I'm a current physics major and considering whether I should minor or double major in math as well. Since I've heard that physics majors need to take upper-division linear algebra and analysis, and I'm currently taking a mulitvariable calculus course, should I be spending time trying to understand single and multivariable calculus through rigorous proofs?
I say this: A great biologist really knows chemistry... a great chemist really knows physics, a great physicist really knows math... what a great mathmatician knows... I don't really know. (and btw... I wouldn't even venture to call myself a great physicist.) That said... the more math you know the better. nowadays,with nano-tech, the more bio and chem you know the better...(geez, the more English you know the better so you don't have bad grammer on forums and can have intelligent conversations with non-scientists.) But of course, we all go brain dead at certain points.... I chose to minor in chem and math when I was in undergrad... and some of the math classes (boundary value problems, complex analysis) were really good...of course, my brain couldn't hold in those proofs very long (or any derivation for that fact), but the "thought-process" behind them is good to know... so try... but balance, (if you LIKE it, spend time on it).
In my opinion, one does not need to know the proofs by heart, just be able to use then if required. One of the powers of physics and math is that your skills will allow you to carry the proofs to end just by using your logics. Let's take an example. Although few people has memorized the derivations of the basic motion formulas for motion in 2D, most of them can combine them rather quickly and get the necessary version of it simply because one knows the math.
I think the better question is if you need to know the reasoning behind proofs. No different conjectures have the same proof. However, they might use similar reasoning to construct the proof.
You don't need to know "proofs" and in being able to derive them, as a physicist. However, you do need to know the range of validity of a particular mathematics, so that you know when not to use something. So in that case, you do need to have an idea of how something came about. Again, as I've mentioned repeatedly, if you want mathematics advice in becoming a physicists (or an engineer), I highly recommend reading the Foreword by Mary Boas in her "Mathematical Methods in the Physical Sciences" book. That book probably gives you all the basic necessary mathematics that you would need as a physicist at the undergraduate level. Zz.
I'm using that book right now for mathematical physics. The course is a pain, but very useful, since I'm not cluttered with math for the sake of math, like it seems to be mostly taught. Instead, I'm cluttered with math that directly applies to physics. If you have a course like that at your school, take it. If not, at least get that book.
yea i already have the book by boas so i guess i should focus more on that than trying to learn proofs.
I own this book. I found that was very difficult to learn from it because it was written with less proofs. Nonetheless, it is a very good reference book. I recommand A Course In Mathematics for students of Physics by Bamberg & Sternbery. The first volume is theory of maths, and the second volume is actual applications using topology and differential forms.
The short answer is no. A physics major does not need to know math proofs. You can absolutely get through physics with a knowledge of Calculus 1, 2, 3, Vector Analysis, and Linear Algebra and Differential Equations. A physics major should take partial differential equations too; one could list other math courses that a physics major "should" take, but that's the courses I would say should be necessary. I was a Physics BS and a Math BS and graduated with honors. I'm now in finance and working on an MS Finance. A physics major would greatly benefit from taking a course on proofs; these type courses are sometimes called transition to advanced math courses, analysis, or simply intro to mathematical proofs. I will say that as a student who completed over 180 credit hours at his undergraduate institution with courses in math, physics, chemistry, electrical engineering, computer engineering, organic chemistry, economics, accounting, finance, etc, the most useful course I ever took was my course that used the book How To Prove It A Structured Approach by Daniel J Velleman. It teaches you how write proofs, how to think, and inherently how to read proofs. It teaches you a methodical way of thinking. A similar course could be taken from a philosophy department; the math dept. does not have a monopoly on logic and proof courses. I would tell you to take a course on how to read and write proofs for you own personal benefit and knowledge, just like I would tell you to take a sociology course and history course - necessary information I would say! If you are a physics major, try to decide if you want to major in math. I did both, and it's challenging. I know you can do it if you want it! If you feel you will get a physics PhD and you know all you love to do is learn physics, I would go for a math BS too. But I have not met anyone as an undergraduate who fits that criteria. Maybe you are special. If you can complete a math and physics degree in four years, I would do it, but it will make your life much harder, you'll have less free time, maybe no free time, and you'll always be doing math work. I tell you I would do it because I have no regrets for having done it, and I don't even want to do a physics phd anymore. I would be "better off" now had I majored in accounting and economics with a math minor, but I loved math and physics at the time, and I needed something to cater to my ego to help me believe I was smarter than everyone else, and alas, math and physics did just that. By better off, I am implying that given my current goals, I would be closer to them had I studied accounting, econ, etc. But as I would say to my girlfriend when I was battling with whether to do a physics Phd or econ phd or medical school, if I were study econ, I'd probably be reading physics in my free time, just like I was reading econ in my free time when I was studying physics. Now that I've been out of undergrad math/physics for a while, I can tell you I love economics and finance, and that's what I want to do. When I was studying physics, I had trouble getting motivated to study E&M. I hated the text we were using. I had motivation problems not until my last year. Now that I am studying econ/finance, I am motivated again. I was this excited and motivated when I started in physics, but I think at this point, I can say with some confidence, that I will stick with economics/finance. I just like it. I may get a law degree, but only for the perceived job I may get from it; not because I enjoy studying the material like I enjoy economics.