How Do You Study Physics & Maths?

[wifi]

Greetings everyone, I'm new to physics forum.

From what I have seen thus far in a swift perusing of the site, there seems to be an ample number of enthusiasts, students, professors, etc. that have a good handle on learning physics and mathematics. My question to you is this: How do you do it?

To be more specific, what technique(s)/method(s) do you employ that, when tastefully applied, seem to make the learning process easier/efficient.

Of course, there are many factors that play important roles in learning any subject. For instance, passion, interest, and raw talent may arguably be considered preordained capacities within the confines of which we must work. With this aside, I seek only the insight that lies within your honest assessment.

 

[hsetennis]

Hi and welcome.

I have a feeling that people will generally give you a mostly similar answer: be an attentive listener, read thoroughly, participate in discussions, work out all the practice problems, write well thought-out reports, and do sufficient revision before assessments. Some may suggest working in groups. Of course how to study may deviate slightly for specific stages of education.

But let's say one knows this already. All the great mathematicians and physicists (and great people for that matter) have a quality in common. They have conviction and enthusiasm for what they do, whether they get their motivation from family, friends, God, intrinsically, competitively, or even by some moving book/movie. I personally, use Nike's slogan, "Just Do It" to push myself.

I'm not sure if I answered you question through and through. Let me know if you have a specific question.

 

[Curve Shifter]

For mathematics? Repetition. Devoting 2-5 hours daily to working textbook problems. I was lucky enough to attend a school where I had access to calculus professors several hours a day. Their offices adjoined the math study room where I've basically lived for the past 2-1/2 years, and having them constantly available to clarify concepts was PRICELESS.

When studying specifically for an exam, I set aside 4-5 hours the day before to working EVERY problem in the chapter review section, whether assigned or not. I spend 5-10 mins daily reviewing 4 handwritten pages of commonly used theorems, log properties, integrals, derivatives and trig identities. I also never walked into a test cold without spending at least 15 minutes reviewing chapter concepts.

For physics? Not as much repetition working problems as it seems to me after the first treatment of friction, the problems become more diverse and complex. So learning the process for specific problem types is not as important as basic problem solving skills and conceptual understanding to figure out WHICH formulas to apply more than HOW (as the problems were generally simpler mathematically than the ones being covered in Calc once you figured out what question was actually being posed). More time spent on reading for conceptual understanding. Reading was mostly NOT the text accompanying the class (which was jargonistic nearly to the point of being unintelligible to non-PhD's). Spent a lot of time doing informal research on things covered in class that I found personally interesting. Also spent time gleaning, writing and re-writing formula crib-sheets in Word for myself and classmates.

Anyway, that's how I got through Trig/Calc/Physics. Your mileage may vary.

 

[thegreenlaser]

I personally tend to do a lot more reading and thinking than I do practice problems. I find that if I understand the underlying concepts and I understand where the problem-solving methods come from, solving problems becomes relatively straight forward. Basically I read the theory until I really understand it (which often involves going through the derivations myself to make sure that I really do understand where everything is coming from). Then I do a few practice problems to make sure that I really do understand the material as well as I think I do. That last step is usually a small portion of my time, but it's really important because I often find that I didn't really understand things as well as I thought, and so I have to go back and look at the theory.

On the topic of practice problems, I find that it's more useful to "pick and choose" rather than just doing every problem in the book (If you spend a lot of time reading the theory, you realistically probably won't have anywhere near enough time for that). I tend to look at a problem and think my way (briefly) through the steps of the solution. If I'm confident in every step and I'm confident that I can do every step, I move on to the next problem because I'm probably not going to gain a lot by actually going through it. With time and practice I've gotten good at reading a question and then saying either "Okay, I know exactly how to solve this" or "Huh, I need to think about this some more." I find I can save a lot of time by only doing the second type.

I think the most important thing I've found is learning to be good at self-assessment. Knowing how well you understand something is a very valuable skill, and it will help you to allocate your time in the best way possible.

 

[wifi]

Thanks for the input, I value your responses.

I think I can relate most to greenlaser insofar that I tend to focus much more on comprehension of the underlying theory and derivations, as opposed to working through problems. Ideally, I'd like to do a fair amount of both - but with the time constraints and several additional classes which accompany the academic setting, we must strive for what works best.

One of my weak-points is that, when taking notes while working through a text, I have considerable difficulty reformulating the material into my own words. Nevertheless, I trudge through while accumulating essentially what are word-for-word morsels of what I've found important through my reading. I fear that I am merely memorizing the material, thus lacking true understanding. I constantly remind myself of Einstein - "If you can't explain it to a six-year-old you don't understand it yourself."

I've gotten an A's in many math/physics classes while doing so, but it's been a terrible struggle. I'm quite aware that the method is extremely inefficient, but I can't seem to find anything else that works. I desperately want to change fundamentally the nature of the process at which I learn things, and I am willing to work as necessary. Any suggestions?

 

[Von Neumann]

Thanks for the input, I value your responses.

I think I can relate most to greenlaser insofar that I tend to focus much more on comprehension of the underlying theory and derivations, as opposed to working through problems. Ideally, I'd like to do a fair amount of both - but with the time constraints and several additional classes which accompany the academic setting, we must strive for what works best.

One of my weak-points is that, when taking notes while working through a text, I have considerable difficulty reformulating the material into my own words. Nevertheless, I trudge through while accumulating essentially what are word-for-word morsels of what I've found important through my reading. I fear that I am merely memorizing the material, thus lacking true understanding. I constantly remind myself of Einstein - "If you can't explain it to a six-year-old you don't understand it yourself."

I've gotten an A's in many math/physics classes while doing so, but it's been a terrible struggle. I'm quite aware that the method is extremely inefficient, but I can't seem to find anything else that works. I desperately want to change fundamentally the nature of the process at which I learn things, and I am willing to work as necessary. Any suggestions?

It seems contradictory to say that you strive for comprehension, yet you copy mindlessly out of a textbook. Try "chunking" through the sections of the chapter, and paraphrasing the important info in your notes.

 

[wifi]

It seems contradictory to say that you strive for comprehension, yet you copy mindlessly out of a textbook. Try "chunking" through the sections of the chapter, and paraphrasing the important info in your notes.

I'm sorry for wasting your time :(

 

[turbo]

When I was in engineering school (eons ago), I took lecture notes in the margins of my texts, so that my lecture notes were right next to the appropriate text. That made it easier for me to study, since I had the profs' take on the material in the textbook. If your notes are in separate notebooks, it will be harder to reconcile them with the texts, unless you have a really good memory for the context of the lecture material.

That was my big "aha!", plus I got premium prices for my used textbooks. I did this in non-engineering courses, too, and the guy that bought my anthropology text bumped into me during the next semester and said "the professor tells the same jokes every year!" Good notes are essential, and keeping them in the context of the textbooks were key, for me. Good luck, wifi.

 

[dipstik]

i try to prep for a test a week in advance, typcially rewriting my cheat sheet once while going through my notes, again after going through the book, and again after re working homework and examples.

i will spend a day just going over notes and making a consides sheet from those
another day going through the book and working out the example
and a day or two sometimes more) to re do all of the homework for that class, making sure the solutions match my solutions. i try to do all this a few days before the exam, so i can talk to the professor about discrepencies etc. well before the exam.

also, programming your calculator to have functions to plug values into is very helpful, for some of the longer equations that are used repeatedly. sometimes finding a program that can do what you need, like symbolic eigenvalues, vectors, are helpful, since my TI-89 doesn't come with a way of getting symbolic eigen values/vectors out of the box.

on the night before the exam and the day of i just try to relax. it is important to not panic if you don't know something on the test, and just calmly skipping it until you have time for it later let's you keep cool for the parts you do know.

most importantly, after the first mid term you will know how the professor likes to test. if you noticed that the teacher asked reworded homework problems, i would try to get homework solutions on my next cheat sheet for the next midterm/final. if they do derivations, put some of those on your cheat sheet etc.. for some of my courses the professor asked fairly difficult homework problems on the exam, so i just printed out the homework solutions really small and made sure i knew which problems were where so i could just plug and chug.

 

[wifi]

When I was in engineering school (eons ago), I took lecture notes in the margins of my texts, so that my lecture notes were right next to the appropriate text. That made it easier for me to study, since I had the profs' take on the material in the textbook. If your notes are in separate notebooks, it will be harder to reconcile them with the texts, unless you have a really good memory for the context of the lecture material.

That was my big "aha!", plus I got premium prices for my used textbooks. I did this in non-engineering courses, too, and the guy that bought my anthropology text bumped into me during the next semester and said "the professor tells the same jokes every year!" Good notes are essential, and keeping them in the context of the textbooks were key, for me. Good luck, wifi.

Thank you! - I definitely can see myself doing that when the fall semester rolls around!

I'm particularly interested in improving my efficiency in regards to self-studying techniques, since I'm mainly teaching myself out of textbooks during the summer. Do you have any suggestions concerning this method of learning?

 

[wifi]

i try to prep for a test a week in advance, typcially rewriting my cheat sheet once while going through my notes, again after going through the book, and again after re working homework and examples.

i will spend a day just going over notes and making a consides sheet from those
another day going through the book and working out the example
and a day or two sometimes more) to re do all of the homework for that class, making sure the solutions match my solutions. i try to do all this a few days before the exam, so i can talk to the professor about discrepencies etc. well before the exam.

also, programming your calculator to have functions to plug values into is very helpful, for some of the longer equations that are used repeatedly. sometimes finding a program that can do what you need, like symbolic eigenvalues, vectors, are helpful, since my TI-89 doesn't come with a way of getting symbolic eigen values/vectors out of the box.

on the night before the exam and the day of i just try to relax. it is important to not panic if you don't know something on the test, and just calmly skipping it until you have time for it later let's you keep cool for the parts you do know.

most importantly, after the first mid term you will know how the professor likes to test. if you noticed that the teacher asked reworded homework problems, i would try to get homework solutions on my next cheat sheet for the next midterm/final. if they do derivations, put some of those on your cheat sheet etc.. for some of my courses the professor asked fairly difficult homework problems on the exam, so i just printed out the homework solutions really small and made sure i knew which problems were where so i could just plug and chug.

Thanks dipstik,

When you say "cheat sheet", do you mean essentially all the relevant info formatted concisely in one place?

 

[chipotleaway]

I read textbooks and watch the MIT/Yale lectures and then try to explain it all to myself both in writing and orally as if I'm trying to teach someone else. If something doesn't make sense or I don't 'intuitively' understand it, then I'll search the net or go on PF. I do the problems after I know I have a good understanding of all the concepts.

 

[dipstik]

Thanks dipstik,

When you say "cheat sheet", do you mean essentially all the relevant info formatted concisely in one place?

yeah, when you are allowed a page or 2 for the test. even when they say open book open notes i will make a cheat sheet. make sure it is well organized and you know where everything on it is. i typcially have to rewrite it a few times to avoid little notes in the magins etc.

 

[wifi]

I read textbooks and watch the MIT/Yale lectures and then try to explain it all to myself both in writing and orally as if I'm trying to teach someone else. If something doesn't make sense or I don't 'intuitively' understand it, then I'll search the net or go on PF. I do the problems after I know I have a good understanding of all the concepts.

I agree that being able to fluently explain a concept or idea is the keystone to deep understanding, but I'm having trouble attaining the self-awareness required to differentiate between memorization and true understanding (if that makes sense).

 

[Von Neumann]

I'm sorry for wasting your time :(

You're not wasting my time. In fact, I'm trying to help.

I personally believe that it's endlessly helpful to be highly critical of oneself - It's best to find the "holes" in your knowledge, as opposed to having another student or professor do so. Constantly question and go beyond what is asked in the textbook. Understand the motivation for concepts and ideas. If something doesn't make sense, find a different explanation online or from another textbook. Take different perspectives. Search for alternate solutions.

 

[wifi]

yeah, when you are allowed a page or 2 for the test. even when they say open book open notes i will make a cheat sheet. make sure it is well organized and you know where everything on it is. i typcially have to rewrite it a few times to avoid little notes in the magins etc.

I've never had classes that allowed the use of cheat sheets.

Although, I do find the idea of making one beneficial.

 

[andryd9]

Hi, Wifi.

I'm going to say something a bit different here. I actually start with the problems and work backward. I learn what each problem is asking me to do before I have any idea how to do it, and then begin to look through the text for clues. This can help with getting stuck on the import of text. Good luck:)

 

[chipotleaway]

I agree that being able to fluently explain a concept or idea is the keystone to deep understanding, but I'm having trouble attaining the self-awareness required to differentiate between memorization and true understanding (if that makes sense).

Well for me, if I understand something, I should be able to explain it and actually know what I'm talking about. Of course there's stuff you have to memorize (first principles) but the point is to 'intuitively' understand that so that when you learn other stuff, you can see how it follows from the first principles and you won't have to memorize all the extra baggage because you then should be able to derive it yourself.

 

[Aimless]

I'm probably not a good example to use, since I often skipped lectures, turned in late assignments, hardly ever studied, and was pretty much the definition of the lazy, unmotivated student - but I still managed to make it through so perhaps I can offer a counter-perspective regarding how I personally learned physics (since my experience was rather different from the conventional wisdom in this regard).

First, I found working in groups to be counter-productive. If I didn't understand something after reading the textbook or listening to my professor, I found that I was unlikely to come to any greater understanding talking with equally confused fellow students. Sure, if you bounce things around enough in a study group you might eventually, collectively be able to work out how to produce an answer to the problem at hand, but that doesn't mean that you, personally, understand all of the details of each step of the problem - which mean that when a similar problem comes up on a test you'll be out of luck.

Second, I'm not an auditory learner, so I often found lectures to be a waste of time (even for my graduate level courses). My goal in attending the lectures would typically be just to get my bearings on what material the class was currently covering, after which I'd learn the material on my own. Part of the reason for this is that I cannot learn things sequentially; I have to be able to see the big picture first before the details start to make sense (this is exactly opposite of the way most material is taught in lectures).

Third, for me, memorization was pointless. Again, this is because I can't understand something without seeing the big picture - without coming to grips with how it's interconnected with everything else I know. Memorizing the process for solving a single, individual problem never helped.

So, when I set about to learn something, I often followed a procedure similar to what andryd9 described. The first thing I'd do is look at the assigned problems and try to figure out exactly what I did and did not understand about each one. Once I knew what I didn't know, I'd start back-searching through the text looking for examples and relevant information until such time as I could properly anchor the problem to things I did understand. Then I'd reverse course, and start working forward (in other words, trying to solve the problem) until I got stuck, at which point I'd reassess things and start working backwards again. Eventually, I'd come to grips with what the problem was about and be able to solve it (and, in the process, understand how to solve an entire class of related problems). At no point in this process did I ever try to memorize formula or solution techniques (actually, for my undergrad level courses, I often tended to re-derive the necessary formula in the margins of the test if they weren't already given to us).

As for studying for tests, I didn't. (As I said, I was pretty much the example of lazy, unmotivated student.) If I didn't understand something after going through my process for solving problems, I was unlikely to come to a new understanding by cramming the night before. The only test I ever really made any concerted effort to study for was quals; my study habits there were to work through copies of past tests so that I knew what to expect, and then prior to each exam refresh myself on all of the relevant concepts. (I'll admit that I did some memorization of formula here, but that's primarily because, one, there was so much to cover, and two, I already understood the material, I just needed to refresh myself about it so that I had it ready come test time.)

The one thing I find interesting about this is that the process I used to solve problems as a student is the same process I still use today when working through papers and trying to understand someone else's research.