How long would it take to learn Algebra I to Calculus II?
October 26, 2020 5:24 PM Subscribe
I am a Social Science student and I am finding statistics to be quite valuable and exciting. I am beginning to think that pursuing a Master's in Statistics (or Biostatistics) or Data Science focus woule be an ideal degree, especially if I can somehow combine it with Sociology/Political Science in government or tech companies with a social aspect to it. Yet, I have always been slow with maths and I struggle with it at times - currently working on Algebra I so far.
How long would it take to learn Algebra I to Calculus II as well as Linear Algebra and higher end Statistics courses? Would it take anywhere from two to three years? Especially from a standpoint where I am slower at maths and need to take my time with it. So far I am enjoying Algebra I, but I am still a bit slow with it, and not entirely sure if I would find Calculus exciting or too difficult. Yet, I would love to be able to understand advanced Statistics and combine it with Political Science and Sociology in terms of academic research/government research or even get involved with tech companies with a social/environnmental/health aspect. I am not sure if I am being realistic here in wanting to transition over to advanced Statistics since my educational background is in Sociology and Political Science, but I think I am willing to put in the effort and learn mathematics. Just not sure if it would take a very long time since I have a learning disability/slower processing speed with things.
How long would it take to learn Algebra I to Calculus II as well as Linear Algebra and higher end Statistics courses? Would it take anywhere from two to three years? Especially from a standpoint where I am slower at maths and need to take my time with it. So far I am enjoying Algebra I, but I am still a bit slow with it, and not entirely sure if I would find Calculus exciting or too difficult. Yet, I would love to be able to understand advanced Statistics and combine it with Political Science and Sociology in terms of academic research/government research or even get involved with tech companies with a social/environnmental/health aspect. I am not sure if I am being realistic here in wanting to transition over to advanced Statistics since my educational background is in Sociology and Political Science, but I think I am willing to put in the effort and learn mathematics. Just not sure if it would take a very long time since I have a learning disability/slower processing speed with things.
I teach graduate level statistics in the social sciences. I'm not sure you need the full sequence of high school math before taking stats. Often you can pick up what you need along the way. I would talk with the faculty teaching the biostats courses you're interested in and ask how best to prepare.
posted by shadygrove at 7:24 PM on October 26, 2020 [1 favorite]
posted by shadygrove at 7:24 PM on October 26, 2020 [1 favorite]
I agree with shadygrove that you don't need the full high school math sequence to learn statistics - it's a pretty separate field from calculus/linear algebra/etc. I took calculus and statistics classes in high school, but I'm pretty sure that the stats class didn't have calc as a prereq.
I'd also consider how much you want a formal understanding of things like calculus, linear algebra, etc, vs. just knowing enough that you can use it effectively. I've found calculus and linear algebra super useful in understanding control theory, but the practical skills were super different from what was taught in classes. I found my calculus class to be a ton of memorizing applications of different formulas, but I've gotten way more value out of having an intuitive understanding of derivatives and integrals, and I essentially never use the formulas that were the focus of the class. Similarly for linear algebra, there are a ton of really beautiful connections between linear algebra and real-world processes, but from people I've talked to who took linear algebra classes, those applications and connections almost never come up in classes :( As someone who also struggles with formal math classes a lot, I found that it was way more effective for me to focus on applying the math to things I was interested in and learning it as I went than it was to take the formal classes.
If you're interested in data science, I think the marginal value of Calculus II once you've taken Calculus I is very small, especially compared to taking a intro programming class (particularly one that focuses on Python). I don't think I'd really recommend Calc II to anyone who isn't planning to be a mathematician or is intrinsically interested in calculus.
Sorry if this is a little more adjacent to your question than you'd like, but I do hope it's useful to consider :)
posted by wesleyac at 8:11 PM on October 26, 2020 [1 favorite]
I'd also consider how much you want a formal understanding of things like calculus, linear algebra, etc, vs. just knowing enough that you can use it effectively. I've found calculus and linear algebra super useful in understanding control theory, but the practical skills were super different from what was taught in classes. I found my calculus class to be a ton of memorizing applications of different formulas, but I've gotten way more value out of having an intuitive understanding of derivatives and integrals, and I essentially never use the formulas that were the focus of the class. Similarly for linear algebra, there are a ton of really beautiful connections between linear algebra and real-world processes, but from people I've talked to who took linear algebra classes, those applications and connections almost never come up in classes :( As someone who also struggles with formal math classes a lot, I found that it was way more effective for me to focus on applying the math to things I was interested in and learning it as I went than it was to take the formal classes.
If you're interested in data science, I think the marginal value of Calculus II once you've taken Calculus I is very small, especially compared to taking a intro programming class (particularly one that focuses on Python). I don't think I'd really recommend Calc II to anyone who isn't planning to be a mathematician or is intrinsically interested in calculus.
Sorry if this is a little more adjacent to your question than you'd like, but I do hope it's useful to consider :)
posted by wesleyac at 8:11 PM on October 26, 2020 [1 favorite]
I think people are misunderstanding the questions.
The OP has already found statistics to be exciting and valuable (presumably by taking a statistics course) and is now wondering about taking the non-statistics math (and intermediate/advanced statistics) necessary to get into a Master's in Statistics (or Biostatistics) or Data Science program, some of which require calculus or beyond.
posted by Jahaza at 8:19 PM on October 26, 2020 [2 favorites]
The OP has already found statistics to be exciting and valuable (presumably by taking a statistics course) and is now wondering about taking the non-statistics math (and intermediate/advanced statistics) necessary to get into a Master's in Statistics (or Biostatistics) or Data Science program, some of which require calculus or beyond.
posted by Jahaza at 8:19 PM on October 26, 2020 [2 favorites]
How long would it take to learn Algebra I to Calculus II as well as Linear Algebra and higher end Statistics courses? Would it take anywhere from two to three years?
If you have to get the actual academic credits, the answer to this will be found in your university catalogue.
However, many universities do their initial math placement by examination, or some allow a challenge exam of some sort for specific courses. If you can teach yourself some of these things on Khan Academy or something, "how long it would take" will depend only on how much time you are planning to put in. Depending on your learning disability, it might be easier to learn these on your own time where you can control your environment, speed up or slow down the lecture, or repeat certain sections as many times as needed without feeling "behind" in class.
It sounds like you are an undergrad now, if you want to go into a math heavy field in grad school it will be good to pick up as much advanced math as you can with your undergrad degree... with the exception that if you are able to "skip ahead" to a higher level of math and do well in those classes, no one will see that as a bad thing. Basically you want to go as high as you can with math to have a strong application. If you take this route, you might work independently ahead of where you are starting with official credit classes, so the first class you "skip ahead" to will be one you can easily show a good grade in.
Oh, and I guess another reading of your question would be wondering if you can take multiple math classes along the lines of Algebra 2, Calc 1, etc at once -- no, math builds in layers on top of each other, you need to build the bottom layers first (at least at this level, once you get past Calculus people's paths start to diverge more).
Edit: good luck! You remind me of a college friend who really fell in love with math and went on to grad school with it. He wasn't super into it initially and at some point something just clicked, he looked so excited when he told me about his grad school plans. Math past Algebra is really a different animal than what comes before it, so while it's rare for someone to unexpectedly fall in love with math in this way it's not exactly unusual -- you might simply have been exposed to parts of math you never had the opportunity to learn about before.
posted by yohko at 9:39 PM on October 26, 2020
If you have to get the actual academic credits, the answer to this will be found in your university catalogue.
However, many universities do their initial math placement by examination, or some allow a challenge exam of some sort for specific courses. If you can teach yourself some of these things on Khan Academy or something, "how long it would take" will depend only on how much time you are planning to put in. Depending on your learning disability, it might be easier to learn these on your own time where you can control your environment, speed up or slow down the lecture, or repeat certain sections as many times as needed without feeling "behind" in class.
It sounds like you are an undergrad now, if you want to go into a math heavy field in grad school it will be good to pick up as much advanced math as you can with your undergrad degree... with the exception that if you are able to "skip ahead" to a higher level of math and do well in those classes, no one will see that as a bad thing. Basically you want to go as high as you can with math to have a strong application. If you take this route, you might work independently ahead of where you are starting with official credit classes, so the first class you "skip ahead" to will be one you can easily show a good grade in.
Oh, and I guess another reading of your question would be wondering if you can take multiple math classes along the lines of Algebra 2, Calc 1, etc at once -- no, math builds in layers on top of each other, you need to build the bottom layers first (at least at this level, once you get past Calculus people's paths start to diverge more).
Edit: good luck! You remind me of a college friend who really fell in love with math and went on to grad school with it. He wasn't super into it initially and at some point something just clicked, he looked so excited when he told me about his grad school plans. Math past Algebra is really a different animal than what comes before it, so while it's rare for someone to unexpectedly fall in love with math in this way it's not exactly unusual -- you might simply have been exposed to parts of math you never had the opportunity to learn about before.
posted by yohko at 9:39 PM on October 26, 2020
For what it's worth, I just went back and took Calculus through what you're probably considering Calculus 2 in order to take the higher-level math courses in a statistics program. It took me about six months to remember/review enough math to transfer into a Calculus course at a community college without actually paying to take high school level classes (I did Edx courses through Pre-Calculus to review algebra, trig, etc.). I had taken Calculus in high school but really had zero memory of it. Then it took about six months to take the calculus courses, and I threw Linear Algebra in there too. I am also a social sciences person who didn't take much math after high school, though I reviewed high-school level math for the GRE a few times over the years. One thing I'd remark is that when I finally started taking the Calculus sequence I was struck by how easy it was - especially the first half or so of it. If you get to the point where you have finished all the prereqs for a Calculus course, you'll be prepared for Calculus and they should take the class at a manageable rate so as not to be overwhelming.
If you just want a working/practical knowledge of statistics, I think it is true what some people said that you don't need calculus. Calculus in relation to stats seems to be more about understanding why/how the math behind the methodologies works instead of how to apply them. I decided to take all the calculus though because probably like you I just wanted to understand things in more depth and have a more quantitative credential.
posted by knownfossils at 10:06 PM on October 26, 2020
If you just want a working/practical knowledge of statistics, I think it is true what some people said that you don't need calculus. Calculus in relation to stats seems to be more about understanding why/how the math behind the methodologies works instead of how to apply them. I decided to take all the calculus though because probably like you I just wanted to understand things in more depth and have a more quantitative credential.
posted by knownfossils at 10:06 PM on October 26, 2020
I didn’t need calculus to earn my MS in data science. It would definitely help if you wanted to focus on machine learning in your career but my program had one stats course and the rest was hardcore computer programming. Honestly it would be a better idea to take courses in programming rather than math unless you apply for a hardcore data science program where you will be expected to develop algorithms by hand or plan on pursuing a PhD.
So yeah, I would spend time taking programming courses, specially in SQL, Python and R.
posted by Young Kullervo at 8:03 AM on October 27, 2020 [3 favorites]
So yeah, I would spend time taking programming courses, specially in SQL, Python and R.
posted by Young Kullervo at 8:03 AM on October 27, 2020 [3 favorites]
As Salty's list implied, linear algebra isn't a prerequisite for calculus. It's separately desirable for the degrees you mentioned, though.
posted by SemiSalt at 1:08 PM on October 27, 2020
posted by SemiSalt at 1:08 PM on October 27, 2020
It will be difficult. You need to take algebra I, geometry, algebra II/trig, precalc, calc I and calc II. Adding linear algebra and advanced (calc-based) statistics, you need to take and pass 8 classes.
posted by splicer at 2:48 PM on October 27, 2020
posted by splicer at 2:48 PM on October 27, 2020
In some ways our math curriculum is set up to train mechanical and electrical engineers and there is a lot of it you would probably want to skip if you can somehow get away with it. The mathematical content is highly biased towards things that are needed for physics and engineering applications.
For instance I don't think the classic Calculus II curriculum would be very useful for someone interested in statistics or data science. And while Calculus III is all about calculus with multiple variables, which is hugely important for statistics, the way it's presented again focuses heavily on 3 dimensions, different coordinate systems, path and surface integrals -- a strong bias towards tools for physics which are not useful for statistics.
Likewise trigonometry is not very important but manipulating trigonometric formulas is a huge and unpleasant part of algebra II and precalculus, again motivated by applications in physics. And if you can skip geometry somehow, I also can't imagine using much of the standard geometry material anywhere, although it might be valuable to have an introduction to proofs.
A working grasp of calculus (at least at Calculus I level) is essential for a solid understanding of statistics. Integrals and derivatives come up constantly. Finding the expected value of something is mathematically the same thing as computing an integral. (It is of course possible to apply a lot of techniques without using calculus.)
And linear algebra is simply the most useful subject you can learn in higher education, full stop, and is essential to statistics with more than one variable -- i.e. anything you would try to do in the real world.
I would try to figure out the way you can work towards both of these subjects with the least extra effort. But the institution might have certain requirements, and it may be hard to argue your way past them.
(Note this is just my idiosyncratic opinion about what is and isn't important. But I honestly think sitting down with some academic advisors and figuring out "what math can I get away with skipping" is the right way to look at it.)
posted by vogon_poet at 11:19 AM on October 28, 2020 [3 favorites]
For instance I don't think the classic Calculus II curriculum would be very useful for someone interested in statistics or data science. And while Calculus III is all about calculus with multiple variables, which is hugely important for statistics, the way it's presented again focuses heavily on 3 dimensions, different coordinate systems, path and surface integrals -- a strong bias towards tools for physics which are not useful for statistics.
Likewise trigonometry is not very important but manipulating trigonometric formulas is a huge and unpleasant part of algebra II and precalculus, again motivated by applications in physics. And if you can skip geometry somehow, I also can't imagine using much of the standard geometry material anywhere, although it might be valuable to have an introduction to proofs.
A working grasp of calculus (at least at Calculus I level) is essential for a solid understanding of statistics. Integrals and derivatives come up constantly. Finding the expected value of something is mathematically the same thing as computing an integral. (It is of course possible to apply a lot of techniques without using calculus.)
And linear algebra is simply the most useful subject you can learn in higher education, full stop, and is essential to statistics with more than one variable -- i.e. anything you would try to do in the real world.
I would try to figure out the way you can work towards both of these subjects with the least extra effort. But the institution might have certain requirements, and it may be hard to argue your way past them.
(Note this is just my idiosyncratic opinion about what is and isn't important. But I honestly think sitting down with some academic advisors and figuring out "what math can I get away with skipping" is the right way to look at it.)
posted by vogon_poet at 11:19 AM on October 28, 2020 [3 favorites]
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Given your situation, you probably shouldn't try to a by taking multiple math classes at once. But you might get there as easily as Algebra 2/pre-calc, calc 1, calc 2, linear algebra. Three years seems like plenty of time, that can people most of a stats major.
I have taught students that seem much like you although I don't know your specific situation. I will say that what often matters most is wanting to be there and putting in the time. I have seen 'struggling' students outperform confident peers many times.
So I am cautiously optimistic but you will only get the specific details you need from the folks who work for you/your institution. Good luck!
posted by SaltySalticid at 5:46 PM on October 26, 2020 [4 favorites]