How Can I Effectively Teach Myself Advanced Math Skills?

[thetexan]

Ok, I am really hooked now.

I have always enjoyed math and love math problems and everything math. I am enthrawled by the threads here and only wish I could understand it all.

I am a typical layman hobbiest math enthusiast but I haven't done much in the way of real study since high school. I have a good grasp of algebra but I want to learn more.

So here is the question. How can I go about teaching myself more math?

Starting with a good refresher on algebra and trig (I know a little calc but not really much) what is your advise on how to study to increase my math skills? I can go to the local university and check out any math book on any subject imaginable so resources are not an issue.

For example...after math and trig... what would be a path to follow?

Let's say

Pre calc
calc
so on
so on
etc.

Any ideas. Keep in mind I am an amateur but I have desire and time.

 

[atomthick]

From my experience reading a lot of books is not the best option. The way to go to increase your knowledge while keeping your interest in the subject is to find one or two unsolved problems and try to solve them.

The problems must be very easy to understand but very difficult to solve, for example:

Proove that every even number can be written a a sum of two primes.

or a computational problem

Let N be a semiprime number (only two factors) i.e. N = P * Q, find a way to get P or Q in a number of steps proportional to the number of digits of N.

Studying easy to understand but yet unsolved problems will keep you interested in the subject and will get you thrugh almost all domains of mathematics because people have had to use all the known tools of mathematics so far in trying to solve them!

Good luck.

 

[ramsey2879]

Ok, I am really hooked now.

I have always enjoyed math and love math problems and everything math. I am enthrawled by the threads here and only wish I could understand it all.

I am a typical layman hobbiest math enthusiast but I haven't done much in the way of real study since high school. I have a good grasp of algebra but I want to learn more.

So here is the question. How can I go about teaching myself more math?

Starting with a good refresher on algebra and trig (I know a little calc but not really much) what is your advise on how to study to increase my math skills? I can go to the local university and check out any math book on any subject imaginable so resources are not an issue.

For example...after math and trig... what would be a path to follow?

Let's say

Pre calc
calc
so on
so on
etc.

Any ideas. Keep in mind I am an amateur but I have desire and time.

I suggest viewing any of the video topics that may interest you here http://www.khanacademy.org/#browse
What started out as Sal making a few algebra videos for his cousins has grown to over 2,100 videos and 100 self-paced exercises and assessments covering everything from arithmetic to physics and more.

 

[DrummingAtom]

I partially agree with atomthick, but instead of taking a problem that's out of thin air and trying to solve it. I'd go buy Stewart's Algebra and Trigonometry book first.

https://www.amazon.com/dp/0534380298/?tag=pfamazon01-20

This book has whole sections in between chapters on challenge problems. The problems in these sections are thought provoking and difficult but they utilize the concepts from the previous chapters so you have some guidance. I remember spending weeks on problems from those sections and it was very worthwhile when I solved them. These type of problems kept me motivated during self study. Good luck.