Foundations A rigorous approach to learn Mathematics

[tuxscholar]

Hello Intellectuals! So far it seems to be reasonable to learn mathematics in a rigorous way by not solely considering the techniques of problem solving or the applications of a particular subject or concept.

Also to truly appreciate the beauty of mathematical endeavor one need to learn the reasoning behind the origination of concepts in mathematics, so as a beginner it appears to be worthwhile to learn the highly abstract aspects of mathematics like proofs, logic, and topics in pure mathematics (number theory, analysis etc). To be able to acquire such a decent sophistication in mathematics one need to learn the works of the masters like that of Euclid, Euler, Gauss and Hardy, as one says "study the masters not their pupils".

So it's not an academic preaching or pedagogical prescription of any sort but an approach to learn the value of the subject which most of the time seems to be useless (especially pure math). But as the saying goes that beautiful things are useless and useful things are ugly, so it's absolutely worth it to learn pure math.

So as a beginner is it good to start one's mathematical endeavor to learn pure math in a rigorous way from the very start with the help of this works :

• Elements by Euclid
• Elements of Algebra by Euler
• Gelfand's Algebra, Trigonometry and calculus of variations
• Introduction to the Analysis of the Infinite by Euler
• A Course of Pure Mathematics by G. H. Hardy
• Thomas' or Spivak's Calculus
• .....well what can be a decent and rigorous but comprehensive text to learn proof theory or logic as a beginner

Also what would be your approach as a beginner to learn pure mathematics?

 

[.Scott]

I would suggest you start by checking out the work of Procrustes, who created a bed that was the perfect fit for anyone.
* Don't set out a curriculum for yourself that you would hate.
* Recognize that there is no single "Mathematician" target.

The "very start" is no older than age 11 or 12. If you're older than that, you have already started.

From about 2nd grade through college, I was always very good at Math and I was a Math major in college. But I have never considered myself to be a "Mathematician". I latched onto computer programming in High School and that has been what I have followed ever since. Software Engineers do not think about problems in the same way as Mathematicians. And, neither Software Engineers nor Mathematicians think about problems in the same way as their peers.

And it's worth mentioning, especially in these Forums, that Mathematicians and Physicists do not thing about problems the same way either.