Physics Graduate School Without Physics Courses

In summary, Alex is a junior mathematics major who plans on going to graduate school for physics. They are considering studying independently and taking the GRE and GRE Physics subject test to get into a decent graduate program. However, other users are doubtful that this approach will be successful and recommend completing an undergraduate physics degree or taking additional physics courses before applying to graduate school.
  • #1
SecretNile
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Long story short, I am currently a junior mathematics major, and I plan on going to graduate school for physics. My college offers but two, non-calculus based physics courses covering classical mechanics, electricity and magnetism.

Correct me if I'm wrong (please!), but I believe that if I do well on the GRE and GRE Physics subject test, I will be able to get into a fairly decent graduate program (top tier would be nice) without having majored in physics.

I believe that if I studied independently, a few hours every day, that I will have a fairly decent grasp on the material before I take the exam(s).

In essence, my question is this: What books/sources do you recommend I use?

Below is a direct quote from ETS about the subjects covered in the GRE physics test. I would like, at the very least, to know these materials thoroughly, but am very open to any additional materials you should recommend.

Thank you!
Alex

CLASSICAL MECHANICS — 20%
(such as kinematics, Newton's laws, work and energy, oscillatory motion, rotational motion about a fixed axis, dynamics of systems of particles, central forces and celestial mechanics, three-dimensional particle dynamics, Lagrangian and Hamiltonian formalism, noninertial reference frames, elementary topics in fluid dynamics)

ELECTROMAGNETISM — 18%
(such as electrostatics, currents and DC circuits, magnetic fields in free space, Lorentz force, induction, Maxwell's equations and their applications, electromagnetic waves, AC circuits, magnetic and electric fields in matter)

OPTICS AND WAVE PHENOMENA — 9%
(such as wave properties, superposition, interference, diffraction, geometrical optics, polarization, Doppler effect)

THERMODYNAMICS AND STATISTICAL MECHANICS — 10%
(such as the laws of thermodynamics, thermodynamic processes, equations of state, ideal gases, kinetic theory, ensembles, statistical concepts and calculation of thermodynamic quantities, thermal expansion and heat transfer)

QUANTUM MECHANICS — 12%
(such as fundamental concepts, solutions of the Schrödinger equation (including square wells, harmonic oscillators, and hydrogenic atoms), spin, angular momentum, wave function symmetry, elementary perturbation theory)

ATOMIC PHYSICS — 10%
(such as properties of electrons, Bohr model, energy quantization, atomic structure, atomic spectra, selection rules, black-body radiation, x-rays, atoms in electric and magnetic fields)

SPECIAL RELATIVITY — 6%
(such as introductory concepts, time dilation, length contraction, simultaneity, energy and momentum, four-vectors and Lorentz transformation, velocity addition)

LABORATORY METHODS — 6%
(such as data and error analysis, electronics, instrumentation, radiation detection, counting statistics, interaction of charged particles with matter, lasers and optical interferometers, dimensional analysis, fundamental applications of probability and statistics)

SPECIALIZED TOPICS — 9%
Nuclear and Particle physics (e.g., nuclear properties, radioactive decay, fission and fusion, reactions, fundamental properties of elementary particles), Condensed Matter (e.g., crystal structure, x-ray diffraction, thermal properties, electron theory of metals, semiconductors, superconductors), Miscellaneous (e.g., astrophysics, mathematical methods, computer applications)
 
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  • #2
SecretNile said:
Long story short, I am currently a junior mathematics major, and I plan on going to graduate school for physics. My college offers but two, non-calculus based physics courses covering classical mechanics, electricity and magnetism.

After those 2 classes, you'd be lucky if you were able to answer a single question on the Physics GRE unless studying "a few hours a day" is followed by "for about 2-4 years".

No graduate school is going to accept you if you've never taken a real physics course, have a near 0% Physics GRE score (which you will), no letters of recommendation from physics instructors (which you probably wouldn't be able to get), and no physics research experience.
 
  • #3
SecretNile said:
Correct me if I'm wrong (please!), but I believe that if I do well on the GRE and GRE Physics subject test, I will be able to get into a fairly decent graduate program (top tier would be nice) without having majored in physics.

I suggest you read this recent thread which was started by someone who wants to do something similar, skipping an undergraduate degree completely:

https://www.physicsforums.com/showthread.php?t=546911
 
  • #4
Pengwuino said:
After those 2 classes, you'd be lucky if you were able to answer a single question on the Physics GRE unless studying "a few hours a day" is followed by "for about 2-4 years".

^This. Studying "a few hours a day" is a pretty normal pace for someone actually pursing a bachelor's in physics (including lectures and homework), and that usually takes at least 3 years.
 
  • #5
If you really plan on going to graduate school for physics, why not go to a school that has a good undergraduate physics program? It seems like you're trying to do this the hard way and in doing so are setting yourself up for disappointment.
 
  • #6
OK, what I don't get is that you plan to go to grad school in physics, but you don't actually major in physics... Or you don't plan to actually take physics courses...
Most people spend four years getting a physics degree. What do you think they do during that time, nothing?? You plan on taking two courses and doing as well as people who are putting in four years of physics. This does not compute...
 
  • #7
@Penguino, bcbwilla

Perhaps I should rephrase. By a few hours a day I mean, potentially, 5-6 hours a day, Sunday-Saturday, throughout the entire year. I am already fairly confident in my classical mechanics, and am currently studying electromagnetism. That should save at least a little bit of time.

It should also be noted that I am a 4.0 student, and that I am used to fast-paced learning. I learned Pre-Cal, Calculus I, II, and III in roughly 1.5 months.


@Choppy
I was accepted to UIUC as a transfer student last year, but was unable to attend due to unexpected medical bills in the family. I have considered finishing my degree in mathematics and then taking some undergrad physics courses at another institute before applying, but I would much rather save the time and teach myself.


@jtbell
Thanks ;)
 
  • #8
SecretNile said:
Correct me if I'm wrong (please!), but I believe that if I do well on the GRE and GRE Physics subject test, I will be able to get into a fairly decent graduate program (top tier would be nice) without having majored in physics.

Yes, you are wrong.

SecretNile said:
I believe that if I studied independently, a few hours every day, that I will have a fairly decent grasp on the material before I take the exam(s).

No, you won't

SecretNile said:
In essence, my question is this: What books/sources do you recommend I use?

Below is a direct quote from ETS about the subjects covered in the GRE physics test. I would like, at the very least, to know these materials thoroughly, but am very open to any additional materials you should recommend.

The material I recommend is an undergraduate degree in physics. The GRE is not a walk in the park, and even majoring in both physics and math, I can tell you that they ask you questions that you would have never studied before as a physics major (unless you are R. P. Feynman). I am sorry, but you kind of offend me thinking that a couple hours a day will be equivalent to all the heart wrenching, head banging years I spent to just get my degree, let alone getting into grad school. Unless you apply oversees where they don't take GRE scores, you will still need a physics professor write you a letter of rec (like was stated earlier).

I also kind of find it weird how people think "hey, I'm really really good at math, physics should be easy" because its a completely different skill. You have to build a physics intuition from the ground up. I didn't go to math grad school because I am horrible at proofs. Its a completely different skill, and most "proofs" in physics would give mathematicians heart attacks, and most proofs in math seem useless in physics when you can "show" its true without a proof.

I don't mean to burst your bubble, but it will take way more than a few hours a day for a year.
 
  • #9
I don't think it's the actual degree that is the big deal. The issue is recommendation letters. Also, it helps to take classes and be able to say you got an A in such and such class and 3.9 physics gpa, etc.

I was planning on doing something similar, but I had planned to take more physics classes. I ended up going for math, instead. I am still trying to learn physics on the side because it's close to the math that I am doing, but grad school in math didn't leave much time for that. So, I think maybe I'm still about 3 classes short of having the equivalent to an undergraduate degree in physics after about 7 years of studying physics in my spare time (although I know bits and pieces of some graduate level topics in physics). So, as yet, I have been unable to do both, to the extent that I had intended.


I also kind of find it weird how people think "hey, I'm really really good at math, physics should be easy" because its a completely different skill. You have to build a physics intuition from the ground up. I didn't go to math grad school because I am horrible at proofs. Its a completely different skill, and most "proofs" in physics would give mathematicians heart attacks, and most proofs in math seem useless in physics when you can "show" its true without a proof.

I don't think this is quite true. It's a different skill, but not completely different. There can be a lot of overlap between physics and math, depending on what you do. As I see it, there's no sharp division between math and physics. It's more of a continuum with a lot of variation within each field. Theoretical physicists are closer to mathematicians, for example, and mathematical physicists ARE mathematicians who study physics or problems motivated by physics. And there are people like string theorists, who, I think, are basically non-rigorous mathematicians.

Of course, part of the problem is that physicists and mathematicians don't talk to each other as much as they should.

Math majors usually make good physics majors. The trouble is that it takes a lot of additional effort to learn physics, not that they aren't good at it. In some cases, people find they are just better at one than the other, though.
 
  • #10
A BS in physics is ~40 hours of work a week for 32 weeks a year for 4 years: a little over 5000 hours.

5 hours a day for 7 days a week for 52 weeks is 1820 hours. So you're arguing that without instruction, you can still learn the material 3x faster than a typical person who goes on to get a PhD in physics.

While I won't say this is impossible, I sure wouldn't bank on it. Just as I wouldn't bank on winning the lottery as a financial plan.

If you want to go to grad school in physics, you need to take physics classes as an undergrad.
 
  • #11
SecretNile said:
@penguino, bcbwilla

Perhaps I should rephrase. By a few hours a day I mean, potentially, 5-6 hours a day, Sunday-Saturday, throughout the entire year. I am already fairly confident in my classical mechanics, and am currently studying electromagnetism. That should save at least a little bit of time.

Well now you're being half-way realistic. Yes, you're looking on the order of years (plural) in terms of studying. One thing that must be pointed out, however, is that I have NEVER EVER EVER EVER heard of anyone being able to do this. I think most people will say that most of their real physics understanding doesn't come from just going through textbooks, but through interacting with professors, other students, and doing experiments as well (oh by the way, do you plan on doing purely theoretical physics?). I mean, getting an answer from solving a problem is nice, but over the years I found myself constantly asking others and professors "what the heck does this mean?"

There is a fantastic way of figuring out whether or not you stand a chance. Go to ETSs website, find the practice physics GRE tests, and just have at it (Actually, here is the link: http://www.ets.org/Media/Tests/GRE/pdf/Physics.pdf [Broken] ). If your confident in your classical mechanics, you should find the classical mechanics problems fairly easy (and by easy, finish each within 60 seconds). This it not a joke either, you have about 1-2min per question on the physics GRE to do decent. You can also take the entire test, under test conditions (180 minutes I believe?). They give you the answers, you score yourself, and see how well you do. If you got a 50% or so given their percentile calculations for that practice test, great! If you get single digits, you are not even close to prepared.

It should also be noted that I am a 4.0 student, and that I am used to fast-paced learning. I learned Pre-Cal, Calculus I, II, and III in roughly 1.5 months.

That's really not relevant. Were you formally tested on all of those classes?
 
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  • #12
I took a look at that test - I would say the practice test is substantially easier than the real deal.
 
  • #13
homeomorphic said:
The issue is recommendation letters.
I'm working with one of my professors to get an internship setup. It would be physics research at another school.

Pengwuino said:
If your confident in your classical mechanics, you should find the classical mechanics problems fairly easy.
I did, and do. Though I only went through about half of them.

Pengwuino said:
Were you formally tested on all of those classes?
Yes. I made perfect or nearly perfect scores on all of them.

Vanadium 50 said:
A BS in physics is ~40 hours of work a week for 32 weeks a year for 4 years: a little over 5000 hours.

5 hours a day for 7 days a week for 52 weeks is 1820 hours. So you're arguing that without instruction, you can still learn the material 3x faster than a typical person who goes on to get a PhD in physics.

While I won't say this is impossible, I sure wouldn't bank on it.
Thank you for actually using numbers. I realize it will be extremely, extremely hard to accomplish. I'm hoping that since I already have the mathematics, applying it to concepts will go faster than if I were learning both simultaneously.
 
  • #14
SecretNile said:
It should also be noted that I am a 4.0 student, and that I am used to fast-paced learning. I learned Pre-Cal, Calculus I, II, and III in roughly 1.5 months.
There's a big difference between lower-division and upper-division courses.

Since you're still in your junior year, why not just add physics as a second major or possibly as a minor? You could probably cram everything in before you graduate. At the very least, you should take classical mechanics, e&m, quantum, and statistical mechanics.
 
  • #15
I'm a biologist, but I did try the physics GRE years back (much easier than the Biology GRE). I 've no idea about physics grad school (probably much harder than biology grad school), but if you just want to try taking the test, maybe:

Basic Mechanics: Kleppner & Kolenkow (the absolute best)
Fancy Mechanics: Fetter & Walecka (just the first half), supplemented by Landau & Lifgarbagez when Fetter & Walecka are confusing
E&M: Dugdale
Waves: Lewin
Thermo & Stat Mech: Schroeder, supplemented by Kardar when Schroeder is confusing
Modern Physics: Beiser (just read quickly), supplemented by the special relativity parts of Rindler for concepts
QM: Griffiths, supplemented by Peebles and Shankar when Griffiths is confusing
 
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  • #16
Dear SecretNileI posted a long sequence of what books/knowledge/skills you should have for grad physics and beyond at: https://www.physicsforums.com/showthread.php?t=540829
At the top there is a short 8 page document for those at about the junior level interested in particles and fields (with a Word document), and then there is a long sequence of posts of a long Word document for going from junior level math/physics to grad physics and beyond (math/physics texts/references/key ideas/key skills). This, later, sequence is the sequence I have edited, thanks to great feedback and have available now. I haven't posted the reduced material yet, but I can email it to you (akalaniz AT gmail.com).

(Both documents are there in that post, just scroll down.)

(Note: Part 1 of the long document is on the limits of physics and math. Then Parts 2 & 3 are about the book lists and topics lists.)

I feel the pain of some the other people who have replied. I got a piece of crap BS in physics from a liberal arts college, and got my butt kicked in grad school UT Austin. I ended up getting a pilot's license and joining the Air Force. Later, at the Air Force Research Laboratory in Albuquerque, I spent 4 years relearning my undergrad physics and undgrad math with the tutelage of a bunch of PhDs. It was mostly me that did self guided learning, but thanks to the PhDs, I had a heads up on what was required in grad school.

After 4 years of self learning, I left the Air Force and knocked out a 4.00 MS Math, 36 hour non-thesis.

Then it was back to physics grad school. The math helped, but not as much as you would think. Physics intuition/skills takes a lot of hard work. For example, Griffiths is a typical author of junior level E&M, and Jackson is the gold standard for graduate school. There's not much more in Jackson than in Griffiths when it comes to theory, but applications are far deeper in Jackson. It took me years working at an accelerator after my PhD to begin to appreciate the depth and beauty of Jackson.

That file I can send you is also about filling the gap between pure (almost useless) math and math that physicists really need but can't get for lack of good sources.

I hope this is helpful,

Alex
 
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  • #17
atyy said:
Basic Mechanics: Kleppner & Kolenkow (the absolute best)
Fancy Mechanics: Fetter & Walecka (just the first half) or Landau & Lifgarbagez (very to the point)
E&M: Dugdale
Waves: http://www.youtube.com/watch?v=9kSUGGIQPJU&feature=list_related&playnext=1&list=SP854AA255B15C574C
Thermo & Stat Mech: Schroeder or Kardar
Relativity: Rindler (only special relativity parts)
Modern Physics: Beiser (just read quickly)
QM: Griffiths, supplemented by Peebles and Shankar whenever Griffiths is confusing
Thank you! That will be incredibly helpful. :)

aalaniz said:
That file I can send you is also about filling the gap between pure (almost useless) math and math that physicists really need but can't get for lack of good sources.
Thank you! I will email you shortly.
 
  • #18
I have a suggestion of something that would probably be much more straightforward. If it is theory that you are interested in, you might try to apply to graduate school for mathematics to departments that have a lot of mathematical physicists, or professors that are both physics and math professors, etc. Then you can keep pursuing your math degree, take the math GRE, and then learn physics in graduate school. Furthermore, some departments may let you have someone in the physics department as your adviser.
 
  • #19
SecretNile said:
I have considered finishing my degree in mathematics and then taking some undergrad physics courses at another institute before applying, but I would much rather save the time and teach myself.

It's very possible that should you be accepted to a physics grad program, they will require you to complete a bit of "catch up" work before starting grad-level classes. So taking a few classes at another institution may not be a waste of time. And it would likely help your PGRE scores, too.
 
  • #20
The most important thing is not how much time you spend learning the material. It's the quality of that time.

At least in my university, if you were a "good" student : going to all the lectures, taking all the notes and doing all the homework, you would be wasting a lot of time with minimal benefit. Only a part of the lectures are useful, only a part of the books are worthy to read, only a part of problems are worthy to be solved. Hence, if you spend your time wisely, if you're good at self learning, I think you could easily self learn all the necessary physics in a year.

As of textbook recommendations, I would suggest picking books which cover mostly the most important, fundamental topics, without going into details. However, those fundamentals should be explained in a deep fashion. What is more, the books should be written in a formal, mathematical way, with just a few sentences of additional explanation. This would make the books (or, actually, top universities lecture notes might be even better) with relatively small amount of pages, which would give you some extra time, however, that time should be used for slow reading, thinking extensively about all the fundamental concepts. In my opinion, not only for GRE, but for physics in general, it's not how many concepts, how many equations and how many various details you know that matters, but how deeply you understand the very fundamentals. With them you can derive the details when needed yourself.

For example, for mechanics my suggestion would be :
http://www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf
It seems it's from Cambridge, Mathematical Tripos, hence it should be designed for mathematicians. It also looks clear and short, but at the same time deep and it seems it covers all the most important concepts.
 
  • #21
Monocles said:
I have a suggestion of something that would probably be much more straightforward. If it is theory that you are interested in, you might try to apply to graduate school for mathematics to departments that have a lot of mathematical physicists, or professors that are both physics and math professors, etc. Then you can keep pursuing your math degree, take the math GRE, and then learn physics in graduate school. Furthermore, some departments may let you have someone in the physics department as your adviser.
I'll consider this and talk to my advisers about it. Thank you ;)

lisab said:
It's very possible that should you be accepted to a physics grad program, they will require you to complete a bit of "catch up" work before starting grad-level classes. So taking a few classes at another institution may not be a waste of time. And it would likely help your PGRE scores, too.
I've fought myself over questions like this. Why would they accept me if I had to catch-up? There's plenty of applicants that don't need this special treatment. But, wouldn't scoring well on the PGRE without having had formal classes show dedication and a good work ethic?

I think I'll try to get in without formal classes. Then I'll either be accepted, accepted and have to catch up, or declined. If I'm declined I'll take the classes at another institute and then reapply. At least the classes won't be as hard if I've already (attempted) to learn the material...

Obis said:
The most important thing is not how much time you spend learning the material. It's the quality of that time. . . Hence, if you spend your time wisely, if you're good at self learning, I think you could easily self learn all the necessary physics in a year.

. . .In my opinion, not only for GRE, but for physics in general, it's not how many concepts, how many equations and how many various details you know that matters, but how deeply you understand the very fundamentals. With them you can derive the details when needed yourself.
I agree wholeheartedly. As one of my math professors said, "Math has a shelf life. You will forget these equations in a few months, or a few years. The concepts are what stay with you. The equations in math are not nearly as important as the concepts." I think the same will hold for physics.

Thank you for your input. I will definitely take your advice and peruse some lecture notes.
 
  • #22
Obis said:
The most important thing is not how much time you spend learning the material. It's the quality of that time.

At least in my university, if you were a "good" student : going to all the lectures, taking all the notes and doing all the homework, you would be wasting a lot of time with minimal benefit. Only a part of the lectures are useful, only a part of the books are worthy to read, only a part of problems are worthy to be solved. Hence, if you spend your time wisely, if you're good at self learning, I think you could easily self learn all the necessary physics in a year.

As of textbook recommendations, I would suggest picking books which cover mostly the most important, fundamental topics, without going into details. However, those fundamentals should be explained in a deep fashion. What is more, the books should be written in a formal, mathematical way, with just a few sentences of additional explanation. This would make the books (or, actually, top universities lecture notes might be even better) with relatively small amount of pages, which would give you some extra time, however, that time should be used for slow reading, thinking extensively about all the fundamental concepts. In my opinion, not only for GRE, but for physics in general, it's not how many concepts, how many equations and how many various details you know that matters, but how deeply you understand the very fundamentals. With them you can derive the details when needed yourself.

For example, for mechanics my suggestion would be :
http://www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf
It seems it's from Cambridge, Mathematical Tripos, hence it should be designed for mathematicians. It also looks clear and short, but at the same time deep and it seems it covers all the most important concepts.

I agree that at times lectures are a waste of time if your good at self-studying. But what i don't completely agree with is that doing a lot of problems can be a waste of time. The general consensus is that the more problems you do the better?
 
  • #23
In my opinion, this general consensus is wrong. Solving a lot of relatively simple problems makes you good at solving simple problems in a small amount of time. Being able to solve simple problems in a quick manner doesn't make one a good physicist/mathematician. It's the ability to solve very hard problems that does it, while the time required is also important, but not too much. Hence is much better to solve fewer, but harder, deeper problems, that require not some direct application of an equation, where you don't even need to understand that equation and concepts used, but that require a clear understanding, creativity. The useful problems can be relatively easy, too, however, what is important is that they should check your ability to relate, analyse, compare, explain in your own words, etc. Most of the problems I see as assigned homework are not like that : they check your ability to directly use a formula or a computational algorithm, your ability to add, subtract, multiply and not lose a minus sign. Solving such problems is mostly a waste of time.

Generally, I think that solving problems is overrated, while reading and trying to understand theory is highly underrated. It's a matter of an individual's learning style and various other subjective things, of course, but I find that the most effective way to learn for me is around 90% reading theory and 10% solving problems.
 
  • #24
Why not save yourself the hassle and apply to a two-year Master's program in Europe? (Germany, France or the UK, if you can afford it!)

Check this one out. I have checked and they require either a Math or Physics degree along with the appropriate GRE subject test.
 
  • #25
Obis said:
Generally, I think that solving problems is overrated, while reading and trying to understand theory is highly underrated. It's a matter of an individual's learning style and various other subjective things, of course, but I find that the most effective way to learn for me is around 90% reading theory and 10% solving problems.

I find it very hard to believe that you are successful with this strategy. May I ask how far along you have gotten?

What we call "solving problems" is really "doing calculations" (a textbook problem is merely a calculation chosen for its pedagogical value), and that's a large part of a physicist's job. Reading about theory is a little like watching someone else lift weights; it has some utility, in that one should know what the proper form and technique is, but it's no substitute for lifting weights yourself.
 
  • #26
If the reading is passive, without raising questions, without trying to generalize, without trying to relate with everything else you already know, without trying to imagine, without trying to prove theorems yourself in your mind before reading the proof and so on, then yes, the analogy with watching somebody else lift weights is a very accurate one.

Solving problems is a good and necessary thing, I agree, however, I mostly see it as a way to test your knowledge, find holes in your understanding, get used to the technical side of various computations, etc. However, at least for me, the understanding comes from reading, however, mostly the direct reading of the books takes about 10% of the time spent, the rest 90% are thinking and trying to "play" with the information read. Hence, sometimes reading a single page of concentrated text can take more than an hour.
I'm simply saying that reading theory deserves more credit and attention than it gets.
 
  • #27
You didn't answer my question. How far have you gotten with this strategy of yours? A permanent position? A postdoc? A PhD? An MS? A BS? Sophomore year? High school?
 
  • #28
Solving problems is how you learn physics. This is really how you test yourself to see if you really know what is going on. You can understand Maxwell's equations mean, but that doesn't mean you know electromagnetism.
 
  • #29
I don't want to answer that, because it makes not too much difference. Even if I were in high school now, the fact that I learn more from reading than solving problems would still be true, at least that's the way I see it.
 
  • #30
Understanding your own understanding is an ability that can be learned and improved. Hence, theoretically, at some point, you don't even need to solve problems to check your understanding, you simply see your own understanding's weak points.

Once again I'm not against solving problems, but I don't think it's the only way to learn physics or any other subject. Anyway, active reading is in some sense problem solving, where you solve problems imposed directly or indirectly by the text, or by yourself.
 
  • #31
Obis, please answer Vanadiums question...
 
  • #32
Obis said:
I don't want to answer that, because it makes not too much difference. Even if I were in high school now, the fact that I learn more from reading than solving problems would still be true, at least that's the way I see it.

I think it actually does make a difference if you are in High School or a PhD in Physics. You might think you know a lot, but if you can't solve the problems, then there are obviously gaps in your learning. Solving problems is when you really have to think hard about what you know and don't know. And if they are good problems, then solving them should give you tremendous insight into the subject that you just can't get by reading a book.
 
  • #33
I am a 6th year grad student in math (PhD in August if things go well--adviser says he thinks I can graduate this year, but otherwise, I will face the dreaded 7th year and possible lack of funding, but I promise I will have a PhD in two years at most), and I have some sympathy with what Obis is saying, although I am not in complete agreement. Of course, he also realizes that solving problems is necessary. I think it's complicated issue, so it's hard to do it justice here.

Math and physics are similar enough that I think that the fact that I do math doesn't make that big of a difference, plus, I do physics-related math and have studied a fair amount of physics, too.

There are a couple problems with active reading, though. First of all, what you want to do is get your OWN perceptions into it as much as possible. Of course, you need the book because your own perceptions aren't quite enough to come up with the subject by yourself. So, active reading can be good, but you don't want to be too dependent on the textbook. Trying to do problems before reading everything carefully can get you more involved in the process from the start.

But, you have to do what works, depending on the situation. Sometimes, you might need to do more reading first. Sometimes, the problems won't be good problems. Sometimes, the textbook sucks, and all the textbooks on the subject suck, so you need to be more self-sufficient and try to come up with as much of the theory on your own as possible. It just depends.

There's something to be said about thinking about the theory. In high school and early undergrad, I had more of a "just do the problems" approach. Then, at some point, I started thinking about the theory more, and it was a lot more effective in terms of my understanding and retention of the material. Then, in grad school, I shifted back more towards doing problems, but still retained a lot of the thinking stuff over. So, you need to do both, I think. Sometimes, when you do the problems, you do some of the thinking you need, but it's not always enough.
 
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  • #34
Obis said:
I don't want to answer that, because it makes not too much difference. Even if I were in high school now, the fact that I learn more from reading than solving problems would still be true, at least that's the way I see it.

Yes, but it would not be relevant advice for someone who is working on problems many years more advanced.
 
  • #35
Let me elaborate a little on what lead me to use the "active reading" approach a little less and be more problem-oriented, recently.

First, my qualifying exams when I started graduate school impressed upon me the point that you want to be good at DOING real analysis, say, rather than just understanding the theory. You have to know the tricks to doing the problems, and so on. You want to be able to move beyond the existing theory to be able to create your own. Of course, this can go both ways. Someone else told me that they needed to do more reading and understand the concepts, rather than practicing the problems. For me, I already knew all the concepts, so what was left was just to practice problems. But that was because I had already laid the groundwork in terms of thinking about the theory enough.

Secondly, while working on my thesis, I found that I understood the theory that I personally came up with much better than the theory that I "actively read". So, I am now taking the attitude that I don't like to read as much, if I can avoid it, because when I come up with it, it makes so much more sense and is much easier to remember and much more intuitive. Of course, this was something I was aware of all along, but working on a big research project drove it home a lot more because, when you are doing research, you have to think about the big picture more. When I used to read books, I was more focused on doing things one step at a time, rather than making a whole plan for how the theory should unfold. So, now when I read stuff, I try to approach it more as if I am doing research, but the book or paper is giving me hints to help me if I get stuck.
 

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