Which is more difficult: pure or applied mathematics?

[chiro]

Forgive me, I only took some courses in math and am not a mathematician, but what do applied mathematicians actually do? I look at the programs for applied mathematicians and it seems that, although they're heavy in computer programming work, they have to take a bunch of analysis classes and proof based numerical analysis, differential equations, statistics/probability, etc.

That's for university-wise, but what about in the workplace? My previous assumption was that they are basically engineers, but what would be the point of taking analysis classes, then? Surely there's some use in them after college... and I don't know what people in mathematical finance do either.

I assume you need to know the methods from the inside out in order to apply them, unlike an engineer?

Applied mathematicians usually take specifications of some particular problem, then use the appropriate mathematics to do some analysis and then typically communicate the main results and more importantly the interpretation of what the results mean for their target audience.

A few examples:

An actuary might be asked to go through the design of a new insurance product to see how probable the company might be to go bankrupt. So the actuary away, probably uses an industrial strength modeling program, does some analysis, and then gives a presentation outlining his findings and recommendations in plain english terms. Most of the board members have probably done at most some calculus and a business statistics course.

Another example could be an analyst working in fisheries. The analyst might be asked what his recommendations for the fishery are to maximize their intake of fish, but do so in a way that they will regenerate more fish in time for the next harvest. So in this example the analyst uses a difference equation to model fish intake and out-take at a particular time and presents their findings to management giving their recommendations.

There are a lot of examples, but I think its important to realize that in a lot of situations, applied mathematicians are not just mathematicians, they're communicators. It's no use deriving a great formula if you can't break it down for others less literate in math.

 

[Liquid7800]

I think thinking of new (unsolved), practical/applied problems or pioneering/discovering a new pure mathematics field require equal amounts of creativity, computer science ties very closely between the two fields.

No matter the field though----someone on these forums said it somewhere a while back, "its one thing to solve problems in a field and quite another to contribute to a field"

 

[Outlined]

Pure math is more about problem solving, theorem proving and mathematical reasoning.

Applied math is about learning procedures/recipes to solve problems, so a part of the thinking has already been done for you. You have to make modifications to the problem so that it fits the right recipe/procedure.

The 1st one is more difficult than the 2nd one.

 

[jasonRF]

Pure math is more about problem solving, theorem proving and mathematical reasoning.

Applied math is about learning procedures/recipes to solve problems, so a part of the thinking has already been done for you. You have to make modifications to the problem so that it fits the right recipe/procedure.

The 1st one is more difficult than the 2nd one.

It seems that "applied math" means different things to different folks. A friend of mine got his PhD in applied math. He was required to take all of the core analysis, algebra and topology courses with the pure math PhDs. After the core, then he took the courses on probability theory, statistics, math finance, etc. His education was NOT about learning recipes!

jason