a teacher who cancels class half the time? We have four units to cover in our calc III class. We started on Aug. 31, have only six class sessions left (twice per week) and we haven't even taken the second test yet... >_< I've taught myself to teach out of the book, like I can just "get" the concepts without any additional assistance besides the textbook. (Taught myself gradients and iterated integrals today, I find it fascinating that math seems to be a never-ending learning process, and I never wanna stop learning.) So I don't need a teacher to learn, but I still gotta take the tests just like everyone else. He always starts teaching 20 minutes late too. It'a a shame that my learning of math is slowed by this.

I had this same teacher for Calc II, and we missed so much class time that we had to drop parametric equations, the disk/shell methods, and quite a few other things. And parametric equations are essential in Calc III... I'm just hoping something really stupid doesn't happen like I'll have to repeat Calc III only because of my teacher canceling half the classes, which I have no control over (I already have to take a credit overload next semester...) And if he just bags some of the later material, I (and the rest of my class) will probably encounter that material later in our studies and have no fucking clue what it means.

As far as actual math goes, as much as I like math... fuck finding the normal vector to a vector-valued function at given points. There's so much to calculate and it's some of the hardest algebra I've ever seen... the tangent vector, the derivative of the tangent vector, the magnitude of the derivative of the tangent vector... with trigonometry it's not so bad cause of trig identities, but for algebraic functions... just no.

(Also I'm taking Linear Algebra next semester, I know it involves matrices but other than that I don't know what to expect...)
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"Listen, Harvard. I'm a billionaire. And most of you are gonna graduate, and move back in with your parents! I'm gonna tell you somethin', though. We [all] have something in common: we're all gonna die. No matter whatcha' do, no matter whatcha' do with your lives, you're dead! You're dead! You're dying. You're gonna die, all of you, dead. You, dead. You, dead, all of you."
-Nathan Explosion

[-Sparks-]

I REALLY like math. Always liked it my whole life, I'll never forget my 770 score on the Math SAT's (missed one question... FFFFFFFFFFFFFUUUUUUUUUUUUUUUUUUUUUU...)

But how do I deal with a teacher who cancels class half the time? We have four units to cover in our calc III class. We started on Aug. 31, have only six class sessions left (twice per week) and we haven't even taken the second test yet... >_< I've taught myself to teach out of the book, like I can just "get" the concepts without any additional assistance besides the textbook. (Taught myself gradients and iterated integrals today, I find it fascinating that math seems to be a never-ending learning process, and I never wanna stop learning.) So I don't need a teacher to learn, but I still gotta take the tests just like everyone else. He always starts teaching 20 minutes late too. It'a a shame that my learning of math is slowed by this.

I had this same teacher for Calc II, and we missed so much class time that we had to drop parametric equations, the disk/shell methods, and quite a few other things. And parametric equations are essential in Calc III... I'm just hoping something really stupid doesn't happen like I'll have to repeat Calc III only because of my teacher canceling half the classes, which I have no control over (I already have to take a credit overload next semester...) And if he just bags some of the later material, I (and the rest of my class) will probably encounter that material later in our studies and have no fucking clue what it means.

As far as actual math goes, as much as I like math... fuck finding the normal vector to a vector-valued function at given points. There's so much to calculate and it's some of the hardest algebra I've ever seen... the tangent vector, the derivative of the tangent vector, the magnitude of the derivative of the tangent vector... with trigonometry it's not so bad cause of trig identities, but for algebraic functions... just no.

(Also I'm taking Linear Algebra next semester, I know it involves matrices but other than that I don't know what to expect...)
_________________

"Listen, Harvard. I'm a billionaire. And most of you are gonna graduate, and move back in with your parents! I'm gonna tell you somethin', though. We [all] have something in common: we're all gonna die. No matter whatcha' do, no matter whatcha' do with your lives, you're dead! You're dead! You're dying. You're gonna die, all of you, dead. You, dead. You, dead, all of you."
-Nathan Explosion