Mathematics Major

College Majors
1

<p>I am very interested in majoring in math. Whenever I have free time, I take make up integrals and solve them or I take out my calc book and learn new stuff. I don't think I like applications as much as I enjoy solving a problem for the heck of solving it. Can someone out there help me differentiate between applied and general math? Also, I'm concerned that as a math major I won't have the opportunities to grow financially as a business major, or an engineering major could. If I do major in math, I want to go to graduate school. How would going getting a doctorate in mathematics as opposed to going to med school or business school affect me? What are the opportunities that one has with a PhD in mathematics? Where can I work? What would I do? (Also, I don't like the idea of teacher or professor)</p>

<p>Thanks much :)</p>

2

<p>I am a Pure Math major myself. Im a Junior right now.</p>

<p>The difference between Applied Math and Pure Math (General Math) is that Applied Math focuses on the applications of math in the real world while Pure Math focuses on the theory and the abstract part of it.</p>

<p>I too, hate applied math. It just seems too dull, boring and in reality, Applied Math is Pure Math but dumbed down for its applications.</p>

<p>Also, I'd like to touch a little part regarding math. First of all, all the math you have seen up to now has nothing to do with Pure Math. What im trying to say is that when you finish with the easy classes such as Calc1-2-3, Differential Equations, etc. Math takes a very sharp turn and goes to be all theory. In my opinion, I loved the sharp turn and I enjoy theoretical math. </p>

<p>Many people will come to this post and say how the math you have seen up to now is VERY different to real advanced math (which i just did) but dont let that discourage you. You have to try it by yourself and see if you're cutout for it. Theres no other way.</p>

<p>When I was in High School, I was always fascinated by math and I was told how the math I was doing in High School is no way near advanced math. Anyways, I decided to be a math major and try it out by myself. Turns out that advanced math is way different than anything I did before, BUT I really enjoy advanced maths so like I said before, theres no way to tell but to try it.</p>

<p>So, the fact you like tackling Calculus problems (such as integration) etc, is a good indication that you may like being a math major. However, that doesnt mean that Pure Math is for you, BUT it doesnt mean it isnt either. If you get what I mean?</p>

<p>If I wasnt clear, just say so.</p>

<p>Hopefully someone else will touch on the other questions you asked.</p>

<p>Note: Being a Math major rocks. You get this big respect from ALL other majors. lol.</p>

3

<p>Acere's post is really good, and I agree with pretty much everything what s/he said.</p>

<p>I'm almost done with my freshman year as a math major, and so far I have really liked it. I haven't taken much advanced math yet, but here's my suggestion.</p>

<p>After you're done with classes like calculus (or "easy classes" as Acere have described), I'd strongly advice you to take a class that uses proofs at more of an elementary level (i.e. the class that actually teaches you how to write a proof). For example, I took elementary number theory (mathematical field that deals with integers) this term, and although the materials themselves weren't too difficult, it is still relatively challenging (but not INSANELY challenging) if you're exposed to proofs for the first time, and your professor knows that you're writing proofs for the first time, so s/he won't get mad at you if you can't even solve a simple stuff. This way, I think you're far more confident in writing proofs when you get to take advanced math classes, such as analysis, abstract algebra, topology, and etc. Your school should offer a class like this; I'd look for classes that have names like "Introduction to proofs" or "Discreme Math" (which is also a good course if you're thinking of computer science). </p>

<p>And as I've mentioned, I haven't taken a lot of advanced math classes yet, so I might be wrong.</p>

<p>Also, you might want to take a look at this topic; this might answer some of the questions you've asked (but probably not all of them): <a href="http://talk.collegeconfidential.com/other-college-majors/506851-mathematically-inclined-looking-some-info-majors.html%5B/url%5D"&gt;http://talk.collegeconfidential.com/other-college-majors/506851-mathematically-inclined-looking-some-info-majors.html&lt;/a&gt;&lt;/p>

<p>And being a math major does rock. You get this weird stare from people whenever you tell that you're a math major, like "WHY??? I HATE MATH!" And I'm starting to enjoy that :)</p>

4

<p>NorthWestLover's is also full of wisdom. By the way, im a "he"! :)</p>

<p>Here's something I was thinking about. If you like math, even if you dont do a pure math major, chances are that the major you choose will be science oriented and therefore the major's requirement will require the first math classes (such as the calculus series, diff eqs, etc). So you can't go wrong taking those classes even if you're unsure of which specific major to go into.</p>

<p>NorthWestLover mentioned something very important. Most universities have a class that basically introduces you to advanced mathematics. taking that sharp turn from applied to theory. In my university, the name of such class is "Introduction to Advanced Mathematics", I have talked to other math majors from other universities and the name varies, such as "Intro to Proofs" its all the same class. This is the class that will tell YOU if you like pure math or not. If you dont, there's nothing bad about it, not everyone is cutout for it. You always have the chance to go the physics (or similar) route and still apply your math skills. Anyways, like I said, this class will let you know what advanced mathematics is really like. It will talk about many diverse and fun topics. It wont go in dept but it will touch many topics such as predicate logic, set theory, relations, induction, sequences, proofs, functions as relations, cardinality, real number and limits, etc. As you can see, this is a very diverse class. After this class, you WILL know if pure math is for you.</p>

<p>About being a math major, it does rock but sometimes you get too conscious of it and get cocky (i do) but what the hell, after all, im a math major. (haha im joking :) )</p>

5

<p>I'd recommend all math majors to pick up a minor or a double-major. The reason is that pure math does not really teach you a lot besides various "thinking" skills. A second concentration in e.g. business or computer science gives you a background in a subject in which you can apply all the problem-solving and analytical skills you have acquired in your math classes and will come in very handy if you eventually want to work right out of college. Many students decide that they need a break from school after college and work for one or two years before going to graduate school.</p>

<p>I really encourage you to consider a math major, but I will discourage you from assuming that you will get a PhD in math before you have taken your first theoretical math class.</p>

6

<p>Thank you. Thanks a lot to all of you, I learned some stuff I wasn't even looking for because I wasn't aware of the difference between high school and college math. One thing intrigues me though, if the math is so different, what is the math that we learn in high school used for in college (the calculus, diff eqs, etc)?</p>

7

<p>I think you might be misunderstanding what people mean when they say that math is different. Math in college is different mainly in its approach to the subject. For example, one of the first tasks of a real analysis course is to go back and rigorously prove all of the concepts you have learned in your calculus courses. I'm betting your book glossed over the proof of the intermediate value theorem. In analysis, you will use facts about continuous mappings and connected sets to prove this theorem. Linear algebra, on the other hand, builds on what you learned about systems of equations to develop a general theory of linear operators. There are a wide range of topics in college level math: algebra, analysis, topology, number theory, etc. The one commonality which sets these topics apart from high school math is the concept of mathematical proof.</p>

8

<p>Weasel sums it up pretty well. Just to hint at the rigor behind the proofs, I would like to mention that real analysis does not just prove the stuff you learned in calculus. You go back even further, proving stuff we take for granted about numbers. How can one go about defining the real numbers? Can we be sure that every root of a positive real number is again a real number? Answering these questions involves a lot more work than one might think at first glance.</p>

9

<p>For PHD Mathematics majors, the starting salary at various investment firms and hedge funds is in the 150K-200K range.....FYI</p>

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<p>Could you provide a source?</p>

11

<p>Wegmanstuna,</p>

<p>Do you have a source?</p>

<p>Even according the US BLS, the top 10% of Mathematicians made $132,910.</p>

<p>[url=<a href="http://www.bls.gov/oco/ocos043.htm%5DMathematicians%5B/url"&gt;http://www.bls.gov/oco/ocos043.htm]Mathematicians[/url&lt;/a&gt;]&lt;/p>

<p>I'm not sure if Financial institutions automatically grant mathematicians "associate" positions--which could explain the salary range.</p>

12

<p>Mathematicians who have useful knowledge easily make more than that at hedge funds but quant positions are VERY competitive. I dont think its a good idea to get a phd in math if that's your only goal.</p>

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<p>Here's just a random example of an opening at an investment bank for a PhD holder: Model</a> Validation Quant- U.S. Investment Bank/ New York - New York</p>

<p>To be quite honest, I was even being moderate when I gave the last salary range for a PHD in finance; it could be more like 500K if you really know your stuff. That said, there is a trade-off and that is the 5 years or so that it takes to earn a PHD. I think someone said earlier, that shooting for a PHD for finance is not a wise decision. It would be much more lucrative for one to enter finance right after undergraduate. Case in point, however, is that there are very lucrative opportunities for PhD’s other than doing research and/or teaching.......</p>

14

<p>ive done linear algebra and induction in my HS. I really like them and yes there totally different from Calculus. Pure Math Rox lol</p>

15

<p>INTERESTED IN MATH? Oh lord :)</p>