Intro Math Rigorous math/physics self teaching material?

[Quantaliinuxite]

Hi guys,

So, I'm a high school senior about to graduate, and because of reasons, I most likely will not be attending a college next year. However, I will apply to colleges next year for a Physics major. In the meantime, I would like to use my time wisely, and I was thinking that the smart thing to do would be to get as comfortable as possible with as advanced mathematical tools as possible by the end of this year to be able to comfortably go through my first couple of years in college -- and possibly finish in three years. So my thinking is that I should go through a regular math major curriculum while reading the Feynman lectures on physics over the year. If you think that that would not be the right thing to do over this year, please let me know. Otherwise, any textbooks/courses/opportunities you can recommend are more than welcome.Thank you!

 

[Stephen Tashi]

to get as comfortable as possible with as advanced mathematical tools as possible by the end of this year to be able to comfortably go through my first couple of years in college -- and possibly finish in three years.

It's unlikely you can thoroughly teach yourself vector calculus, linear algebra, and differential equations in one year.

If you don't take any courses at community college, what's the plan for finishing college in 3 years? Taking lots of courses per semester? - going to summer school? You need to have a certain number of credits on your record.

As a general rule, self-taught people are not comfortable! - at least they are not more comfortable that students who are not extensively self-taught. Typically a self-taught person hits some roadblocks in his self-teaching, so his knowledge of a given subject is uneven. As a worst case, he might sail his way through the first five weeks of a college course effortlessly, become over confident, and get hopelessly lost in the last part of the course.

 

[verty]

I was thinking that the smart thing to do would be to get as comfortable as possible with as advanced mathematical tools as possible by the end of this year to be able to comfortably go through my first couple of years in college...

One possibility is Edwards & Penney: Calculus, Early Transcendentals Matrix Version (6th Edition).

 

[snatchingthepi]

If you want a good book for teaching mathematics as applied to physics, try Mary Boas' "Mathematics Methods for the Physical Sciences".

 

[jedishrfu]

Ther are also the Openstax.org books on math and physics that may be helpful too.

and the mathispower4u.com website of short math videos.

 

[MidgetDwarf]

Make sure you have the basics down to a T. The basics include algebra,geometry,trig.

What was the last math class you took. Was the material in the class at an adequate level or was it more of the "dumb down" stuff?

Going over the above topics again, to feel in holes, is probably the best thing you can do.

I like Serge Lang: Basic Mathematics.

The Feynman Lectures are nice. But they can be a bit hard to learn from, even for people that have taken physics classes at the university.

I won't dissuade you from reading them. But supplement it with a standard intro physics textbook.

 

[OJ Bernander]

Brilliant (dot org) has online self-study courses at several levels. Their format is to have a paragraph of explanation, immediately followed by a question (and answer) so you don't read too far without checking your understanding.
They are under $100 for a one-year subscription, and with some googling, you should be able find a 20% discount code, last I checked. Just make sure to unset the auto-renew after a day or two.