Is Derivation Equivalent to Proof in Mathematics?

[DrummingAtom]

Problems in books that say "Show that" or "Derive this" does that qualify as a "Proof"? I spend most of my study time working on the "Show that" problems. Are these the types of problems similar to the problems found in upper level classes(like Analysis)?

Thanks.

 

[Office_Shredder]

Certainly if you show something is true or derive an equation that qualifies as a proof, as long as you actually proved it. All of higher level mathematics is essentially proving things, despite the mass of equation solving you see in lower level classes. So those are the types of problems you can expect to see if you mean 'will I have to prove things in an analysis class?', but the actual flavor and difficulty of the problem, and the techniques that you have to use are wildly different depending on subject

 

[Fredrik]

I consider the words "show" and "derive" to mean exactly the same as "prove". However, physicists will often do something really sloppy and call it a "derivation".

 

[AC130Nav]

I consider the words "show" and "derive" to mean exactly the same as "prove". However, physicists will often do something really sloppy and call it a "derivation".

On the other hand, are you sure those aren't mathematicians masquerading as physicists? Like Hawking.

 

[specone]

If you have a statement that is known to be true and you "derive" a new expression using valid methods then the initial statement implies the derived statement so it is true.

 

[Tac-Tics]

A proof is just evidence something is true.

In math, evidence is having showed the steps involved to logically take the assumptions and reach the conclusion. Math tends to be more absolutist. If you can't prove beyond a shadow of a doubt your theorem is true (or that it is false), you must not speak of it at all.

In science, evidence is an experiment or a strong case for it to be true. It's closer to what you might find in a court of law. Generally, you can get away with making very strong assumptions without proof, so long as there is no direct evidence against you. In a scientist's eyes, the Riemann Hypothesis is true.

To derive is just another way to say you get a conclusion from taking logical steps. It's pretty much a synonym. Just as a theorem is a lemma is a corollary.