calculus as window into Buddhism is a narrow engineering perspective?
Calculus vs Statistics
- Thread starter Septimus Prime
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calculus as window into Buddhism is a narrow engineering perspective?
"That stem all converges into calculus , and ai is just prob and stats"
Seems like engineering colloquialisms
Seems like engineering colloquialisms
Since you can't understand probability or statistics without calculus, it's probably more important to study calculus. However, combinatorics and discrete mathematics (including basic probability theory) should be better integrated into pre-college education in the US.
I have studied and implemented convolutional neural networks myself, I can assure you it is probability and statistics.
Also, I am not an engineer. I am a computer scientist.
you need to learn calculus first to understand Bachelor level prob&stat course. You also need to learn calculus to understand basically most courses in science and engineering and even beyond that. It's the basis of pretty much everything. With that said after you graduate, statistics and your data presentation skills on top of that are far more useful skills but you need to get there first.
For daily use? Statistics. It's important to understand, at least qualitatively, sample sizes, normal distributions, standard deviations, and basic probability. We have so much data being thrown at us from news articles, blogs, forum posts, etc. that it's helpful to think about both what the data means and how it's represented. I think calculus is much more interesting though.
On a somewhat related note there is an ongoing debate on the most effective way to teach calculus. Historically it has been a taught as pattern-recognition - recognize the type of problem and choose a technique from the toolbox. But these methods only work for certain problems. With the advent of Mathematica and other symbolic computation programs there has been an increased interest in numerical techniques that apply to all problems. It will be very exciting to see how the old pen-and-paper techniques are balanced with the numerical methods in the upcoming years.
On a somewhat related note there is an ongoing debate on the most effective way to teach calculus. Historically it has been a taught as pattern-recognition - recognize the type of problem and choose a technique from the toolbox. But these methods only work for certain problems. With the advent of Mathematica and other symbolic computation programs there has been an increased interest in numerical techniques that apply to all problems. It will be very exciting to see how the old pen-and-paper techniques are balanced with the numerical methods in the upcoming years.
Calculus is important for STEMy fields, Statistics is important for life. So yeah, if we can only teach one, Statistics all the way.
Although I was always amused that, at least in my college, calculus wasn't considered "real" math. As in, the math majors were doing discrete and number theory and stuff, and the calculus courses were more for physics and engineering majors.
Although I was always amused that, at least in my college, calculus wasn't considered "real" math. As in, the math majors were doing discrete and number theory and stuff, and the calculus courses were more for physics and engineering majors.
Good for you, ai is not just cnn's
It includes plenty of work all over mathematics and understanding why cnn's even work isn't a well understood problem so I doubt you know what the hell you're talking about
For instance, You can pose a lot of learning problems through differential geometry lens and go from there
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Probability and statistics, and calculus itself, describes work "all over mathematics," whatever you think you're describing is not at all mutually exclusive with calculus.
...differential geometry is a method to model probability and statistics.
Definitely statistics. I have a math degree, and while calculus is fantastic for fundamentally understanding a lot of things that exist in the world, statistics is something people are more likely to actually USE and ENCOUNTER on a daily basis.
If you're going to be imprecise and just say calculus is everywhere so everything is calculus, you might as well just say math is important.
Calculus is what you spend 15 years studying math for. Algebra, Geometry, Trigonometry all come together. I loved those courses so much.
So you've gone from saying my view of maths is "narrow, engineering specific" to now "imprecise" and overly broad?
I'm not being imprecise, btw. I'm using the very definition of calculus: the study of change. Notice how the post you are upset about said most (not all) and I even provided, in the preceding post, a STEM/Math subject that ISN'T the domain of calculus (i.e. boolean algebra). Dunno what you're going on about.
Let's just agree to disagree
Mostly the narrow perspective was precisely
Stem converge to calculus
And AI is just prob and stats
That's only true if you blanket calc as everything and just wrong for the AI statement, it comes off like a engineer's view of mathematics
Stem converge to calculus
And AI is just prob and stats
That's only true if you blanket calc as everything and just wrong for the AI statement, it comes off like a engineer's view of mathematics
Yes, I understood how you disagree, hence why I said let's agree to disagree. You have noted over several posts that you think I'm being too broad, clearly I disagree but I saw them, given how I responded to them directly. No need to further clarify.
That's generally called information geometry , these things have names for a reason
Either way, you can use many formalisms to solve a problem, that doesn't make them the same field
I have no idea. When I was in high school most of us only took Algebra 1 lol. You only took pre cal or something if you were considered advanced in math. Curriculum has changed a lot.
The most difficult math I use irl is figuring out a certain percentage of a total so I know how much to tip lol.
The most difficult math I use irl is figuring out a certain percentage of a total so I know how much to tip lol.
I don't think calculus is relevant for most people. It would make more sense as a first year requirement for STEM majors at university.
Stats is much more urgent and should be learneD as early as possible.
Stats is much more urgent and should be learneD as early as possible.
Also an engineer. As much as I love calculus a fundamental understanding of statistics would really help this world.
AI uses a lot of calculus or techniques that form the basis of calculus. Basically all forms of function optimization on a computer are the result of iterative applications of the derivative!
I think the mathematics progression is effective, but it can feel disjointed in the beginning. Here's how I think of it:
Arithmetic (how to add, subtract, multiply, divide 1, 2, 3...)
Algebra (arithmetic but with a, b, c...)
Trigonometry (application of algebra to triangles)
Analytic Geometry (application of algebra to Cartesian coordinates, including triangles)
Calculus (application of algebra to rates of change and areas - can be applied to objects from trigonometry and geometry)
Linear Algebra (more in depth look at linear equations from algebra - can be taken directly after algebra, but can be applied to problems from geometry and calculus)
There are also multiple levels of courses. For example, calculus is encountered later in studies as real analysis.
My main problem with this configuration is that the math I actually, really really wanted to learn, I didn't wind up learning until super late in college, purely by chance. Turns out, boolean algebra really doesn't fall very neatly into that structure, and as I'd been programming since I was a kid, that was something I didn't even know I wanted to know. I actually wound up taking boolean algebra by chance to fill a math requirement (so I wouldn't have to take differential calculus, actually) and it was like drinking a huge gulp of cool water. Honestly one of my favorite classes I ever took at any level of school.
I really don't have much of a solution for the progression of math, other than to say I felt like it was very wrong for how I learned growing up.
Boolean algebra would fit after algebra. If you don't mind answering, what were the prerequisites for boolean algebra at your school?
Well, they flat out didn't offer it in my highschool, but they offered calc 1 (integrated) and calc 2 (differential) and trig. At UT, there were no prereqs for Boolean Algebra IIRC. But my major, comp sci, didn't recommend it, they recommended multiple calculus courses. That boolean algebra course came at just the right time and really bridged a lot of gaps in knowledge for me and made later EE courses I took outside my major actually doable. That class laid a lot of ground work for me to go off in a direction I had been wanting to go in for a very long time.
It was a from the ground up course assuming no knowledge of boolean algebra, it was one of the best taught classes I ever took. The professor who taught me was really great.
In primary school: calculus, just because its pretty much a prerequisite for learning even the simplest Newtonian physics. And ideally you'd want to get this prerequisite done as fast as possible so you can actually start learning proper physics as early as possible.
Calculus is also pretty much a prerequisite for a lot of statistics. Even something as simple as the expected value of a continuous distribution is defined as the integral of the probability density function of the distribution. So learning calculus first seems like a good idea even if you want to learn statistics.
In both of these cases, schools try to get around it by using weird, mathematically incorrect tricks. And in my experience, all that did was completely confuse me because the way physics were taught just didn't make any sense from a mathematical point of view. No wonder most people get the impression that physics is just about memorizing equations when the education system fails to give them the tools to actually understand where these equations come from.
Calculus is also pretty much a prerequisite for a lot of statistics. Even something as simple as the expected value of a continuous distribution is defined as the integral of the probability density function of the distribution. So learning calculus first seems like a good idea even if you want to learn statistics.
In both of these cases, schools try to get around it by using weird, mathematically incorrect tricks. And in my experience, all that did was completely confuse me because the way physics were taught just didn't make any sense from a mathematical point of view. No wonder most people get the impression that physics is just about memorizing equations when the education system fails to give them the tools to actually understand where these equations come from.
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If you are going to do math/engineering/physics, probably calculus (but it's kind of a moot point because you are going to learn statistics too).
For normal people, I think statistics is far more important. More people need to think of the world as a stochastic system.
For normal people, I think statistics is far more important. More people need to think of the world as a stochastic system.
I have a physics Ph.D, but I'd probably pick stats. Even the physics actually turned into stats at some point for me though :) tinged with lots of calc. But since I left the field I hit stats a lot and calculus... basically never. You're bombarded by statistics constantly.
If you're in any technical/science job Calculus, everything else Statistics. As far as importance goes I'd say Calculus, once you get it more or less the world really opens up to you. Stats are important though, I would say it's not a matter or choosing what but when. Everybody should know them at a basic level.
If I had to choose between calculus and statistics, I would opt for statistics, because while the two are mostly unrelated in low-level math, statistics is much easier to create an intuition for in people who don't have a solid foundation in math, because it's entirely derived and expressed by counting. It's something that might take a little time to come around to, but is immensely important, especially as statistical methods are used just as much as higher math in all areas of science.
BUT if I were not constrained to those two choices, I would actually say some kind of linear algebra instead, over both stats and calculus, as it can be taught without any calculus, and as a subject it's so essential to other areas of math that it seems criminal to wait so long before actually delving into it.
BUT if I were not constrained to those two choices, I would actually say some kind of linear algebra instead, over both stats and calculus, as it can be taught without any calculus, and as a subject it's so essential to other areas of math that it seems criminal to wait so long before actually delving into it.
What type of primary school teaches statistics or calculus. I saw calculus for the first time in high school and statistics only in second year of university.
I took both. We should all take both.
I think calc is more important to develop problem solving ability. It's more challenging in general.
Statistics is fairly cut and dry (at least at the intro levels). I had 1 semester of it and it was enough. Although I retook it in college and it is indeed very useful.
I think calc is more important to develop problem solving ability. It's more challenging in general.
Statistics is fairly cut and dry (at least at the intro levels). I had 1 semester of it and it was enough. Although I retook it in college and it is indeed very useful.
Definitely stats, and I say that as an engineer. Also, analysis is a much better name than calculus.
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until recently it was only really taught at alevels. it's stuff like differentiation and integration.
Calculus is awesome. Take calculus and a physics class then watch the world open up.
But also why not both? People should learn all sorts of things and it shouldn't be limited to things that are useful for jobs.
But also why not both? People should learn all sorts of things and it shouldn't be limited to things that are useful for jobs.
I legit thought stats was boring. Took Calc 1 in high school. Got my math minor along with my bachelor's in college (took Calc 1, 2, 3, linear algebra and stats).
In high school, I took physics and calc at the same time and I really wanted to do the math from Calc class in Physics (instead of how they taught it in Physics class), but they wouldn't let me.
In high school, I took physics and calc at the same time and I really wanted to do the math from Calc class in Physics (instead of how they taught it in Physics class), but they wouldn't let me.
Basic stats is far more important then basic calc for the average joe.... but you need to have a good understanding of calc to get anything more out of stats so let's call it a wash.
calculus is useful for mechanical and electrical engineering, and a tiny tiny bit in microeconomic modeling
statistics is useful in every natural and social science, finance and economics, and in not becoming a sucker
statistics is more useful than calculus in general. yall should learn both though
discrete/combinatorial math and number theory and Boolean algebra are all more useful than calculus or trigonometry also
statistics is useful in every natural and social science, finance and economics, and in not becoming a sucker
statistics is more useful than calculus in general. yall should learn both though
discrete/combinatorial math and number theory and Boolean algebra are all more useful than calculus or trigonometry also
As someone who took classes for both, I always found statistics to be the most useful in day-to-day life. Being able to accurately interpret studies, polls, historical data, and trends is something every adult needs to do.
I'm really good at calculus but absolutely hate statistics.
My personal bias aside, I can see how statistic might actually be more useful in general.
My personal bias aside, I can see how statistic might actually be more useful in general.
Calculus was the only time I enjoyed math class. Statistics is more useful though.
I don't often use more than basic algebra day to day, so calculus doesn't come up often.
I don't often use more than basic algebra day to day, so calculus doesn't come up often.
They should leave these until college when they're optional and not make everyone do them in school.