Pure vs. Applied Mathematics. (1 Viewer)

[Forbidden.]

Simple question.

 

[darkliight]

I voted pure, but I have a question that this poll just reminded me about. Are computer science and stats considered pure, applied, or seperate fields??

 

[Forbidden.]

Depends,

e.g. if I'm solving an augmented matrix using Gaussian Elimination then Backward Substitution on paper because of some simultaneous equations then I consider that pure mathematics.
If I interpet a holiday expenses as a simultaneous equation then solve it as above then find out whether a solution is possible or not I can spend a certain amount of money that's applied.

 

[Affinity]

Depends,

e.g. if I'm solving an augmented matrix using Gaussian Elimination then Backward Substitution on paper because of some simultaneous equations then I consider that pure mathematics.

Thats call drudgery.. not mathematics

 

[Trebla]

From my own impressions:
Pure mathematics seems to be characterised by rigour and very abstract concepts. This can include complex analysis, number theory and abstract algebra.
Applied mathematics tends to have some context into other fields such as Physics, Biology and Engineering because they are often used for applications of modelling. A lot of it involves partial differential equations and vector calculus.

I think Statistics is a different field of mathematics in its own right...

 

[Sonata]

im thinking of applied since it applies to reality in a way, still dunno how pure maths works

 

[sicmacao]

i still dont really know what the difference is

The divide between applied and pure maths can be quite blur. The names applied and pure are artificial. Often problems that arise in Pure mathematics can have great ramification in the physical world. Moreover problems that occur in applied maths can be so challenging can create a new theory which would be researched by pure mathematicians.

For example number theory are considered a classical pure mathematics subject. Prime numbers have important application in crytography which is used in security systems in banks and internet.

 

[sicmacao]

i still dont really know what the difference is

Visit the following url
http://www.maths.unsw.edu.au/students/future/sycourseoverview.html

You may get some idea about about their differences.

 

[sicmacao]

When I was an undergraduate, I used to think that pure mathematics is a branch of mathematics that can be investigated by using a pen and a piece of paper only while applied mathematics requires a lot of other equipment like computers, boat, and a knowledge of another science.

 

[Affinity]

You know you are doing pure maths when you don't see numbers more than 10.

 

[Aerath]

Pure is easier to do.

 

[darkliight]

dont think i know any pure maths then :S

Calculus?

 

[Iruka]

Calculus?

Would you consider numerical integration to be pure maths, then?

I think the distinction between applied and pure is rather arbitrary, and essentially, not a very interesting question, as I like both. (although I haven't had much opportunity to learn applied maths yet.)

 

[Slidey]

Pure maths in high-school is awesome.

By university, you realise the pure maths you did in highschool is actually applied maths, and the pure maths you do at uni is retarded.

Thus, applied maths.

 

[darkliight]

Would you consider numerical integration to be pure maths, then?

I don't tend to think of particular pieces of mathematics as either pure or applied. My personal definition goes something along the lines of:

Applied mathematics starts with a practical problem, and ends with a piece of mathematics to solve (or approximate a solution to, show there is no solution to, etc) said problem.

Pure mathematics starts with some definitions, and asks "what can we deduce?", "can we generalise this?", etc.

Obviously, there is overlap. Also, an applied question may lead to interesting pure questions, and vice versa. To make things more complicated, entire fields are motivated by applied questions (game theory for instance), so I guess I would consider those fields applied in that case. As for numerical integration? On its own, sure, I would consider it pure. It wasn't that long ago it was all we had for calculating area and volume. If you start with a practical application in mind and your solution to the proplem happens to involve numerical integration (or whatever), then you're engaging in applied mathematics imho.

It's why I chose pure over applied. I couldn't give a stuff how cheaply farmer brown can build his fence for, but I like knowing that given some random function, I can have a go at trying to find a minimum.

 

[humphdogg]

Pure maths in high-school is awesome.

By university, you realise the pure maths you did in highschool is actually applied maths, and the pure maths you do at uni is retarded.

Thus, applied maths.

did you get boned over by analysis 1?


pure maths ftw.

 

[tommykins]

omg i love maths so much.

There are things that just drain my love for math. Especially harder 3u inequialities.

 

[Slidey]

did you get boned over by analysis 1?


pure maths ftw.

I wouldn't say boned as much as mututal dislike. Stat, ODE's and PDE's were good though. Good luck with analysis 2 and 3. Hahahaha.

 

[humphdogg]

I wouldn't say boned as much as mututal dislike. Stat, ODE's and PDE's were good though. Good luck with analysis 2 and 3. Hahahaha.

meh, i'm on a 90-ish average for analysis 2 so far. it's easier than analysis 1 imo.

and well, stats, ode's, and pde's really don't interest me at all. extremely bored by 2405, and i doubt 2406 will be any better... theory of pde's will probably be interesting though.

did you number theory and cryptography? i would've thought that would be relevant for a compsci student.

 

[sicmacao]

Would you consider numerical integration to be pure maths, then?

I think the distinction between applied and pure is rather arbitrary, and essentially, not a very interesting question, as I like both. (although I haven't had much opportunity to learn applied maths yet.)

Numerical integration which is a subbranch of Numerical analysis is applied maths. As the speed of the computer gets faster, numerical analysis are now of equal importance to theoretical mathematics.

However numerical integration can often yield some nice formula approximating transcendental numbers like pi or e which is popular in HSC questions and appears also in various problem solving books.