Quick questions on studying math and physics?

College Majors Science Majors
1

<p>So basically, I should spend time on thinking and applying what I've learned and do problems more so than just reading it right?
what do u think about these questions?</p>

<p>1) Is it more important to understand all the concepts presented in a specific textbook rather than worrying about every little word in the textbook right? How would I know that some concepts are presented in a textbook that isn't in another textbook though? </p>

<p>2) When would I know when to read/look at lecture notes besides just reading the textbook and which combination of textbooks to use on specific areas within in one topic? And which problems to do since there are different problems in every textbook or lecture notes?</p>

<p>3) What's the difference between all the same level, same topic textbooks out there if the concepts are the same? For example, Jackson and Schwinger, where both are graduate level EM books. </p>

<p>4) And also, is it necessary for me to master everything in halliday/resnick first of all? Or can I just pick up individual topics with individual undergrad level books in topics such as thermodynamics, waves, optics, etc. So far, my high school only uses the mechanics and em sections for physics C. And I don't think colleges really use the other sections of that book for topics like waves/optics/quantum mechanics.</p>

<p>5) Are Feynman's lectures as useful as a regular textbook? Or just a fun aside reading? </p>

<p>6) Does this advice apply to studying math as well?</p>

<p>thanks a lot.</p>

2

<p>any ideas?</p>

3

<p>1) You don’t look at just one textbook, no book is complete.
2) Do the assigned problems. Or find a webpage for a class that is using that book and do the problems assigned there.
3) Differences in approach, problem difficulty, writing style, etc. Griffiths for example often includes important points within problems rather than in the text. I hate Griffiths for this reason. One quantum text may include scattering, another may not. One e&m book may cover special relativity, another may not.
4) The physics GRE is 75% Halliday and Resnick level stuff, so it’s worth it to study as much as possible.
5) I’ve only read Six Easy Pieces and didn’t care for it.
6) Math is all about practicing.</p>

<p>Here is an article I was reading yesterday. The important part (for you) is the section about halfway down where he starts talking about idiot savants:</p>

<p>[Views</a> From An Affirmative Activist](<a href=“http://www.aas.org/cswa/status/2000/JANUARY2000/Georgi.html]Views”>http://www.aas.org/cswa/status/2000/JANUARY2000/Georgi.html)</p>

<p>My point is that many many physics books and classes are all about math methods and problem-solving methods for certain types of problems, but they usually aren’t about physics, per se. For example, get a copy of the book “Thinking Physics,” it’s full of physics brain teasers (there are many such books and I recommend buying them all). Studying physics formally didn’t always prepare me for those puzzles, because they aren’t about equations or formulae or solving for a variable, they are about what happens in the physical world and why. Books like that will do you more good at this point than rushing to get to grad-level texts, IMO. If you want to get ahead, just master Halliday and Resnick level physics and college-level differential and integral calculus. That would put you a year ahead of most other physics majors.</p>

4

<p>Thanks.

  1. Isn’t physics just about practice too though? How do you know which set of textbooks to use then?</p>

<p>2) I thought that picking up specific introductory texts was better than using halliday/resnick? For example, using kleppner and purcell, instead of using the mechanics/em chapters in halliday/resnick. Like, I don’t see a point in doing everything in halliday/resnick when there are better introductory undergraduate books in every topic. For example, like using shankar for qm. </p>

<p>3) I’m already taking multi/diff in high school at this point, so regarding studying physics, I should spend more time thinking and applying what I’ve learned rather than just reading the text right?</p>

<p>4) And so, understanding the concept is more important reading every single word?</p>

<p>5) Wouldn’t I understand the physics behind everything, unlike the idiot savant, as I read through the text and actually am able to do the problems? </p>

<p>thanks.</p>

5

<p>1) Solving certain types of problems involves a lot of practice, yes, but solving problems in physics texts and actually understanding physics are not necessarily the same thing. For example, the math involved in working with gyroscopic precession is not that bad, you’ll find the necessary math in a Halliday and Resnick-level text. The problems involved can get hairy but you can rely on the math to get you through. Now, that said, understanding the PHYSICS of gyroscopic precession can make you crazy. My classical mechanics text was written by a very good physicist at Harvard and he writes that trying to solidly understand it gives him a headache, and he can only really understand aspects of it. This is a non-relativistic, non-quantum problem, yet people still argue over the physics of it. Being great at the math is great but the real world is where the rubber meets the road. A lot of this may not make sense now.</p>

<p>2) Shankar is not an introductory text. It is suitable for an upper-level undergrad or grad course in quantum mechanics.</p>

<p>The qm found in Halliday and Resnick level texts is almost always a very mickey mouse version of things, since they can’t assume any linear algebra knowledge on the part of the reader (linear algebra is usually taken second year if at all), and linear algebra is the language of qm. Not that it’s not worth reading as an intro to basic concepts.</p>

<p>I don’t like Halliday and Resnick, for that level I prefer Physics for Scientists and Engineers, much better. However, Halliday and Resnick includes many good real-world example problems. Thing is, those problems come from the book The Flying Circus of Physics, which everybody should own.</p>

<p>Let me break it down in case it’s not clear. Physics majors take in their freshman year a sequence of intro calc-based physics, spanning intro-level classical mechanics, e&m, optics, wave. Halliday and Resnick and similar level books are for this sequence. Then they will take dedicated classical mechanics, e&m, etc. classes. Every textbook they buy for ALL of these classes will say “Introduction to…” Whatever on the cover. IT DOESN’T MEAN IT’S REALLY AN “INTRODUCTORY LEVEL” BOOK. You’ll see grad-level books that assume prior knowledge labeled as introductions, etc. I don’t know where they get the nerve calling themselves introductions, but it’s a tradition that nobody seems to care about.
3) Get solid on integral calc if you’ve already done differential. I’m assuming you’re solid on trig. Since you’ve done multivariable, next would come vector analysis, differential equations, and linear algebra. But studying real-world physics is great for building up your physical intuition. This could be books like the Flying Circus of Physics or it could be going to science museums and working on fully understanding the physics of the demonstrations. Theme parks are great for building up your physical intuition also. It may seem that studying a bunch of macroscopic non-e&m, non-qm, non-relativistic phenomena aren’t helping you in “real physics,” but by building up your understanding of things like force, velocity, acceleration, centripetal force, normal force, gravitational fields, friction, vectors (where forces are pointing, etc.), is all helping towards your understanding of all physics. Many e&m and qm phenomena have classical analogs, and understanding one helps you understand the other.
4) You already seem far enough ahead that worrying about your strategy of how to study RIGHT NOW is kind of pointless, spend more time looking at where you want to go to college, what kind of undergraduate research you may be able to participate in (right now, since high schoolers get involved in ug research too). Work out which classes you can skip with AP or CLEP credit, which ones you <em>shouldn’t</em> skip, etc.
I suggest taking up programming. Get a book on Python and start learning. I think that’s a more valuable use of your time at this moment than trying to figure out how to study upper-level texts. Why? Programming is becoming a skill that every physicist kind of needs. Even pure experimentalists need to make a program in LabVIEW or MATLAB every now and then, it’s not just theorists who program. Most of my class mates who do ug research do at least some programming, and often that is what they are primarily doing.
5) Well, put it this way, I took a semester of honors e&m and afterwards I didn’t know anything more about e&m than I did when I started. So what did I learn? Lots of math stuff, almost all vector analysis stuff for e&m with some differential equations I hadn’t seen before, some I had, and some other Fourier type stuff similar to what I’d done before. In principle, I could have known nothing about e&m <em>before</em> starting the class and still done well, since the whole class was math methods in e&m and I’d already taken vector analysis. Most problems didn’t rely on me using any kind of physical intuition.</p>

<p>It was all important stuff, I needed to have taken it, but it didn’t advance my conceptual understanding of the physical forces and phenomena in e&m very much. This is not true of every upper level class or text though.</p>

6

<p>lol sorry I should specify my background more clearly.
I’m going to Cornell in the fall and according to friends the math placement test goes up to linear algebra diff and multi.
I already took multi and differential equations so I was planning on studying linear algebra over the summer so I could start with analysis in the fall. As for physics I took physics C already so I’ll be taking waves and optics in the fall skipping mechanics and email.</p>

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<li><p>I thought that I should study more advanced physics. Like I’m in the middle of Griffiths email and I could understand it well enough to solve most problems on the problem sets for this tnx on lot ocw.is physical intuition really that important? I was just planning on reading Feynman lectures over the summer to establish a stronger foundation in general physics besides just mechanics and email.</p></li>
<li><p>Do contests necessarily determine how well you would do as a professor in the future? I’m not that good with contests like usapho and usamo. And math contests too like arml I didn’t have that much practice before junior year with math team type problems. Do these play a big role in the future if I intend on majoring in math and physics?</p></li>
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<p>Thanks a lot</p>

7

<p>Any ideas?</p>

8

<ol>
<li><p>Well, I think it’s important. Physics isn’t all about math. But building up an intuitive understanding physics takes time and can be done alongside learning all of the math. I don’t really know what else to say about this!</p></li>
<li><p>I don’t even know what you’re talking about. Usually, college admissions people care about what you did in high school but once you’re accepted nobody cares. When you are applying to grad school, grad school admissions people will care only about what you did as an undergrad (you may as well be a high-school drop-out that got their GED as far as they are concerned), but once you’re in grad school nobody will care. When applying for post-docs, people care primarily about what you did in grad school and maybe what you did as an undergrad (if it stands out in some way like some publications or your undergrad school has an impressive name like MIT) but your grad school work is far more important. I can’t imagine anybody caring about what you did in high school by the time you apply for tenure track positions (if tenure track positions still exist by that time).</p></li>
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<p>If, as you say, you’re already accepted Cornell, then your high school experiences (unless you flunk out) officially don’t matter to anyone anymore, congrats!</p>

9

<p>thanks.</p>

<p>1) The reason I asked about contests was is it a measure of your natural talent in mathematics and physics or is it mostly based off of practice and hard work? Like, I can do those problems, but I don’t have enough practice to be able to do it well enough for higher contests like usamo. Like how essential is natural talent in succeeding in physics and math like prominent scientists like Einstein or Feynman?</p>

<p>2) As for self studying, so basically, if you look at the problems and you can do them then that means that you understand the physics in the book right? And I just use a bunch of other texts to cover whatever topic is missing in one book that is in another? And the fastest way to do physics is to just finish a chapter and do the problems and move on gradually like that?
And if I want to like want to understand the conceptual idea behind it I can just side-read some other book?</p>

10

<p>1) You should really ask Einstein or Feynman! You can still be good, even great, even Nobel-worthy in physics without reaching their level. I heard a Nobel prize winner say words to that effect, so don’t worry.
2) Most of what you said is correct except like I said, a lot of the problems in these books are really math problems where some of the variables have constraints imposed on them by physics. You can be a wizard at the math and still struggle to really understand the physics, gyroscopic precession is a good example. Or quantum physics. The good part is that you can rely heavily on the math (my classical mechanics prof called it “flying by instruments,” like when a pilot flies in the clouds or in pitch blackness and has to rely entirely on instruments to know what’s going on). In qm, “shut up and calculate” is a motto some people have.</p>

<p>That said, from what I know about physics and its history, my opinion is that new theoretical advances require people with intuition and understandings (at least in part) of what is happening physically. Then the math can come later. Like Einstein was guided by intuition first of all, imagining riding alongside a light ray and what that would be like. Later, for general relativity, he had to go out and learn the math necessary, and a lot of other mathematicians and mathematical physicists helped guide him to his final theory. Even then, after publication, it took other mathematicians and mathematical physicists to do things like solve his equations and so forth.</p>

<p>My point is that there is plenty of room at the table for people who are very strong math-wise but weaker intuition/physical understanding wise, and there is also room for people who aren’t the best at math. Like Cavendish. IIRC, Bohr was supposedly nothing special at math, but he had a lot of ideas.</p>

11

<p>thanks. Just one more thing.</p>

<p>Is natural talent or hard work more important in the long run? I think I have more natural talent than most people, I can understand most things fast and apply them well enough, but then there are prodigies that either get where they are through their families with a lot of resources or money or they’re just the kinds that go to college when they’re 7. </p>

<p>When you go out and do research in math and physics fields, how would you prove to be better than everyone else? Is it just mostly hard work? And only a sufficient amount of natural talent needed to understand the material is enough in general?</p>