Fundamental Mathematics

[Ryan Rudolph]

Hello all.

I'm rather discontent with my overall mathematical understanding, and I was wondering what some of you believe are the most basic and fundmental mathematical principles to be able to excel at some of the more complicated forms of math like Calculus and so on.

[DHodges]

In math, more complex ideas are built up from simpler ones, so it's always good to have a very firm grasp of the basics.

Set theory is fundamental. That's a basic that you should have a good grasp on, for just about anything mathematical.

Calculus actually only has a few basic underlying ideas - the infinitesimal and integration/differentiation.

Other fields of math will have other basic ideas - for instance, for statistics you need to have a grasp on the concept of a random variable, which is generally not considered in calculus.

[MindExpansion]

Is it necessary always necessary to learn the basics in order to understand the more advanced?

As long as someone can fully understand the basics, they can always build up and learn the more complicated. Is there a limit, why? Is that limit what separates the average from the superior or is it the belief?

[Ryan Rudolph]

Dhodges wrote:

In math, more complex ideas are built up from simpler ones, so it's always good to have a very firm grasp of the basics.

Do you know of an all encompassing mathematics textbooks that takes the reader from the very basics into the very complicated? what are some of the best books out there in your opinion?

Or anybody else for that matter, thanks.

[Elizabeth Isabelle]

Try this.

[Ryan Rudolph]

Elizabeth,

yes, the content of that entire website is what I'm looking for, but I'd prefer it wrapped up in one book.

[MindExpansion]

Thanks liz!:)

[HUNTEDvsINVIS]

Don't you think it is a bit unrealistic to make such an attempt? Maths is not just about learning that A is B and B is C etc... It involves complex abilities to actually picture things in your mind and in many different ways. Some people just picture the graphs and the starting points and logical proceedings immediately and have a whale of a time learning very quickly. Also every "rule" in maths can be applied in a hundred different ways...thus we used to get 20 sums to do in a day to test and identify all the possibilities.

[Ryan Rudolph]

HUNTEDvsINVIS wrote:

Don't you think it is a bit unrealistic to make such an attempt?

No, I may agree if I had absolutely no mathematical skills at all, but I’ve taken pre-calculus many years ago, and I did fairly well. However, I had to work very hard, and at the time I didn’t understand how the actual math related to the scientific theories as a whole. So I’d like to experiment a bit, which I’ve actually been doing, and I haven’t had too many difficulties.

My strategy should work, mathematics builds on simpler principles, so if I can start from the most rudimentary forms of math, and slowly build on that, then more complicated forms of will make more sense due to its progressive nature.

[HUNTEDvsINVIS]

ok cool, just keep in mind that it will indeed probably take long. I was good in algebra, loved log sums, but struggled with the graphs and geometry and trig sucked. I found algebra to be more logical. The visual representations of some graphs were absolutely strange to me. I was not satisfied with "Just learn that that is the shape of the graph" from the teacher.