Ask a Mathematician!

[uppi]

Any suggested reading about statistical mechanics?

*Okay, so maybe there is sufficient prompting to model thermodynamics with such spaces, but I hope the point about constructs not necessarily being applicable was made.

Sorry, I can't recommend anything. The course material and even the textbook I read on the subject was in German.

Yes, constructs are not necessarily applicable, but it is quite hard to find any mathematical construct that has not yet been used (or abused) for some application outside of pure mathematics.

Depends on how it is handled.. I don't think screaming would help though. I would have a problem setting something (like a number) equal to it unless it was understood that "=infinity" is not an equivalence relation, but a statement about {positive} divergence (as in we're no longer dealing with a huge number). It may turn out for a given scenario that the infinite-dimensional case can be well-approximated by a finite-dimensional case if it can be shown that the infinite case is convergent.

This careful reasoning about convergence is exactly what physicists usually don't bother with. Until proven otherwise we just assume it converges and go right ahead. If we notice along the way that it doesn't, we try another approach, but as long as a technique works we don't care much about proving that it is applicable.

 

[Leoreth]

Leoreth was on the ball with this one.

Hehe.

Got the joke only after you pointed it out. Oh my.

New question: do you have a favourite math joke?

 

[ParadigmShifter]

What's purple and commutes?

An Abelian grape.

 

[Rashiminos]

What's purple and commutes?

An Abelian grape.

Are there any non-abelian food groups?

 

[ParadigmShifter]

Hot cross product buns?

 

[pi-r8]

This careful reasoning about convergence is exactly what physicists usually don't bother with. Until proven otherwise we just assume it converges and go right ahead. If we notice along the way that it doesn't, we try another approach, but as long as a technique works we don't care much about proving that it is applicable.

At the risk of a huge over-generalization, I would say that physics requires more creativity, while mathematics requires more rigor.

 

[Akkon888]

RPN or in-fix?

 

[uppi]

At the risk of a huge over-generalization, I would say that physics requires more creativity, while mathematics requires more rigor.

I wouldn't say that physics requires more creativity. I think you need quite some creativity to think of a new proof. I would rather say that physics requires the ability to approximate, to determine which terms are important and which can be neglected.

Without simplifying a problem by dropping the irrelevant effects, you don't get very far in physics. So you have to leave behind the mathematical rigor and focus on the important part while ignoring the unimportant. To distinguish these is one of the main skills of physicists.

In mathematics the quest for absolute proofs does not allow for approximations, so you have to be rigorous and cannot just drop unimportant terms. Almost proving a theorem does not count for anything.

 

[IdiotsOpposite]

RPN or in-fix?

I looked up RPN and am honestly surprised anyone speaks of that with a straight face.

 

[SpiritWolf]

u ready?

What's your survival strategy for real analysis? It has a nasty tendency to break people.

 

[IdiotsOpposite]

My strategy - figure out what book I'm assigned, and read every chapter of it before the class begins.

Twice.

 

[pi-r8]

I wouldn't say that physics requires more creativity. I think you need quite some creativity to think of a new proof. I would rather say that physics requires the ability to approximate, to determine which terms are important and which can be neglected.

Without simplifying a problem by dropping the irrelevant effects, you don't get very far in physics. So you have to leave behind the mathematical rigor and focus on the important part while ignoring the unimportant. To distinguish these is one of the main skills of physicists.

In mathematics the quest for absolute proofs does not allow for approximations, so you have to be rigorous and cannot just drop unimportant terms. Almost proving a theorem does not count for anything.

Sure, I agree. But don't you think that being able to "bend the rules" like that is a form of creativity? Not to mention the creativity involved in designing good experiments.

 

[azzaman333]

Why are statisticians so much better than mathematicians?

 

[gangleri2001]

I don't know if is it me that I'm stupid or that the concept is really hard to get. You see, an operator's arity is a concept easy to get for the most common forms of it (nullary, unary and binary), but it's hard to get when you reach ternary level. I assume that ternary operators work pretty much like a transistor, but what about quaternary or other n-ary operators? And what about a multary (that accept many arities)? I cannot imagine operators like these but maybe you can enlighten me.

 

[uppi]

Sure, I agree. But don't you think that being able to "bend the rules" like that is a form of creativity? Not to mention the creativity involved in designing good experiments.

Of course it is a form of creativity. But I also consider the ability to apply the rules in new ways to get a new proof a form of creativity. So I wouldn't say one group is more creative than the other.

 

[Integral]

u ready?

What's your survival strategy for real analysis? It has a nasty tendency to break people.

I shivered when I saw that picture.

No lie.

--

My strategy - figure out what book I'm assigned, and read every chapter of it before the class begins.

Twice.

Bad way to read Rudin.

The good way to read Rudin:

Start at page one. Read until you come to the word Theorem. Do not read the proof. Prove it yourself. Or at least try. If you get stuck read a line or two until you see what to do.

Thrust, repeat.

If you make it through the first six or seven chaptors like this then there shall be no power in the verse that can stop you. Enjoy graduate school. You half way there.

 

[Atticus]

Rudin isn't probably the easiest book to read as the first one on the subject. I'd recommend Avner Friedman's Foundations of Modern Analysis, which is a bit simpler.

Of course it's given that you don't read math books. You must try proving things yourself.

 

[Rashiminos]

u ready?

What's your survival strategy for real analysis? It has a nasty tendency to break people.

You've had a calculus course. Some of the material will be familiar, but now you have to deal with the why.

(Actually, if you've had a discrete math course where proofs were done, you already have a good beginning).

 

[ParadigmShifter]

Analysis isn't hard, it's just weird applying rigour to topics which previously haven't required it.

You can always post in my maths thread in sci/tech if you want help.

 

[IdiotsOpposite]

Analysis isn't hard, it's just weird applying rigour to topics which previously haven't required it.

You can always post in my maths thread in sci/tech if you want help.

Hehe, actually, if I ever need help with something, I usually ask the people at Physics Forums. Sometimes I help other people out there too.