<p>What kind of person does applied math compared to the kind of person that does pure math? I’m confused about this distinction and am wondering what career paths/opportunities are characteristic of each.</p>
<p>Applied Math = the first three dimensions
Math = the rest.</p>
<p>That’s the best explanation I ever got. The courses should really help to differentiate the two, check them out on Mocha-- [Welcome</a> - Mocha](<a href=“http://brown.mochacourses.com%5DWelcome”>http://brown.mochacourses.com)</p>
<p>Applied math focuses more on how the concepts are used in subjects like physics, econ, biology, computer science, and so on, as well as fields such as insurance (statistics and probability are big here).</p>
<p>Pure math is less interested in making connections to how the concepts will be used and more on generalizing the concepts. To an extent, one may say it’s “learning for learning’s sake.”</p>
<p>So it depends on your interests and how abstract you like things. I took statistics within the applied math department (APMA1650 and APMA1660) rather than in the math department because I felt that’s one topic I’d be more interested in applying. On the other hand, I’ll take differential equations (MATH1110) in the math department instead of a comparable course in the applied math department because I have no real interest in methods to approximate solutions for physical sciences.</p>
<p>As modestmelody said, Mocha may help you the most here. I feel that one can, by the nature of applied math, find a wider variety of career options, but it also depends on where you focus (partial differential equations? statistics? computational biology?).</p>
<p>i’m interested in AM-econ…is that looked down upon by people double concentrating in econ and math or by the mathematical econ concentrators (or more importantly, graduate schools and employers) as less rigorous or just different?</p>
<p>The ScB seems to be the equivalent of an AB in each of Applied Math and Econ. So from that standpoint, it seems you’d be losing a bit of depth in applied math to gain a broader view on the concept. It’s not as rigorous as an Applied Math or Math ScB, but it’s more rigorous than an AB in either. The AB program is a bit lighter but gives you more freedom with other courses. I feel that it’s more what you make of it and what else you take to complement it than the name of the concentration. For example, many grad schools that I’ve looked at don’t care about the name of your degree nearly as much as your background.</p>
<p>So I’d believe that it’d be more along the lines of “different” than less rigorous, but maybe others could give an opinion?</p>
<p>Sounds like I would definitely be more interested in an ScB, then, which is what I’ve been thinking. If I did go to graduate school, it would either be for a Ph.D. in Economics (or perhaps, though less likely, Finance) or an MBA, so in that case, would AppliedMath-Econ with additional Applied Math classes (to compensate for the comparatively reduced rigor of the concentration) provide enough background to impress top Economics graduate programs? If I did choose that path, I’d want to be competitive for top places like Harvard/MIT. So would that be an optimally viable option, or would perhaps mathematical economics suit me better? I’d also like to keep open the option of working in finance post-graduation, and the computing classes in the AM-econ concentration do a nice job integrating CS into the curriculum, something that might be left out in Mathematical Econ. Is the middle ground here just a personal, customized form of either of these concentrations? Or do you guys have any other suggestions?</p>
<p>First of all, when examining all choices you make, employers and graduate schools are not looking for the same thing, so lumping them together is silly. </p>
<p>Applied Math is not “looked” down upon. Applied Math is, as its name suggests, more practical and applicable. On the contrary to being “looked down” upon by employers, it might be more valuable to you than pure math, which gets theoretical. </p>
<p>One of my best friends is a brilliant math wiz(Intel Finalist) and he doesn’t have much interest in Applied Math and prefers pure Math. But he’s not actually aiming for employment. He’s looking to go to become a professor in Mathematics someday. Apparently once one delves deep enough into pure Math you start to understand it on a level that can’t really be explained or grasped by those who have not. </p>
<p>So, in terms of employers: Depends what kind of job you get–but I imagine that applied math might be more useful and applicable. </p>
<p>In terms of Grad School: This simply depends on whether or not you want to go to Grad School for Math or Applied Math.
If you meant Medicine/Law/Business School, then really it’s not going to make much of a difference for admissions, though you might find applied math, again, more useful.</p>
<p>ETA: Okay you updated while I was updating mine so, in regards to your newer post:</p>
<p>1) If you want to go to Grad School for Econ…get a degree with Econ in it (whether Econ alone or Applied Math-Econ) and make sure to do research with it.
2) If you’re shooting for an MBA, then choose whichever you like better. Don’t worry about which will be more impressive–worry about which ones you enjoy more and which ones you’ll do better in.</p>
<p>Just my two cents and iterating on what everyone has said thus far:</p>
<p>I have not taken any APMA courses. But Math is fairly theoretical here after you are done with Calc 3 (It can get theoretical here if you take 200/35 but mainly 35). I honestly would try to take a good mix of Math-APMA-Econ courses if you are trying to goto grad school for this kind of stuff. I love Math here because you really get a chance to think about the proofs, why things functions they way they do. And in reading period (a week - or two off to study for your finals) you can really spend time mastering the subject at hand. Math here teaches you how to think in an abstract way (versus the plug n chug, memorization found in earlier math courses). I think taking all APMA courses might make you good at plug n chug but you may miss the complex machinery running everything-which is math- behind it.</p>
<p>So in short math is good here because you can understand why things function the way they do, and then you can learn how to change the “program” to fit your needs.</p>
<p>Don’t forget to sign up for a few courses in english and writing too. You don’t want to be out there discovering all these new beautiful things and not have a way of clearly expressing your inventions.</p>
<p>are there any MATH courses in particular you would recommend for their ability to hone this understanding of proofs? I already took multivariable calc and linear algebra and we spent basically 0 time covering proofs, so what classes are you referring to?</p>
<p>Well I am going to assume you are in high school. Just sit in (shop) Math 52 regular linear algebra, and Math 54 honors linear algebra (shop atleast 2 classes) and look at a problem set. I feel that Highschool math is very different from college math in the sense that the teachers are trying to get you to think like an actual mathematician. (And no proofs in linear algebra? what the hell ??).</p>
<p>The short answer is “both”. Anyone interested in hiring you for math skills (of the kind used in economics, finance industry or such) will be interested in whether you have the mental infrastructive and problem solving background from the theoretical courses, and also in your ability to program computers and use standard software tools. With that said, you have to evaluate applied math programs carefully because many of the curricula are far out of date. Pure math is more flexible but will not leave you with much of an ability to compute on real world data sets. Math and computer science combination doesn’t touch numerical or scientific computing all that much. So you might need to pick and choose to fill out your background omnivorously.</p>
<p>Math and Applied Math are separate departments at Brown, but down the street from each other. Applied would have some overlap with CS , CogSci, and others.</p>
<p>Given that I’m an AM-Econ concentrator, and that I’m going to grad school doing more or less the same thing, I’d say that your major’s denomination matters less than what courses you’ve taken to demonstrate depth of knowledge and interest. Between AM-Econ, CS-Econ, Mathematical Economics… they all try to give a more quantitative introduction to Economics, and each can be a successful path to all the options you have mentioned. To be honest with you, I think you’ll get things figured in due time, but not necessarily right now. Shop around, compare classes, see how you perform in them and then adapt your interests/expectations.</p>
<p>By the way, if you’re done with your calculus + linear algebra sequence, MA101 is an excellent way to get a rigorous introduction to write proofs (and just about any courses in mathematical analysis).</p>
<p>As mentioned above, Math 52 and 54, linear algebra, (more 54) and 101, real analysis, (which is recommended before taking any higher level courses, especially for freshmen) would help working with more rigorous proofs. Even in APMA1660, we did do some proofs, though not as many as one would have done in the pure math equivalent.</p>
<p>I did multivariable calculus and linear algebra in high school, and while I was told I wouldn’t have to, I plan to take honors linear algebra next spring, just for the experience.</p>
<p>Uroogla: This is something I’m debating - whether or not to take the honors calc / linear classes. I’m a prefrosh right now and just finished an analysis class. I did multivariable last semester and am doing linear algebra as a distance course right now. I really dug analysis and am liking linear, but multivariable wasn’t my thing. Then again, maybe I would like it if explored from a more theoretical angle.</p>
<p>justwondering09:
If you decide to take multivariable calculus again, you’d want to take 35, which is supposedly more theoretical, though not as much as 54 is. If you plan to concentrate in math (or anything that requires multi and linear as prereqs), unless you can get credit from the institution at which you took them as distance courses, it seems that you would instead need to take a course that shows an understanding of the material. I’m wary about taking abstract algebra before a solid, theoretical linear algebra course, thus my decision to take 54. My high school class covered some topics, but I got a thorough enough understanding of linear that I was able to assist a friend in 52, despite having never explicitly covered some of the topics. I’ve heard that 35 isn’t as good a course as 54 is, and any analysis course, as well as differential equations and partial differential equations would demonstrate competence in the subject (according to the current head of the math department). However, with your interest in analysis, it might be good to ensure you have a solid foundation both on the concepts of multivariable calculus and on proof techniques and the way of thinking needed for higher level analysis classes.</p>
<p>I have a friend who did not take either multi or linear here, and started in 153 (abstract algebra). He did alright in the course, and it was less the concepts from earlier courses that were needed than the way of thinking.</p>
<p>So I advice you to talk with the math department (and take what they say with a grain of salt), shop 35, 54, or both and get a feel, and consider registering for 113 (complex analysis) or 101 (real analysis). The latter may be boring for you, though it’s recommended for students before taking a higher level course, particularly in analysis. It comes down to how comfortable you are with the material and with proofs and abstraction.</p>
<p>I’m a prefrosh considering majoring in math. I haven’t done anything past BC Calc, so I’ll obviously be taking Multivariable/Linear Algebra next year. I’ve heard that it’s a good idea to take 54 if you’re going to major in math, so would I be at a serious disadvantage in 54 if I take 18 instead of 35? (Although I love math and like the look of 35, I haven’t had much in the way formal proofs yet. I’m worried that class would probably be too heavy-handed for me.)</p>
<p>Neither linear nor multi are dependent, so from the standpoint of concepts, either 18 or 35 is fine. With that said, I believe 35 would be helpful towards 54. 18 isn’t likely to get you much experience with formal proofs. While 35 may be on the difficult side, 18 won’t really help you with preparation for 54. It depends on what other courses you’re considering taking, but Brown supports exploration and challenging oneself through its Open Curriculum. There are worse things than being in a course that’s a bit too challenging, because one can argue (and people have) that one learns more through doing poorly than through doing well (more about oneself, at least).</p>
<p>I’m not in high school. I just finished my freshman year and might transfer to Brown next semester.</p>
<p>My linear algebra class was crap, to summarize. Though my previous school is really well regarded, the class was called “Introduction to Linear Algebra and Differential Equations” and focused almost entirely on computations. We spent 2/3 of the semester on LA and 1/3 on DiffEq. Because it was so rushed, no one got a really good understanding of the material and would just cram the night before, memorizing how to compute null spaces, etc. without really understanding what we’re doing. So, I could probably get credit for linear algebra technically, but I’m wondering if it would be worth my while to retake the course, maybe Honors Linear Algebra at Brown to provide a better foundation? Is a strong foundation in this class really important, or would it be better to just move on with Differential Equations and APMA stuff?</p>
<p>Thank you, Uroogla! Just out of curiosity, do you happen to know which textbooks are used for each course (18 and 35, that is)?</p>
<p>airbag:
The introduction courses within the Applied Math department cover some linear algebra from a more numerical standpoint, so if you’re worried about the basic concepts, those would be covered in APMA0350 and APMA0360 (0r 330/340). If you want a broad theoretical perspective, MATH0540 would be decent, but this likely wouldn’t help you too much unless you wanted more pure math courses. This coming fall, the differential equations textbook focuses a lot more on linear algebra; in a case like that, it would likely help, but I’m taking this course before honors linear. 52 would likely not be that much better than any course you’ve taken; it might be a bit more theoretical, but it is designed to keep in mind that most students will have trouble with proofs. Differential equations are fall only, while honors linear is offered fall and spring, so you would have time to consider. One can make an argument for taking 54 and not taking it; it comes down to a question of what your personal goals are.</p>
<p>thefunnything:
This spring the book used for 18 was [Amazon.com:</a> Calculus: Early Transcendentals (Stewart’s Calculus Series): James Stewart: Books](<a href=“http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts/dp/0495011665%3FSubscriptionId%3D04MMFA32FTGTSY3WJGG2%26tag%3Dmocha01-20%26linkCode%3Dxm2%26camp%3D2025%26creative%3D165953%26creativeASIN%3D0495011665]Amazon.com:”>http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts/dp/0495011665%3FSubscriptionId%3D04MMFA32FTGTSY3WJGG2%26tag%3Dmocha01-20%26linkCode%3Dxm2%26camp%3D2025%26creative%3D165953%26creativeASIN%3D0495011665). I do believe 35 uses a different book, though. 20 (which is for physicists and engineers) does use a different book. For some courses, the books change depending on the year and professor, but I don’t believe 18 (or 35) would change very often.</p>