<p>Haha, no problem Acere, gotta stick up for my fellow math majors ;)</p>
<p>And I agree with Ken285. To tell you the truth, I don't even care if other majors are harder or easier. I like my major, and I'm happy. It's only when people put your major down and tell you you'll never get a job with it that you get defensive, and feel the need to say why yours is better. Hell, I even get defensive when people tell my friend who's majoring in English Writing she'll be living in a cardboard box. She's a damn good writer, and I'll be the first in line to get her books signed when she gets published.</p>
<p>Shackleford, definitely take some more advanced math in graduate school. Go for some kind of algebra - it's an awesome departure from Calculus and analysis, and in my opinion it gives you that same fulfilling starting-from-scratch feeling as analysis does (then again, if you don't like that starting-from-scratch feeling Number Theory is pretty awesome too!).</p>
<p>Since we seem to be going on a tangent, I'll take the opportunity to say, ultimately as a field of study math (pure) will never be as challenging as physics.* And to those who keep on saying "physics is applied math”, you would be partially right if you meant physics was applied math and wrong if you meant physics is a subset of math. </p>
<p>Please tell me where in math the foundations to problems such as nuclear energy, gravity or jet propulsion lie. Math is a tool/language used by physicists, nothing more and nothing less. It is used by them to explain things in detail, to defend/prove what they say and serve as a common ground in logically sharing their ideas. </p>
<p>If someone says something in the pure math world all they do is write down the proofs. If everything is logically and mathematically sound, that’s the end of the story. If that was true about physics, Stephen Hawking would probably be one of the greatest scientists ever -- he is not. There are just too many people trying to put holes in what you say and too many ways to disprove it, not least in a lab.</p>
<p>There are many un-answered questions in physics because they truly are very difficult ones.
At the end of the tunnel, you will find that pure math is nothing more than art, in which case you can make the argument that da Vinci found it more difficult to produce The Last Supper, than he did trying to build any of his flying machines.</p>
<p>*This is not an argument about under-grad programs.</p>
<p>I disagree with your characterization of math as easy.You say that "in the pure math world all they do is write down the proofs." When you put it that way, of course it sounds easy. The fact is that proofs don't just throw themselves in front of you. Fermat's Last Theorem wasn't proved for over two centuries, and there are still many unsolved problems that are just as elusive for mathematicians today.</p>
<p>In fact, the proof process is much like what you describe for physics. Proofs at the level of math being discovered now are not simple ones found in the math textbooks you have seen so far. Actually, they are closer to the length of your textbook. Many are hundreds of pages. Nobody just accepts them after one reading, though of course they'd like to. Mathematicians review and criticize each other's work in order to throw out the flaws in the proof and get the solution down to the most elegant form possible. The way we go about showing our results may be different, but the process of accepting the results is pretty much the same. (Besides, knocking proofs is a dangerous move for a supporter of a subject that has completely empirical results and nothing more).</p>
<p>And I can't stand when people say math is just a tool for sciences. You are closer when you say that math is art. But to say it's nothing more is just wrong. Art can only beautiful. Math can be both beautiful and correct. Math is more like formalized thinking. It really is behind everything you see and experience. Sciences, being the study of specific areas of the world, can't help but employ the math found in those areas. Math is a consequence of choosing to study physics, not a choice by physicists to solve their problems.</p>
<p>One prerequisite for me in grad school is Intro. to Complex Analysis. How hard will that be?</p>
<p>Also, since I am a physics major, what advanced math do you recommend? I believe tensors (used in relativity) are covered in Abstract Algebra? Maybe?</p>
<p>I haven't taken that yet, but I hear that it's pretty difficult. It's basically redoing Real Analysis to include complex numbers, so if you remember how much complex numbers can botch up other subjects you know how complicated this could get. But I also hear it's an area that's really popular in contemporary research, so it could also be really interesting.</p>
<p>I haven't herd of tensors in mathematics, and I'm not sure what they are in Physics, so I can't answer your second question. Sorry.</p>
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Again, someone explain to me how do engineers/physicists have the same mathematical knowledge as a math major when all engineers/physicists have to take is calc1-2-3, differential equations and (sometimes) linear algebra. This is without taking into account that they may take some other math classes as electives but the same argument can be said with a math major taking engineering/physics electives. (which i am).
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<p>I don't recall anyone ever actually making that assertion.</p>
<p>Nevertheless, most engineers (and physicists, I'm sure), even in undergrad, learn (and use) a lot more math than you give us credit for. For one, there's probability theory and statistics - which is usually taken with the math department. </p>
<p>Mostly though, we learn a considerable amount of math in our engineering courses. Sure, I never took the math department's course in Fourier Analysis, but I assure you after three signal processing courses, I have a pretty firm grasp of the subject. Yes, I never took the math department's course on Partial Differential Equations, but I have some understanding of it (and its applications) after taking my Electromagnetics and Modern Physics courses.</p>
<p>But again, I don't buy into the idea the difficulty of a subject is determined entirely by its mathematical complexity (e.g. if this were so, law would necessarily be "easier" than accounting). I'm just trying to clear up some misconceptions math majors may have of engineers.</p>
<p>My Physics teacher told me that most of mathematics was derived from Physics experiments, discoveries, etc. e.g. Newton invented (I like to think discovered, but w/e) calculus to prove the motion of the planets (that is true, right?).
And plus Physics is Math + other stuff; Math is just math... Therefore Math is a subset of Physics.</p>
<p>Your physics teacher is wrong. This may have been the way things were in the 17th century, but it's the 21st century now. Pick up a standard graduate math text and see how much of a role the material plays in physics. Nowadays, the math is developed about 30 or so years before it actually finds application. For example, differential geometry was greatly criticized before its role in general relativity was found.</p>
<p>I think math and physics are of about the same difficulty, although math requires a mind that can handle more of the abstract. The people who say that math is easy are simply ignorant and haven't seen pure math. This is understandable, I suppose, since most undergraduate departments of mathematics tend to create their courses so that they can be easily applied to other areas. Earlier this year, we learned fourier analysis on arbitrary locally compact abelian groups, in particular p-adics. Anyone who claims that math is easier than physics hasn't seen this.</p>
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One prerequisite for me in grad school is Intro. to Complex Analysis. How hard will that be?
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<p>Not terribly difficult as long as you know real analysis well. I have heard complaints from people who couldn't greatly understand residue calculus, but I really didn't see where their points of complaint were. Complex Analysis is rather easy, though, if you know power series well, since all holomorphic (i.e., complex differentiable) functions emit a power series expansion, unlike the reals.</p>
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Also, since I am a physics major, what advanced math do you recommend? I believe tensors (used in relativity) are covered in Abstract Algebra? Maybe?
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<p>Tensors are covered in differential geometry, and at a more abstract level than you'll ever see in physics. Tensors are (very) roughly multi-dimensional analogs to linear transformations. Let V be a vector space and let f be a map from V^k to R. We say that f is a k-tensor on V if f is linear in each variable, i.e. multilinear. Physicists deal more with tensor fields than anything, so the mathematical area of tensor analysis tends to a bit more abstract than what is used in physics.</p>
<p>You're right in a sense. Much of math was invented to help solve physics problems: problems whose solutions couldn't be found until that math was invented (i.e., physics being built upon math).</p>
<p>"And plus Physics is Math + other stuff; Math is just math... Therefore Math is a subset of Physics."</p>
<p>Your set theory is a little weak (maybe not used much in Physics courses?). A set is a subset of another set if everything in that first set is also in the second set. Not all math is used by physics, but all the math that physics uses is (prepare to be surprised) math. If anything physics is a subset of math, but I don't believe it's that easy.</p>
