Math Majors

<p>truthfully as possible…would anyone care to comment on two topics that I find troubling in the world o’ math.
(and please, please, please, lets not make this a Larry Summers discussion in any way)
I ask these questions in the spirit of true inquiry- and hope that the discussion can be as free of PC spin as possible.
First of all: I have the perception that math is rather less hospitable to women students.
and secondly: perhaps related to the first,
many math professors lack the language skills in english to instruct satisfactorily…making math study at a high level unnecessarily frustrating for students, and i suspect…for women students especially, for whom communication skills are often more important.</p>

<p>In response to sjmom2329 (since I don’t know how to quote on these forums), the answer to your question is that some of it is applied math and some of it is pure math, but it doesn’t matter in the least. A mathematics problem is a mathematics problem, and whether or not someone defines themself as a pure mathematician or an applied mathematician, whether or not they can solve the problem is much more dependent on their particular background in mathematics.</p>

<p>There are numerous problems that are considered to be “applied mathematics” problems because they are problems that come up in physics, chemistry, biology, computer science, etc., but at their heart they are mathematics problems. A physicist might have a problem and not have the proper mathematical background to solve it, so he’ll take it to a mathematician (pure or applied) and explain the relevant parts for them to solve it.</p>

<p>I participated in an REU this summer where we were dealing with a general relativity problem. Now, I haven’t taken a course in relativity (nor have I taken any physics courses since high school), and so I didn’t understand the physical implications of the problem. However, my background in differential geometry was enough for me to get some progress on the problem, and with the help of my teammates (who also have no physics background) solve the problem.</p>

<p>I might be in the same situation this summer. I’ve applied for a position at the NSA in which I would be in a group of 25 students solving unsolved problems for the agency. Some of these problems will likely be cryptography problems (although their exact nature is classified, and so even I don’t know what they’ll be until I’m actually at the NSA - assuming I get security clearance). But the fact of the matter is that we’re a bunch of college students and although we have strong backgrounds in mathematics, we are not experts in cryptography. I would imagine we’ll be briefed on the nature of the problems and given crash courses in cryptography to help us understand the problems, but we’ll really be doing a lot of pure math.</p>

<p>But at the same time, I was told that some of the problems are in algebra, geometry, analysis, number theory, and other areas that are more pure math. The NSA does have pure mathematics problems that it needs to solve. So does Wall Street. So does the rest of the world.</p>

<p>People seem to draw some big line between pure and applied mathematicians, when in actuality the difference in functionality is probably something few people realize. A typical pure mathematician can do the job of a typical applied mathematician at about 80% - they’re great problem solvers and they have a very deep background to help them, but they’re not quite aware of some of the implications of the math in the other areas. And a typical applied mathematician can do the job of a typical pure mathematician at about 80% - they are very specialized and have a great depth of knowledge in one area of mathematics, but they lack a broader background necessary for some problems.</p>

<p>Some people think that there’s a great divide between pure mathematicians and applied mathematicians, and that one can’t do the other’s job. This is completely false. Once you have the training in one area, if you want to go over to the other side of the fence, the supplemental education needed isn’t very much. And I would assume it’s much easier for a pure mathematician to become an applied mathematician; they would only need to get a basic education in the area in which they want to specialize, whereas an applied mathematician will have to get foundations in all areas of mathematics to have a good background, and that can be troublesome.</p>

<p>Again, my posts are turning out to be much longer than I have intended them to become. Summarizing, someone shouldn’t see a job that says “research” in the title and say, “But my daughter Suzie is a pure mathematician, and so there’s probably an applied mathematician out there that’s more well suited for the job. Suzie isn’t going to be able to get a job! Oh no!” Sure, an applied mathematician is more likely to get a job in a physics laboratory than a pure mathematician. But there are pleanty of places that are borderline that employ many pure mathematicians to solve their problems, and a student wanting to study pure mathematics shouldn’t worry that there won’t be a job for them any more than the next person (since we are in a time when there’s more and more college graduates and there’s more and more competition to get jobs).</p>

<p>Emengee, we are basically in agreement. My point was that there are few jobs, other than academia, which really are about “pure math.” As background, my H has a bachelor’s degree in pure math, and a master’s in applied. His employment hasn’t really been about pure math, i.e. solving equations or developing proofs, but his math background provides a framework for problem solving that has served him well. There are a variety of ways to use a degree in math, and it’s a wonderful way to develop analytical skills. At the moment, our older son is a physics major, who will probably double major in math. A strong math background can’t hurt in any field, even in areas like social science research or business.</p>

<p>Of course there are very few jobs out there that are “about” pure math. Other than academic institutions, there are very few places out there that will develop new pure math research just for kicks. We are certainly in agreement. I just wanted to press the issue for anyone else reading this that a degree in pure mathematics will get you very far in life, and there are pleanty of jobs out there that a pure mathematician can take. There are a lot of people out there that feel like a degree in pure math is a road directly to academia, and there’s nothing else out there for a pure mathematician. This is simply false, and I know that you agree with this, but I wanted to press the point so that anyone else reading the forum will take that message home with them.</p>

<p>My daughter majored in Math and is currently in graduate school. A good book to read for aspiring Mathematicians is “101 Careers in Mathematics” edited by Andrew Sterrett and published by The Mathematical Association of America. The book profiles 101 people who majored in math. It tells where they went to undergraduate and graduate school (if applicable) and what they are doing now.</p>

<p>Aside from the obvious ones (Stanford, Berkeley, Harvard, Princeton, Harvey Mudd, Cal Tech, MIT), which schools particularly stand out with respect to their pure math departments? And which schools for applied math? Are there schools that are good in one but not the other? Or does it really matter, with a math major pretty much the same wherever you go?</p>

<p>Why has no one brought up the fact that math majors don’t necessarily have to work in a math related field? I know of math majors working in completely unrelated fields, just like I know of history majors working in other fields. For what it’s worth, I believe I’ve read that math majors are among the highest scorers on the LSAT…</p>

<p>Pesto:</p>

<p>Chicago and Duke have great math departments. Duke came in third in the Putnam competition this year and did very well in the past two years. Among public unis, Michigan, Wisconsin, UIUC stand out.
Among LACs, some schools that have great math departments that will be very adequate for most undergraduates. Williams and Swarthmore come to mind.</p>

<p>Thanks, Marite. Chicago and Swarthmore were already on the list because of personality fit, and I thought I had heard Chicago’s math was good, but I wasn’t sure. The big public U’s are probably not the right fit, no matter how good. Brown used to have good applied math but I’m not sure how good the pure math is there – that’s also on the list. Someone has suggested that we look at Dartmouth as well, but again, I know nothing about their pure math. </p>

<p>I believe our sons were both at PROMYS last summer so that gives you some idea about the kind of math depth we’re looking for. Emengee’s discussion of applied vs. pure math has been very helpful as my S does not yet know which branch of math is more his cup of tea.</p>

<p>I probably have links somewhere to discussions of math schools on CC before this, but I don’t think they get into the distinction between pure and applied math. If anyone has any other suggestions, that would be great.</p>

<p>The University of MD, College Park has a very strong math department as well.</p>

<p>:)</p>

<p>Chicago’s math program is one of the best in the country. :)</p>

<p>I will be attending Chicago next year, and math as a major is definately an option, though classics and biology are there, too. I am sure the toughest of the three subjects will be weeded out, but none are easy.</p>

<p>Pesto: One thing to note is that Brown has separate pure math and applied math departments (I’ll be starting as a graduate student in their pure math deparmtment next year). Since your S doesn’t seem to be sure if he prefers pure math or applied math, you should look into the programs and see how everything works. Just looking at the website gives me the impression that it’s easy to major in one and take courses in the other. I would definitely assume that since your S would have two full departments from which he can pick courses, it would be a great place for him to be.</p>

<p>And as far as how good the program is, although they do not rank undergraduate programs in mathematics, their graduate programs are both in the top 30. I think applied math is in the high teens and the pure math is in the mid to high 20’s. If you’re looking for anything ranked between 10 and 40 or so, how well the student fits with the school is probably more important than minor differences in rankings of programs. Although the results of college are extremely important, the time spent at college is probably even more important.</p>

<p>Thanks, emengee, for all your posts on this thread. They have been incredibly helpful.</p>

<p>i’ll be interested to see the responses. I intend to major in math</p>

<p>I was a pure math major and found it great preparation for law school.</p>

<p>Thank you this information is great. My son is a junior this year who plans on majoring in math and would also like to minor or double major in music. This will help us as we begin our college search.</p>