How much of the material (formulas, etc.) do you need to memorize?

[Ascendant78]

I am just finishing up my first physics course this semester (as a physics major). Although there did seem to be a lot to soak up this semester, I didn't feel like it was too bad. I am just curious though, is there a resource that has a list or other type of reference material that shows you what formulas and such that you need to memorize for this and future courses in physics? I memorized everything from this semester even though our professor gave us the option of reference cheat sheets. However, I know as time goes on, trying to memorize it all will be impractical, but would like to know what I should be memorizing and what can just be referenced back to as necessary?

 

[Vanadium 50]

The idea is not to memorize. The idea is to remember.

 

[Ascendant78]

The idea is not to memorize. The idea is to remember.

Well, I feel that explanation is a bit ambiguous. Someone could remember the method used to solve a work-energy problem involving linear oscillations, but if they didn't have the formula memorized, remembering a method would do little good unless they were allowed to use a reference sheet (which I know many professors later on will not allow).

If you meant it is more important to memorize the concepts rather than just memorizing formulas, that is what I do. I usually memorize the formulas indirectly by learning the concepts. However, I know for the physics GRE I will need to have a lot of formulas memorized, I'm just not sure which ones.

If you could clarify your statement for me, I'd really appreciate it.

 

[IGU]

I'd say the idea is to understand the material. If you do, you should be able to rederive any formulas you need. If you are memorizing things, you are taking a shortcut that avoids understanding, although it can make things faster at times.

 

[Ascendant78]

Ok, I found a site giving an example of what I was talking about. Not sure if links are alright to post on here, so excuse me if they aren't: http://www.phys.ksu.edu/personal/eschultz/GRE%20Home.htm

That url has a 14-page list of formulas it indicates need to be known for the GRE physics test. So, clearly there is some memorization involved. Is it practical to expect to know all those formulas?

Here is a link with a more reasonable list, but they seem to indicate it is just a start and that you would want to add more: http://www.physicsgre.com/viewtopic.php?f=13&t=1065

I feel a bit overwhelmed with how much we are expected to memorize, but I guess since I still have two more years before I'll need to actually take the exam, I will have a lot of courses (as well as time) to work on them. However, I still haven't found any consistency in what I should actually memorize.

 

[Vanadium 50]

The strategy of memorizing a bunch of formulas is rarely successful. Even the link you posted to says "But, this is not simply memorization. When memorizing the formulas don't just memorize the formulas as in there's an m over r or something like that. Ask yourself, does this make sense? Do the units make sense? Analyse them! You will remember the formulas much better if you aren't simply memorizing them and instead making sense of them!"

 

[IGU]

I feel a bit overwhelmed with how much we are expected to memorize, but I guess since I still have two more years before I'll need to actually take the exam, I will have a lot of courses (as well as time) to work on them. However, I still haven't found any consistency in what I should actually memorize.

Seriously, you should memorize exactly none of it. You will learn the physics behind the formulas. Then when you go through a list like this you'll see it as a shorthand for what you need to know. You'll look at it and go "uh huh, uh huh, yes, ..." You'll have worked through the physics so many times in solving problems that the formulas are just shorthand for what you know.

And if you do memorize things rather than understand them, all you'll be able to do with what you know is pass bad tests. Good tests determine whether you understand the material, not whether you know some formula and can guess when to apply it.

 

[Ascendant78]

The strategy of memorizing a bunch of formulas is rarely successful. Even the link you posted to says "But, this is not simply memorization. When memorizing the formulas don't just memorize the formulas as in there's an m over r or something like that. Ask yourself, does this make sense? Do the units make sense? Analyse them! You will remember the formulas much better if you aren't simply memorizing them and instead making sense of them!"

Thanks for the information and I do get that the priority is to grasp the concepts before trying to learn the formulas. Perhaps the word "memorize" wasn't the best word for me to use. I was simply thinking that no matter how well you grasp the concepts, you'd still need to know the formulas that go along with it.

I think I am just thinking too far ahead. It is just that with all the linear oscillation information we have been looking at lately, a lot of it has just been learning formulas that go with the concepts, but there doesn't seem to be an intuitive way of remembering the formulas just by the concepts alone.

From what I can see, most of the information I've found says to do as many official practice physics GRE tests you can, then figure out what you need to learn from there and learn it. I'm thinking I should probably just leave it at that for now and just focus on studying what I am learning now.

 

[Ascendant78]

Seriously, you should memorize exactly none of it. You will learn the physics behind the formulas. Then when you go through a list like this you'll see it as a shorthand for what you need to know. You'll look at it and go "uh huh, uh huh, yes, ..." You'll have worked through the physics so many times in solving problems that the formulas are just shorthand for what you know.

And if you do memorize things rather than understand them, all you'll be able to do with what you know is pass bad tests. Good tests determine whether you understand the material, not whether you know some formula and can guess when to apply it.

I posted before I saw this post of yours, but completely understand what you are saying. I think it ties right into the whole thinking too far ahead thing I just mentioned.

The main reason I was asking is that I want to make sure I know everything I should know, but no matter how much I learn, I keep finding more to learn. I know I could spend 24/7 studying the material from my class, from opencourseware variations of the material, from Morin's mechanics book, along with multiple other sources. I am just trying to set a boundary for myself that will be reasonable, but am not sure how much is adequate.

 

[ParticleGrl]

Well, I feel that explanation is a bit ambiguous. Someone could remember the method used to solve a work-energy problem involving linear oscillations, but if they didn't have the formula memorized, remembering a method would do little good unless they were allowed to use a reference sheet

You should remember the major formulas, and then how things relate. i.e.- Let's look at your linear oscillator- "linear" should clue you in that F = -kx (why the negative sign? How else would we get oscillations?).

So, ma = -kx. The right side doesn't depend explicitly on time, so we remember that we can integrate-

[tex] \int m \frac{dv}{dt} dx = -\int kx dx [/tex]

Using [tex] dx = vdt[/tex] and integrating, we get

[tex] \Delta \frac{1}{2}mv^2 = -\Delta \frac{1}{2}kx^2 [/tex]

So the only formula I had to remember to do the problem was F=ma, BUT I had to remember how to think through the physics, and it only took a moment. The formulas all come from somewhere, and as you learn more, you'll get good at making the connections you need .

 

[AlephZero]

That url has a 14-page list of formulas it indicates need to be known for the GRE physics test. So, clearly there is some memorization involved. Is it practical to expect to know all those formulas?
...
I feel a bit overwhelmed with how much we are expected to memorize

Even if you igmore the good advice already given, you are saying that memorizing 14 pages of information in 3 years is "overwhelming"? Seriously?

That probably works out at less than one "formula" per day, on average. I doubt that anybody can succeed in any academic subject if they can't remember information at a faster rate than that.

 

[Ascendant78]

You should remember the major formulas, and then how things relate. i.e.- Let's look at your linear oscillator- "linear" should clue you in that F = -kx (why the negative sign? How else would we get oscillations?).

So, ma = -kx. The right side doesn't depend explicitly on time, so we remember that we can integrate-

[tex] \int m \frac{dv}{dt} dx = -\int kx dx [/tex]

Using [tex] dx = vdt[/tex] and integrating, we get

[tex] \Delta \frac{1}{2}mv^2 = -\Delta \frac{1}{2}kx^2 [/tex]

So the only formula I had to remember to do the problem was F=ma, BUT I had to remember how to think through the physics, and it only took a moment. The formulas all come from somewhere, and as you learn more, you'll get good at making the connections you need .

Thanks. The initial formula you posted is an easy concept for me, but I'm still trying to fully grasp how the wavelength relates to everything else (w=sqrt(k/m), f=2pi/w, etc.). Then again, we did just cover the topic for the first time this morning.

Seems like the further I get into calc (and the more practice I have with that), the easier it will make this as well. I'm not to the point yet where I fully understand how all the things relate like you did above (though I got what you did with the integration), but good to know that I will be able to do so later on. I appreciate the feedback.

 

[Ascendant78]

Even if you igmore the good advice already given, you are saying that memorizing 14 pages of information in 3 years is "overwhelming"? Seriously?

That probably works out at less than one "formula" per day, on average. I doubt that anybody can succeed in any academic subject if they can't remember information at a faster rate than that.

When did I ever say I was ignoring the advice? I simply asked for clarification. No need for the snide remarks.

Also, yes I was serious. Keep in mind I am just finishing my first physics course this semester. So that many pages of material, most of which I know nothing about at this point, did seem like a lot. You are also attempting to oversimplify the material considering that is merely the formulas that go along with all the concepts that they will pertain to.

I have a 7 month old daughter right now, so I am trying to find a balance between my studies and her. If it weren't for her, I would put the majority of my time into this and it would be a walk in the park. However, I am limited on time as I am not going to neglect my daughter for my education. So, I really don't appreciate your attitude when I am simply trying to get some feedback from those who have been where I'm at now.

 

[sus4]

A lot of the times, in the earlier physics classes, you can get by without even memorizing some of the mainstream equations. If you get a good intuitive understanding of everything, it often can be boiled down to making sure the units work out right. I usually only memorize any equation that I can't derive, OR anything that takes too long to derive and that I find useful often.

 

[member 392791]

You usually ''memorize'' the equations by just doing problems and you use the same equation so many times that it sticks

 

[Ascendant78]

Thanks for the additional feedback.

What about constants? I'm not talking the basics like pi or e, but things like the speed of light in a vacuum, constant of gravitation, proton/electron mass ratio, Avogadro constant, and things like that? Things where the only way you could know those values is if you memorized the numbers? To what extent are we expected to know those types of values?

 

[Vanadium 50]

This sounds a lot like "what's the bare minimum I need to remember". Do you think this is a winning strategy?

 

[jtbell]

What about constants?

I can't speak for other professors, but my policy on exams has always been to give students values of physical constants if they need them, or tell them they can look them up on the inside cover of their textbook (the relevant ones are usually listed there).

In practice, I naturally remember the ones that I use often: speed of light, Planck's constant, Newton's gravitational constant, Avogradro's number, etc.

 

[Ascendant78]

This sounds a lot like "what's the bare minimum I need to remember". Do you think this is a winning strategy?

If I took a bare minimum approach, I wouldn't have been the top in my class in Chem I, Chem II, Physics I, Calc I, and Calc II. I can assure you, I do not take a minimum approach, but I do appreciate you making sure I wasn't looking for an easy out that would hurt me later on.

I am merely trying to be practical with my time. If there is no need for me to memorize certain constants, I would rather try to put my studies into other materials. I am trying to utilize some opencourseware for linear algebra (not offered at my current college), opencourseware for multivariable calculus (I'll be taking it online next semester), opencourseware for physics (in conjunction with my current class), learning to work with Mathematica, learning Linux (Ubuntu), brushing up on my foreign language for placement next year, need time for my calculus, and need time for my family in between all that. Oh, and I haven't even had time to start learning latex yet or any computer programming, which I have been told it would be good to get a head start on now, at least with latex.

I am actually trying to do the exact opposite of what you asked. However, due to time constraints, I am trying to figure out the most efficient way to allocate my time to studies.

 

[Ascendant78]

I can't speak for other professors, but my policy on exams has always been to give students values of physical constants if they need them, or tell them they can look them up on the inside cover of their textbook (the relevant ones are usually listed there).

In practice, I naturally remember the ones that I use often: speed of light, Planck's constant, Newton's gravitational constant, Avogradro's number, etc.

Thanks for the information. From what I just read about the physics GRE from the main website, it seems like most of the constants will be provided there as well. So, I'm assuming the ones I *should* know from the courses I'll end up memorizing from frequent use. The rest will most likely be provided.

 

[Vanadium 50]

Your "will this be on the test?" mentality might well get you a good grade in introductory classes. It probably will not get you through the GRE and it will certainly not get you through graduate school. Likewise, thinking about memorizing numbers and equations is the wrong way to go about it. You want to learn by working a lot of problems and derivations and remember what you did - not memorize a bunch of facts.

 

[ZombieFeynman]

Some combinations of constants you really should remember. How else will you be able to do order of magnitude estimates on the fly?

hBar*speed of light ~ 2000 (eV)(angstrom)

(mass of proton)/(mass of electron) ~ 2000

(mass of electron)*(speed of light squared) ~ 0.5 MeV

radius of Earth ~ 6 million meters

bound energy of H ground state ~ 13.6 ev

kBoltzman * (300K) ~ 1/40 of an ev

Nitrogen boils ~ 70K, helium at ~4K

1 GHz E&M wave is ~3m radio wave

radius of Milky Way ~ 60,000 light years = 15 k parsec

(bohr magneton)*(1 tesla) ~ 60 micro eV

These and many more "rules of thumb" you really should have in your head at all times by the time you are a grad student. When you hear many talks, numbers will be thrown around and you MUST have some way of comparing and making sense of them.

 

[clope023]

Memorization and understanding are not mutually exclusive.

I also think clarification on what is meant by memorization is needed.

For instance, sitting and trying to memorize maxwell's equations simply by repeating the names of the symbols will be useless.

However, if you remember the relationship between the permeating and rotating fields than you will memorize and understand them.

 

[Ascendant78]

Memorization and understanding are not mutually exclusive.

I also think clarification on what is meant by memorization is needed.

For instance, sitting and trying to memorize maxwell's equations simply by repeating the names of the symbols will be useless.

However, if you remember the relationship between the permeating and rotating fields than you will memorize and understand them.

I attempted to clarify myself in the 3rd post down from the top, but from some of the comments made after it, it seems like I didn't.

To reiterate and clarify, I typically study the concepts through formulas and working problems in order to indirectly memorize the formulas. I don't just stare at arbitrary formulas to memorize something without understanding what it is, where it came from, why it works, etc. However, a part of fully understanding the concepts is knowing what formulas are used for those particular concepts, so despite how some people might perceive the matter, some level of memorization is necessary. I am well aware that one of the most effective ways to study the material is through a full understanding of the underlying concepts, though it seems many people assumed I didn't and was just looking to scrape by. If I knew some people were going to automatically assume I was incompetent, I would have clarified myself in my original post.

I guess a good way to demonstrate my perception on this matter is like this... How far have most of you memorized the numbers for pi? I'm assuming most only went for 3-8 digits at most, because anything past that is not going to serve most of us much purpose. Now, whether someone memorized those numbers through seeing them in problems, through mnemonics, or some other method, it is still memorization nonetheless. Now, if you took the time to memorize constants like pi, e, Avogadro's constant, and any others that you came across in your studies to say 30 decimal places, would you see that as a productive way to spend your time? Of course not, because there is no need to. That is why I started this thread, to try and understand what is worthwhile to memorize and what is pointless to memorize because you'll most likely never need to know it off the top of your head. I figured not wasting time studying things I don't need to study would open myself to studying things that I do.

 

[Student100]

I guess a good way to demonstrate my perception on this matter is like this... How far have most of you memorized the numbers for pi? I'm assuming most only went for 3-8 digits at most, because anything past that is not going to serve most of us much purpose. Now, whether someone memorized those numbers through seeing them in problems, through mnemonics, or some other method, it is still memorization nonetheless. Now, if you took the time to memorize constants like pi, e, Avogadro's constant, and any others that you came across in your studies to say 30 decimal places, would you see that as a productive way to spend your time? Of course not, because there is no need to. That is why I started this thread, to try and understand what is worthwhile to memorize and what is pointless to memorize because you'll most likely never need to know it off the top of your head. I figured not wasting time studying things I don't need to study would open myself to studying things that I do.

I think you're missing the point a lot of good posts here make. Do you know the method in which Archimedes calculated pi, do you understand the reasoning behind it? If I were to suggest the inequality n*tan(180/n degrees) > Pi > n*sin(180/n degrees) would you know where I'm coming from?

It's fine to memorize things, and if you work through enough problems you'll likely recall from memory many things. That ain't the point, however, the point is a deeper understanding of the material, it's relation and purpose.

There is no steadfast list of things you need to memorize, or things that are irrelevant to memorize. You should try to understand as much as possible.

 

[Ascendant78]

I think you're missing the point a lot of good posts here make. Do you know the method in which Archimedes calculated pi, do you understand the reasoning behind if. If I were to suggest the inequality n*tan(180/n degrees) > Pi > n*sin(180/n degrees) would you know where I'm coming from?

It's fine to memorize things, and if you work through enough problems you'll likely recall from memory many things. That ain't the point, however, the point is a deeper understanding of the material., it's relation and purpose.

There is no steadfast list of things you need to memorize, or things that are irrelevant to memorize. You should try to understand as much as possible.

Thanks for the information. As far as pi, the most I have learned about it previously is that it is the number you get if you divide a circle's circumference by it's diameter. I know I still have much to learn, which is why I'm trying to figure out the best approach to learning it all. Seems the best approach from what people are saying is just tons of practice combined with a true understanding of where the formulas come from and why they work.

 

[Student100]

Thanks for the information. As far as pi, the most I have learned about it previously is that it is the number you get if you divide a circle's circumference by it's diameter. I know I still have much to learn, which is why I'm trying to figure out the best approach to learning it all. Seems the best approach from what people are saying is just tons of practice combined with a true understanding of where the formulas come from and why they work.

There's a thousand ways to derive pi, some better than others, Leibniz series, using the radius, cutting a circle into quadrants... Ect it's just an example.

If you see something in math or physics that might be easy to apply but seems strange or random, dig deeper into the logic behind it. Have you looked into the history of things like e? What it actually means? How it is expressed...? Things like that. I don't really know how to put it into a simple to understand statement, but the deeper you dig into things the more you actually know, not just memorize.

 

[Ascendant78]

There's a thousand ways to derive pi, some better than others, Leibniz series, using the radius, cutting a circle into quadrants... Ect it's just an example.

If you see something in math or physics that might be easy to apply but seems strange or random, dig deeper into the logic behind it. Have you looked into the history of things like e? What it actually means? How it is expressed...? Things like that. I don't really know how to put it into a simple to understand statement, but the deeper you dig into things the more you actually know, not just memorize.

Yes, I get what you are saying, and it actually annoys me when I can't look at something in a way that makes sense to me conceptually. For example, when I first saw simple harmonic motions a couple days ago, our instructor never taught us why certain formulas work. So, when I saw omega=sqrt(k/m), it was bothering me that I didn't understand why omega(w) was the only part we needed to include in this equation with k and m (since the position function is Acos(wt+Θ). I kind of understand it now, but it is still a work in progress.

Anyway, both my chemistry and my physics professors told me it is impractical to expect to remember all of the material as there is simply way too much to be able to remember. However, neither was able to give me a clear answer as to what should and shouldn't be known off the top of your head. Hence my thread.