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Algebraic statistics formulae are available, not just for the Calculus. At my university they taught both.
There are no solutions, only trade-offs. - Thomas Sowell
A day can really slip by when you're deliberately avoiding what you're supposed to do.
- Calvin (Bill Watterson, Calvin & Hobbes)
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Maybe. Would learning to become proficient in a language like "R" actually teach the necessary subsets of Calculus used in the statistical packages available through the R libraries?
R (programming language) - Wikipedia[^]
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Not anymore than using a cake mix teaches someone how to bake a cake from scratch.
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PIEBALD is right. There's a difference between someone who knows what's going on under the hood and a script kiddie.
The difficult we do right away...
...the impossible takes slightly longer.
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I found that as the tick interval got smaller, and the corresponding frame rate got higher, all the computing seemed to get simpler. What can happen when you only move (at a rate of) a few pixels at a time?
"Before entering on an understanding, I have meditated for a long time, and have foreseen what might happen. It is not genius which reveals to me suddenly, secretly, what I have to say or to do in a circumstance unexpected by other people; it is reflection, it is meditation." - Napoleon I
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Universities would have to change their curriculum based on HS kids not having calc. I went to a small Catholic grade school which didn't get around to algebra by 8th grade. When I went to HS, I was behind a year in math, which means I never got to calc in HS. As a comp sci major at Penn State, I had to take three semesters of physics, starting first sememster. Well, Physics 101 required some calc. Fortunately I had a few friends who taught me enough calc to get by with a decent grade. If universities still expect a calc background leaving HS, this would be a disaster. Fast forward to today where my son is already taking calc as a junior in HS...
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PSU Steve wrote: As a comp sci major at Penn State...If universities still expect a calc background leaving HS
One would normally presume that to be successful in STEM university program that one should have at least already been excelling in that before.
But STEM is less that 20% of university degrees.
So attempting to require it all high school students both is not needed and is certain to cause problems for those that are not excelling in the pre-req math in the first place.
Might be better to discuss if universities should require all students to take some statistics rather than those that hypothetically require calculus now.
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swampwiz wrote: Statistics is the basis of Data Science
It is not clear to me how this statement is connected the posted link. I consider that term to be a specific type of profession/expertise. Certainly one is going to need a level of expertise in mathematics to specialize in Data Science.
But looking only at the article...
I doubt Calculus in any normal high school is on the standard curriculum path for most students.
So it is now and should remain for those that excel in that which came before.
In high school statistics should already be introduced in various science classes. And those and least some of them should already be on a standard curriculum path.
Not sure that I think that high school students should have a full class on just statistics.
Also not clear to me that a class just for programming for the standard curriculum is a good idea either.
I also question the implied assertion in the article that all students at a university will be required to take calculus. Googling (briefly) does not suggest that.
modified 9-Nov-23 13:46pm.
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I apply "data science" when the user says one thing, and the data and/or logs say another.
"Before entering on an understanding, I have meditated for a long time, and have foreseen what might happen. It is not genius which reveals to me suddenly, secretly, what I have to say or to do in a circumstance unexpected by other people; it is reflection, it is meditation." - Napoleon I
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A couple of things related to the referenced article:
1. the article is from 2014; world seems to be going the same even if high school curriculum didn't change in the last 10 years. Besides article was referring only to US and high-school curricula vary from place to place.
2. the author wants to introduce both statistics and computer science. As most of us, programming practitioners, would agree, there is no real "computer science"; just a bit of craftsmanship and flavor of the day buzzword(s) - structured, object-oriented, functional, agile, extreme, cloud, as-a-service, etc.
In the interest of full disclosure, I hold one of those "computer science" degrees. Uni taught me many things one of them being that computers are not (yet) a science.
One more example that maybe we shouldn't give much importance to journalists.
Mircea
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Mircea Neacsu wrote: computers are not (yet) a science.
Computer science is not programming. Computer science deals with algorithms, complexity, etc., and has a firm basis in mathematics. Programming, on the other hand...
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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While I see your point, allow me to argue that the vast majority of graduates of "computer science" programs will not practice the Computer Science you are talking about. Also I don't see how Computer Science would be taught at high school level. Nor do I see why it should.
Mircea
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Mircea Neacsu wrote: the vast majority of graduates of "computer science" programs will not practice the Computer Science you are talking about
Agreed. However, a competent programmer will have been exposed to the product of computer science. He/she/it will know algorithms, have some idea of their complexity (time, memory, etc.), and have an idea of when they should be used.
Mircea Neacsu wrote: Also I don't see how Computer Science would be taught at high school level.
Schools could use it to replace Latin as a subject that requires logic and discipline but is totally useless in the modern world. 
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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Daniel Pfeffer wrote: Schools could use it to replace Latin
De gustibus non disputandum est 
Mircea
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Daniel Pfeffer wrote: Computer science deals with algorithms, complexity, etc.
And the techniques used for creating computers. Time-sharing, data storage, etc.
Not so much applying computers to different domains.
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Define calculus.
I don't understand why double integrals are a required part of doing science.
Do I really need to know Euler projections to be able to reason about and collect data?
Or, how to formulate arguments for and against the calculation of an area, bounded by formula that contains i.
None of this has made me a better scientist.
Doing the legwork and chugging along until I gather enough high quality data, that's what made me a scientist.
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I think it's good to have some understanding of the maths which can be a tool in helping to show patterns in data - but in the end it still requires, or did require until the advent of AI, a human eye/brain/experience to be able to see patterns.
Maths is not my strong point and I used to work as a production analyst with medical data - I was able to spot trends in data that some of the more mathematically competent scientists were not able to spot because I knew how to plot the data in graphs and interpret the "story" the graph was telling.
Plotting data in graphs is something of a skill in itself as, depending on the choice of graph, trends can be exposed to the eye that even sometimes advanced statisticians cannot see in the raw figures.
“That which can be asserted without evidence, can be dismissed without evidence.”
― Christopher Hitchens
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Oh, we're talking about maths.
I see, I agree with that notion 100%.
It's probably lost in translation, but the difference between discrete calculus and theoretical calculus are like day and night. Calculus refers to theoretical calculus, no exceptions.
Or else my former professor will rise from the grave and fail me from beyond, just to spite me.
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Doesn't that assertion confuse statistics (data we have) with probability (data we should have got if it followed the rules) ?
Calculus follows the latter idea of `simple rules will predict complex data`.![Rose | [Rose]](https://codeproject.global.ssl.fastly.net/script/Forums/Images/rose.gif)
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it seems you have the answer to your own question .
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IF COVID taught us ANYTHING is that scientist rarely agree when they don't want to agree.
What I mean is this.
From the first data that the CDC posted many data scientists tracked projections and posted the results to have nearly everyone say they were wrong. I watched at virologists who had 1000's of case studies under their belts get slammed as quacks. I too ran the same calculations and came to the same conclusions and lost respect for people who just discounted the math out of hand.
Roll forward to just this year when the real final numbers came out and nearly all of the people who were mocked and dismissed were right. The numbers told us then and tell us the same thing today the difference is now people agree.
We assumed these statistics, from the majority, were from people, with a high understanding of the math. Turns out the majority were wrong and the few got it right....
So the question to me is
Does knowing Calculus make you a good data scientist?
NO emphatically not.
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I'd say calculus would be needed, but it somewhat depends on the definition of a data scientist. It's certainly possible to be proficient in statistics without needing to get to a deep level of understanding.
Are you the engineer designing the plane or the pilot flying it?
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On a side note, I've often wondered why getting a CS degree requires calculus when few programmers ever use it.
CS is based on logic more than math. I minored in philosophy as an undergrad, and the symbolic logic classes I took taught me a lot more about logic than I ever learned in math or CS classes. That served me well, I use logic in every programming project, but I've never had to integrate anything (which is good, because I've forgotten how).
I think there's long been a misunderstanding about what CS is based on. It's logic not math, Turing wasn't doing math when he invented the programmable computer, he was reading analytic philosophy (Bertrand Russell, in particular) and imagining an automated logical machine based on that. Digital computers are logical machines, they can do math because logic is the foundation of math.
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Calculus is actually pretty easy. One thing that really surprises me is how many music majors claim they don't like math. In reality, Calculus I and Music Theory Two are probably about the same level of difficulty. Things really don't start getting ugly in the math world until you reach junior level ABET engineering courses and apply the Calculus you learn. Calculus I-III and even DiffEq generally aren't that hard depending on *where* you take them, but at some point, you will be expected to apply it and things get more difficult there.
To answer your question, I'm guessing one can skate by in the world of Data Science without knowing Calculus and used pre-boxed algorithms and/or numerical analysis techniques to make observations. After all, a person can write a 3D game now without necessarily knowing classic Physics or Linear Algebra since that person can likely rely on a gaming engine to do that "hard stuff". I think much of Data Analysis these days might be in using low-level Tensor Flow or higher-level Auto ML or super easy regression analysis packages. You don't necessarily need to have a deep understanding of how these things work to use wrapper libraries.
With that said, don't avoid Calculus. It's much easier than you think and there are probably software tutors out there...
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So my wife wanted to leave me 3 years ago. For over a year I drank about 20 standard drinks a night. Recently it's been 3-5, one cocktail while I cook, one with dinner and one in the evening. I went to the GP and he told me I have 70% kidney function and my liver is waving a white flag. So I just gave up, that day. I'll still have the odd cocktail when I take my wife to dinner, but that's it.
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