FWIW my experiences with MathAcademy roughly overlap OP’s: it’s really hard work and adult life seriously interferes with making speedy progress (notice their own success stories are with teenagers who can devote hours upon hours on racing through the - very good - curriculum).
They say 1 point is equivalent to 1 minute of work and that you should earn at least 45 points a day. Well, for me 1 point is nowhere near 1 minute of work: I’m sloppy and sometimes downright stupid so it’s 1,5 minutes at best and often much, much more.
Banging your head against a wall every day for more than an hour (sometimes much more) just to get to what they consider to be the minimum of 45 points is no fun, and probably even counterproductive. I managed to keep it up for four months and made reasonable progress during that time (on getting back to where I was at the end of High School, 30 years ago) but it also burnt me out. I’ve now scaled it back to 30 minutes (not points!) a day. As a result my progress is now glacial.
Also, they’re very much of the “just do lots of problems and you’ll learn mathematic concepts and principles by osmosis” school of math instruction. For me I had to buy a textbook to get some extra explanation.
The good thing is that the problems seem well thought out and the spaced repetition system definitely works (for me, anyway).
I’m going to keep it up, because I have enough disposable income to afford it (though it is much too expensive for what it is) and I really want to bring my math skills up to a level where I can follow along the math in ML papers (and also because math, it turns out, is kind of elegant and interesting). I could go the self-study route, but then I’d have to spend time and effort guiding myself and figuring out what it is I needed to work on. If nothing else, MathAcademy is good at taking care of this for you so you can focus on the math itself.
Any pointers on useful textbooks in this space? I seem to have difficulties finding one that is at the right level (not too easy, not too hard) or that provides a way to gauge your level and start accordingly at a later chapter or whatever.
I decided start with Calculus I on MathAcademy because that was the last thing I did in High School. MathAcademy disagreed and told me to do PreCalculus and even bits of Algebra II first, but I knew better (MathAcademy was right and in hindsight I should’ve just started the Foundation courses to build up my pretty weak algebra skills again).
For Calculus I simply use the textbook that’s recommended at the link above. As far as I can tell, it’s good. I don’t do the problems, though - for that I use MathAcademy.
I'm biased, but very fond of the open-access introductory textbooks used where I studied. The department was very much pure maths, but the intro classes were accessible to general liberal arts students. I think the texts are relatively unique in that they're very proof oriented, yet with a pedagogical style that doesn't assume the reader is a future graduate student.
For linear algebra, we used the relatively standard Friedberg Insel and Spence [2], but I hear good things about https://hefferon.net/linearalgebra/.
[1] Link is off university domain, since apparently it was at some point turned into a bit more hardcore textbook oriented towards those going onto graduate studies in mathematics. If curious: https://www.amazon.com/Calculus-Analysis-Euclidean-Undergrad...
Not a textbook, but https://betterexplained.com is an awesome resource for gaining intuition, its author's approach is very unlike others I've encountered.
For proofs and introductory real analysis, I highly recommend Prof. Jay Cummings' books at the awesome price of about $20 on Amazon for freaking 400 page books. If anything, just buy it to support the guy.
Yeah, I only have a goal of 25 points a day, Monday through Saturday, and I still usually take more than half an hour (though usually less than an hour) per day.
I actually feel that 25 points may be a bad choice as it makes me spend too much energy picking lessons that will barely add up to 25 so I can be done with my daily. Probably causes me to review or whatever when maybe I don't need to?
You can do all of that without paying a monthly fee. You just need a library card (or know of a person called Anna and her archive ;) ) and a list of books. These are the ones I used:
Precalculus by Axler
Calculus (Ninth Edition) by Thomas
Linear Algebra by Lay
How To Prove It by Velleman
Understanding Analysis by Abbott <--- I'm currently here
Much, much, much cheaper than paying $50/month. What I've spent most on so far has been printer paper and fountain pen ink because I do exercises by hand instead of using a tablet/iPad but in total this expense has been waaaaay under $50.
The #1 resource needed for self-learning is motivation, and for many people it's a lot more difficult to come by than money. What you're paying $50 a month is not information, but a system that encourages you to keep doing it
You can do that manually. Say for example you learn integration by trig sub today and you do 30 problems from a book. Next week you do some more trig sub problems. Then 2-3 weeks after that you do some trig sub problems and then in a few months you do some. You can do spaced rep manually. Is mathacademy more efficient? I don't know. It's too early to say. But what I do know is millions of people have learned mathematics with books, pen and paper for hundreds of years.
I've recently gotten back into math and I'm really struggling with your approach. I find it particularly difficult to get an accurate view of how well I'm doing and where I am. Most concepts I ingest easily, and I demolish any exercises in the books I read, find on the internet, ask AI for, or scribble down myself randomly. I repeat them a couple of times to make sure. All is well. Cute green checkmarks abound. Categories marked as mastered. Pride bordering on arrogance. I move on. A week later I'm handed new concepts. The house of cards collapses. I haven't mastered any of the things. There are gaping holes in the information I was given and I wasn't knowledgeable enough to notice.
The author doesn't seem to share my difficulties either. His are of motivation and those seem to maybe be addressed by the resource he used and specifically sharing his progress with other users. For $50 I expect more than polished KhanAcademy, promises like "accelerates the learning process at 4X the speed of a traditional math class" (if anything I want to slow down), and a progress tracker to post pictures of on X. If I wanted to be told I'm amazing, how long my streak is, and to learn nothing I'd use duolingo.
What you describe is entirely normal in my experience learning lots of stuff and teaching many others. It might help you to let go of the idea that learning is a linear process where you master one topic and move on to the next. As I learn more I'm continually getting a deeper understanding of basic material I "mastered" decades ago. I often tell my students I don't think their understanding is complete but it is sufficient to move on, and the later material will help them get a better understanding. And it does!
When do you do exercises, do you refer back to sections in the book or examples? If so, this is a bad habit. Try to do exercises without looking back. This will force you to use your memory. Also don't be too quick to check solutions for things you're stuck on.
Everyone who does mathematics feels the way you do when learning something new. It's a normal feeling. Don't get disheartened. Push through it.
Sounds like you'd really like MA. It will drill you on things until you actually know them. There's no green checkmark as such either - everything will be tested again spaced repetition style. You will be slowed down until you can actually use the previous concepts properly.
Mostly sympathetic here, but your duolingo comment is a bit too harsh. Anecdotal counterpoint: my high-schooler used duolingo last summer to skip a year of instruction and get into AP Spanish as a junior, and got into the Spanish National Honors Society, and earned a fluency certificate. (I know most high school language classes churn out students who can't speak a lick, but her school is excellent and she has working fluency - which she credits largely to using duolingo to catch up.) IOW, YMMV.
$50 a month is just not that much money, though. It's maybe a percentage point or two of the average US person's take home pay. And if this even doubles the speed at which I learn what I need to, then I'm saving myself many hundreds of dollars of the equivalent of my time.
You can, but you will spend a lot of time figuring out what it is that you need to study and where your weak points are. MathAcademy does that for you so you can spend your precious studying time on, well, what you need to study.
I think it’s very expensive, and the correct price should be €$25/ month at most, imho, but its spaced repetition system definitely provides value over self study.
You can discover your weaknesses yourself by doing problem sets then checking solutions. You'll notice what kinds of questions you keep getting wrong, then you make a note to study that area again or you do more problems in that area. You don't need a computer algorithm for this.
I also have to suspect that the depth of the knowledge you get from reading real textbooks (and working the problems) is more profound than you're ever going to get from a MOOC, no matter how well put together.
I'm a bit behind you - I'm just finishing up my (third lol) re-read of my old undergraduate calculus textbook but one of these days I'm going to get around to real analysis. I'm pretty sure that a really good understanding of calculus still puts me in the top 5% of American adults.
$49 seems a surprisingly high amount for something aimed at students and learners - I appreciate the content may be good, but it's effectively 3 times a Netflix subscription.
It's meant to be something you stick with in the "long term" by its nature, and yet an annual subscription is $500 - this is just completely unrealistic for any student. Someone in a lower end job hoping to "up skill" is going to really struggle with this.
I get why some people would not want to pay this, but it’s also not at all unreasonable to pay 50 USD.
It might be 3x a Netflix subscription, but Netflix is, for many, just wasting our time, whereas learning math could mean you can get a better job (higher salary, more interesting projects, future proofing yourself), then suddenly the 50 dollars per month is negligible.
I also get that in the end all this is available for free scattered around the internet and libraries, but having guidance, having a system that helps you actually do the learning is also very valuable.
I believe their rationale is that a private tutor costs more than this per lesson, and they're targeting the people who will pay for a tutor once/twice a week for themselves or their children.
I tend to agree with you, it seems like they could be wayyy more competitive on price but I also understand where they're coming from.
They’re not a private tutor, though. They don’t explain very much and there certainly isn’t a way to ask questions.
As I said elsewhere, to me they’re about twice as expensive as they should be.
There are cases where it's not the student who is paying. Definitely all the younger students, since that's covered by parents by default. I got it covered for a while under work's learning budget. I'm sure there are other groups I can't think of right now.
Having once been poor I understand you, but this is missing the bigger picture. If you're going to improve at mathematics you need to put serious time into it.
Instead of an hour of extra work every day, you're doing math instead. At minimum wage that's around two grand lost over a year. Even if MathAcademy was free.
Also, I recall seeing MathAcademy being free if you can demonstrate financial need.
The latest trend in educational software seems to be relatively high pricing. See e.g., Mentava, which sells for $500 USD/mo (not a typo). AoPS online courses are $28/lesson (though Beast Academy can be had for $100/yr). By comparison, this ($49) is in the realm of reasonable.
If this kind of pricing helps these services be sustainable over the long term, it's probably not a bad thing.
While it assumes a level of competence of basic algebra, it essentially mimics a self-study math major and provides links to lecture recordings, widely used textbooks, problem sets, and answer banks to said problem sets. You obviously have to be self-motivated, but it beats paying $50 per month for the service OP's post links to.
> but it beats paying $50 per month for the service OP's post links to.
I used this with my kids.
The $50 a month to make it easy is worth it for many people, and is downright cheap compared to many approaches.
Now, there's other options-- Khan is also great and free. But always having a bite-sized chunk to do, immediate feedback, spaced repetition, etc-- it's pretty good.
I recently stopped my MathAcademy subscription: I went from halfway through Math Foundations II through to near the end of Linear Algebra. I stopped because I realised I wasn't really learning maths, I was just learning to answer the questions by rote.
The way that they pretty much completely omit all the explanation, proofs and discussion you get in traditional maths education really limits its utility once you get to more advanced content. I think the reason for a lot of the positive reviews is that their approach works really well early on when you're revising the basic end-of high-school stuff.
I'm surprised Kahn Academy hasn't been mentioned. It's free and from my experience pretty good. Though I'm not a parent or teacher so I can't speak from either of those viewpoints.
If you need to get into math and are not really motivated I can recommend 3blue1Brown by Grant
Sanderson (https://www.3blue1brown.com/). The best part is not only, that he explains math problems in an easy way, but also show how to approach math problems in general. I think it’s one of the best sources to start with Math.
Not sure I’d want to use it as my only resource, but as supplementary material it’s excellent. He really explains concepts well (some better than others though, though this is likely a ymmv issue).
If you are recommending 3B1B from a pov of someone who has already once been past college level math, it's certainly commendable, but does not help someone who has not.
I used math academy for several months. I was curious and wanted to try it out since it’s a problem I’ve also worked on in the past. Th system is good, the fractional spaced repetition is a nice system and really reduces the spaced repetition overhead. Still IMHO, it provides nowhere near the value of the $50 a month pricing. But again I also know a lot of higher level mathematics and can work my way through a topology book on my own, so I’m probably not in the target audience. Still, I would think that even for people wanting to get into math or high school students this would still be a very steep price.
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They say 1 point is equivalent to 1 minute of work and that you should earn at least 45 points a day. Well, for me 1 point is nowhere near 1 minute of work: I’m sloppy and sometimes downright stupid so it’s 1,5 minutes at best and often much, much more.
Banging your head against a wall every day for more than an hour (sometimes much more) just to get to what they consider to be the minimum of 45 points is no fun, and probably even counterproductive. I managed to keep it up for four months and made reasonable progress during that time (on getting back to where I was at the end of High School, 30 years ago) but it also burnt me out. I’ve now scaled it back to 30 minutes (not points!) a day. As a result my progress is now glacial.
Also, they’re very much of the “just do lots of problems and you’ll learn mathematic concepts and principles by osmosis” school of math instruction. For me I had to buy a textbook to get some extra explanation.
The good thing is that the problems seem well thought out and the spaced repetition system definitely works (for me, anyway).
I’m going to keep it up, because I have enough disposable income to afford it (though it is much too expensive for what it is) and I really want to bring my math skills up to a level where I can follow along the math in ML papers (and also because math, it turns out, is kind of elegant and interesting). I could go the self-study route, but then I’d have to spend time and effort guiding myself and figuring out what it is I needed to work on. If nothing else, MathAcademy is good at taking care of this for you so you can focus on the math itself.
I decided start with Calculus I on MathAcademy because that was the last thing I did in High School. MathAcademy disagreed and told me to do PreCalculus and even bits of Algebra II first, but I knew better (MathAcademy was right and in hindsight I should’ve just started the Foundation courses to build up my pretty weak algebra skills again).
For Calculus I simply use the textbook that’s recommended at the link above. As far as I can tell, it’s good. I don’t do the problems, though - for that I use MathAcademy.
For calculus, three options to see if you like a particular author's style of explanation: http://people.reed.edu/~mayer/math111.html/math111.pdf - the most pedagogical http://people.reed.edu/~mayer/math111.html/math111.pdf - the most beautiful https://people.reed.edu/~jerry/111/calc.pdf - the most technical
For introduction to mathematical analysis and proof: http://people.reed.edu/~mayer/math112.html/math112.pdf
For multivariable calculus: https://www.stat.rice.edu/~dobelman/notes_papers/math/calcul... [1]
For linear algebra, we used the relatively standard Friedberg Insel and Spence [2], but I hear good things about https://hefferon.net/linearalgebra/.
[1] Link is off university domain, since apparently it was at some point turned into a bit more hardcore textbook oriented towards those going onto graduate studies in mathematics. If curious: https://www.amazon.com/Calculus-Analysis-Euclidean-Undergrad...
[2] https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/...
Art of Problem Solving is the best. I started with Prealgebra and it just flows. The best textbooks I have found.
I actually feel that 25 points may be a bad choice as it makes me spend too much energy picking lessons that will barely add up to 25 so I can be done with my daily. Probably causes me to review or whatever when maybe I don't need to?
Precalculus by Axler
Calculus (Ninth Edition) by Thomas
Linear Algebra by Lay
How To Prove It by Velleman
Understanding Analysis by Abbott <--- I'm currently here
Much, much, much cheaper than paying $50/month. What I've spent most on so far has been printer paper and fountain pen ink because I do exercises by hand instead of using a tablet/iPad but in total this expense has been waaaaay under $50.
It's a business premised on teaching people things faster by understanding research around learning.
If the math it teaches is the math you need or want to learn, its likely an efficient way to learn it.
So, you are paying for efficiency. Like using Pimsleur rather than spending a year in France.
The author doesn't seem to share my difficulties either. His are of motivation and those seem to maybe be addressed by the resource he used and specifically sharing his progress with other users. For $50 I expect more than polished KhanAcademy, promises like "accelerates the learning process at 4X the speed of a traditional math class" (if anything I want to slow down), and a progress tracker to post pictures of on X. If I wanted to be told I'm amazing, how long my streak is, and to learn nothing I'd use duolingo.
Everyone who does mathematics feels the way you do when learning something new. It's a normal feeling. Don't get disheartened. Push through it.
I think it’s very expensive, and the correct price should be €$25/ month at most, imho, but its spaced repetition system definitely provides value over self study.
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I'm a bit behind you - I'm just finishing up my (third lol) re-read of my old undergraduate calculus textbook but one of these days I'm going to get around to real analysis. I'm pretty sure that a really good understanding of calculus still puts me in the top 5% of American adults.
It's meant to be something you stick with in the "long term" by its nature, and yet an annual subscription is $500 - this is just completely unrealistic for any student. Someone in a lower end job hoping to "up skill" is going to really struggle with this.
It might be 3x a Netflix subscription, but Netflix is, for many, just wasting our time, whereas learning math could mean you can get a better job (higher salary, more interesting projects, future proofing yourself), then suddenly the 50 dollars per month is negligible.
I also get that in the end all this is available for free scattered around the internet and libraries, but having guidance, having a system that helps you actually do the learning is also very valuable.
I tend to agree with you, it seems like they could be wayyy more competitive on price but I also understand where they're coming from.
Instead of an hour of extra work every day, you're doing math instead. At minimum wage that's around two grand lost over a year. Even if MathAcademy was free.
Also, I recall seeing MathAcademy being free if you can demonstrate financial need.
If this kind of pricing helps these services be sustainable over the long term, it's probably not a bad thing.
While it assumes a level of competence of basic algebra, it essentially mimics a self-study math major and provides links to lecture recordings, widely used textbooks, problem sets, and answer banks to said problem sets. You obviously have to be self-motivated, but it beats paying $50 per month for the service OP's post links to.
I used this with my kids.
The $50 a month to make it easy is worth it for many people, and is downright cheap compared to many approaches.
Now, there's other options-- Khan is also great and free. But always having a bite-sized chunk to do, immediate feedback, spaced repetition, etc-- it's pretty good.
The way that they pretty much completely omit all the explanation, proofs and discussion you get in traditional maths education really limits its utility once you get to more advanced content. I think the reason for a lot of the positive reviews is that their approach works really well early on when you're revising the basic end-of high-school stuff.
MF II and III were great for revision of late high school maths, yes.
https://www.khanacademy.org/math/multivariable-calculushttps://www.khanacademy.org/math/differential-equationshttps://www.khanacademy.org/math/linear-algebra
https://www.khanacademy.org/math/calculus-2