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I am in my late 20s learning mathematics using Khan Academy. I have always passed my math with borderline grades.

Since last year I have joined Khan Academy, I have learned voracious and re-learn every single thing from scratch.

I would like to know after learning all the math topics on Khan Academy, what level of mathematics am I equipped with? i.e. High school/college/undergraduate?

How can I further my understanding in math?

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  • $\begingroup$ In answer to your last sentence: To further your understanding your best bet would be going to college. If that's not an option, then you could try MIT's OpenCourseWare. They have lecture notes, homeworks, and even video lectures for certain courses. Along those same lines are edX, Coursera, and the Ximera Project. If you'd like to know roughly what topics you should be learning, I tried to make a... $\endgroup$ – user137731 Jan 4 '15 at 23:37
  • $\begingroup$ roadmap for learning undergraduate topics last week which you can look at (though I didn't quite finish because the question was put on hold). Note though that the main benefit of university is that there is someone checking over every bit of work you do. If you're trying to learn on your own, you're handicapped in this regard. $\endgroup$ – user137731 Jan 4 '15 at 23:38
  • $\begingroup$ @Bye_World sadly, I lie in a similar situation as the OP. I've found MIT courseware disheartening. Many times you run into a course, you're excited and you'll then see random bits of content missing. Solutions missing, maybe notes, or assignments etc. $\endgroup$ – gideon Jan 5 '15 at 14:50
  • $\begingroup$ @gideon You could use Internet archive to get books on topics that are missing are learn from them. $\endgroup$ – A---B Aug 27 '17 at 17:00
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My experience with Khan Academy is that it has decent coverage of K-12 mathematics, and increasingly spotty coverage the more advanced you get. In answer to the question, I would say that mastering the Khan Academy materials would put you ready to take a GED (high school equivalency exam) or SAT (college entrance exam). You would also have hit-and-miss knowledge of calculus and additional advanced topics. It's no substitute for taking the courses at an accredited college or university.

For example, I've taught flip (upside-down) calculus classes where the students view lectures from online sources that I've aggregated. Khan Academy videos alone would not enable anyone to pass the course; some topics get decent coverage while others are completely omitted.

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  • $\begingroup$ It may be worth mentioning that a good function of Khan Academy at the university level is to give another lecturer's perspective on a particular topic. I found some of the videos on multivariable calculus to help quite a bit when it came to studying for exams. $\endgroup$ – Bib Jan 4 '15 at 17:56
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    $\begingroup$ @vadim123 how is it compare to A-Levels? GCE A Levels? $\endgroup$ – ilovetolearn Nov 23 '15 at 4:48
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    $\begingroup$ Khan Academy is constantly adding resources, and their advanced mathematics topics are already significantly more complete than 2 years ago when this answer was posted. $\endgroup$ – Zaz Aug 12 '16 at 17:25
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    $\begingroup$ @youcanlearnanything: It covers A-level material very well now; I can't think of anything I saw in A-levels but not on Khan Academy. $\endgroup$ – Zaz Aug 12 '16 at 17:26
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I've used Khan Academy here and there while earning my degree in mathematics to reinforce my understanding of topics that were covered hastily during lecture etc. I enjoy it because I can focus specifically on those topics that I want to focus on.

However, Khan Academy is better used, in my opinion, as an ancillary resource. I think subscribing to a structured course, such as those offered through MIT's open courseware program, might be a better idea. If nothing else, those structured courses are likely to more thoroughly cover each subject, which helps you avoid holes in your understanding of each subject.

As I have begun to teach myself advanced topics in my spare time, I've found that working my way through books while supplementing with online materials works best. Perhaps that is just me? I think having lots of exercises really helps reinforce my understanding of ideas. For example, I can absolutely understand the definition of continuity offered in analysis. However, reading the definition and the proof and understanding both is much different than sitting down and working my way through a dozen delta-epsilon proofs. This coursework is often missing when using online material, hence my reasons for guiding my studies with textbooks.

If your concerns are more broad - something along the lines of "what topics should I study if I want to give myself the rough equivalent of an undergrad degree in mathematics" - then your best bet is to pick out a few course catalogs from some top programs and systematically study each subject in whatever way works best for you.

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    $\begingroup$ I am not sure if this applies to everyone. After moving on to a new topic, I seem to forget what I have learnt in the previous topics. For each math skill in Khan Academy, you have to attempt 3 times before you are considered to "master" the skill. Did I really learn Math the correct way? $\endgroup$ – ilovetolearn Jan 5 '15 at 13:31
  • $\begingroup$ I intend/am learning in the following order Algebra 1 -> Geometry -> Algebra 2 -> Trig -> Pre-Calculus -> Calculus $\endgroup$ – ilovetolearn Jan 5 '15 at 14:05
  • $\begingroup$ That sounds like the standard order. And again, adapt that however best fits your learning style and needs. I stick to my recommendation that getting your hands on a textbook is a good idea so that you can have lots of practice problems. $\endgroup$ – 123 Jan 5 '15 at 15:06
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Khan Academy tends to oversimplify some topics, so that they can be easily understood by newcomers. Although this is totally understandable, when you study at a university you want to emphasize more in some things..

That being said, the only way (imo) to gain the most from Khan Academy is by following your class lectures and keep watching the parts, you have difficulty in undestanding during class. This way you can benefit from the simplicity of the lessons, and as Bib mentioned in a comment above, it will sometimes give you a different perspective on a difficult math theory for example.

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