Why do I have to take "Calc-Based Physics"as a Math major?

[micromass]

I'm afraid I have to disagree, there are a handful of elite Mathematicians doesn't have Physics knowledge/background. It is absurd to even say someone doesn't deserve to be a mathematicians, just because their lack of interest in Physics. With all due respect, I believed those who only cares about the applications of Mathematics, doesn't deserve to be a Mathematician-- considering they only viewed math as a mere tool. No offense, here is just my $0.02.

You are very naive. That's ok. Back when I started my undergrad I hated applications of mathematics. I actively avoided them. But boy, I regret that attitude so much now.

Take functional analysis. It's a very cool field of research. But can one really understand it without knowing QM? I don't think so. How is somebody supposed to understand topology or differential geometry without the physical applications of stuff like measuring the Earth or GR. How is somebody supposed to understand even calculus without seeing it in action in physics? Sure, you think you understand it, but do you really know the relevance of Stokes' theorem? I didn't until I studied more physics.

Talk about great mathematicians, you'll find that many great mathematician knew their physics very well. Von Neumann was very aware of QM. Hilbert did research on GR. Euler, Gauss, Laplace all had applications in mind. Do you really think you can be a mathematician without knowing some physics? Perhaps you can, but I guarantee that you will regret this attitude later in your life.

 

[Crush1986]

Well, the fact is, general physics made absolutely no sense to me in high school, i barely survived with a B- by doing a lot of hand outs without UNDERSTANDING why. i.e. why force is F=ma. my teacher just threw a list of formula and tell me to apply it. that's why I don't know if calc-based physics would be the same. It was a nightmare in gen. phys.

F=ma will still be the starting point for almost everything in freshman physics. You're going to have to take it a physical fact of life at first. If you ever take more advanced mechanics you'll see more of why f=ma is a fact of life. The good news is most everything else you'll be able to prove using it, not much else should be, "thrown" at you.
My advice, give it a chance and give it your all. Physics strengthened my mathematical skills many times fold. A lot of math majors I know felt the same and decided to go for the physics minor. In fact every math major I met in undergrad physics went for the physics minor now that I think of it.

 

[Akorys]

Micromass, you say that physics helps in understanding the motivation for certain math fields, of which I've no doubt. However, studying mathematics already gives you a large number of courses to choose from, and additionally the recommended stat courses. If one wants to be a math major, surely they do not need to learn quantum mechanics, general relativity, etc, or they may as well do a minor/ double degree? While I'm sure it is helpful, I wonder as to the extent of physics courses you're recommending for math majors?

 

[Integreat]

You are very naive. That's ok. Back when I started my undergrad I hated applications of mathematics. I actively avoided them. But boy, I regret that attitude so much now.

Take functional analysis. It's a very cool field of research. But can one really understand it without knowing QM? I don't think so. How is somebody supposed to understand topology or differential geometry without the physical applications of stuff like measuring the Earth or GR. How is somebody supposed to understand even calculus without seeing it in action in physics? Sure, you think you understand it, but do you really know the relevance of Stokes' theorem? I didn't until I studied more physics.

Do you really think you can be a mathematician without knowing some physics? Perhaps you can, but I guarantee that you will regret this attitude later in your life.

I think there's a misconception here-- that I'm "afraid"of physics because of the "math" part. if anyone claim to be a mathematician but afraid the math, they might as well as NOT call themselves a mathematician. Perhaps you're right, Ill probably enjoy physics one day. although someone had already answered my true concern-- but once again, really boils down to-- is it going to be just memorizing formulas like i did in high school, because i did physics like that. but i don't understand anything at all, please allow me to use the good ol' example: F=ma. why is F=ma, how did they derived it. why is acceleration of gravity is -9.8m/s^2, where did the s^2 came from and why is it squared.

As you see I'm not that type of person who just take whatever the teacher told without asking "why," i like to understand the nature of everything. i.e. why do we use integration by substitution when dealing with a "differentiated" composite function.

I guess the reason why I'm having the "FEAR" of physics and applying math on it is because my high school experience, where I just memorize a colossal of formulas without truly understanding their nature. As I've said before, I barely survived Gen. Physics with a low B in high school. I'm just affraid that it'll be the same with calc-based physics.

But after reading your respond it made me feel better now.

 

[max1995]

I think there's a misconception here-- that I'm "afraid"of physics because of the "math" part. if anyone claim to be a mathematician but afraid the math, they might as well as NOT call themselves a mathematician. Perhaps you're right, Ill probably enjoy physics one day. although someone had already answered my true concern-- but once again, really boils down to-- is it going to be just memorizing formulas like i did in high school, because i did physics like that. but i don't understand anything at all, please allow me to use the good ol' example: F=ma. why is F=ma, how did they derived it. why is acceleration of gravity is -9.8m/s^2, where did the s^2 came from and why is it squared.

As you see I'm not that type of person who just take whatever the teacher told without asking "why," i like to understand the nature of everything. i.e. why do we use integration by substitution when dealing with a "differentiated" composite function.

I guess the reason why I'm having the "FEAR" of physics and applying math on it is because my high school experience, where I just memorize a colossal of formulas without truly understanding their nature. As I've said before, I barely survived Gen. Physics with a low B in high school. I'm just affraid that it'll be the same with calc-based physics.

But after reading your respond it made me feel better now.

When you do proper physics (starts once calculus is introduced into it) you should learn things like this, I am from the uk and until I got to university level (known as college in the US) we did plug and chug physics where we just had to use the formulas because you needed more maths than what we were taught at high school.

But once you hit university level, all the things you want to find out in bold will come through various physics courses (what you will cover derivation wise will depend on your course), yes some physics equations are still given to you at the earlier stage, but that's normally because it requires more advanced maths/physics than you have currently covered so won't understand the derivation with the current level of knowledge but there is no stopping you going and learning it of course

Dont worry it sounds like once you start doing proper physics you will actually enjoy it :D

 

[axmls]

I think there's a misconception here-- that I'm not "afraid"of physics because of the "math" part. if anyone claim to be a mathematician but afraid the math, they might as well as NOT call themselves a mathematician. Perhaps you're right, Ill enjoy physics one day. although someone had already answered my true concern-- but once again, really boils down to-- is it going to be just memorizing formulas like i did in high school, because i did physics like that. but i don't understand anything at all, please allow me to use the good ol' example: F=ma. why is F=ma, how did they derived it. why is acceleration of gravity is -9.8m/s^2, where did the s^2 came from and why is it squared.

$F = m a$ because Newton postulated that there is something called a force that causes objects to accelerate, and that acceleration also depends on the mass of the object. That's not really proven, though there are other formulations of classical mechanics where $F = ma$ can be derived (but it all boils down to making some assumption and seeing if experiments agree with it). $g = 9.8 m/s^2$ because experimentally, the gravitational force is $F = G \frac{M m}{r^2}$, and if $F = m a$, then since these are equal, $a = G \frac{M}{r^2}$. Plugging in known values of $G$, the mass of the Earth, and the radius of the Earth gives $a = 9.8 m/s^2$. The seconds term is squared because $m/s^2 = m/s/s$, i.e. "meters per second, per second"--acceleration tells you how fast the velocity (meters per second) changes per second. Things like this become very clear when you've learned calculus (especially the seconds squared part) and applied it to physics. I believe it is impossible to intuitively understand differentiation until you've seen the relationships between acceleration, velocity, and displacement in classical mechanics. Almost everything you do in first year physics is a result of solving the differential equation $$F = m \frac{d^2 x}{dt^2}$$ with various forces (spring forces, no forces, gravitational forces, etc.)

You will find physicists sometimes treat math very sloppily in the first year (and even onward). Don't be shocked when your professors are manipulating differentials. It's all grounded in proper math somehow, even if it is an abuse of notation.

 

[Mondayman]

I really feel that if where F=ma or the s^2 came from wasn't clear, the course either wasn't taught well or you didn't pay attention. Even in an introductory algebra-based physics class, it's pretty intuitive;

Anyway, introductory classes are guilty of dropping equations out of nowhere with not a lot of motivation. Just "use this in this situation". When you take your first calculus-based physics class, you start deriving these equations yourself, and they begin to make a whole lot more sense.

 

[amys299]

Taking freshman physics isn't going to just be memorizing equations and plugging and chugging if your university is actually teaching actual physics and if you're actually invested in the "why" part. All of physics is "WHY." The reason algebra-based physics had you memorize formulas is because there is an assumption you don't know calculus therefor you cannot fully understand the equations your using. If anything, algebra-based physics is the most useless thing in any curriculum so stop basing your assumption of physics because of algebra-based physics alone.

Also, a graduate mentor once told me no one fully understands F=ma until graduate school. It is more mathematically complicated, but all you will learn in freshman physics is F=dx²/d²t. If this formula has not given you an understanding about how math and physics are related, or what this math actually says about force and in turn what force says about math, you may want to look more in depth at what you learned in math, especially Calculus. When I took Calculus at my university, most of it was theory (the "why") but there was also a heavy emphasis on application.

 

[symbolipoint]

...but once again, really boils down to-- is it going to be just memorizing formulas like i did in high school, because i did physics like that.

No. Physics in college or your university will not be like that.

 

[MidgetDwarf]

I think there's a misconception here-- that I'm "afraid"of physics because of the "math" part. if anyone claim to be a mathematician but afraid the math, they might as well as NOT call themselves a mathematician. Perhaps you're right, Ill probably enjoy physics one day. although someone had already answered my true concern-- but once again, really boils down to-- is it going to be just memorizing formulas like i did in high school, because i did physics like that. but i don't understand anything at all, please allow me to use the good ol' example: F=ma. why is F=ma, how did they derived it. why is acceleration of gravity is -9.8m/s^2, where did the s^2 came from and why is it squared.

As you see I'm not that type of person who just take whatever the teacher told without asking "why," i like to understand the nature of everything. i.e. why do we use integration by substitution when dealing with a "differentiated" composite function.

I guess the reason why I'm having the "FEAR" of physics and applying math on it is because my high school experience, where I just memorize a colossal of formulas without truly understanding their nature. As I've said before, I barely survived Gen. Physics with a low B in high school. I'm just affraid that it'll be the same with calc-based physics.

But after reading your respond it made me feel better now.

You would like Fundamental of University Physics, by Alonso and Finn. It is different than most introductory physics books. DO not purchase the book titled Physics.
Everything is derived, experiments that led to discoveries are given a good coverage. Many topics not introduced in the introductory physics sequence are discussed.

 

[Integreat]

You would like Fundamental of University Physics, by Alonso and Finn. It is different than most introductory physics books. DO not purchase the book titled Physics.
Everything is derived, experiments that led to discoveries are given a good coverage. Many topics not introduced in the introductory physics sequence are discussed.

Very interesting, ill take a look, thanx

 

[jtbell]

Hi, why do I have to take calculus based physics, if I'm a math major?

Probably because it's a required course. If you are not happy with that, complain to your department.

Or go to a different university. I checked two that came first to the top of my head: Michigan and Ohio State. Neither requires math majors to take the calculus-based intro physics sequence, although Michigan does "strongly recommend" it.

 

[symbolipoint]

Or go to a different university. I checked two that came first to the top of my head: Michigan and Ohio State. Neither requires math majors to take the calculus-based intro physics sequence, although Michigan does "strongly recommend" it.

A mathematics undergraduate program might not require a set of courses in Physics. The institutions would specify a list of "cognates" to choose from, which are of high mathematical content, meaning courses outside of the Mathematics department and which rely very much on Mathematics for their understanding. These are things like Finance, Business Management, Economics, PHYSICS, Chemistry, Computer Science, Engineering.

 

[GHZ2016]

I know that a lot of people have said things of this nature, but I think you're underestimating the relationship that most physicists and physics students have with mathematics. A lot of people are interested in physics precisely because of their love for mathematics. Mathematics is not just a tool, it's the way to translate the world around you into something understandable and manipulatable. Topics like classical mechanics or electrodynamics were awe-inspiring for me exactly because of the beautiful mathematics involved. Not only that, but they completely changed my relationship with mathematics and rigor and helped me to better understand where the original ideas came from and how new ideas are developed. If you think that there is such a thing as math for math's sake that is completely divorced from the physical world and the attitudes that have driven physics, I think that's more a mark of naivete and a lack of really understanding either at this point in your education. That's completely alright and even understandable, since you seem quite young, but you will find that you will be much better served intellectually and personally if you don't go about shutting down whole fields or areas of thinking based on a very small bit of experience with them. There's a lot of wonderful things to learn about in the world, and a lot of topics will surprise you so long as you remain open to them. If you approach something with only an attitude of being bitter that you have to do it in the first place, you're setting yourself up not to like it and you might miss something really cool.

Best of luck in your studies.

 

[Fervent Freyja]

I know that Micromass is from Europe

I wonder, do Russians prefer or dislike being called European or Asian, or do they consider themselves exclusively Russian?

 

[Fervent Freyja]

math isn't about application, it's the beauty behind it.

The beauty behind it? Do you mean the natural world around you? The value of mathematics is that it meets human needs and has given us higher chances of survival with it's applications. The quality of life has improved for the majority of the world because of it. What would the human condition look like without it never being applied throughout history? Not a world that I would ever want to witness, and that's saying something. Physics will do even more for humankind one day.

I think you will regret the choice, I know that I do. But, they may not let you into this course anyway. It's not intended for mathematics or science majors, but serves as an option for other majors to take that could satisfy their general requirements. My university recommended reading material for the course is "Physics for Dummies"- I'm not kidding. This course will probably need to grade on a curve, but if you are as competent as you say in mathematics and do too well then you may be considered by your peers as the 'curve wrecker'.

 

[max1995]

The beauty behind it? Do you mean the natural world around you? The value of mathematics is that it meets human needs and has given us higher chances of survival with it's applications. The quality of life has improved for the majority of the world because of it. What would the human condition look like without it never being applied throughout history? Not a world that I would ever want to witness, and that's saying something. Physics will do even more for humankind one day.

I think you will regret the choice, I know that I do. But, they may not let you into this course anyway. It's not intended for mathematics or science majors, but serves as an option for other majors to take that could satisfy their general requirements. My university recommended reading material for the course is "Physics for Dummies"- I'm not kidding. This course will probably need to grade on a curve, but if you are as competent as you say in mathematics and do too well then you may be considered by your peers as the 'curve wrecker'.

Most people don't study maths or physics to increase our chances of survival etc. Almost all researchers who do mathematics/physics do it because they love it. There is definitely a beauty in mathematics, I know of no mathematics researchers at my university that do it for the applications to industry.

If you think maths as just a tool then I guess youll never understand when someone says there is a beauty in the mathematics but there is :)

 

[Fervent Freyja]

Most people don't study maths or physics to increase our chances of survival etc. Almost all researchers who do mathematics/physics do it because they love it. There is definitely a beauty in mathematics, I know of no mathematics researchers at my university that do it for the applications to industry.

If you think maths as just a tool then I guess youll never understand when someone says there is a beauty in the mathematics but there is :)

Young man, do not get smart and you should drop the straw man argument. Mathematics are manipulative cognitive skills that must be taught; therefore, they meet the definition of a tool. Everyone here is trying to communicate the importance of understanding the applications behind the tools, which can give more creative foresight.

I was pointing out the most valuable results that have stemmed from mathematics in recent history, and its contribution to, you know, people. I wasn't talking about your egocentric view on the beauty of it. I did not state that the catalyst for developments in mathematics came from human needs. Just that, great mathematicians were able to work at a level ahead of their time, and those principles were utilized by others to benefit humanity. I see beauty in tools that can improve the lives of people, particularly of those that still suffer.

Push that pencil and boost about your superiority all you want, but remember that you were simply lucky to be born in an environment that provided you the opportunity to even learn mathematics. You do not owe anybody charity or have to go out of your way. But, ungratefulness to the extent I see in juveniles today is disgraceful and disturbing. Kudos to the nurse that used simple equations in administering the drugs and IV that saved a childs life today.

 

[George Jones]

From "A Mathematician's Apology" by pure mathematician G.H. Hardy:

There are many highly respectable motives which may lead men to prosecute research, but three which are much more important than the rest. The first (without which the rest must come to nothing) is intellectual curiosity, desire to know the truth. ... It may be fine to feel, when you have done your work, that you have added to the happiness or alleviated the suffering of others, but that will not be why you did it. So if a mathematician, or a chemist, or even a physiologist, were to tell me that the driving in his work had been the desire to benefit humanity, the I should not believe him (nor should I think the better of him if I did). His dominant motives have been those which I have stated, and in which, surely, there is nothing of which any decent man need be ashamed.

Notes: 1) here "apology" means "explanation" or "defence" and is not an expression of regret; 2) I don't agree with the sexist language.

 

[symbolipoint]

From "A Mathematician's Apology" by pure mathematician G.H. Hardy:
Notes: 1) here "apology" means "explanation" or "defence" and is not an expression of regret; 2) I don't agree with the sexist language.

Nice quotation of that mathematician, but the language was not picked to be sexist. The pronouns as applied there function for all genders. The pronouns used are typical. Women and others are not excluded.

 

[max1995]

Young man, do not get smart and you should drop the straw man argument. Mathematics are manipulative cognitive skills that must be taught; therefore, they meet the definition of a tool. Everyone here is trying to communicate the importance of understanding the applications behind the tools, which can give more creative foresight.

I was pointing out the most valuable results that have stemmed from mathematics in recent history, and its contribution to, you know, people. I wasn't talking about your egocentric view on the beauty of it. I did not state that the catalyst for developments in mathematics came from human needs. Just that, great mathematicians were able to work at a level ahead of their time, and those principles were utilized by others to benefit humanity. I see beauty in tools that can improve the lives of people, particularly of those that still suffer.

Push that pencil and boost about your superiority all you want, but remember that you were simply lucky to be born in an environment that provided you the opportunity to even learn mathematics. You do not owe anybody charity or have to go out of your way. But, ungratefulness to the extent I see in juveniles today is disgraceful and disturbing. Kudos to the nurse that used simple equations in administering the drugs and IV that saved a childs life today.

But maths isn't just a tool for some people and all these applications you speak of were developed, on the whole, from pure interest for the subject so without that there may not even be the applications. Many of the researchers I have come across in industry and academia have said they arent really in that area for its applications but just for pure interest in the subject. An example of this my tutor is currently doing research into dynamics of bubbles and she says the applications could be more targeted delivery systems of chemotherapy drugs but also said while that is great, her main interest is just to further the knowledge in that subject are. Also you say 'everyone is trying to put across the importance of application' but I view it more as putting across the importance of being open minded when approaching new subject areas

I never boosted about my superiority either nor an I ungrateful for everything I have in my life today (especially as a lot of it comes from my hard work). I also wasn't 'getting smart with you' I was just stating the reason that, from what I have observed and read about, a lot of maths and physics applications are about today. You seemed to say that the only real reasons people do maths is to benefit society but this simply isn't the case

Anyway this is straying from the point of the thread.

 

[symbolipoint]

max1995, good show!

 

[axmls]

But maths isn't just a tool for some people and all these applications you speak of were developed, on the whole, from pure interest for the subject so without that there may not even be the applications. Many of the researchers I have come across in industry and academia have said they arent really in that area for its applications but just for pure interest in the subject. An example of this my tutor is currently doing research into dynamics of bubbles and she says the applications could be more targeted delivery systems of chemotherapy drugs but also said while that is great, her main interest is just to further the knowledge in that subject are. Also you say 'everyone is trying to put across the importance of application' but I view it more as putting across the importance of being open minded when approaching new subject areas

I never boosted about my superiority either nor an I ungrateful for everything I have in my life today (especially as a lot of it comes from my hard work). I also wasn't 'getting smart with you' I was just stating the reason that, from what I have observed and read about, a lot of maths and physics applications are about today. You seemed to say that the only real reasons people do maths is to benefit society but this simply isn't the case

Anyway this is straying from the point of the thread.

Of course many (most?) mathematicians aren't super interested in applications directly. And there's nothing wrong with that. I think that the point the others were trying to get across was that students should never intentionally shut out the prospect of application-based math, and more importantly, a lot of students underestimate how much it can help your math skills to see the math applied to something or to see the historical reasons for the development of that math in the first place. There can be a deeper understanding gained by looking at how the math is applied, if only because it boosts motivation. Micromass mentioned general relativity with differential geometry and quantum mechanics with functional analysis, for example. Likewise, it makes sense to learn physics in general in order to better understand calculus.

 

[max1995]

Of course many (most?) mathematicians aren't super interested in applications directly. And there's nothing wrong with that. I think that the point the others were trying to get across was that students should never intentionally shut out the prospect of application-based math, and more importantly, a lot of students underestimate how much it can help your math skills to see the math applied to something or to see the historical reasons for the development of that math in the first place. There can be a deeper understanding gained by looking at how the math is applied, if only because it boosts motivation. Micromass mentioned general relativity with differential geometry and quantum mechanics with functional analysis, for example. Likewise, it makes sense to learn physics in general in order to better understand calculus.

Sorry just re read a point I made and it wasnt very clear, I totally agree with you on not shutting out application based maths (hell I study maths and physics aha)