07 August 2008

Math in Climatology

I'm doing my best to keep the math to a minimum here, because one can indeed understand a lot of the fundamentals without it, also because I know many people suffer from math anxiety. Then a large contribution from the fact that I know if I start down the road towards using math, I'll use a lot of it.

Now, on the math anxiety side, I highly recommend Sheila Tobias' Overcoming Math Anxiety. Unlike your probable expectations, she is not some outsider who never had the problem herself. She had a big case of it, but decided that physics was interesting and she'd bite the bullet and try to learn the math needed. She did, along the way dealing with a number of anxieties and false impressions about mathematics. One of the major problems shared by many people is the notion that only certain 'special' people can do mathematics. If you're talking the seriously hard core stuff that wins Fields Medals, that's probably true. If you're thinking about the level that I'm using here, the answer is ... nonsense. Anybody without a serious learning disability can learn this, regardless of age, gender, race, religion, part of world you live in, etc.

Here's a sampling of courses or material that one would almost certainly encounter on the way to being able to study climatology professionally:

Algebra I
Algebra II
Differential Calculus
Integral Calculus
Calculus of Several Variables
Probability and/or Statistics
Ordinary Differential Equations

That's just warming up. You'd also likely encounter several of:
Linear Algebra
Partial Differential Equations (probably multiple courses)
Complex Analysis
Numerical methods (probably multiple courses)
Statistics (in a multi-term sequence)

... and probably several more that aren't leaping to my mind right now.


sylas said...

Just to contribute to the maths anxiety... Tensor Analysis. Apparently this is needed if you want to deal adequately with rotating fluid dynamics in a spherical Earth, for example.

Anonymous said...

A good math background is of tremendous value for all branches of science. Climate science makes much use of it, in large part because it involves so much physics.

But I must point out that a famous quote from Feynman about physics, applies to mathematics as well: "Physics is like sex. Sure, it may give some practical results, but that's not why we do it."

EliRabett said...

Math is useful, but learning how to think clearly about a problem, recognize first, second and even third order physical implications and tie up the loose edges is even more important. If you learn how to do this

a. You protect yourself against trivial mathematical errors

b. You may not even need the math. I remember one argument where having proven that 2+2 .LT. 5 some clown wanted to know why I had not used calculus

Robert Grumbine said...

duae: Tensor analysis is a good idea, but probably not a requirement. Adrian Gill's Atmosphere-Ocean Dynamics and Joseph Pedlosky's Geophysical Fluid Dynamics both make little or no mention of tensor analysis. Vector calculus and Partial Differential equations abound. Also in the good idea department is Variational Calculus.

Eli: Absolutely. Math (for us in science) is a tool to solve problems with, not an end in itself. Far more important than adding 2+2 to get a number close to 4 is to know why you want to be adding, and why it is 2 and 2 that you want to add.

A future post will go in to some examples where you don't need to know a thing about mathematics or statistics to recognize that the answer is irrelevant because the person set up the wrong problem.

And thanks for the welcome to the 21st century, though it may be premature. More a techno-penguin here to your techno-bunny.