does maths ability have a shelf life?

[sasguru]

Arithmetic is the oldest branch of Mathematics.

You buffoon.

simplest

[Moscow Mule]

What's the difference between learning and understanding? If you've understood something you've learnt it IMHO.

I think they are different.

To give a related but somewhat flippant example;

Learning is when you know the 1 is more than 0.
Understanding is when you can prove it.

It's quite easy to learn the proofs and derivations for Maxwell's Equations of Electromanetism.
Understanding the theory behind them is something I never learned at uni and probably never will.

[Diver]

Arithmetic is the oldest branch of Mathematics.

You buffoon.

So it's all like "Sums" and stuff like?

[Xenophon]

So it's all like "Sums" and stuff like?

WHS

[BlasterBates]

i'm struggling with some accountancy concepts, aswell as derivs maths

to skill up i've gone back to real basics such as probability. i've got through an excellent probablility book. which i'll have to read again. next i'm going to revisit calculus. after that differential equations.

i used to be good at pure maths and hopeless at applied, now i have to have a concrete example to be able to grasp the abstract stuff

i've effectively become more stupid

The difficulty with derivs maths is not the mechanical turning the handle, it the assumptions, you need to understand i.e. the entire theory is based on perfectly hedged portfolios and the price of risk. When you understand that it is then straightforward. A key principle is discounting, i.e. 1£ in a years time is worth less than £1 today because you can invest it and earn £1.05 in a years time.

[expat]

I think they are different.

To give a related but somewhat flippant example;

Learning is when you know the 1 is more than 0.
Understanding is when you can prove it.

It's quite easy to learn the proofs and derivations for Maxwell's Equations of Electromanetism.
Understanding the theory behind them is something I never learned at uni and probably never will.

Quite so. You will have to learn it first, before you can understand it.

Other branches of knowledge are not always so demanding: as you grow more mature (hopefully) and broaden your knowledge and experience, you may well find that in some spheres you can understand more, while not needing to learn so much in order to do so. Maths and physics are not like that, and never get easy.

More flippant example: learning is knowing that a tomato is a fruit. Understanding is knowing that you wouldn't put it in a fruit salad.

[xoggoth]

Yeh. Thing add up completely differently to when I were a lad. I blame the vodka.

[Spacecadet]

Just accept you're a div and move on...

what about Grad and Curl?
(perhaps my favourite Mathematics book at uni)

[Spacecadet]

I think they are different.

To give a related but somewhat flippant example;

Learning is when you know the 1 is more than 0.
Understanding is when you can prove it.

It's quite easy to learn the proofs and derivations for Maxwell's Equations of Electromanetism.
Understanding the theory behind them is something I never learned at uni and probably never will.

when you understand something you can fill in some of the gaps in your learning and accelerate further learning.

Take calculus and newton laws of force and motion. I was taught them completely seperately and we were expected to simply learn the equations for acceleration, velocity and distance etc... Newtons laws would be examined in the Applied/Mechanical mathematics paper, calculus in the pure, 2 different exams, 2 different teachers.
However, if you understand mathematics, you can see clearly how newtons equations are all built up using calculus, this saves you the bother of having to memorise them for the exam as you can simply derive them as required.

Problem with learning and understanding is that teaching is usually done with the aim of getting the kids past the exams, not to give them a thorough understanding of the subject.

[Churchill]

Just accept you're a div and move on...

MOD!!!!!