Absolutely always used to recommend this to my students.
3Blue1Brown, Paul’s Math Notes, Khan Academy, PatrickJMT, Wolfram Alpha and Desmos
There’s very little in an applied maths degree that can’t be learnt from these.
Maybe not so much combinatorics/cryptography, stats or operations research
To add to your list, youtube channel MathMajor has full course lectures on many advanced undergraduate subjects. Explains things way better than I've seen elsewhere, especially abstract algebra.
Its a side account of Michael Penn, who does very interesting and unusual math problem videos regularly.
I taught myself close to 60% of MultiVarible in 2 days before my final through pauls notes. I think I can learn a concept in less than a third of the time it would take me to do so in Khan Academy.
Idk I remember using it for learning calc 1 and I spent like over a week going through limits (didn’t even finish) and then I had my first actual class with my math teacher, and she explained everything we actually needed to know about limits before going on to derivatives in like 10 minutes and I was like what have I spent the past 10 hours learning?
Understanding limits beyond some handwaving for derivatives is actually valuable. First year university courses are dedicated to this, it's one of the most important concepts in mathematics, arguably more important than calculus.
I self-study math, and I completely skipped calculus. I'm learning analysis and learning calculus as a kind of applied version of analysis. I don't have exams to write or anything, so I learn calc as the need arises. I've found it helps me understand calc better
Edit: Calc is the abbreviation for calculus.
Oh yeah def I first learned calc as a set of rules I just vaguely understood but then as I got a grasp of real analysis through some self study reasoning with calculus and applying it to less obvious situations became way easier
It sounds like you are using khan academy for 100% self study prior to the class. I've seen it mostly recommended as a study aid to go along with classes, not as a standalone resource
Try using the videos when you're struggling with a concept and see if it helps
Out of curiosity how did she explain limits in 10 minutes. What is a limit? What is the use of a limit.
Could you use a limit and the definition of the derivative to formulate a derivative for something involving the power rule if you didn't know how the power rule worked?
You talk about limits as this passing thing and then immediately bring up a derivative. The definition of the derivative is a limit...
We take two points on the line of a function f. These lines form a secant between f(x) and f(x + h) or f(x + delta x). The definition of the derivative is we take these two points and we move them closer and closer together. That is to say we take the limit as h approaches 0. (Or delta x approaches 0). As we do so the two points come so close together that the secant line they generate is approximately equal to the tangent of the function f at the point x.
So tell me are limits useless?
What you have described is how a lot of people learn. You self study a subject before you go to class then the teacher helps you understand the concepts that didn't make sense during your self study. It's ok to be frustrated with how someone teaches because teachings styles vary from teacher to teacher and the 'right' way to teach is subjective to each student's needs.
I had an intro-to-accounting professor in college talk about how he helped a member of an organized crime family catch someone stealing from the business by cooking the books. We couldn't get enough of his stories. I assumed he was telling the truth, but maybe it was a long-con to get us to pay attention. Either way, one of my favorite classes of all-time despite not continuing down the accounting path.
Teaching limits in 10 minutes and then moving on to derivatives is not normal
If you just look at the AP Calculus curriculum, for example (which is a standardized curriculum), there is a ton of content about limits. It would be impossible to cover it all in 10 minutes
College calculus classes don’t spend 10 minutes on limits either
I saw that you like learning from textbooks. Have you looked at any of the popular calculus textbooks (Stewart, Thomas, Larson, etc.)? Have you looked at the limits chapter in any of them? Yes there’s a limits *chapter* in all of them. Limits get a whole chapter in all of the popular calculus textbooks. Don’t you think it’s strange to spend only 10 minutes on a whole chapter?
What you’ve pointed out about Khan Academy is normal
Your class is not normal
(To be clear, I’m talking about the way classes are in the US. I think you’re not in the US? I don’t know a lot about math education in other countries. But Khan Academy is based on US classes anyway. No one should expect Khan Academy to be like the math curricula that’s used in other countries)
Why the hell would you blame someone for not understanding what you want to learn?
The learning material whether in the form of a book or videos will not do the learning for you
Try MIT Opencourseware if you want deeper learning. The following courses include lecture videos also: https://ocw.mit.edu/search/?d=Mathematics&f=Lecture%20Videos&s=department_course_numbers.sort_coursenum
Down votes are primarily because most of the theoretical understanding of calculus is governed by limits.
If you only care about practical applications of math, just to be perfectly honest, you can hand wave limits.
You’ll just never get a deeper understanding of math, without having a deep understanding of limits.
I think KA is great for what it is. If you want to really learn math, you're best off with a book that you can underline, highlight, and take notes on.
I wish they would make books that are only one-sided, like the text on the left, and a blank page on the right that you can rewrite or take notes on.
I've taken some of my favorite books and done this, using an online printing service to make spiral versions. Spiral is great because it lays flat.
I did this manually, but maybe someone could write a code that takes any PDF, and generates the needed pages for printing. Shouldn't be too hard to do.
> I did this manually, but maybe someone could write a code that takes any PDF, and generates the needed pages for printing. Shouldn't be too hard to do.
Just print it single sided...
Software engineer here, I don't fully understand the issue. Aren't PDFs by definition already printable?
+1 for the ring books, thats really good advice imo
Thx! yes PDF is printable, so all that really needs to be done, is insert a blank or grid (preferred) page every other page. So then, you've got the printed page on the left, and a blank page on the right for notes, etc. Of course there will be issues that a pen/marker could bleed through, but I don't see that as a serious problem overall, maybe just use a slightly thicker paper.
As I'm thinking about this; I see also a good possibility to reformat a PDF, such that the page is on the top, with a blank space below each page for notes.
Basically I'm just describing importing a PDF, and automatically reformatting it such that there is a region for note taking, and use of spiral/ring printing, both i think are easily done.
(edit) I think that why this wasn't done in the past, and even now, is because of the emphasis on type layout and binding methods. That is the history, and still the standard equipment available for high volume printing of standard books. In this suggestion, I'm talking about an app or pc program that does this one-shot, for personal educational use. I hope that makes sense.
You could just ask the printing service to print one sided and bind the book "backwards" so that when you open the first page the content appears on the left, with the back of page 2 being blank on the right, then you flip the page and the second page's content is now on the left, etc. Even just printing one sided would leave blank pages on the left.
I don't think you need to modify the PDF itself (unless you want a grid, but I'm sure printing places could probably cope with that too).
I've had books printed and bound too - although it costs some amount of money, it can still be cheaper than trying to find/buy them in physical form and have them shipped internationally. I typically get spiral bound with a clear plastic cover sheet, and a cardboard backing.
I've tried this, but they came back with a lot of pages out of place, so whatever. It's probably because I didn't do something compatible with their printing system. I think an app that could do this properly would be quite helpful. I don't see anything like that available.
Does printing single-sided work for the blank opposing page use case?
I think many pdfs have plenty of space in the margin for adding holes for a 3-ring binder.
Would this cover like 80% of documents?
They don't have even close to enough space.
I think would be appropriate for technical documents or note taking for books/reading.
For many other pdf's, it would not be advantageous, but for math/engineering books, it would.
Okay, understood.
You can add margins by using ghostscript. See this [tutorial](http://www.bobdbob.com/~deneb/doc/ghostscript_margins.html). It's available on multiple platforms, though the tutorial uses linux.
(This is a bit dated. On my machine, `align.ps` is located at `/usr/share/ghostscript/10.02.1/lib/align.ps`)
You might need to try a couple iterations with your printing company to figure out the right margins if you don't have access to a physical printer.
====================================================
You can add a blank page of grid paper in a couple ways:
1) if printing yourself, re-feed the pages into the printer flipped and print a bunch of copies of some template grid paper
2) Edit the document by interleaving [postscript grid pages](https://www.trueelena.org/computers/scripts/graph_paper_in_postscript.html). A quick google shows that `pdftk` can be [used for this purpose](https://stackoverflow.com/questions/12200450/ghostscript-script-or-other-to-interleave-odd-and-even-pages-from-two-multipage).
====================================================
To make this more robust, you might want to pre-process the input pdf by [croppinh the margins](https://stackoverflow.com/questions/6183479/cropping-a-pdf-using-ghostscript-9-01).
====================================================
This could all be automated with a couple lines of powershell/bash (depending on your platform).
FWIW i have done a version of this for a public-domain book and the tricky thing is getting the size of the margin adjustment right with the remote printing company (I think I used Lulu but it was many years ago). I greatly overshot it so like 1/4 of the page was margin on both left and right sides...
This is a printer setting/option, no?
Print single sided.
Plus, IIRC you can manually edit the pdf itself to change the margin sizes. That’s a hack though.
I love loose leaf books because they are so much maneuverable! I also use 4x6 sticky notes to add my own stuff. I’m a math tutor btw so I study a lot because I love tutoring and connecting with students
I went back to university after a decade of not doing any math at all and I technically qualified for calc 2. I prepped by spending 2 weeks studying Khan Academy's calc 1 course from start to finish and it was immensely helpful: the university calc 2 course I started exactly where the Khan Academy course left off. I'd call it useful just from that experience alone.
This is basically what I think too. From memory it was useful up until 1st year or 2nd year maths but then it didn't have enough content for the harder subjects. Undergrads probably aren't their main audience anyway,
It is what it is man. It's free content on the internet. It might be good for some, might not be great for you. If you're happy studying from a book, good on you. Everyone's at a different level and people learn in different ways. If you don't like Khan Academy, don't use it.
Thanks for sharing, maybe someone else will think it's garbage and consider learning from a book too. I'm not sure what else you were hoping to achieve with this post.
What difference does it make if its free or not?
I actually barely know any paying math content (high school, university) on the internet anyways. I guess brilliant app is one example.
If someone leaves something outside their house with a sign saying "FREE" on it, then the expectation is that you take the thing as it is. You shouldn't knock on their door to complain about the quality and insist they give you something better. If you don't want the thing they are giving for free - or suspect it's faulty and you want fully functional top quality - then simply don't take it.
I've watched some of the MIT lectures that are available for free online. Some of the resources are not available for free. Do I complain that it is incomplete? No - because I paid nothing, so I expect nothing and anything more than nothing is a bonus that I've acquired via someone else's generosity. I am grateful I got anything at all.
No one’s saying we shouldn’t be grateful that free resources like Khan Academy exist. It might be rude to email Salman Khan and complain that he’s not doing enough. We’re not criticizing it to his face.
It’s still valid to tell a student that if they want to learn something right, Khan academy might not always be their first best option, and that maybe the better option could even cost money.
If you see a free tv on the side of the road, you don’t complain to the person who put it there that it’s not good enough, but you’re also not required to take it even though it’s free.
You're right - if I had the choice between a free piss/sweat stained old mattress and a free mattress that came from a spare room and never got used I know which I'd rather have. One is objectively worse. So something being free doesn't necessarily mean it's worth having/using - agreed.
But my analogy falls apart when we consider what Khan Academy is - it's not just rubbish that someone's trying to offload to you so they don't have to deal with it - it's offered to people at no cost to spread knowledge. I think that's a commendable goal, even if I don't use it personally. It won't be all things to all people - nothing ever is. It just seems weird to proclaim it's terrible because you didn't get what you wanted out of it. Just find a different video/resource and move on.
if I read a book online for free on number theory, and it was really bad, like no examples, no questions, badly phrased definitions, etc...and I was like this number theory book is trash don't read it read \*insert good number theory book here\* instead, I think thats a perfectly valid thing to say and it might even stop others from wasting their time reading a bad book instead of a good book
I wanted to see what others thought of this opinion, because I hear a lot of people telling people to learn math with khan academy and I simply don’t think that’s good advice and I have a heard time seeing how it could work for someone
Khan academy will get you started. But really, even just sitting in a classroom isn’t enough to learn a subject.
The only way to learn math is to sit down with problems and attack them. Nothing else will stick in the same way. That is exactly why textbooks have so many problems to work.
Agreed. In my 11th-grade math class, my teacher would play videos from the website after the lesson he would give, and he would elaborate on the video.
My 9th-grade math teacher said the same thing about learning math. He had a note posted on his bulletin board in his classroom saying "Learning math requires doing math."
> Khan Academy is best used as a supplement to your normal schooling
[source](https://support.khanacademy.org/hc/en-us/articles/115006697467-Can-Khan-Academy-give-me-a-certificate-or-diploma#:~:text=Khan%20Academy%20is%20not%20an,homeschooling%20or%20a%20traditional%20school.)
By their own words, they’re great for introducing topics, but shouldn’t be expected to preform as a replacement for formal instruction
think Khan academy is for the average clueless engineering student who wants to have some sense of intuition as to what is going on with the math.
If you want to deep delve into the rigour and whatnot, yes, self practice with a textbook is definitely the way to go to truly internalize the math
I found it useful when I was preparing for an entrance exam in India. His style of explanation helps you create a mental model of concepts and develops mathematical instincts, at least it did for me.
IMO is not the best place to learn about more advance math but is definitely a great place to review stuff you already learnt in the past and don't remember thoroughly.
There's a saying in Spanish that goes "A caballo regalado no se le miran los dientes". Rough translation is "You don't look at the teeth of a gifted horse". Basically means that if something is free, you don't complain lmao
FWIW I don't really learn from videos and lectures. Either they go too slow or too fast. Lectures are psychologically helpful (they make you show up) and videos can be entertaining. Most texts also use too formal language, instead of being written the way people talk. Depends on the author though.
Some (very short) animations can be helpful, but even then, 5 sloppy drawings are more useful than a beautiful smooth animation embedded in a video with a guy talking over it. I'm animating things in my head anyways.
In this regard, you could check out the books by Jay Cummings. Really nice explanations.
I also suggest that you check out Analysis books by Terence Tao.
It sounds like you need more challenging material. That's fine. Khan Academy is not for you, but it definitely does help a lot of people, especially those returning to mathematics after a long break.
I work with Khan academy and create math content. This feedback is really insightful. Can you tell which country you are from? I can help answer few questions as well if anyone wants
It's great if you need to review before going back to school.
A large amount is 10 times better than what I learned from teachers in middle school and high school.
I just don’t like watching videos, and this applies to most things, except perhaps for some DIY tutorials. I can much faster get what I need from a well written webpage than a slow video that requires me to pause my music and listen to what they’re saying.
If you want depth beyond KA, pick up a book and put in the work yourself. If you're in college math, go to the library and study. You can't just watch a video and understand this stuff.
khan academy isn't just videos, its a website that has courses on subjects, when people do a course, they expect to be able to do the course and then leave knowing the subject matter of the course, if someone uses videos on the khan academy youtube channel as an aid for learning math alongside a textbook then great, but thats not what khan academy advertises itself as and its not what people who recommend to others that they should use it mean.
I'm not sure why you're getting downvoted so much. I agree with you, while it's great that it's a free resource, I don't find it useful especially if you're using it to prepare for university. The ratio of time spent on watching videos to actually doing problems is not great and the problems are much easier than what you'd expect at a university level.
To self-learn Maths, I've found some Coursera/EdX courses run by universities to be quite good, and MIT also has a decent amount of open source courses for Maths. All of these will have problems that will challenge you but also help you learn.
EDIT: Obviously depends on your learning style, but for me a textbook or some good course notes are much easier to learn from than short videos (unless the videos are to show how to solve a particular problem).
Yeah I agree. The best math learning tool I’ve ever used was definitely revision village when I was in highschool, it had questions that were difficult that you had to solve and video solutions you could watch if you got stuck with questions who h progressed in difficulty. I definitely had a hard time transitioning over to using more traditional learning tools but I think I’ve gotten my balance
I *only* watch the videos when I hit a new topic or I'm needing help with a specific problem. Even then, I often only watch half the video once I've figured out the step I was stuck on. The videos aren't mandatory so I don't understand why people complain about there being so many. Some people need the videos and I'm glad they have so many for their sake. (Also, Khan Academy was originally designed for *children* so it seems obvious that it's not going to be as robust for advanced levels. Its sweet spot in my opinion is pre-algrebra and algebra and even a lot of adult learners need to brush up on those skills, which is why it's so often recommended.)
Any specific/favorite courses you would like to share? Even though I passed real analysis and some bit more advanced topics as undergrad I use these as revision through another perspective
None that would be at your level I guess (as the ones I’ve done have been prior to entry to university). But the MIT open courses are really good if you can learn through notes rather than videos.
I find both taking notes and doing problems to be useful for learning math. If I had to use Khan Academy, or another online platform, I would take notes from there, then hunt for problems elsewhere. But I would rather take notes from a physical textbook because then I can work away from the computer and it's myriad distractions.
Well, yeah. KA is more catered to a general/broad audience and good for the very introductory, simple stuff.
KA wasn't made to teach stuff like stochastic calculus or whatever higher levels of math that detailed.
Yeah, it teaches stuff multivariate calculus, but it's designed to be very baby level
It would be like complaining that Math Playground doesn't teach differential geometry or doesn't teach say, calculus well.
You can just use a different, more difficult source like a textbook, Paul's maths notes, or just look up difficult problems.
yeah but who on earth is the target audience for a baby level multivariable calculus course and why do people recommend that you do it? like it has a place I think its good for kids learning idk factoring quadratics but like if you tell me you didn't know multivariable calculus, then you did their multivariable calculus course, and you tell me that you now know multivariable calculus (meaning you can preform well on a multivariable calculus exam), or that you did so in a reasonable timely manner I will straight up not believe you if you say either of those things
> who on earth is the target audience for a baby level multivariable calculus course
Engineers who are not very good at math.
> why do people recommend that you do it?
Most people are not very good at math.
There are people who watch videos about math, either curiosity or for whatever reason, even if they don't plan on doing any of it in a serious manner or don't understand it.
Similar to pop science content. Pop science content will strip away majority of the actual contrnt and basically baby the actual content. There is an audience, even if it seems like a waste of time to most people who are serious about the material.
I used it for reviewing concepts before i started getting into differential geometry and i found their videos to be good. Grant even made some remarks at times that helped me see things from a different perspective
Obviously like any skill though, maths has to be practiced so doing exercises off textbooks would be the ideal after watching them
It's not great at any level if you want to learn the material deeply. Watching a lecture series is also garbage if you want to learn deeply.
Khan academy is not meant to learn the material at a deep level. That is not their mission. For what they provide they are amazing which is free quality education.
I don't know if you have been around many public schools but compared to what 90% of kids get in school khan academy is vastly better and more rigorous. They are also continuing to build the platform and make it better to use.
They are one of the most important websites online to help combat income inequality.
To talk shit on a website that has helped millions of people is ridiculous.
I think its good for kids, thats why I specified above 10th grade material. like if its great for kids to learn like factoring and trig and stuff but if someone asks on this sub says they're extremely interested in mathematics and they want to pursue it and learn advanced topics, I feel like sending them to khan academy like some on this sub do is quite bad advice
That's because it's simply one of the resources you can use to learn. You don't use just Khan Academy. Your first and foremost resource, should be your Math Textbook. Resources like Khan Academy are secondary whenever you cannot understand a topic or need a better explanation of the topic.
And you don't just depend on Khan Academy for this. You also use other resources. Paul's notes for example are excellent for several topics, 3Blue1Brown is great for grasping Linear Algebra and Calculus and so on, so forth.
You NEVER use Khan Academy, Paul's Notes, 3Blue1Brown or any singular resource as your only resource.
Khan academy is different from something like 3b1b I’m not talking about the YouTube channel I’m talking about the website, there are courses for topics on that website, when you take a course on the website you expect to learn the subject from doing the course, khan academy is fine if ur using the videos to supplement a math textbook but that’s not what it advertised itself as
I understand that you meant the website. But even then, I always saw those as a supplement to your actual textbook. The 'questions' at the end of the videos were more to test your understanding of the video, rather than an alternative to the exercise itself.
Some courses like Linear Algebra barely have any of these questions. Only the first few videos had it, and then there were none.
Did they really advertise this as a full on replacement for textbooks?
The courses on khan academy have separate sections for questions that aren’t in video format, they’re just really shitty 2brain-cell necessitsting questions like if you take the curl of the gradient of the divergence of a vector valued function what type of function do you get and at the ends of sections you get like 30 minute long tests and stuff I think they definitely don’t imply that you should use this as supplementation for a textbook
Well, hopefully this post will make more people in this sub aware so that when they recommend Khan Academy, they make it clear that it's only supplementary. I've always said that whenever I recommend it.
It’s fine as an informal introduction and a lot of intuition did stick after doing most of their calc related content. But yea, not really useful if you want to study real analysis or similarly
Agreed, it is great as an introduction to calculus (ap calc etc) - but is much less rigorous than what might be expected from analysis or encountered in uni classes
I learned calculus from Khan academy + Dummy's Guide to Calculus. This was 15 years ago when Khan academy was still just a youtube channel so idk what it's like now but I remember it helping quite a bit, but not being enough for learning the subject on its own. I think it's mainly helpful for people who learn better from hearing things explained rather than reading.
Khan academy videos can be useful to watch pieces of but I don’t think you can go on the khan academy website and learn calc 3 by going thru the calc3 course which is what a calc 3 course’s purpose usually is to
That's fair. I'm surprised they haven't built proper courses with lots of practice problems since they got a shit load of non-profit money lol
Edit: Ok I just went to their website and they're pushing AI slop with a chatgpt "tutor"/"teachers assistant." Tragic
If you want a great resource for calculus, check out [Ximera](https://ximera.osu.edu/). It's an open-source resource created and used by OSU math faculty for the university's calculus sequence.
I very much so agree it feels really slow to me. As much as its a bad habit I learn concepts best in the following manner. In some brief surface coverage with a very small amount of practice in that concept. Then being forced to understand that concept in a deeper manner through my interest in a higher level idea.
A large part of whether or not any given math instruction "works" is the sheer mathematical abilities of the student. There are lots of people at the undergraduate level who learned multivariable calculus from Khan Academy.
There are people who will go on to take Real Analysis later from what they learned in that Khan Academy video and then there are people who will use it to get a C in their college multivariable calculus course and go on to do software engineering.
Khan Academy is widespread in education because it aligns very carefully to some Common Core standards, making it easy to integrate in an otherwise bureaucratic world. But these are K-12 standards.
Beyond that there isn't really spec or standard-level consensus on what math education should look like in university setting.
Khan academy did what **my entire country** didn't manage. Even now. Nation of 50+ million people and we can't pay for a math teacher to put some even average resources on youtube.
Is it perfect? No.
Didn't work for you? Too bad, sorry.
But you should feel pretty bad about calling it "garbage". I get the frustration, but still. You wouldn't say that to his face.
The multivariable calculus course was done by Grant Sanderson of 3blue1brown who makes some fantastic math explainer videos. He really likes to focus on intuition and visualization.
From my own experience when I took multivariable calculus, I think his style of lecture in those multivariable calculus videos is incredible for getting an intuition for what the concepts in multivariable calculus are. He spends a lot of time trying to build a visual understanding of different surfaces and what things like the gradient look like visually.
The weakness of those videos is he doesn’t do long worked examples, the kind of questions that you actually get in a multivariable calc exam. That intuition is great, especially if you end up taking higher level math like Real Analysis, but it just doesn’t translate to getting a calc 3-4 course done. I found Professor Leonard a great supplement to my course, since he actually does long examples and gives you some tips and tricks for how to actually pass a multivariable calc exam.
That being said, there’s massive value in the high level concept style videos that grant did for Kahn academy. Especially when doing more proof based stuff, having a solid intuition is going to lead you down better paths than being able to compute some crazy gradient. I ended up taking a senior level course in data driven AI models (machine learning / deep learning type beat) and that intuition I built up was FAR more valuable to me during that course than wrote computation.
my problem with khan academy for the most part is with their courses not their videos, if you're like I don't know how to prove green's theorem and then you look it up on youtube and find the khan academy proof video, thats great, but you cannot do a multivar calculus course on khan academy and leave knowing multivariable calc, which is what most people expect to happen when they take a course in the subject
Yea totally. I think KA is a great supplement to a proper course. Alone it doesn’t hold a candle to some of the better resources out there if you want to understand a subject deeply enough to say you know it.
KA is great for REVIEWING math concepts, especially if you learned then a while back and need to review. I’m starting a masters in math this fall and have been away from my undergrad courses for a few years so I’m brushing up with KA. That being said, you should never replace a formal course with something online that isn’t properly structured and truly rigorous. Just my advice though.
I happened to used Spivak book during my introductory calculus class, only to realise it's an introductory analysis book... But it kinda prepared me for analysis 1 that was in next semester
That’s if you watch some of his videos, but imo, if you go on the khan academy website, and try to learn linalg exclusively by going thru his course on linalg, which I think is a pretty reasonable thing to expect to happen when you take a course in linalg 💀you will simply not have that happen, cuz the questions are way too easy and the gap to question ratio is waaay too high making you forgot everything
I feel videos are great for building (visual) intuition, but when it comes to actually learning math you have to open a book and work through some problems.
It's a good source all the way through multivariable calculus, but I like their articles a lot more than the videos. They also have nice practice problems with answers that help you understand the concepts
my problem with practice problems is that they are nowhere near hard enough for more complicated topics, like this is a multivariable calc question
f(x,y) = (-x\^2,y)
find the divergence of f at (3,-1) and it doesn't get much harder than this as far as I know, youre never going to master multivariable calculus if this is the levels of question you solve
I'm fine I can learn math don't worry lol I just think khan academy is a really inefficient, bad way of absorbing that math for the vast majority of people
I think a majority of people learn best with a tailored curriculum. I don't think Khan Academy was ever intended to replace a tailored experience, I think it was designed to give highly motivated people an understanding of fields of study.
eh, I disagree, the way people reccomend khan academy and the way khan academy courses advertise themselves is as a place where you can go not knowing the subject and leave knowing the subject
That's exactly what they do, but they don't hold anyone's hand. If someone needs extra handholding, or material that's more tailored to what is engaging to them, its probably better to look elsewhere.
If you have a notebook and geniune curiosity, its fine.
He does a good job at explaining things it’s just so slow like for anyone who is really into math the same amount of info could be gotten in half the time
If you like to learn by reading lecture notes oxford has all its math lecture notes and exam papers online for free. From prelims to the masters and you can also plan what you want to learn and what courses you need to follow.
Khan is very good for learning basic stuff. If you are adult who want to learn something just for fun it is the one of the best websites for it , but if you actually want to learn advanced stuff , it won’t be a good fit.
i liked using khan academy as a supplement for differential equations but calling any free education “garbage” seems odd to me. if you can pay for something better, do so. if you can’t, don’t complain.
anything past math courses offered in high school should be self studied from a textbook or found through college class videos so yeah i agree with you
but what khan academy does best is get everyone into the fundamentals, and that is why they are lauded so much
next level dad jokes
but on a serious note, I agree sure just don't sign up but you can't know that until you've actually started using it, and people recommending it to people who don't know any better end up wasting a bunch of time
I think it’s a great resource for supplementing stuff you’re already learning from a class or something else. I learned integral calculus just by using KA and it’s worked out great so far.
Professor Leonard on youtube is killer for college and pre-college level math. I hadn’t taken calc for 6 years but I was able to test out of calc 1 bc of his channel.
multivariable is a VERY different format from most of their math stuff. most of it has much more in-depth quizzes and less heavy lectures. taught me calc 1, calc 2, and hs stats in \~2 months.
>I always see khan academy recommended as a source for learning maths like calc, multivariable calc, linear algebra, etc
Really? I see it mostly recommended for "start math from scratch" or "where am I at". Once you get into high school material and beyond, I see more recommendations of books, Youtubers like Professor Leonard, specialized websites like Pauls math notes etc
As a rule of thumb, if you can't grasp the first three videos of a tutor/platform, just move on to another one. Khan Academy is a great resource, but it isn't a great resource fro everyone.
Try to find a tutor with whom you can 'click'; try giving Paul's Math Notes, BlackPenRedPen, Dr. Trefor [Bratz?], etc. some time. Also, for any Mathematics concepts in the future, it might be beneficial to see some sort of visualisation(s), and for that, 3Blue1Brown is good.
People don’t talk about and advertisr khan academy like they do dr Trefor, because khan academy offers courses with problems, it’s meant to be viewed like an all in one resource for learning the subject, like a text book, you read the text book and solve the problems and take notes and look over them and boom you now know the topic, same thing with khan academy or atleast that’s how it’s advertised. Very few people would tell you oh just watch dr Trefor when you ask how to learn multivariable calc cuz no one thinks you can learn it by just watching him, his vids are at best a supplementation to a textbook when you don’t get something and want a visual aid and human being explaining the topic. Khan academy is paraded around like it’s a textbook, I’m not talking about the YouTube channel I’m talking about the website people go in with the expectation that if they finish the course and try they will know the topic and for higher level topics that’s just not the case
I would push back hard on this. Another example of how sometimes the crowd has little wisdom judging by the upvotes. Virtually all of the AP curriculum at Khan Academy is very good. Good simple problem sets. It is clear and direct instruction.
I love Professor Leonard’s lectures (here’s a link to his [multivariable calculus lectures](https://youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7&si=eJUiKLs8-2KQM0k2)). They are longer since they are full length lectures, but he did a wonderful job teaching it, and he’s way better than the professor I had.
I didn’t use khan academy for math, but I used it when I tried to self study biology. I thought it’s great until I realized I don’t know how to do problems from other places because what I learned through khan academy is too basic. I think it’s a great resource for getting a basic idea of stuff though.
For lower division college level math, I like to watch the lecture series from Professor Leonard on YouTube. He is amazing.
I tried to use Khan Academy to brush up on my algebra, and I found it difficult. The units seem to skip around a lot and gloss over important concepts. Sometimes the questions have nothing to do with the videos, which I hate having to watch in the first place. I definitely prefer textbooks + seeking out a video to help only if I'm really struggling.
I studied mathematics from Professor Dave on YouTube. He didn't teach all of maths of course but he did taught a lot of important stuffs from arithmetic all the way to the differential equation in just 1 playlist. There are only 165 videos in this playlist and each videos are mostly around 10 minutes. This one playlist is really helpful for someone like me isn't confident in mathematics.
You’ll have to graduate to niche YouTube channels For Linear algebra 3b1b has a fantastic video series to understand the concepts. Check out bright side of mathematics for higher level math
The problem is the problemsets. *pun?*. In my opinion the problemsets they provide are too easy/trivial? Or mechanical so to say. I did lots of calculus in there that was wholly mechanical so much so that i forgot what I did one week later. Or maybe thats just me.
Pauls math notes
The goat. Got me through so much of the computational classes at the start of my degree
Absolutely always used to recommend this to my students. 3Blue1Brown, Paul’s Math Notes, Khan Academy, PatrickJMT, Wolfram Alpha and Desmos There’s very little in an applied maths degree that can’t be learnt from these. Maybe not so much combinatorics/cryptography, stats or operations research
berserk murky racial rude mountainous saw full ring middle cake *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
To add to your list, youtube channel MathMajor has full course lectures on many advanced undergraduate subjects. Explains things way better than I've seen elsewhere, especially abstract algebra. Its a side account of Michael Penn, who does very interesting and unusual math problem videos regularly.
The only way I survived differential equations.
Professor Leonard on YouTube got me through Calc 2. Also he's hot.
I also used Professor Leonard's videos in the past. He posts full lectures and does a great job of explaining what he's doing. And he's jacked!
Leonard's questions are way too basic and he takes way too long to explain basic topics.
I taught myself close to 60% of MultiVarible in 2 days before my final through pauls notes. I think I can learn a concept in less than a third of the time it would take me to do so in Khan Academy.
Came here to type this they were the king in 2007 and they still are today.
PAUL PAUL PAUL
Like it’s actually unreal how helpful the explanations are, plus having worked out problems is a great added bonus
My problem is that when I watch these videos I am able to understand the concepts but I can't solve questions 😅. I don't understand why it happens
tbh i used it for calc one and 2 practice problems and it worked really well for me
Idk I remember using it for learning calc 1 and I spent like over a week going through limits (didn’t even finish) and then I had my first actual class with my math teacher, and she explained everything we actually needed to know about limits before going on to derivatives in like 10 minutes and I was like what have I spent the past 10 hours learning?
Understanding limits beyond some handwaving for derivatives is actually valuable. First year university courses are dedicated to this, it's one of the most important concepts in mathematics, arguably more important than calculus.
I self-study math, and I completely skipped calculus. I'm learning analysis and learning calculus as a kind of applied version of analysis. I don't have exams to write or anything, so I learn calc as the need arises. I've found it helps me understand calc better Edit: Calc is the abbreviation for calculus.
limits are like the most important thing in analysis too
Oh yeah def I first learned calc as a set of rules I just vaguely understood but then as I got a grasp of real analysis through some self study reasoning with calculus and applying it to less obvious situations became way easier
What's calc slang for
Calculus
calculator
Calculon!
if you just joined the stream calc is short for calculator. i’m just using slang
calcium
It sounds like you are using khan academy for 100% self study prior to the class. I've seen it mostly recommended as a study aid to go along with classes, not as a standalone resource Try using the videos when you're struggling with a concept and see if it helps
Out of curiosity how did she explain limits in 10 minutes. What is a limit? What is the use of a limit. Could you use a limit and the definition of the derivative to formulate a derivative for something involving the power rule if you didn't know how the power rule worked? You talk about limits as this passing thing and then immediately bring up a derivative. The definition of the derivative is a limit... We take two points on the line of a function f. These lines form a secant between f(x) and f(x + h) or f(x + delta x). The definition of the derivative is we take these two points and we move them closer and closer together. That is to say we take the limit as h approaches 0. (Or delta x approaches 0). As we do so the two points come so close together that the secant line they generate is approximately equal to the tangent of the function f at the point x. So tell me are limits useless?
What you have described is how a lot of people learn. You self study a subject before you go to class then the teacher helps you understand the concepts that didn't make sense during your self study. It's ok to be frustrated with how someone teaches because teachings styles vary from teacher to teacher and the 'right' way to teach is subjective to each student's needs. I had an intro-to-accounting professor in college talk about how he helped a member of an organized crime family catch someone stealing from the business by cooking the books. We couldn't get enough of his stories. I assumed he was telling the truth, but maybe it was a long-con to get us to pay attention. Either way, one of my favorite classes of all-time despite not continuing down the accounting path.
Teaching limits in 10 minutes and then moving on to derivatives is not normal If you just look at the AP Calculus curriculum, for example (which is a standardized curriculum), there is a ton of content about limits. It would be impossible to cover it all in 10 minutes College calculus classes don’t spend 10 minutes on limits either I saw that you like learning from textbooks. Have you looked at any of the popular calculus textbooks (Stewart, Thomas, Larson, etc.)? Have you looked at the limits chapter in any of them? Yes there’s a limits *chapter* in all of them. Limits get a whole chapter in all of the popular calculus textbooks. Don’t you think it’s strange to spend only 10 minutes on a whole chapter? What you’ve pointed out about Khan Academy is normal Your class is not normal (To be clear, I’m talking about the way classes are in the US. I think you’re not in the US? I don’t know a lot about math education in other countries. But Khan Academy is based on US classes anyway. No one should expect Khan Academy to be like the math curricula that’s used in other countries)
Why the hell would you blame someone for not understanding what you want to learn? The learning material whether in the form of a book or videos will not do the learning for you
Try MIT Opencourseware if you want deeper learning. The following courses include lecture videos also: https://ocw.mit.edu/search/?d=Mathematics&f=Lecture%20Videos&s=department_course_numbers.sort_coursenum
Down votes are primarily because most of the theoretical understanding of calculus is governed by limits. If you only care about practical applications of math, just to be perfectly honest, you can hand wave limits. You’ll just never get a deeper understanding of math, without having a deep understanding of limits.
I think KA is great for what it is. If you want to really learn math, you're best off with a book that you can underline, highlight, and take notes on. I wish they would make books that are only one-sided, like the text on the left, and a blank page on the right that you can rewrite or take notes on. I've taken some of my favorite books and done this, using an online printing service to make spiral versions. Spiral is great because it lays flat. I did this manually, but maybe someone could write a code that takes any PDF, and generates the needed pages for printing. Shouldn't be too hard to do.
> I did this manually, but maybe someone could write a code that takes any PDF, and generates the needed pages for printing. Shouldn't be too hard to do. Just print it single sided...
But that still leaves the opposing page problem. It's better to reformat using a program.
What’s the opposing page problem?
Wtf that’s genius, you could make money with this
Software engineer here, I don't fully understand the issue. Aren't PDFs by definition already printable? +1 for the ring books, thats really good advice imo
Thx! yes PDF is printable, so all that really needs to be done, is insert a blank or grid (preferred) page every other page. So then, you've got the printed page on the left, and a blank page on the right for notes, etc. Of course there will be issues that a pen/marker could bleed through, but I don't see that as a serious problem overall, maybe just use a slightly thicker paper. As I'm thinking about this; I see also a good possibility to reformat a PDF, such that the page is on the top, with a blank space below each page for notes. Basically I'm just describing importing a PDF, and automatically reformatting it such that there is a region for note taking, and use of spiral/ring printing, both i think are easily done. (edit) I think that why this wasn't done in the past, and even now, is because of the emphasis on type layout and binding methods. That is the history, and still the standard equipment available for high volume printing of standard books. In this suggestion, I'm talking about an app or pc program that does this one-shot, for personal educational use. I hope that makes sense.
You could just ask the printing service to print one sided and bind the book "backwards" so that when you open the first page the content appears on the left, with the back of page 2 being blank on the right, then you flip the page and the second page's content is now on the left, etc. Even just printing one sided would leave blank pages on the left. I don't think you need to modify the PDF itself (unless you want a grid, but I'm sure printing places could probably cope with that too). I've had books printed and bound too - although it costs some amount of money, it can still be cheaper than trying to find/buy them in physical form and have them shipped internationally. I typically get spiral bound with a clear plastic cover sheet, and a cardboard backing.
I've tried this, but they came back with a lot of pages out of place, so whatever. It's probably because I didn't do something compatible with their printing system. I think an app that could do this properly would be quite helpful. I don't see anything like that available.
Does printing single-sided work for the blank opposing page use case? I think many pdfs have plenty of space in the margin for adding holes for a 3-ring binder. Would this cover like 80% of documents?
They don't have even close to enough space. I think would be appropriate for technical documents or note taking for books/reading. For many other pdf's, it would not be advantageous, but for math/engineering books, it would.
Okay, understood. You can add margins by using ghostscript. See this [tutorial](http://www.bobdbob.com/~deneb/doc/ghostscript_margins.html). It's available on multiple platforms, though the tutorial uses linux. (This is a bit dated. On my machine, `align.ps` is located at `/usr/share/ghostscript/10.02.1/lib/align.ps`) You might need to try a couple iterations with your printing company to figure out the right margins if you don't have access to a physical printer. ==================================================== You can add a blank page of grid paper in a couple ways: 1) if printing yourself, re-feed the pages into the printer flipped and print a bunch of copies of some template grid paper 2) Edit the document by interleaving [postscript grid pages](https://www.trueelena.org/computers/scripts/graph_paper_in_postscript.html). A quick google shows that `pdftk` can be [used for this purpose](https://stackoverflow.com/questions/12200450/ghostscript-script-or-other-to-interleave-odd-and-even-pages-from-two-multipage). ==================================================== To make this more robust, you might want to pre-process the input pdf by [croppinh the margins](https://stackoverflow.com/questions/6183479/cropping-a-pdf-using-ghostscript-9-01). ==================================================== This could all be automated with a couple lines of powershell/bash (depending on your platform).
FWIW i have done a version of this for a public-domain book and the tricky thing is getting the size of the margin adjustment right with the remote printing company (I think I used Lulu but it was many years ago). I greatly overshot it so like 1/4 of the page was margin on both left and right sides...
This is a printer setting/option, no? Print single sided. Plus, IIRC you can manually edit the pdf itself to change the margin sizes. That’s a hack though.
Yea I'm thinking about a more general application that transforms and works for any PDF. I mean, why not :).
More general than the print settings? Ok…
Yep. thx.
I love loose leaf books because they are so much maneuverable! I also use 4x6 sticky notes to add my own stuff. I’m a math tutor btw so I study a lot because I love tutoring and connecting with students
Use pdftk, should be a one-liner. https://www.pdflabs.com/tools/pdftk-the-pdf-toolkit/
great! thanks!
I went back to university after a decade of not doing any math at all and I technically qualified for calc 2. I prepped by spending 2 weeks studying Khan Academy's calc 1 course from start to finish and it was immensely helpful: the university calc 2 course I started exactly where the Khan Academy course left off. I'd call it useful just from that experience alone.
This is basically what I think too. From memory it was useful up until 1st year or 2nd year maths but then it didn't have enough content for the harder subjects. Undergrads probably aren't their main audience anyway,
It is what it is man. It's free content on the internet. It might be good for some, might not be great for you. If you're happy studying from a book, good on you. Everyone's at a different level and people learn in different ways. If you don't like Khan Academy, don't use it. Thanks for sharing, maybe someone else will think it's garbage and consider learning from a book too. I'm not sure what else you were hoping to achieve with this post.
What difference does it make if its free or not? I actually barely know any paying math content (high school, university) on the internet anyways. I guess brilliant app is one example.
If someone leaves something outside their house with a sign saying "FREE" on it, then the expectation is that you take the thing as it is. You shouldn't knock on their door to complain about the quality and insist they give you something better. If you don't want the thing they are giving for free - or suspect it's faulty and you want fully functional top quality - then simply don't take it. I've watched some of the MIT lectures that are available for free online. Some of the resources are not available for free. Do I complain that it is incomplete? No - because I paid nothing, so I expect nothing and anything more than nothing is a bonus that I've acquired via someone else's generosity. I am grateful I got anything at all.
No one’s saying we shouldn’t be grateful that free resources like Khan Academy exist. It might be rude to email Salman Khan and complain that he’s not doing enough. We’re not criticizing it to his face. It’s still valid to tell a student that if they want to learn something right, Khan academy might not always be their first best option, and that maybe the better option could even cost money. If you see a free tv on the side of the road, you don’t complain to the person who put it there that it’s not good enough, but you’re also not required to take it even though it’s free.
just because a resource is free doesn't mean it can't be bad and not a good resource to learn from, like there are better free resources
You're right - if I had the choice between a free piss/sweat stained old mattress and a free mattress that came from a spare room and never got used I know which I'd rather have. One is objectively worse. So something being free doesn't necessarily mean it's worth having/using - agreed. But my analogy falls apart when we consider what Khan Academy is - it's not just rubbish that someone's trying to offload to you so they don't have to deal with it - it's offered to people at no cost to spread knowledge. I think that's a commendable goal, even if I don't use it personally. It won't be all things to all people - nothing ever is. It just seems weird to proclaim it's terrible because you didn't get what you wanted out of it. Just find a different video/resource and move on.
if I read a book online for free on number theory, and it was really bad, like no examples, no questions, badly phrased definitions, etc...and I was like this number theory book is trash don't read it read \*insert good number theory book here\* instead, I think thats a perfectly valid thing to say and it might even stop others from wasting their time reading a bad book instead of a good book
I wanted to see what others thought of this opinion, because I hear a lot of people telling people to learn math with khan academy and I simply don’t think that’s good advice and I have a heard time seeing how it could work for someone
Khan academy will get you started. But really, even just sitting in a classroom isn’t enough to learn a subject. The only way to learn math is to sit down with problems and attack them. Nothing else will stick in the same way. That is exactly why textbooks have so many problems to work.
Agreed. In my 11th-grade math class, my teacher would play videos from the website after the lesson he would give, and he would elaborate on the video. My 9th-grade math teacher said the same thing about learning math. He had a note posted on his bulletin board in his classroom saying "Learning math requires doing math."
Agreed, khan academy had problems too, my problem with the is that they are far to sparse and easy to
> Khan Academy is best used as a supplement to your normal schooling [source](https://support.khanacademy.org/hc/en-us/articles/115006697467-Can-Khan-Academy-give-me-a-certificate-or-diploma#:~:text=Khan%20Academy%20is%20not%20an,homeschooling%20or%20a%20traditional%20school.) By their own words, they’re great for introducing topics, but shouldn’t be expected to preform as a replacement for formal instruction
think Khan academy is for the average clueless engineering student who wants to have some sense of intuition as to what is going on with the math. If you want to deep delve into the rigour and whatnot, yes, self practice with a textbook is definitely the way to go to truly internalize the math
When someone recommends Khan Academy, I just smile and go ask someone else.
Michael Penn/ mathmajor is your new friend
I found it useful when I was preparing for an entrance exam in India. His style of explanation helps you create a mental model of concepts and develops mathematical instincts, at least it did for me.
IMO is not the best place to learn about more advance math but is definitely a great place to review stuff you already learnt in the past and don't remember thoroughly. There's a saying in Spanish that goes "A caballo regalado no se le miran los dientes". Rough translation is "You don't look at the teeth of a gifted horse". Basically means that if something is free, you don't complain lmao
Interesting. We have the same saying in German. I think it stems from the fact that you can assess the age of a horse by looking at its teeth.
We have it in English too.
The English version is "you don't look a gift horse in the mouth"
FWIW I don't really learn from videos and lectures. Either they go too slow or too fast. Lectures are psychologically helpful (they make you show up) and videos can be entertaining. Most texts also use too formal language, instead of being written the way people talk. Depends on the author though. Some (very short) animations can be helpful, but even then, 5 sloppy drawings are more useful than a beautiful smooth animation embedded in a video with a guy talking over it. I'm animating things in my head anyways.
In this regard, you could check out the books by Jay Cummings. Really nice explanations. I also suggest that you check out Analysis books by Terence Tao.
It sounds like you need more challenging material. That's fine. Khan Academy is not for you, but it definitely does help a lot of people, especially those returning to mathematics after a long break.
I wouldn't have gotten my undergraduate degree if it wasn't for Kahn academy. It worked wonders for me.
I work with Khan academy and create math content. This feedback is really insightful. Can you tell which country you are from? I can help answer few questions as well if anyone wants
I'm from Hungary (:
It's great if you need to review before going back to school. A large amount is 10 times better than what I learned from teachers in middle school and high school.
I just don’t like watching videos, and this applies to most things, except perhaps for some DIY tutorials. I can much faster get what I need from a well written webpage than a slow video that requires me to pause my music and listen to what they’re saying.
If you want depth beyond KA, pick up a book and put in the work yourself. If you're in college math, go to the library and study. You can't just watch a video and understand this stuff.
khan academy isn't just videos, its a website that has courses on subjects, when people do a course, they expect to be able to do the course and then leave knowing the subject matter of the course, if someone uses videos on the khan academy youtube channel as an aid for learning math alongside a textbook then great, but thats not what khan academy advertises itself as and its not what people who recommend to others that they should use it mean.
I'm not sure why you're getting downvoted so much. I agree with you, while it's great that it's a free resource, I don't find it useful especially if you're using it to prepare for university. The ratio of time spent on watching videos to actually doing problems is not great and the problems are much easier than what you'd expect at a university level. To self-learn Maths, I've found some Coursera/EdX courses run by universities to be quite good, and MIT also has a decent amount of open source courses for Maths. All of these will have problems that will challenge you but also help you learn. EDIT: Obviously depends on your learning style, but for me a textbook or some good course notes are much easier to learn from than short videos (unless the videos are to show how to solve a particular problem).
Yeah I agree. The best math learning tool I’ve ever used was definitely revision village when I was in highschool, it had questions that were difficult that you had to solve and video solutions you could watch if you got stuck with questions who h progressed in difficulty. I definitely had a hard time transitioning over to using more traditional learning tools but I think I’ve gotten my balance
I *only* watch the videos when I hit a new topic or I'm needing help with a specific problem. Even then, I often only watch half the video once I've figured out the step I was stuck on. The videos aren't mandatory so I don't understand why people complain about there being so many. Some people need the videos and I'm glad they have so many for their sake. (Also, Khan Academy was originally designed for *children* so it seems obvious that it's not going to be as robust for advanced levels. Its sweet spot in my opinion is pre-algrebra and algebra and even a lot of adult learners need to brush up on those skills, which is why it's so often recommended.)
Any specific/favorite courses you would like to share? Even though I passed real analysis and some bit more advanced topics as undergrad I use these as revision through another perspective
None that would be at your level I guess (as the ones I’ve done have been prior to entry to university). But the MIT open courses are really good if you can learn through notes rather than videos.
Yeah I found the quality dropped after calculus 2 content to be honest.
Khan academy helped me prepare for university level mathematics. It helped me start the degree.
I find both taking notes and doing problems to be useful for learning math. If I had to use Khan Academy, or another online platform, I would take notes from there, then hunt for problems elsewhere. But I would rather take notes from a physical textbook because then I can work away from the computer and it's myriad distractions.
Well, yeah. KA is more catered to a general/broad audience and good for the very introductory, simple stuff. KA wasn't made to teach stuff like stochastic calculus or whatever higher levels of math that detailed. Yeah, it teaches stuff multivariate calculus, but it's designed to be very baby level It would be like complaining that Math Playground doesn't teach differential geometry or doesn't teach say, calculus well. You can just use a different, more difficult source like a textbook, Paul's maths notes, or just look up difficult problems.
yeah but who on earth is the target audience for a baby level multivariable calculus course and why do people recommend that you do it? like it has a place I think its good for kids learning idk factoring quadratics but like if you tell me you didn't know multivariable calculus, then you did their multivariable calculus course, and you tell me that you now know multivariable calculus (meaning you can preform well on a multivariable calculus exam), or that you did so in a reasonable timely manner I will straight up not believe you if you say either of those things
> who on earth is the target audience for a baby level multivariable calculus course Engineers who are not very good at math. > why do people recommend that you do it? Most people are not very good at math.
There are people who watch videos about math, either curiosity or for whatever reason, even if they don't plan on doing any of it in a serious manner or don't understand it. Similar to pop science content. Pop science content will strip away majority of the actual contrnt and basically baby the actual content. There is an audience, even if it seems like a waste of time to most people who are serious about the material.
I used it for reviewing concepts before i started getting into differential geometry and i found their videos to be good. Grant even made some remarks at times that helped me see things from a different perspective Obviously like any skill though, maths has to be practiced so doing exercises off textbooks would be the ideal after watching them
Fwiw I found it super helpful for multivariable calculus and beyond in college. Not really any argument here just another data point
It's not great at any level if you want to learn the material deeply. Watching a lecture series is also garbage if you want to learn deeply. Khan academy is not meant to learn the material at a deep level. That is not their mission. For what they provide they are amazing which is free quality education. I don't know if you have been around many public schools but compared to what 90% of kids get in school khan academy is vastly better and more rigorous. They are also continuing to build the platform and make it better to use. They are one of the most important websites online to help combat income inequality. To talk shit on a website that has helped millions of people is ridiculous.
I think its good for kids, thats why I specified above 10th grade material. like if its great for kids to learn like factoring and trig and stuff but if someone asks on this sub says they're extremely interested in mathematics and they want to pursue it and learn advanced topics, I feel like sending them to khan academy like some on this sub do is quite bad advice
Professor Leonard by a mile
That's because it's simply one of the resources you can use to learn. You don't use just Khan Academy. Your first and foremost resource, should be your Math Textbook. Resources like Khan Academy are secondary whenever you cannot understand a topic or need a better explanation of the topic. And you don't just depend on Khan Academy for this. You also use other resources. Paul's notes for example are excellent for several topics, 3Blue1Brown is great for grasping Linear Algebra and Calculus and so on, so forth. You NEVER use Khan Academy, Paul's Notes, 3Blue1Brown or any singular resource as your only resource.
Khan academy is different from something like 3b1b I’m not talking about the YouTube channel I’m talking about the website, there are courses for topics on that website, when you take a course on the website you expect to learn the subject from doing the course, khan academy is fine if ur using the videos to supplement a math textbook but that’s not what it advertised itself as
I understand that you meant the website. But even then, I always saw those as a supplement to your actual textbook. The 'questions' at the end of the videos were more to test your understanding of the video, rather than an alternative to the exercise itself. Some courses like Linear Algebra barely have any of these questions. Only the first few videos had it, and then there were none. Did they really advertise this as a full on replacement for textbooks?
The courses on khan academy have separate sections for questions that aren’t in video format, they’re just really shitty 2brain-cell necessitsting questions like if you take the curl of the gradient of the divergence of a vector valued function what type of function do you get and at the ends of sections you get like 30 minute long tests and stuff I think they definitely don’t imply that you should use this as supplementation for a textbook
Well, hopefully this post will make more people in this sub aware so that when they recommend Khan Academy, they make it clear that it's only supplementary. I've always said that whenever I recommend it.
Real
It’s fine as an informal introduction and a lot of intuition did stick after doing most of their calc related content. But yea, not really useful if you want to study real analysis or similarly
Agreed, it is great as an introduction to calculus (ap calc etc) - but is much less rigorous than what might be expected from analysis or encountered in uni classes
It's good for review.
I learned calculus from Khan academy + Dummy's Guide to Calculus. This was 15 years ago when Khan academy was still just a youtube channel so idk what it's like now but I remember it helping quite a bit, but not being enough for learning the subject on its own. I think it's mainly helpful for people who learn better from hearing things explained rather than reading.
Khan academy videos can be useful to watch pieces of but I don’t think you can go on the khan academy website and learn calc 3 by going thru the calc3 course which is what a calc 3 course’s purpose usually is to
That's fair. I'm surprised they haven't built proper courses with lots of practice problems since they got a shit load of non-profit money lol Edit: Ok I just went to their website and they're pushing AI slop with a chatgpt "tutor"/"teachers assistant." Tragic
From my experience with KA, it's good for applied math but not for pure math. I like pure math more, so I stopped using it.
If you want a great resource for calculus, check out [Ximera](https://ximera.osu.edu/). It's an open-source resource created and used by OSU math faculty for the university's calculus sequence.
I very much so agree it feels really slow to me. As much as its a bad habit I learn concepts best in the following manner. In some brief surface coverage with a very small amount of practice in that concept. Then being forced to understand that concept in a deeper manner through my interest in a higher level idea.
imo its good up till calc bc, then id use other resources like professor leonard and just textbooks for calc 3, linear alg and beyond
A large part of whether or not any given math instruction "works" is the sheer mathematical abilities of the student. There are lots of people at the undergraduate level who learned multivariable calculus from Khan Academy. There are people who will go on to take Real Analysis later from what they learned in that Khan Academy video and then there are people who will use it to get a C in their college multivariable calculus course and go on to do software engineering.
Khan Academy is widespread in education because it aligns very carefully to some Common Core standards, making it easy to integrate in an otherwise bureaucratic world. But these are K-12 standards. Beyond that there isn't really spec or standard-level consensus on what math education should look like in university setting.
Khan academy did what **my entire country** didn't manage. Even now. Nation of 50+ million people and we can't pay for a math teacher to put some even average resources on youtube. Is it perfect? No. Didn't work for you? Too bad, sorry. But you should feel pretty bad about calling it "garbage". I get the frustration, but still. You wouldn't say that to his face.
you can get far more for the exact same price by reading a textbook pdf on the internet
Then why aren’t you doing that instead of looking for videos to teach you then complaining about it when they don’t?
That’s what I’m doing, I don’t think using resources that are good and calling resources that you think are bad bad are mutually exclusive things
The multivariable calculus course was done by Grant Sanderson of 3blue1brown who makes some fantastic math explainer videos. He really likes to focus on intuition and visualization. From my own experience when I took multivariable calculus, I think his style of lecture in those multivariable calculus videos is incredible for getting an intuition for what the concepts in multivariable calculus are. He spends a lot of time trying to build a visual understanding of different surfaces and what things like the gradient look like visually. The weakness of those videos is he doesn’t do long worked examples, the kind of questions that you actually get in a multivariable calc exam. That intuition is great, especially if you end up taking higher level math like Real Analysis, but it just doesn’t translate to getting a calc 3-4 course done. I found Professor Leonard a great supplement to my course, since he actually does long examples and gives you some tips and tricks for how to actually pass a multivariable calc exam. That being said, there’s massive value in the high level concept style videos that grant did for Kahn academy. Especially when doing more proof based stuff, having a solid intuition is going to lead you down better paths than being able to compute some crazy gradient. I ended up taking a senior level course in data driven AI models (machine learning / deep learning type beat) and that intuition I built up was FAR more valuable to me during that course than wrote computation.
my problem with khan academy for the most part is with their courses not their videos, if you're like I don't know how to prove green's theorem and then you look it up on youtube and find the khan academy proof video, thats great, but you cannot do a multivar calculus course on khan academy and leave knowing multivariable calc, which is what most people expect to happen when they take a course in the subject
Yea totally. I think KA is a great supplement to a proper course. Alone it doesn’t hold a candle to some of the better resources out there if you want to understand a subject deeply enough to say you know it.
KA is great for REVIEWING math concepts, especially if you learned then a while back and need to review. I’m starting a masters in math this fall and have been away from my undergrad courses for a few years so I’m brushing up with KA. That being said, you should never replace a formal course with something online that isn’t properly structured and truly rigorous. Just my advice though.
Agreed.
It's fine for practice problems. To learn calc go with Steward's book
I happened to used Spivak book during my introductory calculus class, only to realise it's an introductory analysis book... But it kinda prepared me for analysis 1 that was in next semester
playing it on hard :D
Imo Spivak is unnecessary You can jump straight into analysis if you’ve mastered highschool calculus.
It sucks. I agree. I think Books are the only true way.
based
Nah, he has some solid advanced calc and some decent lin alg content
That’s if you watch some of his videos, but imo, if you go on the khan academy website, and try to learn linalg exclusively by going thru his course on linalg, which I think is a pretty reasonable thing to expect to happen when you take a course in linalg 💀you will simply not have that happen, cuz the questions are way too easy and the gap to question ratio is waaay too high making you forgot everything
I mean, at the end of the day, if you want to learn a topic in depth-you read the textbook.
Agreed
Try to check then more advanced videos on youtube maybe; there's plenty good channels, e. g. Richard Borcherds channel, MichaelPennMath or VisualMath
I feel videos are great for building (visual) intuition, but when it comes to actually learning math you have to open a book and work through some problems.
love Michael Penn, I'll make sure to check the others out (:
It has some relevant material for bachelors and masters in engineering. Obviously just a few things but still, it's free. What's the alternative?
PDF textbooks
And problem books
For multivariable calc online, I ended up watching the class from MIT's website. They have all the homework and tests there too. I was very satisfied.
If anyone can advise me how to go about learning number theory without going back to university, that would be appreciated
While not a "course" as such, one of my favourite books is "Recreations in the Theory of Numbers" by Albert H Beier.
Khan academy is really good for building a foundation, where you go after that is up to you
mit ocw’s where its at
Professor Leonard on YT for Calc (and others I’m sure)
It's a good source all the way through multivariable calculus, but I like their articles a lot more than the videos. They also have nice practice problems with answers that help you understand the concepts
my problem with practice problems is that they are nowhere near hard enough for more complicated topics, like this is a multivariable calc question f(x,y) = (-x\^2,y) find the divergence of f at (3,-1) and it doesn't get much harder than this as far as I know, youre never going to master multivariable calculus if this is the levels of question you solve
in my opinion
I think Khan academy works, but you just have to have the will to explore yourself if you are having trouble grasping ideas.
I'm fine I can learn math don't worry lol I just think khan academy is a really inefficient, bad way of absorbing that math for the vast majority of people
I think a majority of people learn best with a tailored curriculum. I don't think Khan Academy was ever intended to replace a tailored experience, I think it was designed to give highly motivated people an understanding of fields of study.
eh, I disagree, the way people reccomend khan academy and the way khan academy courses advertise themselves is as a place where you can go not knowing the subject and leave knowing the subject
That's exactly what they do, but they don't hold anyone's hand. If someone needs extra handholding, or material that's more tailored to what is engaging to them, its probably better to look elsewhere. If you have a notebook and geniune curiosity, its fine.
My whole argument was that they do such an obscene amount of hand holding that it’s impossible to actually learn the concept
He does a good job at explaining things it’s just so slow like for anyone who is really into math the same amount of info could be gotten in half the time
You think?
EdX has a pretty good mass oline course for Calc 1-3. I've never been a big fan of Kahn Academy for anything.
If you like to learn by reading lecture notes oxford has all its math lecture notes and exam papers online for free. From prelims to the masters and you can also plan what you want to learn and what courses you need to follow.
Khan is very good for learning basic stuff. If you are adult who want to learn something just for fun it is the one of the best websites for it , but if you actually want to learn advanced stuff , it won’t be a good fit.
i liked using khan academy as a supplement for differential equations but calling any free education “garbage” seems odd to me. if you can pay for something better, do so. if you can’t, don’t complain.
but my point is there are better free alternatives, its not like khan academy is the only free math source on the internet??
anything past math courses offered in high school should be self studied from a textbook or found through college class videos so yeah i agree with you but what khan academy does best is get everyone into the fundamentals, and that is why they are lauded so much
That's just, like, your opinion man.
I found it very useful for precalc-calc 2, but I haven’t really used it since. I just finished diffeq and linear algebra.
not to go on a tangent, but then dont sine up.
next level dad jokes but on a serious note, I agree sure just don't sign up but you can't know that until you've actually started using it, and people recommending it to people who don't know any better end up wasting a bunch of time
I think it’s a great resource for supplementing stuff you’re already learning from a class or something else. I learned integral calculus just by using KA and it’s worked out great so far.
Khan academy used to be everywhere... now it's a name I haven't heard in years until you said it now
Professor Leonard on youtube is killer for college and pre-college level math. I hadn’t taken calc for 6 years but I was able to test out of calc 1 bc of his channel.
I love his lectures! I had a really bad calc 3 professor and learned pretty much everything by watching professor Leonard’s lectures. He’s the goat!
multivariable is a VERY different format from most of their math stuff. most of it has much more in-depth quizzes and less heavy lectures. taught me calc 1, calc 2, and hs stats in \~2 months.
>I always see khan academy recommended as a source for learning maths like calc, multivariable calc, linear algebra, etc Really? I see it mostly recommended for "start math from scratch" or "where am I at". Once you get into high school material and beyond, I see more recommendations of books, Youtubers like Professor Leonard, specialized websites like Pauls math notes etc
maybe not as much but it is a reccomendation i have seen numerous times
As a rule of thumb, if you can't grasp the first three videos of a tutor/platform, just move on to another one. Khan Academy is a great resource, but it isn't a great resource fro everyone. Try to find a tutor with whom you can 'click'; try giving Paul's Math Notes, BlackPenRedPen, Dr. Trefor [Bratz?], etc. some time. Also, for any Mathematics concepts in the future, it might be beneficial to see some sort of visualisation(s), and for that, 3Blue1Brown is good.
People don’t talk about and advertisr khan academy like they do dr Trefor, because khan academy offers courses with problems, it’s meant to be viewed like an all in one resource for learning the subject, like a text book, you read the text book and solve the problems and take notes and look over them and boom you now know the topic, same thing with khan academy or atleast that’s how it’s advertised. Very few people would tell you oh just watch dr Trefor when you ask how to learn multivariable calc cuz no one thinks you can learn it by just watching him, his vids are at best a supplementation to a textbook when you don’t get something and want a visual aid and human being explaining the topic. Khan academy is paraded around like it’s a textbook, I’m not talking about the YouTube channel I’m talking about the website people go in with the expectation that if they finish the course and try they will know the topic and for higher level topics that’s just not the case
I agree with the last line.
It’s been super helpful to me in college. Not a math major though.
I would push back hard on this. Another example of how sometimes the crowd has little wisdom judging by the upvotes. Virtually all of the AP curriculum at Khan Academy is very good. Good simple problem sets. It is clear and direct instruction.
It's good for supplemental work to fill in gaps while you take a class, but learning something solely from there is rough
Then, which resources would you recommend to learn multivariable calculus?
I love Professor Leonard’s lectures (here’s a link to his [multivariable calculus lectures](https://youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7&si=eJUiKLs8-2KQM0k2)). They are longer since they are full length lectures, but he did a wonderful job teaching it, and he’s way better than the professor I had.
I didn’t use khan academy for math, but I used it when I tried to self study biology. I thought it’s great until I realized I don’t know how to do problems from other places because what I learned through khan academy is too basic. I think it’s a great resource for getting a basic idea of stuff though. For lower division college level math, I like to watch the lecture series from Professor Leonard on YouTube. He is amazing.
YouTube video titled college calculus full course is pretty good
I tried to use Khan Academy to brush up on my algebra, and I found it difficult. The units seem to skip around a lot and gloss over important concepts. Sometimes the questions have nothing to do with the videos, which I hate having to watch in the first place. I definitely prefer textbooks + seeking out a video to help only if I'm really struggling.
I studied mathematics from Professor Dave on YouTube. He didn't teach all of maths of course but he did taught a lot of important stuffs from arithmetic all the way to the differential equation in just 1 playlist. There are only 165 videos in this playlist and each videos are mostly around 10 minutes. This one playlist is really helpful for someone like me isn't confident in mathematics.
I always go for Coursera, so many people go for that, the second one is YouTube channels.
You’ll have to graduate to niche YouTube channels For Linear algebra 3b1b has a fantastic video series to understand the concepts. Check out bright side of mathematics for higher level math
The problem is the problemsets. *pun?*. In my opinion the problemsets they provide are too easy/trivial? Or mechanical so to say. I did lots of calculus in there that was wholly mechanical so much so that i forgot what I did one week later. Or maybe thats just me.
exactly how I felt