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January 22nd, 2012, 04:57 AM  #1 
Joined: Jan 2012 Posts: 2 Thanks: 0  The natural structure of mathematics
As I understand it, mathematics is a study that is founded on the principles of logic and set theory and branches out into specialized fields. I was just wondering about what that structure would look like. It seems like there might be significantly different ways to do this since there is often more that one way to prove something. How do you see this? Here's a rough idea of what I mean. This isn't meant to be complete, and definitely isn't totally accurate. But, it's 5 am here and I need to get some sleep Thanks for the input everyone. I. Fundamentals a. Logic b. Set Theory II. Arithmetic a. Addition b. Subtraction c. Multiplication d. Division e. Exponentiation III. Numbers a. Integers & Number Theory b. Rational Numbers c. Irrational Numbers d. Transcendent Numbers e. Imaginary Numbers f. Complex Numbers IV. Geometry & Trigonometry a. Two Dimension i. Flat Space ii. Curved Space b. Higher Dimensions V. Calculus a. Differentiation b. Integration 
January 22nd, 2012, 05:00 AM  #2 
Joined: Jan 2012 Posts: 2 Thanks: 0  Re: The natural structure of mathematics
I wish I could edit that list, it doesn't show the structure well. Anyone know how I could do that? Even if I can't fix this post, it would be good for the future. Roman numerals are primary sections Letters are 2nd level sections i tally's are 3rd level sections 
January 22nd, 2012, 06:45 AM  #3  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: The natural structure of mathematics Quote:
 
January 22nd, 2012, 10:51 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 15,758 Thanks: 844 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: The natural structure of mathematics
I think that the natural structure would be a DAG, not a list.


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