Teaching myself math with Khan Academy.... Advice?

[ToneCoole]

Hello, PhysicsForums. Right now, I am studying high school mathematics on Khan Academy, and it is working out great! I also read all of the articles and do the excersizes and I write down everything that I see. I feel that I will achieve mastery of Algebra, Geometry, and Trigonometry in no time. I know that Khan Academy has courses on differential, integral, and multivariable calculus, as well as differential equations and linear algebra. I have heard that Sal's coverage over these higher level courses are spotty, so I would like some advice. When I get to Khan Academy's course on Calculus, should I also use MIT OCW, and online math notes while I use Khan Academy, or after? I also own a copy of Calculus: An Intuitive and Physical Approach, and I plan on reading through it and doing all of the exercizes. Remember, I want to achieve complete mastery of these higher level subjects.

Please give me advice on what I should do. Thanks for any that you give me, I appreciate it.

 

[fresh_42]

Here's a post I've written for a similar question about self-study.
https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947

I think you should take the time and read the links. Maybe some are beyond your current scope, i.e. have topics for college courses, but the insights on our forum here should be valuable in any case, at least the first four and the last three of those listed. I can't imagine learning only online, but this might be a personal attitude. However, you should check out the link with the (free) books and see whether they can be of help or whether you understand them. In general these links address the transition time from high school to college but openstax also has books for your specific situation.

 

[ToneCoole]

Thanks for that. Not only do I want to master calculus before I graduate, but I also want to master differential equations and linear algebra, and I want to learn some abstract algebra, topology, and partial differential equations concepts. I want to do this because I want to get a PhD in Physics, and I want to get a head start on all of those things.

 

[opus]

I think it could possibly depend on your learning style. For me, watching videos wouldn't cut it. What I hear goes in one ear and out the other. So I have to read books and do problems to make it stick. Not sure how this method would fair for upper level mathematics as I am only in college algebra and trigonometry.

 

[phinds]

Thanks for that. Not only do I want to master calculus before I graduate, but I also want to master differential equations and linear algebra, and I want to learn some abstract algebra, topology, and partial differential equations concepts. I want to do this because I want to get a PhD in Physics, and I want to get a head start on all of those things.

Admirable goals, but don't get caught up in the rush to get to all of those things to the detriment of really learning any of them solidly. Do LOTS of problems in each area of study before moving on.

 

[ToneCoole]

For me, it depends on who is doing the video. My learning style is pretty different from most people.

 

[ToneCoole]

Ok, I read all of the links you posted here, and added all the books to my amazon shopping list. It will cost quite a bit, but I plan on finding a job soon anyway.

 

[fresh_42]

Ok, I read all of the links you posted here, and added all the books to my amazon shopping list. It will cost quite a bit, but I plan on finding a job soon anyway.

The books are free and downloadable. I think they also offer to sell a printed version which might be cheaper than on amazon. If not, then don't forget to use amazon from here!

 

[opus]

Openstax is great. I have the college algebra, precalculus, and physics pdfs downloaded to my laptop. They help a lot when I need a fresh view of something or different explanation. My university just started using openstax for calculus I and the book is only $30.

 

[Stephen Tashi]

I also want to master differential equations and linear algebra, and I want to learn some abstract algebra, topology, and partial differential equations concepts.

When we first began to appreciate math, there is an intoxication and addiction to it. We can't get enough. Enjoy the feeling while it lasts. Hope that it doesn't completely wear off after you've hit some rough spots.

 

[ToneCoole]

I am a sophomore in high school. Do you think this is feasible? I am a very fast learner, and can focus on one thing for a long time.

 

[fresh_42]

I am a sophomore in high school. Do you think this is feasible? I am a very fast learner, and can focus on one thing for a long time.

If you don't start to read too many different books at the same time, the only limitation is your fun, time and how often you get stuck, assumed you recognized if you haven't understood something. In any case you can always come here and ask, get your solutions checked or even just discuss concepts.

 

[ToneCoole]

I plan on studying math for several hours a day; 10 if I can. I will read, reread, and practice each chapter until I understand them, and then move on to the next.

 

[fresh_42]

Don't underestimate the fun part! Simple curiosity is often the key to real understanding. So as long as all is ToneCoole in Wonderland, everything is fine. Don't let it get Dante's Inferno

Here's another article worth to read: http://www.ams.org/publications/journals/notices/201707/rnoti-p718.pdf which has some good advice in it.

 

[ToneCoole]

I will have fun with it! A smaller reason that I'm doing this is to challenge myself. I also have Asperger's Syndrome, and this is one of my "Special Interests".

I feel that I could learn some of the easier subjects in a month, and the harder subjects will take much longer.

 

[fresh_42]

Experience tells me that there are realms which are easier and others which are more difficult. This might depend less on the subjects as on personal favors. E.g. at school we are trained to do calculations and algorithms along certain schemes. Numbers wherever you look, and all of a sudden all numbers are gone and only $-1,0,1,2$ are basically left. And some students never heard about vector spaces at school, so linear algebra appears difficult to them, although it isn't in an objective sense. Or take topology as an example. The basic concept is pretty simple, yet it contains a lot of strange sets, examples up to highly complicated constructions. People who like algebra are often bad at numerical analysis and vice versa. Of course there are exceptions, but don't be surprised if some fields are more fun than others.

 

[Dr. Courtney]

https://www.physicsforums.com/insights/resources-high-school-math-home/