How can I effectively relearn physics and math through self-study?

[s8on95]

Hello, I'm 19 currently second year in college,

After one quarter of taking on many math/science classes and struggling in them, I've realized how my knowledge is both shallow and fragile, even in the subjects I've already learned. I currently wish to reestablish my knowledge from the ground up, especially in mathematics and would like some recommendation for good textbooks from which to use for self learning. I would like enough textbooks to be able to have an intuitive understanding (like that of Feynman's), as well as a complete understanding (as I've heard of Spivak's Calculus book).

Additionally, I like to play games (everything is a game with the right perspective!) so it would be helpful to set up the learning like some sort of game with objectives. That is, I want to know how I can be self-assured that I have mastered a certain material. I think the biggest problems in learning (self learning specifically) are you don't know what you don't know and you don't know if what you do know is wrong!

 

[snatchingthepi]

That's a pretty tall order you're asking. First and foremost, what mathematics do you want to reestablish, and what other areas of science are you looking towards? What is your current background for math/science? What are you currently studying?

 

[s8on95]

Here's a bit more context:

I mostly wish to reestablish my knowledge of precalculus and calculus, but knowledge of other maths to remember some forgotten "tricks" would help.

I used to be very interested in math and would challenge myself a lot. Since for years ago though, I've been in a phase where I'm somewhat disinterested in life. My learning of precalculus was shallow and my learning of calculus was half-assed (I had gotten by with A's in a rather challenging school, but I consider this only reflecting how low the standards are).

I consider myself decent at problem solving, but not as good at learning and explaining concepts. I am interested in all areas of science and do not wish to limit myself to one area, but I believe math is fundamental to most sciences and thus important to learn.

I have just finished taking a quarter of Multivariable I, Physics (kinematics), Chemistry (quantum mechanics), and Linear Algebra. Doing this has allowed me to visualize how all of them relate to each other at once (how they fit together on a grand scale), but has given me shallow knowledge in each.

 

[snatchingthepi]

I would encourage you to take the single-variable and multi-variable calculus sequence that MIT offers. The OpenCourseWare website has multiple offerings of these courses to follow. They come with problem sets, assignments, solutions, and even tell you what sections to read out of the book. The video lectures are also very good, and there exist multiple forums for people to discuss the course and get help with solutions to problems.

http://ocw.mit.edu/courses/mathematics/

The two courses described will definitely increase the rigour of your basic calculus knowledge and force you to learn those "tricks of the trade" when solving problems. Afterwards, going through the offered courses on linear algebra and differential equations would be a great bet.

For science now, since your interest is mainly mathematical, I would encourage you to study some physics beyond the level of kinematics (which I'm assuming was an introductory course). One of the best ways to learn vector calculus is to study electromagnetic theory in detail. I would refer to other parts of this forum for an introductory text on electricity and magnetism, and then encourage you to take-up Griffiths' book on the subject (there exist others, but I like Griffith's).

I hesitate to suggest further than this, as what I've described between the courses of calculus, the two on linear algebra and differential equations, an introductory EM course, and study of Griffiths' text easily represent a couple years of work if you want to go through it all carefully and studiously.

 

[s8on95]

I think this is plenty for now. I also downloaded "Trigonometry for the Practical Man" to brush up on it. Thanks!

 

[snatchingthepi]

You are most welcome. I hope I helped.