Physics vs Math: Comparing Difficulties

[sutupidmath]

Hi all,

I have been wondering for the last couple of days whether it is just me or is there also anyone out there who finds math relatively easy compared to physics. Albeit someone misunderstands me, i am not claiming that math is a piece of cake for me, only that compared to physics i find it considerably easy.

Specifically, i found Real Analysis, Abstract algebra and even Topology now, relatively easier than my introductory physics courses.

The reason might also be that i spend considerably more time studying math compared to physics, but i just kind of feel that i do not have the necessary/proper mindset(the proper kind of thinking structure) for doing physics. Is there anyone out there in a similar situation?...or would you say that it is simply due to the insufficient amount of time dedicated to fully absorbing the concepts in physics?

Thanks in advance for your input!

 

[kuahji]

I'd have to say neither are really easy :). I struggle more with math, esp. the math dealing with proofs. Those classes just seem to eat massive amounts of time. Physics eats a lot of time as well, but I enjoy it a lot more so I reckon it seems easier because I'm enjoying it more. So yeah, physics is a bit easier than mathematics for me. But it's still insanely hard if that makes sense.

 

[Klockan3]

I have a hard time picking which is easiest. Maths depends a lot on your mind being structured while physics gets easier the more "intuition" you got. But of course a lot of maths gets easier with intuition and a lot of physics gets easier with structure it is just that there is a difference in how important either one of those are.

I know people of both kinds, those who are excellent at maths and can't do physics and those who can do physics but suck at maths.(I don't believe that you can be excellent at physics without being good at maths though)

 

[sutupidmath]

I believe that i do, actually, have a quite structured mind. The very fact that i love 'dry' math,with this i mean pure math (by the way, some of my profs. even joke they say : " 'ME' likes math bare of any use-useless math" )and stuff that is strictly based on pure logic makes me think that my mind simply is not 'programmed' to successfully do physics (which i have no intention of doing physics in the future but...) It's just that physics sometimes makes me feel really dumb. While i have no problem following and also constructing myself 2-3 pages long proofs in math, in many instances i have to spend quite some time to figure out how to solve, what a physicists i suspect would call ''problems of moderate difficulty'...it is frustrating.

 

[cronxeh]

A physicist and a mathematician were staying in a hotel room. During the night, a fire broke out outside of the room. A physicist wakes up, sees the smoke, and immediately fills the room's trash can with water from the bathtub and dumps it on the fire, successfully putting it out. An hour later a fire breaks out again, this time a mathematician wakes up. He notices that the solution already exists, and proceeds to wake up the physicist who puts out the fire.

 

[Rasalhague]

Sometimes I find the math in math easier than the math in physics, namely when physicists use vague, rough-and-ready, short-hand definitions. When I'm new to a subject, I prefer things to be explicit and spelled out; even if that makes for wordier definitions, it can save confusion in the long run. This thread about what "vector" means is good example:

https://www.physicsforums.com/showthread.php?t=374623

I remember posting a similar question myself a while ago.

 

[cronxeh]

Six engineers and six mathematicians are attending a conference and are traveling by train. One by one, each of the engineers goes up to the ticket counter and buys a ticket to the conference. But only one of the mathematicians does. The engineers look puzzled and one of the mathematicians says, "Optimization."

The twelve get on the same car and one mathematician stands at each end of the car. Now the engineers are really puzzled. After a while, the mathematician at one end, yells, "Conductor!" On that cue, all the mathematicians pile into the rest room and lock the door.

The conductor enters the car and announces, "Tickets, please. Tickets!" He passes the engineers and punches each of their tickets. At the end of the car, he notices the restroom is occupied and knocks on the door, "Ticket, please."

The ticket slides out from under the door, he punches it and slides it back, then leaves the car and continues to the next car.

The engineers look at each other and decide how clever the mathematicians have been, and then wink at each other.

They all attend the conference and have a good time. Upon arriving at the train station, one engineer buys a ticket and they giggle at each other. The mathematicians do not buy any. This time again, the engineers look puzzled, and the same mathematician says, "Optimization."

This time all the mathematicians sit down and the engineers have the lookouts. One engineer, peers down a couple of cars and shouts, "Conductor!" Immediately all the engineers pile into the rest room, while the mathematicians just sit there. Once the engineers are in the rest room, one of the mathematicians knocks on the door and says, "Ticket, please." The ticket slides out under the door, the mathematician grabs it and along with the other mathematicians, runs to the other rest room and they lock themselves in.

 

[ishan001]

Six engineers and six mathematicians are attending a conference and are traveling by train. One by one, each of the engineers goes up to the ticket counter and buys a ticket to the conference. But only one of the mathematicians does. The engineers look puzzled and one of the mathematicians says, "Optimization."

The twelve get on the same car and one mathematician stands at each end of the car. Now the engineers are really puzzled. After a while, the mathematician at one end, yells, "Conductor!" On that cue, all the mathematicians pile into the rest room and lock the door.

The conductor enters the car and announces, "Tickets, please. Tickets!" He passes the engineers and punches each of their tickets. At the end of the car, he notices the restroom is occupied and knocks on the door, "Ticket, please."

The ticket slides out from under the door, he punches it and slides it back, then leaves the car and continues to the next car.

The engineers look at each other and decide how clever the mathematicians have been, and then wink at each other.

They all attend the conference and have a good time. Upon arriving at the train station, one engineer buys a ticket and they giggle at each other. The mathematicians do not buy any. This time again, the engineers look puzzled, and the same mathematician says, "Optimization."

This time all the mathematicians sit down and the engineers have the lookouts. One engineer, peers down a couple of cars and shouts, "Conductor!" Immediately all the engineers pile into the rest room, while the mathematicians just sit there. Once the engineers are in the rest room, one of the mathematicians knocks on the door and says, "Ticket, please." The ticket slides out under the door, the mathematician grabs it and along with the other mathematicians, runs to the other rest room and they lock themselves in.

Ha Ha!

However, I think Physics is easier. Personally, I find Physics easy because it can be easily related to real life!

Between, story was really funny! :)

 

[lisab]

I found them equally challenging, but physics homework took far more time than math.

Oh and physics profs were better teachers, in my very narrow experience.

 

[elect_eng]

Personally, I find Physics easy because it can be easily related to real life!

I'd like to visit your neighborhood. Quantum and relativistic effects must be rampant in your part of town. I live in boring old Newtonianville.

 

[Pinu7]

I prefer pure mathematics and rigor over the applied stuff. To me, it is much easier when everything is well defined and no "extra assumptions" are made. I usually skip over many examples in texts(I could usually make them myself) and do most of the proofs. I almost never draw a picture or some kind of illustration unless absolutely necessary.

However, mathematics seems uninspired and I find physics a wonderful mixture of philosophy and mathematics. However, I can not subscribe to the intuitive ideas the pure physicists have. Therefore, I aim to be a theoretical and mathematical physicist.

 

[DukeofDuke]

Physics vs. Math is VERY different from Real Analysis, Abstract Algebra, and Topology versus intro to Newtonian mechanics.

If anyone finds the former set easier than the latter, their education really confuses me...either your school has FAR too low mathematics standards or FAR too high physics standards.

 

[Klockan3]

Physics vs. Math is VERY different from Real Analysis, Abstract Algebra, and Topology versus intro to Newtonian mechanics.

If anyone finds the former set easier than the latter, their education really confuses me...either your school has FAR too low mathematics standards or FAR too high physics standards.

Or he tries to use the same approach in physics as he did in maths, which will fail. The main thing in physics is that they force you to make approximations everywhere which have to be motivated by "In this case this number is so negligible that it wouldn't change the answer more than the margin of error already does". Also they automatically assume that everything takes normal forms, like all functions are smooth and Q=R.

Also the dreaded "Do this make sense?", like if you derived that the sound in your cinema contains enough energy to destroy all of the universe then you should look over your calculations...

 

[Hurkyl]

The main thing in physics is that they force you to make approximations everywhere

One can use approximations in mathematics -- half of the point of calculus is to learn how.

Also the dreaded "Do this make sense?"

One can make sanity checks in mathematics too. "Whoops, if this claim is true, then I can prove 0=1 -- let's look for my mistake..."

 

[Klockan3]

One can use approximations in mathematics -- half of the point of calculus is to learn how.One can make sanity checks in mathematics too. "Whoops, if this claim is true, then I can prove 0=1 -- let's look for my mistake..."

But they are different, firstly you don't approximate anything in calculus except for a small part of the Taylor expansion bits and then you do an exact approximation, something you can't do in most physics problems. There you for the most part assume that it is negligible since your real world experiences tells you that it is so, this goes on till you get to modern physics (No intuition) or graduate level physics(Being formal).

The other one don't have anything to do with your real world intuition, having that something leads to 1=0 just means that it was wrong, this is a standard way to disprove things in maths. A physics comparison with that would be "dimensional analysis", ie if you get that mass equals speed you are wrong.

 

[Ivpoly]

It also how do we define easy, as we sometimes mix tedious with hard. Sometimes these intro courses are just a big con to get you to like math, then when all the fun stops it is usually too late. What books where used for these courses( if I may ask)?

 

[cronxeh]

I don't know what you guys are talking about.

0=1 for large enough value of 0

Speaking of funnies..

Γ(n+1) = n*Γ(n) = n!

Taking n=0, Γ(1) = 0*Γ(0) = 0! = 1, Henceforthhereinto 0 is not a natural number :rofl:

 

[Klockan3]

0=1 for large enough value of 0

That isn't true, 0+0=1 for large enough values of zero.
Though:
$\lim_{0\rightarrow big} 0=1$

 

[sutupidmath]

Physics vs. Math is VERY different from Real Analysis, Abstract Algebra, and Topology versus intro to Newtonian mechanics.

If anyone finds the former set easier than the latter, their education really confuses me...either your school has FAR too low mathematics standards or FAR too high physics standards.

Easy and Hard are relative concepts i would say, the same holds for 'FAR too low" and "FAR too hight''. However, just to give you a clearer picture of their 'difficulty', in my abst. alg course, which I took as a second semester freshman, i made an A, while 5 of the ppl failed it, and only one other person got an A as well out of a class of 14( i appologize if this looks like showing off, the intention is far away from this). I also made an A in my two intro to physics classes.
The only thing i was saying is that i seem to lack the 'intuition' for physics. The lack of 'strict structure' i would say that seems to exist within physics (in terms of the material I've been exposed so far) does not quite fit my way of thinking.

 

[sutupidmath]

Oh and physics profs were better teachers, in my very narrow experience.

Hmmm...now when i think more about it, i believe that actually the lecturer might have played an important role in my lack of affection, i would say, for physics as well. The prof. i had for those two classes, never got into details as to why the stuff in physics works the way it does, but simply he would say ok, this is how it is done. In other words, he almost never explained the physical meaning of what we learned, so it is very probbable that the lack of profound understanding of the concepts has resulted in a lack of intuition for physics as well.

 

[Werg22]

I found them equally challenging, but physics homework took far more time than math.

Oh and physics profs were better teachers, in my very narrow experience.

I find it's the opposite. I am regaled when a math prof shares the need for clarity and precision I have, and curse when a science prof doesn't.

 

[Chronos]

The trouble with physics is you must frame the question before applying the math. The best math in the world will not save you from bad assumptions or hidden variables. Math, however, is in indispensable component of physics. Phyisics without math is like building a house without tools.

 

[sutupidmath]

The best math in the world will not save you from bad assumptions or hidden variables.

I will have to totally agree with you at this point.
Just to ilustrate this point a little bit further, not long ago a friend asked me if i could help him with one of his problems in calc based physics 1 (an intro course).

I don't remeber the exact wording of the problem but it was something like this:

A person, starting from A, moves a distance d north accelerating at x m/s^2 until he reaches point B, then he moves in a circular path with radius r, until he is directly moving east at point C and keeps going until he reaches point D.

we were supposed to find the distance from A to C i think. And i had trouble finding the arch lengh from point B to point C. It turned out that we had to assume that his path north was tangent to the circle(circular path) at point B, which would make him cover an angle of 90 degrees, and then the prob. wouuld have been a piece of cake. Nevertheless, since i was not working under this assumption, but rather that his path could have intersected the circle at any other point, i failed to find the arch length and thus solve the problem.

I think this kind of 'poor wording', i would say, is very common in physics, and i totally dislike this trend.

 

[Klockan3]

I think this kind of 'poor wording', i would say, is very common in physics, and i totally dislike this trend.

It isn't poor wording, it is just that you can't have infinite acceleration.

 

[owlpride]

I can walk a path with corners. Physicists haven't figured out how to model those yet?

 

[DukeofDuke]

I can walk a path with corners. Physicists haven't figured out how to model those yet?

Sorry but instantaneous deceleration would be impossible. So you can't walk a path with corners, your radius will be small but existent.

 

[Klockan3]

I can walk a path with corners. Physicists haven't figured out how to model those yet?

But the guy was obviously running at ~top speed or they wouldn't be talking about acceleration from the start. It takes a bit to accelerate from 0m/s to top speed, while walking is normally seen as almost instantaneous.

Anyway, try to run around a tight corner in a corridor. You will hit the wall every time. What you are talking about is to first stop by the corner, then turn and then continue on walking.

 

[MathematicalPhysicist]

Hmmm...now when i think more about it, i believe that actually the lecturer might have played an important role in my lack of affection, i would say, for physics as well. The prof. i had for those two classes, never got into details as to why the stuff in physics works the way it does, but simply he would say ok, this is how it is done. In other words, he almost never explained the physical meaning of what we learned, so it is very probbable that the lack of profound understanding of the concepts has resulted in a lack of intuition for physics as well.

If you want inspiration, watch Walter Lewin shows, entertaining.

 

[Pinu7]

I can walk a path with corners.

No you can't.

 

[owlpride]

No you can't.

Why not? What prevents me from stopping at a point and then start walking into a different direction?

 

[DukeofDuke]

Why not? What prevents me from stopping at a point and then start walking into a different direction?

My roommate wants to know if you were joking. He has a crap sense of humor. Were you? Or did you seriously ask why you can't turn a corner without decelerating?
(that's the key to the problem, he's not slowing down as he turns the corner).

 

[dacruick]

physics is better.

 

[Heresy]

Why not? What prevents me from stopping instantaneously at a point and then start walking into a different direction at the same speed as before?

The fact that you don't want to rip your body apart by trying.

 

[owlpride]

My roommate wants to know if you were joking. He has a crap sense of humor. Were you? Or did you seriously ask why you can't turn a corner without keeping the same velocity?

Is your roommate about to show me how I would walk along a circular path with constant velocity?

 

[dacruick]

I think the idea that heresy is trying to very subtly and condescendingly imply is that you need a deceleration. The only way for you to be going a certain speed and then to stop instantaneously is if an infinite force is applied to you, hence the ripping apart of your body. But if you measure your distance in steps, You can stop instantaneously because your measurement of distance is discrete. and then you can start at the same speed once again for the same reason.