Ugh How different is introductory physics from high level courses?

[Nano-Passion]

At this point I feel like my classical mechanics I course is an engineering course. While I do enjoy physics, I am much more interested in the theory behind it.. I find myself easily engulfed in calculus but when it comes to physics it is harder to motivate myself. I love proofs and mathematics, and physics is what actually got me started in appreciating mathematics itself.

But at this point I completely hate the way that physics goes on to portray its concepts. I feel like a lot of things are left in obscurity. Its too much of a "hey let's use this, this, and this math formula and try our hardest to conceptualize the problem." I'm an aspiring physics PhD holder, but at this point classical mechanics I is really turning me off. Also keep in mind that I took physics in high school, so that may also affect my level of interest toward classical mechanics I.

I say this especially because I have a midterm soon. I always find myself with the urge to open my calculus book and doing extra problems instead of opening up my physics book. That is certainly not good since I'm planning to pursue theoretical physics.. -_-

How different is introductory physics to some of the higher level physics courses that you take later on? Will it be more theory or will problem-solving be stressed over theory for a while?

 

[Dr_Morbius]

Try watching these videos from MIT. The professor, Walter Lewin, is an engaging instructor who makes this subject fascinating.

http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/

 

[JHamm]

If you need some quick physics inspiration (not exactly what you asked for but seems kind of relevant) see if you can borrow a copy of The Feynman Lectures, he has a unique way of viewing physics and his explanations are artful.

 

[f95toli]

I also found classical mechanics to be extremely boring, and I was not alone.
Don't worry, it will get better and more interesting later.

 

[Nano-Passion]

Try watching these videos from MIT. The professor, Walter Lewin, is an engaging instructor who makes this subject fascinating.

http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/

He also came out with a new book after his retirement, seems interesting:

If you need some quick physics inspiration (not exactly what you asked for but seems kind of relevant) see if you can borrow a copy of The Feynman Lectures, he has a unique way of viewing physics and his explanations are artful.

Thank you, I'll look into it. I read one of his books "six easy pieces" about a year ago, it was amazing.

I also found classical mechanics to be extremely boring, and I was not alone.
Don't worry, it will get better and more interesting later.

Will it also be more theory based or forever intertwined with solving real life problems? I'm guessing it gets more theory based as you approach graduate school?

 

[sandy.bridge]

He also came out with a new book after his retirement, seems interesting:





Thank you, I'll look into it. I read one of his books "six easy pieces" about a year ago, it was amazing.



Will it also be more theory based or forever intertwined with solving real life problems? I'm guessing it gets more theory based as you approach graduate school?

It does get more theory based. However, from my experience they don't diverge from enforcing applications to the concepts. Initial courses do appear more to be "plug and chug" types of problems, because essentially these courses are not designed from merely Physics majors. They are usually designed for students in a diverse range of colleges.

 

[Nano-Passion]

It does get more theory based. However, from my experience they don't diverge from enforcing applications to the concepts. Initial courses do appear more to be "plug and chug" types of problems, because essentially these courses are not designed from merely Physics majors. They are usually designed for students in a diverse range of colleges.

Thank you. ^.^ It just bothers me that physics in my class is taught only as a tool to solve for relatively rudimentary problems. I feel like my professor strips physics of all its beauty. His lectures consists of doing examples in the book and telling us what formulas to use when. I completely despise it. I also have him for calculus too.. I'm definitely avoiding him next semester.

 

[dacruick]

Hi Nano-Passion,

I am halfway through my third year of a 4 year physics degree at the University of Waterloo. I am quite different from you, as academia doesn't really interest me. but I do have an experience that you can take into account. My physics courses for first semester third year were very mathematically intensive, and very theory based, and I only see it trending in that direction. I was much more drawn to my initial courses as the subject matter was more tangible.

 

[sandy.bridge]

Yeah. Professors can really make or break the class. For example, when I initially came to university, I had no aspirations to major in physics. It was the professor of my first physics class that really lit a flame under my cheeks, and got me motivated and interested in a subject (finally).

 

[Nano-Passion]

Hi Nano-Passion,

I am halfway through my third year of a 4 year physics degree at the University of Waterloo. I am quite different from you, as academia doesn't really interest me. but I do have an experience that you can take into account. My physics courses for first semester third year were very mathematically intensive, and very theory based, and I only see it trending in that direction. I was much more drawn to my initial courses as the subject matter was more tangible.

Well I guess one's bad news is another's good news. Thanks for the info. What kind of problems do you have to solve?

Yeah. Professors can really make or break the class. For example, when I initially came to university, I had no aspirations to major in physics. It was the professor of my first physics class that really lit a flame under my cheeks, and got me motivated and interested in a subject (finally).

Same here, I didn't like anything until my senior year of high school when I took physics. The teacher was amazing and obviously had a passion for his subject. He really brought me in physics! I later figured out its the math aspect that I really like of physics. You can say I'm also seduced by the mysteries of physics and the problems that are yet to be solved. =D I love both.

Before my physics professor I was just another follower of society. Yesterday I read my goal in life from high school that I wrote for college.. "I want to be a successful doctor and have a happy family." Oh boy, I've changed so much since then. I have a love for knowledge and wisdom. I no longer plan to base my life around attaining a 9-5 job and money.

 

[lsaldana]

How different is introductory physics to some of the higher level physics courses that you take later on? Will it be more theory or will problem-solving be stressed over theory for a while?

The simple answer is : VERY DIFFERENT. I see the introductory physics courses to be more about problem-solving than anything else. Upper level stuff is way more interesting and even the "applied" courses, like Electronics, have a good amount of theory. Don't give up now, take a couple of upper level courses like Quantum, E&M, Relativity, etc, and you'll see what you want. Upper level Classical Mechanics is also very theoretical, specially if you go deep into Hamiltonian and Lagrangian dynamics. Problem solving is there for sure but let's just say you won't see numbers as in your intro courses...

 

[Nano-Passion]

The simple answer is : VERY DIFFERENT. I see the introductory physics courses to be more about problem-solving than anything else. Upper level stuff is way more interesting and even the "applied" courses, like Electronics, have a good amount of theory. Don't give up now, take a couple of upper level courses like Quantum, E&M, Relativity, etc, and you'll see what you want. Upper level Classical Mechanics is also very theoretical, specially if you go deep into Hamiltonian and Lagrangian dynamics. Problem solving is there for sure but let's just say you won't see numbers as in your intro courses...

Thank you, that was uplifting. What do you mean that you won't see numbers as your intro course? Do you mean there are less numbers and more symbols? Whats the big difference exactly?

 

[dacruick]

Well I guess one's bad news is another's good news. Thanks for the info. What kind of problems do you have to solve?

Well I can tell you the courses I've taken up to this point. Calc 1 through 3, lin alg 1, class mech 1 and 2, math phys 1, quantum 1 and 2, EM 1, optics, thermodynamics, programming, plus my first year physics courses.

The three courses that I took most recently were class mech 2, quantum 2, and math phys 1. Math phys and quantum overlapped in a handful of differential equations. We solved the hydrogen atom in spherical coordinates, whatever that means... For math phys we did legendre polynomials, bessel functions, Fourier series, and a few other topics. In class mech we covered gravitation, rotational kinematics (tensors involved), briefly special relativity, coupled oscillations and I'm probably forgetting something. and in quantum we covered formalism, schrodingers equation, the hydrogen atom, and perturbation theory.

 

[SophusLies]

Before my physics professor I was just another follower of society. Yesterday I read my goal in life from high school that I wrote for college.. "I want to be a successful doctor and have a happy family." Oh boy, I've changed so much since then. I have a love for knowledge and wisdom.I no longer plan to base my life around attaining a 9-5 job and money.

We all had bad classes but what is stopping you from just self studying higher level physics on your own? Especially if you're doing well in that class. If you claim to have such a love for "knowledge and wisdom" then why are you complaining about the class and wasting time from learning what you really want?

I get very annoyed by this kinda stuff because my high school was trash so I had to self study like crazy to make sure I wouldn't fail my first year in college. My high school had more people that either became rappers, gang members, or drug addicts than went to college.

You have an incredible opportunity while in college to learn something, even if it is on your own, take it or leave it. I went to an incredible undergrad school, but guess what? I still had some garbage professors. I could have easily complained, as most did, but I didn't. Instead I just took it into my own hands. Make sure your grade is good then move onto to something that interests you.

If you only knew what some people went through to get into college... I promise you, you would never complain again.

 

[Nano-Passion]

We all had bad classes but what is stopping you from just self studying higher level physics on your own? Especially if you're doing well in that class. If you claim to have such a love for "knowledge and wisdom" then why are you complaining about the class and wasting time from learning what you really want?

I get very annoyed by this kinda stuff because my high school was trash so I had to self study like crazy to make sure I wouldn't fail my first year in college. My high school had more people that either became rappers, gang members, or drug addicts than went to college.

You have an incredible opportunity while in college to learn something, even if it is on your own, take it or leave it. I went to an incredible undergrad school, but guess what? I still had some garbage professors. I could have easily complained, as most did, but I didn't. Instead I just took it into my own hands. Make sure your grade is good then move onto to something that interests you.

If you only knew what some people went through to get into college... I promise you, you would never complain again.

Thing is I don't know where to start. If I were to spend my time on self-study I would put it toward mathematics because I like it more at the moment.

And in response to "learn what you really want." I feel like I don't have time for that. If I have extra time I use all of it doing extra problems in calculus. I feel like its a good investment of my time. This is because, like you, I didn't get much out of high school at all. I don't blame it on my teachers, rather, it was because of my disinterest in knowledge in general; which has changed since. By doing all the extra and harder problems in calculus I feel like I am catching up on my mathematical maturity.

But who knows, maybe its terribly inefficient of my time; if you have other ideas please share!

Well I can tell you the courses I've taken up to this point. Calc 1 through 3, lin alg 1, class mech 1 and 2, math phys 1, quantum 1 and 2, EM 1, optics, thermodynamics, programming, plus my first year physics courses.

The three courses that I took most recently were class mech 2, quantum 2, and math phys 1. Math phys and quantum overlapped in a handful of differential equations. We solved the hydrogen atom in spherical coordinates, whatever that means... For math phys we did legendre polynomials, bessel functions, Fourier series, and a few other topics. In class mech we covered gravitation, rotational kinematics (tensors involved), briefly special relativity, coupled oscillations and I'm probably forgetting something. and in quantum we covered formalism, Schrodinger equation, the hydrogen atom, and perturbation theory.

Very interesting, thanks for sharing. I'm very curious though on how the style of the problems differ from that of classical mechanics I. The most mathematical excitement you might get out of classical mechanics one is basic linear algebraic substitution (in my opinion).

 

[bromden]

We all had bad classes but what is stopping you from just self studying higher level physics on your own? Especially if you're doing well in that class. If you claim to have such a love for "knowledge and wisdom" then why are you complaining about the class and wasting time from learning what you really want?

I really agree with this. You don't even have to study higher-level physics, though. You can just read through and work a lot of problems in your physics text.

Earlier in the thread you said that you liked physics in high school. How is this class any different? I know that your teacher may suck, but that doesn't change the actual content.

By doing all the extra and harder problems in calculus I feel like I am catching up on my mathematical maturity.

But who knows, maybe its terribly inefficient of my time; if you have other ideas please share!

I wouldn't necessarily call being able to solve some tough problems in Calculus I as having mathematical maturity. I have always heard the term used to refer to comfort with proofs and abstraction. If you just enjoy trying to solve these problems, then that's fine, but I would refer to it as "getting good at calculus."

It's never a bad idea to pick up a programming language or two, because it will really benefit you in the future. If you're really forward looking in your math, perhaps pick up a text on mathematical proof techniques.

Very interesting, thanks for sharing. I'm very curious though on how the style of the problems differ from that of classical mechanics I. The most mathematical excitement you might get out of classical mechanics one is basic linear algebraic substitution (in my opinion).

Yeah, there's a lot of linear algebra in more advanced mechanics, but - in addition to what dacruick mentioned - you will also explore the calculus of variations and Lagrange multipliers. You get a couple of formalisms in classical mechanics that are pretty cool and really show you that classical mechanics is pretty elegant. Also, you'll likely study non-linear dynamics and chaos, which are awesome topics, and still developing fields of mathematics. So, don't be so quick to dismiss classical mechanics. There's plenty of excitement to come, you just need to be patient!

 

[Nano-Passion]

I really agree with this. You don't even have to study higher-level physics, though. You can just read through and work a lot of problems in your physics text.

Thing is though, I'm for some reason more inclined to work extra problems in calculus.

Earlier in the thread you said that you liked physics in high school. How is this class any different? I know that your teacher may suck, but that doesn't change the actual content.

I'm still trying to pinpoint the psychology of it all; I always try to single out a couple unconscious reasons influence my paradigms toward things such as physics. I believe one of the reasons is that its basically the third time I'm being introduced to the concepts. Once in physics, once in a intro to physical science course because I was itching for a science course at the moment, and then another time now in College physics.

I wouldn't necessarily call being able to solve some tough problems in Calculus I as having mathematical maturity. I have always heard the term used to refer to comfort with proofs and abstraction. If you just enjoy trying to solve these problems, then that's fine, but I would refer to it as "getting good at calculus."

Oops, I should choose my words more carefully. To reword it, doing a lot of calculus problems makes me feel that I am getting better at math. The reason for that is I realize that the only hard part of calculus is the algebraic manipulation part. Furthermore, you use pretty much the same skills for Calculus I to Multivariable Calculus and Differential Equations. If I am mistaken please direct me towards the right path!

It's never a bad idea to pick up a programming language or two, because it will really benefit you in the future. If you're really forward looking in your math, perhaps pick up a text on mathematical proof techniques.

I try to prove everything I come across in calculus, but I don't think that is enough so I'll heed your advice. Do you have a couple recommendation? I find proofs to be the most fun part of mathematics so I'm looking forward to it. ^.^

Yeah, there's a lot of linear algebra in more advanced mechanics, but - in addition to what dacruick mentioned - you will also explore the calculus of variations and Lagrange multipliers. You get a couple of formalisms in classical mechanics that are pretty cool and really show you that classical mechanics is pretty elegant. Also, you'll likely study non-linear dynamics and chaos, which are awesome topics, and still developing fields of mathematics. So, don't be so quick to dismiss classical mechanics. There's plenty of excitement to come, you just need to be patient!

Haha, yeah.. I told a previous professor of mine that classical mechanics doesn't have enough theory he replied "Are you kidding me!"

To be honest I don't really know the terms you mentioned but they sound neat. Someone passed on a free online version of a linear algebra book, I looked through it and it was pretty cool. I always love how math starts with very simple things such as "algebraic substitution" and builds up into more complex and powerful concepts!

 

[lsaldana]

Thank you, that was uplifting. What do you mean that you won't see numbers as your intro course? Do you mean there are less numbers and more symbols? Whats the big difference exactly?

Just as in other disciplines, concepts become abstracted the further you go into them. As a senior undergrad I can tell you that the classes get more interesting both mathematically and physically. The range of topics one tackles become more broad and the techniques become more rigorous (or at least they can). The reason for this is that the mathematical level one is at during upper level courses is (expected to be) greater than what you had in your first years. Mechanics wasn't very interesting to me until I picked up a copy of goldsteins classical mechanics. Like it's been said before don't put off physics just yet.

 

[Dembadon]

...

Haha, yeah.. I told a previous professor of mine that classical mechanics doesn't have enough theory he replied "Are you kidding me!"

...

Be careful not to confuse "Physics I" with a course on Classical Mechanics. As others have mentioned, they are different. Here's an example from my course catalog:

PHYS 180 PHYSICS FOR SCIENTISTS AND ENGINEERS I
Lecture+Lab: 3+0
Credit(s): 3

Vectors, one and two dimensional kinematics, particle dynamics, work and energy, momentum, rotational mechanics, oscillations, gravitation, fluids, elastic waves and sound.Prereq(s): MATH 181 (Calc).

The following is the sophomore/junior-level physics course on classical mechanics:

PHYS 351 CLASSICAL MECHANICS
Lecture+Lab: 4+0
Credit(s): 4

Newtonian mechanics, dynamics of a particle and system of particles, mechanics of continuous media, methods of Lagrange and Hamilton.Prereq(s): PHYS 180.
Coreq(s): PHYS 301 (Applications of mathematics frequently used in physics, including vector calculus, tensors, linear algebra, ordinary differential equations, partial differential equations and complex analysis.)

As you can see, even though the Physics I course covers some of the same material, it is not at the depth of the classical mechanics course itself. This probably lends to the more "plug-n-chug" nature of the introductory course to which you're referring.

 

[bromden]

Thing is though, I'm for some reason more inclined to work extra problems in calculus.

I'm still trying to pinpoint the psychology of it all; I always try to single out a couple unconscious reasons influence my paradigms toward things such as physics. I believe one of the reasons is that its basically the third time I'm being introduced to the concepts. Once in physics, once in a intro to physical science course because I was itching for a science course at the moment, and then another time now in College physics.

Yeah, seeing essentially the same material treated three times can be extremely boring, especially if you understood it the first time. That being said, the mathematical arguments for why we use the equations we do should be more interesting (and convincing) than what you have had before. Either way, hopefully when you take your next course, it will be more interesting to you.

...To reword it, doing a lot of calculus problems makes me feel that I am getting better at math. The reason for that is I realize that the only hard part of calculus is the algebraic manipulation part.

I would say that solving a lot of problems in calculus makes you better at solving problems in calculus and a better problem solver. But a lot of folks finish up a calculus sequence and can't say what limits (and the special limits of derivatives and integrals) really are. Sometimes these type classes focus too much on rote calculation, and students lose track of the more theoretical parts of calculus.

Furthermore, you use pretty much the same skills for Calculus I to Multivariable Calculus and Differential Equations. If I am mistaken please direct me towards the right path!

I'm not sure I agree with this. Integration (calculus II) is, in my opinion, a completely different beast than differentiation. I could probably find the derivative of almost any function. There is a well defined set of rules for differentiation, and I think it is usually pretty clear which rules to apply. This is not so with integrals. You may try many different approaches, and none of them work. In my opinion, solving integrals improves your problem-solving skills much more than differentiation.

I try to prove everything I come across in calculus, but I don't think that is enough so I'll heed your advice. Do you have a couple recommendation? I find proofs to be the most fun part of mathematics so I'm looking forward to it. ^.^

Going through the calculus proofs is a great step in the right direction for moving into proof-based math. I worked through https://www.amazon.com/dp/0387008349/?tag=pfamazon01-20 for some proof books - they are usually very affordable.

I will forewarn you that physicists aren't always the most meticulous people when it comes to proving things. In my experience, unless the professors felt that the proof was just as important as the result in understanding how something applies to physics, they would usually point us to a reference text for proofs. In general, physicists want to use the results. I find that very satisfying, but not everyone does. I just don't want you to think that when you're using math in your physics classes you will be going through a bunch of proofs.

Haha, yeah.. I told a previous professor of mine that classical mechanics doesn't have enough theory he replied "Are you kidding me!"

Haha. Yeah, you'll get there.

To be honest I don't really know the terms you mentioned but they sound neat. Someone passed on a free online version of a linear algebra book, I looked through it and it was pretty cool. I always love how math starts with very simple things such as "algebraic substitution" and builds up into more complex and powerful concepts!

I agree. Linear algebra is what made me really like mathematics. I found the concepts to be reasonably simple, but it is still a nice course to get your hands dirty with some real proofs.

Be careful not to confuse "Physics I" with a course on Classical Mechanics. As others have mentioned, they are different. ...

Yes, this is an important distinction to make.

 

[Nano-Passion]

Just as in other disciplines, concepts become abstracted the further you go into them. As a senior undergrad I can tell you that the classes get more interesting both mathematically and physically. The range of topics one tackles become more broad and the techniques become more rigorous (or at least they can). The reason for this is that the mathematical level one is at during upper level courses is (expected to be) greater than what you had in your first years. Mechanics wasn't very interesting to me until I picked up a copy of goldsteins classical mechanics. Like it's been said before don't put off physics just yet.

Thank you!

Be careful not to confuse "Physics I" with a course on Classical Mechanics. As others have mentioned, they are different. Here's an example from my course catalog:



The following is the sophomore/junior-level physics course on classical mechanics:



As you can see, even though the Physics I course covers some of the same material, it is not at the depth of the classical mechanics course itself. This probably lends to the more "plug-n-chug" nature of the introductory course to which you're referring.

Oops, I should be more careful choosing my words.

 

[Nano-Passion]

Yeah, seeing essentially the same material treated three times can be extremely boring, especially if you understood it the first time. That being said, the mathematical arguments for why we use the equations we do should be more interesting (and convincing) than what you have had before. Either way, hopefully when you take your next course, it will be more interesting to you.


I would say that solving a lot of problems in calculus makes you better at solving problems in calculus and a better problem solver. But a lot of folks finish up a calculus sequence and can't say what limits (and the special limits of derivatives and integrals) really are. Sometimes these type classes focus too much on rote calculation, and students lose track of the more theoretical parts of calculus.

Thank you so much for the reply. That helped quite a bit. Though I feel practicing a lot of calculus is giving me a grip on the algebraic manipulation (the ones I missed in high school because I didn't like math) I need and I try to do all of the proofy problems.

I'm not sure I agree with this. Integration (calculus II) is, in my opinion, a completely different beast than differentiation. I could probably find the derivative of almost any function. There is a well defined set of rules for differentiation, and I think it is usually pretty clear which rules to apply. This is not so with integrals. You may try many different approaches, and none of them work. In my opinion, solving integrals improves your problem-solving skills much more than differentiation.

Hmm.. that seems intersting. I was always under the thought that integration was much like differentiation except your working backwards. So it just challenges your problem solving skills more? In that case I agree, because once you get the hang of differentiation then it becomes very easy sort of speak. I remember solving *simple* differentiation problems in my sleep. I found that to be very amusing! It actually happened a few times ahahah.

Going through the calculus proofs is a great step in the right direction for moving into proof-based math. I worked through https://www.amazon.com/dp/0387008349/?tag=pfamazon01-20 for some proof books - they are usually very affordable.

Thanks.

I will forewarn you that physicists aren't always the most meticulous people when it comes to proving things. In my experience, unless the professors felt that the proof was just as important as the result in understanding how something applies to physics, they would usually point us to a reference text for proofs. In general, physicists want to use the results. I find that very satisfying, but not everyone does. I just don't want you to think that when you're using math in your physics classes you will be going through a bunch of proofs.

Eh.. I just love knowing how one thing leads to another mathematically. I guess I have to sacrifice some of that in physics courses. =/

Haha. Yeah, you'll get there.

He is a great professor (guy I asked).. he started math when he was 10 years old so it is very intimidating talking about math subjects with him ahaha. Yet he still cares about portraying the beauty of math and physics.

 

[homeomorphic]

That was me. I quit studying physics officially and became a mathematician because of CM and a bad professor. I just lost trust in physicists, basically. I never stopped liking physics or even classical mechanics. It's only physicists that I am wary of, not physics. Often, the same is true in math, though. Too many people doing their best to make sure that the subject is completely boring. They are like vampires, I tell you. Just sucking the life out it. They have some perverse need to make things as ugly and boring as they possibly can. And what's even worse is they are trying to their best to make sure no one has any intuition and everything has to be a mystery that comes from nowhere. I feel bad because a lot of these profs are nice people, but when it comes to math and physics, they are just jaw-droppingly tasteless. I wish I could understand why they do it, and what they could possibly find interesting in math or physics the way they do it.

I probably would have given up on both physics and math by now, if I were to take the easiest path, but the reason why I have not given up is that I can't let these boring people win and continue to suck the life out of both subjects.

 

[bromden]

...
Hmm.. that seems intersting. I was always under the thought that integration was much like differentiation except your working backwards. So it just challenges your problem solving skills more? In that case I agree, because once you get the hang of differentiation then it becomes very easy sort of speak.

(Emphasis mine.)

I think that this is the take-away most people have when it comes to Calculus I and II. Yes, this is true. But it can be very difficult (or impossible) to find the anti-derivative of certain functions in terms of elementary functions. A classic example of the impossibility is the indefinite integral of exp(-x^2). You cannot find an expression for the anti-derivative of this function in terms of elementary functions. There are many functions of which I think it is difficult to find the anti-derivative, though not impossible. As you continue in math, you'll find that some integrals become much more manageable using complex analysis.

I remember solving *simple* differentiation problems in my sleep. I found that to be very amusing! It actually happened a few times ahahah.

Ha, well, that would indicate you have been studying rather diligently.

Eh.. I just love knowing how one thing leads to another mathematically. I guess I have to sacrifice some of that in physics courses. =/

No one is stopping you from pursuing the depths of the mathematics outside class, I just don't want you to expect them to be discussed in great detail in class.

He is a great professor (guy I asked).. he started math when he was 10 years old so it is very intimidating talking about math subjects with him ahaha. Yet he still cares about portraying the beauty of math and physics.

That's very cool. I find it inspiring when someone has held onto passion for so long.

That was me. I quit studying physics officially and became a mathematician because of CM and a bad professor. I just lost trust in physicists, basically. I never stopped liking physics or even classical mechanics. It's only physicists that I am wary of, not physics. Often, the same is true in math, though. Too many people doing their best to make sure that the subject is completely boring. They are like vampires, I tell you. Just sucking the life out it. They have some perverse need to make things as ugly and boring as they possibly can. And what's even worse is they are trying to their best to make sure no one has any intuition and everything has to be a mystery that comes from nowhere. I feel bad because a lot of these profs are nice people, but when it comes to math and physics, they are just jaw-droppingly tasteless. I wish I could understand why they do it, and what they could possibly find interesting in math or physics the way they do it.
...

This is pretty sad, I think. You must have had some horrible professors. I never had any such thing, especially to the point where I would think there is some grand conspiracy of physicists and mathematicians trying to make people hate their fields. I have had a few less than desirable experiences, but I liked the subject enough to push through. I highly doubt that they intend to make anything ugly or boring.
Have you considered that maybe the style that most physicists/mathematicians use to teach just truly doesn't fit your way of learning?

 

[homeomorphic]

This is pretty sad, I think. You must have had some horrible professors. I never had any such thing, especially to the point where I would think there is some grand conspiracy of physicists and mathematicians trying to make people hate their fields. I have had a few less than desirable experiences, but I liked the subject enough to push through. I highly doubt that they intend to make anything ugly or boring.
Have you considered that maybe the style that most physicists/mathematicians use to teach just truly doesn't fit your way of learning?

My post was a bit tongue in cheek. Not ALL of my professors were that way, in fact probably a minority. I have slight disagreements with the way most professors do things, but it's not that big of a deal, most of the time. There were just a few big offenders. Birds of a feather flock together, and that's why I am a topologist. I found a field where my way of thinking is more common. I am also speaking of textbook authors here, who collaborate with some professors in the rape and pillage of mathematics.

It's not that it's a conspiracy. Boredom breeds boredom. Profs teach in a boring way and it gets passed on to the next generation. It's probably a consequence of people not quite thinking independently enough.

Maybe it's not that what is there is so bad. Maybe it has more to do with what is missing.

I think any good math or physics student will have had the experience of making the discovery that some beautiful and intuitive concept had been butchered by their professor/textbook and turned into an incomprehensible, unmotivated monstrosity. Even one such experience is enough to leave a very bad taste in your mouth.

I'm often frustrated by the explanations that I am given, and ultimately, when I am confronted by one that doesn't satisfy me, 95% of the time, I succeed in finding one that does. Then I think, why didn't they just say that? It could have saved me perhaps dozens, or perhaps hundreds of hours of work in extreme cases. Maybe it makes me stronger, but then, there's just too much math to learn and not enough time. I just don't have time for that kind of BS. I can't just practice outsmarting bad pedagogy and unmotivated mathematics all the time. I am supposed to be cranking out publications. I have other things to do with my life. It's a waste.

It's not just about learning style. Of course, they don't cater to my learning style. But I think they aren't really catering to anyone's learning style, except people who are okay with not understanding things very deeply.

There are famous mathematicians who could sympathize with my views:

http://pauli.uni-muenster.de/~munsteg/arnold.html

Maybe I'm not as much against abstraction as he seemed to be (he just died very recently), but abstractions should be "abstracted" from something, and that's a great deal of the problem.

 

[Nano-Passion]

That was me. I quit studying physics officially and became a mathematician because of CM and a bad professor. I just lost trust in physicists, basically. I never stopped liking physics or even classical mechanics. It's only physicists that I am wary of, not physics. Often, the same is true in math, though. Too many people doing their best to make sure that the subject is completely boring. They are like vampires, I tell you. Just sucking the life out it. They have some perverse need to make things as ugly and boring as they possibly can. And what's even worse is they are trying to their best to make sure no one has any intuition and everything has to be a mystery that comes from nowhere. I feel bad because a lot of these profs are nice people, but when it comes to math and physics, they are just jaw-droppingly tasteless. I wish I could understand why they do it, and what they could possibly find interesting in math or physics the way they do it.

I probably would have given up on both physics and math by now, if I were to take the easiest path, but the reason why I have not given up is that I can't let these boring people win and continue to suck the life out of both subjects.

Hahaha.. its funny because your analogy makes complete sense to me. I've always thought in that fashion but dismissed it because I convinced myself that its harder to show your enthusiasm towards math and physics while you try to teach it. In other words, I give them excuses to suck. hehe.

By the way, your a mathematician really? What led you to choose that road if 'vampires' are blocking both of them? Was it because that road a looked better because it had 'vampires' but more rigor? Did you find that rigor helped you battle the 'vampires?'

Excuse my puns, my questions are quiet serious actually.

(Emphasis mine.)

I think that this is the take-away most people have when it comes to Calculus I and II. Yes, this is true. But it can be very difficult (or impossible) to find the anti-derivative of certain functions in terms of elementary functions. A classic example of the impossibility is the indefinite integral of exp(-x^2). You cannot find an expression for the anti-derivative of this function in terms of elementary functions. There are many functions of which I think it is difficult to find the anti-derivative, though not impossible. As you continue in math, you'll find that some integrals become much more manageable using complex analysis.

I find that to be very intriguing... Throughout my life I've been introduced to things that are largely solvable. The fact that higher mathematics such as complex analysis can help you with finding an integral sounds interesting in itself.

By the way, I ended up wasting a lot of time in my calculus test (which I like to believe that I completely aced but I didn't get the results back yet). I found myself erasing everything I've done for the problem a few times because it was the very long way. Luckily I finished the exam in time. But that took out a huge chunk of my time! That scares me because in calculus II integration can often get much trickier. I can't afford the time to approach the problems in the long way.

Ha, well, that would indicate you have been studying rather diligently.

Haha.. it was actually a few times that I have awaken to this. I remember doing very simple things in my dreams, things like the power rule and chain rule (power rule). But of course I would LOVE to remember the rest of my dreams, because unfortunately I only remember VERY small fractions.

No one is stopping you from pursuing the depths of the mathematics outside class, I just don't want you to expect them to be discussed in great detail in class.

Fair enough.

That's very cool. I find it inspiring when someone has held onto passion for so long.

He is a very inspiring professor himself. Its different than other professors, you feel like you get something out of most conversations. I don't even know why he didn't pursue being a mathematician, I have to clarify that with him. But one thing that struck me as inspiring (and scary) is his story of studying 18 hours a day for a whole summer. He shared some funny stories as a side effect.

 

[Nano-Passion]

I think any good math or physics student will have had the experience of making the discovery that some beautiful and intuitive concept had been butchered by their professor/textbook and turned into an incomprehensible, unmotivated monstrosity. Even one such experience is enough to leave a very bad taste in your mouth.

Everything you wrote here runs parallel to what I believe. But you have a very nice way of putting it. This quote above deserves some spotlight, its beautiful and to the point. I too have felt that way as my professor completely and undeniably humiliated the beauty of gravity along with every other concept introduced in the course if I might add. Professors sometimes thoroughly strip concepts of all its history, elegance, and power.

I remember he introduced apparent weightlessness with the apparent distance of objects in water (optics). I wanted to 'face palm'.

 

[csmcmillion]

You should watch Leonard Susskind's course lecture's on Classical Mechanics. He provides much insight into the theoretical side:

 

[homeomorphic]

Hahaha.. its funny because your analogy makes complete sense to me. I've always thought in that fashion but dismissed it because I convinced myself that its harder to show your enthusiasm towards math and physics while you try to teach it. In other words, I give them excuses to suck. hehe.

Well, I'm not judgmental about teaching, actually. I don't care if they are a crappy lecturer as long as they have mathematical insight. They can have the most boring monotone for all I care, as long as their math is interesting. It's mathematics that I am judgmental about, not teaching. I've done some teaching myself and I sympathize with people who have trouble with it. It's not very easy. I've never given teachers a very a hard time when it comes to evaluations. The profs that really piss me off mathematically will get sort of okay marks on everything. If they failed to provoke my rage, then they get pretty much perfect approval on their evaluation. Maybe 9 out of 10 profs will get perfect approval. I don't ask for perfection mathematically, but if their presentation consistently lacks motivation and intuition or is filled with excessively many gruesome calculations, I will eventually get frustrated and angry. There are really not that many "vampires", but still, a lot of times, I know that, although the courses were good enough not to be painful, they weren't quite what they could have been.

By the way, your a mathematician really? What led you to choose that road if 'vampires' are blocking both of them? Was it because that road a looked better because it had 'vampires' but more rigor? Did you find that rigor helped you battle the 'vampires?'

Yes, I am a math PhD student, and I'm supposed to be graduating this year, assuming I don't spend too much time writing long posts like these. I may have to go into math hibernation for a while if I am going to finish. Well, in math, I found, there were actually not very many vampires. I didn't take that many physics classes. There was a certain vampiress who did irreparable damage, along with the vampires who wrote the textbook (Thornton and Marion--the book is despised with a passion by countless physics students, not just me, as you will see if you look at the reviews on amazon).

I'm not sure if rigor had too much to do with it, except there was this attitude that we get to prove everything from scratch. There were typically no theorems that were just quoted, and we had to use them. We proved it all.

 

[victor.raum]

I know exactly what you mean. I'm not personally in school, but I've sat in on a few of my girlfriend's lectures for her first year physics course. It was totally terrible, and very much like that "just giving sample problem & heartlessly listing rules" method that you described in your post.

I'm very into calc and physics. And though I'm not in school, I'm still reading through one of the very stock and standard intro physics textbooks of the day, namely "University Physics" by Young and Freedman. To give an example of how I go about studying from said book, I just read the chapter on work and kinetic energy the other week. However, I didn't do any of the problems at the end of the chapter, and I didn't even bother to read their sample problems which were provided inline in the chapter. Being good at calculus though, I did understand the math very clearly, and being a software programmer I wrote myself a little simulation which had a point-mass dropping or being thrown upward in a field of a=9.8m/s^2 Earth gravity. I had the simulation displaying the point's KE and PE values at any given moment, and I suspect that watching my simulation's KE and PE counters as it ran gave me a much better feel for how KE and PE work in practice than doing any of the book's problems ever would have.

Then I went on and just had a ton of fun fiddling with the equation, like for example I evaluated $${{\rm d} \over {\rm d}t}\left({1 \over 2}mv^2\right)$$ in the context of v being the proper length of a vector, defined as $$v=({\vec v} \cdot {\vec v})^{1 \over 2}$$ The resulting derivative involved a simple chain rule application and gave a very interesting result, though I won't list it here. I did several hours of some more such playing around with the equations in the chapter, and then I moved on. All the while I still never touched a single one of the numerical engineering-style problems or examples in the book (though from the one or two I did glance at, I can't imagine they're very difficult, or for that matter interesting).

I think I'm moving through the book a lot more enjoyably using that method, and at about the same pace any college course would. Plus it's a lot more fun to boot, and what I might be "missing" by not doing the problems I think I'm making up for in other ways.

I always sort of assumed that higher level physics classes used a method more like the one I just described above, but obviously I'm not certain. I'd be curious to know myself.

 

[bromden]

...

I find that to be very intriguing... Throughout my life I've been introduced to things that are largely solvable. The fact that higher mathematics such as complex analysis can help you with finding an integral sounds interesting in itself.

Yeah, complex analysis is pretty cool, and very useful to physics. (I will say, though, with the power contained in Mathematica, you won't use the methods to evaluate integrals as much as the 60-year-old professor who taught my course.)

Also, if you ever take some analysis (it was in our second course in analysis) we discussed other ways of defining integrals, which sounds a little boring, but it allows you to integrate some functions that you couldn't even dream of with your run-of-the-mill calculus II methods.

By the way, I ended up wasting a lot of time in my calculus test (which I like to believe that I completely aced but I didn't get the results back yet). I found myself erasing everything I've done for the problem a few times because it was the very long way. Luckily I finished the exam in time. But that took out a huge chunk of my time! That scares me because in calculus II integration can often get much trickier. I can't afford the time to approach the problems in the long way.

Well, being proficient at figuring out ways to solve problems quickly can be the name of the game in math and physics (even in some of the more advanced classes, though certainly not as much.) The best thing to do is to solve a lot of problems, sure, but you should also understand when certain methods work, and when they don't. I've found that the more practice I have, the less time I spend writing out all the menial steps explicitly. (I.e., I don't recall the last time I wrote out what my u, du, etc., etc. were in a u-substitution problem.) You see a problem, and you just have a good idea of what will work and what won't.

He is a very inspiring professor himself. Its different than other professors, you feel like you get something out of most conversations. I don't even know why he didn't pursue being a mathematician, I have to clarify that with him. But one thing that struck me as inspiring (and scary) is his story of studying 18 hours a day for a whole summer. He shared some funny stories as a side effect.

That's awesome. He sounds like a good professor to keep in contact with, as well. If you want to go to graduate school, you really should always keep your eyes open for good opportunities to build relationships with your professors.

Well, I'm not judgmental about teaching, actually. I don't care if they are a crappy lecturer as long as they have mathematical insight. They can have the most boring monotone for all I care, as long as their math is interesting. It's mathematics that I am judgmental about, not teaching. I've done some teaching myself and I sympathize with people who have trouble with it.

...

I totally understand this sentiment. I could be pretty critical of some of my professors as an undergraduate, but now that I am a TA, I understood more what it's like - and I really sympathize. (Also, with my brother who teaches high school in an under-privileged district; I tell him I don't know how he does it.)

...

There was a certain vampiress who did irreparable damage, along with the vampires who wrote the textbook (Thornton and Marion--the book is despised with a passion by countless physics students, not just me, as you will see if you look at the reviews on amazon).

I'm not sure if rigor had too much to do with it, except there was this attitude that we get to prove everything from scratch. There were typically no theorems that were just quoted, and we had to use them. We proved it all.

You should check out John Taylor's "Classical Mechanics." When I was doing a lab report on chaos theory as an undergraduate, one of my friends recommended that I read his chapter on chaos; I was so blown away. I am going through the rest of his book in preparing for my qualifiers, and I am just as pleased with his treatment of other topics. It is not the most rigorous, but very conversational. When I read it, I feel like I am getting insight into how he thinks about physics. (I also echo another poster's recommendation of the Feynman Lectures.)

Along the same lines of what you said, I think the most valuable thing you can get out of a professor is some understanding about how they, ideally a researcher, think about problems in physics (or math.) I had a professor who could present some absolutely dreadful lectures, but sometimes I would just be blown away at how differently (and insightfully) he approached some of the problems in our text than the author did.

I know exactly what you mean. I'm not personally in school, but I've sat in on a few of my girlfriend's lectures for her first year physics course. It was totally terrible, and very much like that "just giving sample problem & heartlessly listing rules" method that you described in your post.

I'm very into calc and physics. And though I'm not in school, I'm still reading through one of the very stock and standard intro physics textbooks of the day, namely "University Physics" by Young and Freedman. To give an example of how I go about studying from said book, I just read the chapter on work and kinetic energy the other week. However, I didn't do any of the problems at the end of the chapter, and I didn't even bother to read their sample problems which were provided inline in the chapter. Being good at calculus though, I did understand the math very clearly, and being a software programmer I wrote myself a little simulation which had a point-mass dropping or being thrown upward in a field of a=9.8m/s^2 Earth gravity. I had the simulation displaying the point's KE and PE values at any given moment, and I suspect that watching my simulation's KE and PE counters as it ran gave me a much better feel for how KE and PE work in practice than doing any of the book's problems ever would have.

Then I went on and just had a ton of fun fiddling with the equation, like for example I evaluated $${{\rm d} \over {\rm d}t}\left({1 \over 2}mv^2\right)$$ in the context of v being the proper length of a vector, defined as $$v=({\vec v} \cdot {\vec v})^{1 \over 2}$$ The resulting derivative involved a simple chain rule application and gave a very interesting result, though I won't list it here. I did several hours of some more such playing around with the equations in the chapter, and then I moved on. All the while I still never touched a single one of the numerical engineering-style problems or examples in the book (though from the one or two I did glance at, I can't imagine they're very difficult, or for that matter interesting).

I think I'm moving through the book a lot more enjoyably using that method, and at about the same pace any college course would. Plus it's a lot more fun to boot, and what I might be "missing" by not doing the problems I think I'm making up for in other ways.

I always sort of assumed that higher level physics classes used a method more like the one I just described above, but obviously I'm not certain. I'd be curious to know myself.

To be fair, if it is a survey course aimed at a varied audience (other scientists and engineers, etc.), solving problems using physics really is the goal of the course. Many of those students would be bored with more theoretical discussions.

I do think that more advanced physics courses are similar to what you are discussing, but that obviously depends on the lecturer. In my mechanics lectures, the professor would give motivation and go about some basic derivations; in our problem sets, we would be expected to show some of the more important results and relationships ourselves. A particular problem set on non-linear physics and chaos theory was basically "have some fun exploring different properties of chaos." It has been my experience that, in the upper-level courses, there is certainly more discussion of what the deeper physics is.

 

[Nano-Passion]

Well, I'm not judgmental about teaching, actually. I don't care if they are a crappy lecturer as long as they have mathematical insight. They can have the most boring monotone for all I care, as long as their math is interesting. It's mathematics that I am judgmental about, not teaching. I've done some teaching myself and I sympathize with people who have trouble with it. It's not very easy. I've never given teachers a very a hard time when it comes to evaluations. The profs that really piss me off mathematically will get sort of okay marks on everything. If they failed to provoke my rage, then they get pretty much perfect approval on their evaluation. Maybe 9 out of 10 profs will get perfect approval. I don't ask for perfection mathematically, but if their presentation consistently lacks motivation and intuition or is filled with excessively many gruesome calculations, I will eventually get frustrated and angry. There are really not that many "vampires", but still, a lot of times, I know that, although the courses were good enough not to be painful, they weren't quite what they could have been.

Same here actually.

Yes, I am a math PhD student, and I'm supposed to be graduating this year, assuming I don't spend too much time writing long posts like these. I may have to go into math hibernation for a while if I am going to finish. Well, in math, I found, there were actually not very many vampires. I didn't take that many physics classes. There was a certain vampiress who did irreparable damage, along with the vampires who wrote the textbook (Thornton and Marion--the book is despised with a passion by countless physics students, not just me, as you will see if you look at the reviews on amazon). I'm not sure if rigor had too much to do with it, except there was this attitude that we get to prove everything from scratch. There were typically no theorems that were just quoted, and we had to use them. We proved it all.

The word mathematicians usually hits me as someone who does math for a living; someone who develops the theories of mathematics. That is an interesting viewpoint, so if you are a PhD student you are considered a mathematician? Or did you rather mean that you will be one in the future?
[/QUOTE]

I know exactly what you mean. I'm not personally in school, but I've sat in on a few of my girlfriend's lectures for her first year physics course. It was totally terrible, and very much like that "just giving sample problem & heartlessly listing rules" method that you described in your post.

I'm very into calc and physics. And though I'm not in school, I'm still reading through one of the very stock and standard intro physics textbooks of the day, namely "University Physics" by Young and Freedman. To give an example of how I go about studying from said book, I just read the chapter on work and kinetic energy the other week. However, I didn't do any of the problems at the end of the chapter, and I didn't even bother to read their sample problems which were provided inline in the chapter. Being good at calculus though, I did understand the math very clearly, and being a software programmer I wrote myself a little simulation which had a point-mass dropping or being thrown upward in a field of a=9.8m/s^2 Earth gravity. I had the simulation displaying the point's KE and PE values at any given moment, and I suspect that watching my simulation's KE and PE counters as it ran gave me a much better feel for how KE and PE work in practice than doing any of the book's problems ever would have.

Then I went on and just had a ton of fun fiddling with the equation, like for example I evaluated $${{\rm d} \over {\rm d}t}\left({1 \over 2}mv^2\right)$$ in the context of v being the proper length of a vector, defined as $$v=({\vec v} \cdot {\vec v})^{1 \over 2}$$ The resulting derivative involved a simple chain rule application and gave a very interesting result, though I won't list it here. I did several hours of some more such playing around with the equations in the chapter, and then I moved on. All the while I still never touched a single one of the numerical engineering-style problems or examples in the book (though from the one or two I did glance at, I can't imagine they're very difficult, or for that matter interesting).

I think I'm moving through the book a lot more enjoyably using that method, and at about the same pace any college course would. Plus it's a lot more fun to boot, and what I might be "missing" by not doing the problems I think I'm making up for in other ways.

I always sort of assumed that higher level physics classes used a method more like the one I just described above, but obviously I'm not certain. I'd be curious to know myself.

As a word of advice, be VERY careful. Knowing the formulas and the concepts often does very little to the problem solving. Its knowing how to apply them and how to manipulate things around that's the challenge. Problem solving is harder than you think, you should give one of the problems a try. Anyhow if you only read through the concepts then you don't know physics and you haven't done physics.

Take it from someone who went through the same mistake in calculus. I thought I was learning the material till I attempted some problems. Btw, what you did with the equations is pretty cool, but you will soon realize that it isn't what physics I is all about.

 

[homeomorphic]

The word mathematicians usually hits me as someone who does math for a living; someone who develops the theories of mathematics. That is an interesting viewpoint, so if you are a PhD student you are considered a mathematician? Or did you rather mean that you will be one in the future?

The word mathematician means different things in different contexts. I just mean that I do math research, which is not the same things as being a PhD student (typically, only the advanced students do research). Haven't published yet, but I have something almost ready to go that I think will be published at some point.

To be a Mathematician with a capitol m, I guess maybe you have to be a professor or work for some place like Microsoft research doing math or something like that. But, really, professors make their "living" teaching, so it's not much different from being a grad student. Being a grad student is usually a job in itself. We get paid for teaching and other duties, but we'd get kicked out if we flunked all our classes, so, in a sense, we are doing math for a living as grad students