Freethought & Rationalism Archive

Secular Elation · 08-17-2002, 08:11 PM

Is calculus the highest branch of mathematics, or is there a field of mathematics even more advanced?

fando · 08-18-2002, 05:43 AM

Calculus is barely sticking a toe in the ocean of mathematics!

There are actually several branches of mathematics with different problem domains and methodologies. <a href="http://www.encyclopedia.com/html/section/mathematcs_branchesofmathematics.asp" target="_blank">Here's a page</a> that lists most of the mathematic fields. Calculus itself can be as complex as you make it. Example: multivariable calculus of complex numbers.

ohwilleke · 08-19-2002, 02:44 PM

Number theory, abstract algebra, analysis, and topology are the most abstact and theoretical branches of mathematics which wins them prestige within the mathematics community over math which actually has some use. (I had an applied mathematics emphasis in college which was less prestigious than my theoretical classmates).

Number theory consist mostly of finding weird properties and relationships of numbers (especially prime numbers). Abtract algebra is a consideration of the properties of versions of algebra in which the rules are changed in a systematic way from the algebra you new and loved in high school (e.g. algebras in which the order in which you multiple things matters). Abtract algebra is also closely related to another area of higher math called set theory.

Topology is the study of the property of shapes considered mathematically.

Analysis is advance calculus in which among other things, you are much more hypercritical of your underlying assumptions when you prove things than you are in regular calculus.

Steven S · 08-19-2002, 05:53 PM

It's hard to say which branch of math is more advance than another, it doesn't have a tremendous amount of meaning. If you mean advance as in most general than category theory could be the most general piece of mathematics we have right now, AFAIK.
Take a look at Dave Rusin's mathematical atlas:
<a href="http://www.math.niu.edu/~rusin/known-math/welcome.html" target="_blank">http://www.math.niu.edu/~rusin/known-math/welcome.html</a>
He does a pretty good job of explaining a good deal of known math.
I guess I fall somewhere on the analysis/geometry part of the atlas.

Steven S

Starboy · 08-19-2002, 07:10 PM

Nice site Steven S.

Principia · 08-19-2002, 07:23 PM

Actually, here's another math question: what is mathematics?

Splat · 08-19-2002, 08:09 PM

Quote:

Originally posted by fando:
<strong>Example: multivariable calculus of complex numbers.</strong>

Makes me dizzy just thinking about it!

08-17-2002, 08:11 PM	#1
Secular Elation Veteran Member Join Date: Apr 2001 Location: California Posts: 6,196	Simply wondering... Is calculus the highest branch of mathematics, or is there a field of mathematics even more advanced?

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08-18-2002, 05:43 AM	#2
fando Veteran Member Join Date: Sep 2001 Location: Los Angeles Area Posts: 1,372	Calculus is barely sticking a toe in the ocean of mathematics! There are actually several branches of mathematics with different problem domains and methodologies. <a href="http://www.encyclopedia.com/html/section/mathematcs_branchesofmathematics.asp" target="_blank">Here's a page</a> that lists most of the mathematic fields. Calculus itself can be as complex as you make it. Example: multivariable calculus of complex numbers.

08-19-2002, 02:44 PM	#3
ohwilleke Veteran Member Join Date: Jun 2000 Location: Denver, Colorado, USA Posts: 4,834	Number theory, abstract algebra, analysis, and topology are the most abstact and theoretical branches of mathematics which wins them prestige within the mathematics community over math which actually has some use. (I had an applied mathematics emphasis in college which was less prestigious than my theoretical classmates). Number theory consist mostly of finding weird properties and relationships of numbers (especially prime numbers). Abtract algebra is a consideration of the properties of versions of algebra in which the rules are changed in a systematic way from the algebra you new and loved in high school (e.g. algebras in which the order in which you multiple things matters). Abtract algebra is also closely related to another area of higher math called set theory. Topology is the study of the property of shapes considered mathematically. Analysis is advance calculus in which among other things, you are much more hypercritical of your underlying assumptions when you prove things than you are in regular calculus.

08-19-2002, 05:53 PM	#4
Steven S Regular Member Join Date: Jun 2000 Location: Raleigh, NC Posts: 167	It's hard to say which branch of math is more advance than another, it doesn't have a tremendous amount of meaning. If you mean advance as in most general than category theory could be the most general piece of mathematics we have right now, AFAIK. Take a look at Dave Rusin's mathematical atlas: <a href="http://www.math.niu.edu/~rusin/known-math/welcome.html" target="_blank">http://www.math.niu.edu/~rusin/known-math/welcome.html</a> He does a pretty good job of explaining a good deal of known math. I guess I fall somewhere on the analysis/geometry part of the atlas. Steven S

08-19-2002, 07:10 PM	#5
Starboy Banned Join Date: Jun 2002 Location: Tallahassee, FL Reality Adventurer Posts: 5,276	Nice site Steven S.

08-19-2002, 07:23 PM	#6
Principia Veteran Member Join Date: Mar 2002 Location: anywhere Posts: 1,976	Actually, here's another math question: what is mathematics?

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