I'm excellent at math but i can't seem to master physics?

[Klockan3]

Fair enough. However, in most courses you do (or, at least, should) get challenging exercises. If not, then there's something not quite right about the courses you've been taking.

There are some hard stuff, but a wast majority of it is just menial exercising of normal techinques used for doing proofs.

I did this one in my first year, with just the Euclidean algorithm above high school level:
F(n) is the n'th number of the Fibonacci sequence. Ie, F(0)=0, F(1)=1, F(n+2)=F(n+1)+F(n)
Prove that GCD(F(N),F(M))=F(GCD(N,M))

Let R be a unique factorization domain in which every maximal ideal is principal. Prove that every ideal of R is principal.

I've provided Wikipedia links to all the appropriate definitions. If you attempt this problem, then I think you will agree that it requires a bit more than just a knowledge of these defintions.

Assume there is an ideal that isn't principal. This ideal needs to be a sub ideal to a max ideal since all maximal ideals are principal. Since we have an unique factorization this ideal will look exactly like the original ring but with a factor of the generator extra in every object. This means that any sub ideal of this ideal will have a direct correlation with the ideals of the original ring and thus the maximal sub ideals must then also be principal. Which in turn means that our ideal we are looking for must also be a sub ideal of one of those principal ideals.

Thus this process repeats ad infinitum and as such we can never find an ideal which is not principal.

Well, you need some set point to compare to. If you let that set point be the computational mathematics that most people consider maths to be (some calculus, diff eq, maybe basic stat) then yes, the classes I mentioned are indeed quite nontrivial. There are certainly many ways to those types of proofs- which is why me and my peers come up with completely different methods at times. So its pretty fallacious to say you're given a set of instructions, almost a function, and asked to perform that function on a problem.

There certainly are more than one way to solve most of these, but usually you have gone through ways to solve things that are very similar to what you are supposed to solve now and just minor adjustments are needed.

 

[DukeofDuke]

There certainly are more than one way to solve most of these, but usually you have gone through ways to solve things that are very similar to what you are supposed to solve now and just minor adjustments are needed.

The original point of yours I was refuting, was your claim that physics problems had multiple approaches that had to be thought about individually while math was basically plug and chug, with one or two approaches and no intuition.

Even if the math problem is easy, that doesn't mean its a computation problem. In fact, I'd argue that "usually you have gone through ways to solve things that are very similar to what you are supposed to solve now and just minor adjustments are needed" applies just as strongly to physics courses. Its not like they ask you to derive new forms of quantum loop gravity on tests. The stuff in physics classes are equally trivial if you know your basic assumptions and a couple common techniques...just like in mathematics.

As a math physics double major, I DO use my intuition on math proofs to give me sensible direction to my proofs, while other math majors often spend twice as long thinking about an approach. So i still strongly disagree with you- intuition is vital in mathematical undergraduate studies, its not at all repetition of one or two axioms.

 

[Klockan3]

The original point of yours I was refuting, was your claim that physics problems had multiple approaches that had to be thought about individually while math was basically plug and chug, with one or two approaches and no intuition.

You are mixing me with others partly. I never said that mathematics have just one road and that physical problems are more versatile.

The difference is that in physics you require more intuition while in maths you require a more structured approach. Both of these aspects are in both fields, but it makes some people have an inclination towards one or the other of the fields. That is all I said.

 

[union68]

The original point of yours I was refuting, was your claim that physics problems had multiple approaches that had to be thought about individually while math was basically plug and chug, with one or two approaches and no intuition.

Even if the math problem is easy, that doesn't mean its a computation problem. In fact, I'd argue that "usually you have gone through ways to solve things that are very similar to what you are supposed to solve now and just minor adjustments are needed" applies just as strongly to physics courses. Its not like they ask you to derive new forms of quantum loop gravity on tests. The stuff in physics classes are equally trivial if you know your basic assumptions and a couple common techniques...just like in mathematics.

As a math physics double major, I DO use my intuition on math proofs to give me sensible direction to my proofs, while other math majors often spend twice as long thinking about an approach. So i still strongly disagree with you- intuition is vital in mathematical undergraduate studies, its not at all repetition of one or two axioms.

I agree. Dismissing all the exercises and proofs that one encounters in analysis, algebra, etc. as "trivial" is absolute nonsense. It's attitudes like that that scare away potential majors. Imagine how a new budding math major feels when he/she has spent two hours on a proof only to have it called trivial. That really brings down the self-confidence.

It's the trait of elitism and arrogance that I have encountered in many math majors. Many are very nice, helpful people, but some are just way too cool for their own good.

But I don't know why you're bothering to argue with him. He's clearly the next Gauss.

 

[Klockan3]

Ok, ok, I am sorry that I called the proofs in those classes "trivial as long as you have the definitions". Honestly I do not really know, I am really bad at judging things like that. It was mostly as a counter weight against the really anti physics tendencies that were in this thread before I started to post. Personally I have more experience with people complaining about physics problems than maths ones but that can depend on other things.

 

[union68]

It's cool dude, I'm just teasing you.

However, I have tutored mathematics and physics for about 2 years now. I've helped with everything from baby physics to intro E&M, and from beginning algebra to differential equations and linear algebra. And one thing I have learned is to never, EVER call something simple, obvious, easy, or trivial. That is the quickest way to beat a student's confidence into a pulp.

I don't really have much to add to the actual topic, except that mathematicians who look down upon all other sciences as being inferior are fools.

That G.H. Hardy "pure math" elitism really, really pisses me off sometimes.

 

[aPhilosopher]

I don't really have much to add to the actual topic, except that mathematicians who look down upon all other sciences as being inferior are fools.

That G.H. Hardy "pure math" elitism really, really pisses me off sometimes.

They're two different things. Math just isn't a science in that it's not dependent upon empiricism. Math has absolute and unquestionable truth whereas no theory of science will ever have that. The best that we'll be able to say is that we've been trying to break it for some insane amount of years and haven't been able to.

 

[Klockan3]

They're two different things. Math just isn't a science in that it's not dependent upon empiricism. Math has absolute and unquestionable truth whereas no theory of science will ever have that. The best that we'll be able to say is that we've been trying to break it for some insane amount of years and haven't been able to.

Every theory have absolute and unquestionable truth. If EM fields works exactly as described by Maxwell then we can predict with 100% accuracy what will happen. It doesn't matter that the theories might be wrong, as long as you sit in a classroom it is the truth.

The difference you are talking about only comes when you start doing research. Mathematicians do not do experiments, they only have theorists, that is the difference between maths and other sciences.

Edit: And on top of that it doesn't matter if we disprove a lot of what we thought were correct, since the old models obviously worked for a ton of stuff making them still applicable in most cases. Kinda like the Newtonian limit, there is no need to scrap the old results just because you got something new. What you get is a new level of exactness.

 

[morphism]

Assume there is an ideal that isn't principal. This ideal needs to be a sub ideal to a max ideal since all maximal ideals are principal. Since we have an unique factorization this ideal will look exactly like the original ring but with a factor of the generator extra in every object. This means that any sub ideal of this ideal will have a direct correlation with the ideals of the original ring and thus the maximal sub ideals must then also be principal. Which in turn means that our ideal we are looking for must also be a sub ideal of one of those principal ideals.

Thus this process repeats ad infinitum and as such we can never find an ideal which is not principal.

I'm not really interested in continuing the discussion started in this thread. But, for what it's worth, this isn't a correct proof.

 

[DukeofDuke]

math has unquestionable truth if you assume the axioms of the system...very different from unquestionable truth...

and yes, physics is empirical, but that's good enough for people not hung over a certain few crippling questions.

 

[union68]

They're two different things. Math just isn't a science in that it's not dependent upon empiricism. Math has absolute and unquestionable truth whereas no theory of science will ever have that. The best that we'll be able to say is that we've been trying to break it for some insane amount of years and haven't been able to.

That depends on your definition of "science." The definition I adhere to is that a science is a discipline that makes explicit use of the scientific method -- and by that definition, math is certainly a science.

Now I will be the first to admit that my knowledge of the deep foundational subjects is very basic, but isn't there STILL debate over the fundamental axioms of set theory and logic? I could be wrong...

But hey, I'm way off topic now! Ha.

 

[DukeofDuke]

That depends on your definition of "science." The definition I adhere to is that a science is a discipline that makes explicit use of the scientific method -- and by that definition, math is certainly a science.

Now I will be the first to admit that my knowledge of the deep foundational subjects is very basic, but isn't there STILL debate over the fundamental axioms of set theory and logic? I could be wrong...

But hey, I'm way off topic now! Ha.

I am very confused...the scientific method is empirical in nature, fitting observable data with hypothesis. This is not at all what mathematics does- you do not need observations to do mathematics, just axioms. Nature is the final judge of a theory. Mathematics is based on logic and can be derived- but it is impossible to merely derive nature! The best you can do is fit some values on her and work within the box you've created...completely different approaches!

 

[union68]

I am very confused...the scientific method is empirical in nature, fitting observable data with hypothesis. This is not at all what mathematics does- you do not need observations to do mathematics, just axioms. Nature is the final judge of a theory. Mathematics is based on logic and can be derived- but it is impossible to merely derive nature! The best you can do is fit some values on her and work within the box you've created...completely different approaches!

Yes, clearly it does not depend on empirical observations.

Think about the structure of mathematics. You have a group of problems, and you have a feeling that they might be related. So, you do what?

1) Work on the problems, try to get a feel for them.

2) Conjecture a hypothesis.

3) Try and prove it. If it fails, you reformulate your hypothesis. If you are successful, you have established a mathematical theorem.

Contrast this to physics, or any other natural science: you have a group of observations, or data. You have an idea they may be related, and you're looking for that link. What do you do?

1) Work on the data, looking for something to point you in the right direction.

2) Conjecture a hypothesis.

3) Conduct experiments in effort to verify the hypothesis. If it fails, you reformulate. If you are successful, you have established a physical theorem.

Do you see the similarities? Proofs are the mathematician's experiments. I was particularly struck by mathwonk's quote of V.I. Arnol'd in the "So you want to be a mathematician" thread. It's in the very first post, check it out.

I think you have a very narrow view of what the scientific method entails. It's a way of thinking, an approach.

 

[DukeofDuke]

Yes, clearly it does not depend on empirical observations.

Think about the structure of mathematics. You have a group of problems, and you have a feeling that they might be related. So, you do what?

1) Work on the problems, try to get a feel for them.

2) Conjecture a hypothesis.

3) Try and prove it. If it fails, you reformulate your hypothesis. If you are successful, you have established a mathematical theorem.

Contrast this to physics, or any other natural science: you have a group of observations, or data. You have an idea they may be related, and you're looking for that link. What do you do?

1) Work on the data, looking for something to point you in the right direction.

2) Conjecture a hypothesis.

3) Conduct experiments in effort to verify the hypothesis. If it fails, you reformulate. If you are successful, you have established a physical theorem.

Do you see the similarities? Proofs are the mathematician's experiments. I was particularly struck by mathwonk's quote of V.I. Arnol'd in the "So you want to be a mathematician" thread. It's in the very first post, check it out.

I think you have a very narrow view of what the scientific method entails. It's a way of thinking, an approach.

Um...I don't know what you consider to be the scientific method, but I will go ahead and consult the dictionary on this one (Merriam Webster)...

Main Entry: scientific method
Function: noun
Date: circa 1810

: principles and procedures for the systematic pursuit of knowledge involving the recognition and formulation of a problem, the collection of data through observation and experiment, and the formulation and testing of hypotheses


"collection of data through observation and experiment" implies the input of some extraneous source of information. All the mathematical truths are already present in the axioms you are using- you are just rearranging present knowledge in revealing ways. This is far from the scientific method, which attempts to incorporate knowledge that literally was not in existence previously.

 

[union68]

You're consulting a dictionary? Are you serious? You think that helps your argument?

What do you think drives the process to form mathematical results? Unsolved problems! What drives the process to form physical results? Unexplained data or phenomena!

How was the proof of Fermat's Last Theorem formulated? Conjecture->attempted proof. Didn't work? New conjecture->attempted proof. Still didn't work? New conjecture->proved.

How about quantum mechanics, how was that whole thing arrived at? Conjecture->experimental test. Didn't work? New conjecture->experimental test. Still didn't work? Conjecture->experimentally verified.

In both cases, I want you to tell me this isn't the process of scientific inquiry. Tell me this isn't the scientific method.

Holy cow. Actually, you know what...forget I said anything. Clearly Merriam-Webster has the last word.

 

[irises28]

Every theory have absolute and unquestionable truth. If EM fields works exactly as described by Maxwell then we can predict with 100% accuracy what will happen. It doesn't matter that the theories might be wrong, as long as you sit in a classroom it is the truth.

I think you did a bit of rounding on that 100% you say, just like a physicist. Physics is just a model and its not perfect nor does it ever have a chance of being perfect. It doesn't work 100% of the time because it isn't absolute, it can't be. Physics is just an approximation, always getting closer and closer but always just an approximation. Its not anywhere near as beautiful as math because math is absolute.

Edit: And on top of that it doesn't matter if we disprove a lot of what we thought were correct, since the old models obviously worked for a ton of stuff making them still applicable in most cases. Kinda like the Newtonian limit, there is no need to scrap the old results just because you got something new. What you get is a new level of exactness.

Yes they may work for a lot of stuff but they aren't perfect. So you can't really claim to get a new level of exactness. Saying that implies you have the right answer but your calculator doesn't show enough digits. You don't have the right answer though, and it won't ever be right.

With math if you have a proof that is it, you have to leave it because you know its the right answer. Its perfectly exact. Something physics can't ever be.

 

[DukeofDuke]

You're consulting a dictionary? Are you serious? You think that helps your argument?

What do you think drives the process to form mathematical results? Unsolved problems! What drives the process to form physical results? Unexplained data or phenomena!

How was the proof of Fermat's Last Theorem formulated? Conjecture->attempted proof. Didn't work? New conjecture->attempted proof. Still didn't work? New conjecture->proved.

How about quantum mechanics, how was that whole thing arrived at? Conjecture->experimental test. Didn't work? New conjecture->experimental test. Still didn't work? Conjecture->experimentally verified.

In both cases, I want you to tell me this isn't the process of scientific inquiry. Tell me this isn't the scientific method.

Holy cow. Actually, you know what...forget I said anything. Clearly Merriam-Webster has the last word.

Guess and check is not the scientific method. The scientific method is well defined- it involves real world data separate from a set of originating axioms. It involves *observable phenomenon* and its subsequent categorization. Your terms simply do not match the definition, no matter how much you want them to.

Again, mathematics is never experimentally verified. It is *proven* (assuming the axioms hold). Physics is *never* proven, it is merely verified to the point of general acceptance.

Really, they are two separate paradigms. No matter how much you try to force the square peg into the round hole, it won't work...

By the way, your argument from pathos is not very convincing, nor is it appreciated.

 

[union68]

Taking potshots at me by quoting the dictionary complete with date and part of speech wasn't appreciated either. It's belittling and aggravating, and you know quite well what you were trying to do. Therefore, you're not perfectly innocent either, so don't pretend to be.

I think you're taking too narrow of view of the word, and I'm trying to be more general and less strict. But in the end we're ultimately debating semantics...I think we probably both have better things to do with our time.

Neither of us will budge and we're not even on topic anymore, so I think it's time to throw in the towel. Agree to disagree, etc.

No hard feelings.

 

[Klockan3]

I'm not really interested in continuing the discussion started in this thread. But, for what it's worth, this isn't a correct proof.

The only dubious in it is that I skipped to show a few things that are quite elementary and instead just stated them. The proof is correct, but maybe there is a step or two someone would like to have more clarifications on. But like everything you need to draw the line somewhere.

 

[skyazen]

I have the same problem with physics, right now I am taking physics 313 for engineering and I just failed my last test after I studied my butt off. Am I just not capable of doing physics? I was never expose to physics prior to this class. However, I am pretty good with calculus so far. I need some tips and guidance on studying physics, or should I just keep doing practice problems and hopefully I will get better? I am desperate and really need to pass this course. Major in Mechanical Engineering.