<p>Hello people! This is my first post. I need some advice for my minor. I intend to do my major in Economics and minor in mathematics. How do you evaluate it? What are the advantages/disadvantages of this?What kind of career is possible for me after undergrad?would math minor be an advantage for grad school?</p>
<p>I was wondering this too. What weight do minors have? (Do law schools care about them? Say...a double/triple minor) And pros/cons of math minor vs. accounting minor.</p>
<p>I think it's a good idea, and a common plan to major in economics and minor in math. Actually, I can't think of something better to minor in for an econ major. I think grad schools in economics would be a lot happier seeing someone who can stomach some math, because grad schools tend to emphasize research and theory, and a math background is essential for economics theory. However, if you just want a job, I'm sure you could make it without math. I would view a minor as healthy supplementing; but be sure you have some interest in mathematics before you do the minor - econ at an undergrad level requires very little math on average, and not everyone WILL stomach the mathematics.</p>
<p>I think law schools do like to see minors and such, but mainly be sure to have a good GPA. Beyond that, I won't say anything, because I'm not that knowledgeable.</p>
<p>You should definitely consider at least a math minor (if not a double-major) if you might want to go to graduate school in economics.</p>
<p>
[quote]
6. Recommended for Majors Interested in Graduate School in Economics
Math 115 (Calculus I)
Math 116, 116z or 120 (Calculus II)
Math 205 (Intermediate Calculus)
Math 206 (Linear Algebra)
Math 210 (Differential Equations)
Math 302 (Elements of Analysis I)
Econ 303 (Mathematics for Economics)
Econ 317 (Advanced Econometrics)</p>
<ol>
<li>Typical Math Background of Recent Applicants Admitted to the Top 5 Ph.D Programs in Economics
Math 115 (Calculus I)
Math 116, 116z or 120 (Calculus II)
Math 205 (Intermediate Calculus)
Math 206 (Linear Algebra)
Math 210 (Differential Equations)
Math 302 (Elements of Analysis I)
Math 303 (Elements of Analysis II)
Math 305 (Modern Abstract Algebra)
Econ 303 (Mathematics for Economics)
Econ 317 (Advanced Econometrics)
[/quote]
</li>
</ol>
<p>" be sure you have some interest in mathematics before you do the minor - econ at an undergrad level requires very little math on average, and not everyone WILL stomach the mathematics."</p>
<p>How can I be sure that I'll do good in math as a minor? I mean I like math to a certain extent.In school I liked physics. I'm not going to say that I was the brightest student in Math,but I was much better than the average. The reason I intend to do minor in math because I hear all the time that Grad School actually prefers more math which is not found in undergrad economics courses. On the other hand I absolutely love Economics and I intend to go to grad school. That's why I want do my minor in math. Its not necessary in my college to have a minor for completing the BS in Economics. So actually I've to take extra courses for that. But I'm not sure yet that I can digest the math as a minor as its a college level math and not high school.But If I need it in the grad school its better to take the preparation from now. By the way I'm a freshman. So yea..I do have little knowledge regarding all these things.</p>
<p>So can anyone enlighten me how can I be sure that I'll do good in math as my minor? Any indicators for that? Or what will be the math courses like?</p>
<p>I would say just start with one or two math classes and see how it goes. The math sequence gets gradually harder and you will know how far you can comfortably go. Courses through linear algebra and multivariable calculus are taken by majors in many different fields, but real analysis and up is mostly for math majors. </p>
<p>Even if you eventually decide that you do not want to complete the minor, a few extra math courses behind your back will only help you in graduate school.</p>
<p>To the OP - I very much agree with the above; it's a good idea to actually enroll in the courses and try them out; if you don't find yourself appreciating them and/or if they become a problem, drop them. Definitely you should get through some basic linear algebra if you want to consider doing more. </p>
<p>To give you an idea, since you mentioned not knowing -- the key thing about college math, which people tirelessly mention, is that you need to read and write proofs. You shouldn't be intimidated by this, though -- writing a proof is just communicating your reasoning in an appropriate way, which you'll get used to only by practice. </p>
<p>A slight overview of subjects: linear and abstract algebra both deal with the structure of certain objects with familiar binary operations. Linear algebra deals with vector spaces, which you can view as a generalization of vectors as you learned about them in precalculus. The thing is, when you generalize, you end up finding that quite a few things you see (e.g. polynomials) in math have a structure that involves taking finite linear combinations of some basic elements. Abstract algebra just deals with many structures of this nature. And you see a lot of problems in mathematics as special cases of the theory of these structures. The idea is to pinpoint why familiar objects have the properties they do. </p>
<p>Real analysis deals with questions that have a calculus-like flavor -- how continuous functions behave on different subsets of the reals, how they behave on convergent sequences, and eventually you generalize what continuity means. You also develop abstract versions of integration, where you integrate over things other than your favorite Euclidean space. Doing calculus on different objects is imaginably a powerful thing.</p>
<p>"many structures of this nature. "</p>
<p>Well, not all of them have a concept of linear combination. Sometimes, you only have one binary operation, and your structure is comparatively simpler.</p>
<p>
[quote]
A slight overview of subjects: linear and abstract algebra both deal with the structure of certain objects with familiar binary operations. Linear algebra deals with vector spaces, which you can view as a generalization of vectors as you learned about them in precalculus. The thing is, when you generalize, you end up finding that quite a few things you see (e.g. polynomials) in math have a structure that involves taking finite linear combinations of some basic elements. Abstract algebra just deals with many structures of this nature. And you see a lot of problems in mathematics as special cases of the theory of these structures. The idea is to pinpoint why familiar objects have the properties they do.</p>
<p>Real analysis deals with questions that have a calculus-like flavor -- how continuous functions behave on different subsets of the reals, how they behave on convergent sequences, and eventually you generalize what continuity means. You also develop abstract versions of integration, where you integrate over things other than your favorite Euclidean space. Doing calculus on different objects is imaginably a powerful thing.
[/quote]
If I didn't already appreciate abstract math, those two paragraphs would have scared the hell out of me!</p>
<p>Can you advise me some basic stuffs to go through? like the basics of the college level math.Any online resource?I've nothing to do now till class starts.So some self study would help I guess.Or particularly any concept of high school math to review which will be absolutely necessary for college math?That will be helpful too.And thank you guys for helping me out, I really appreciate it.</p>
<p>What's the first math class you would take? Most important for Calculus are limits (some schools cover limits in pre-calc, but they will be introduced in calculus again if you have not seen them before) and elementary functions (polynomials, exponential and logarithmic functions, trig functions and trig identities). If you already had calculus in high school and would take a more advanced class or statistics, I would recommend you enjoy the break!</p>
<p>Yikes, well I was intimidated when starting too -- I guess I wanted to convey the one friendly thing about the math you'll do, though, which is that it pays off tremendously to consider what it is you're trying to do! As in, going into a first course in algebra and saying "OK, that's just another structure I have to learn the properties of and grow familiar with" seems like a way to be less nervous to me at least =] I hope I was at least a bit helpful to the OP!</p>
<p>I'm also sorry, I sort of assumed the OP had calculus in high school! Which isn't fair, different people come from very different backgrounds. </p>
<p>Yeah, enjoy break is good advice, if you've had some calculus. Nothing like being fresh and rested and happy. Because I found that if I looked at things in a calm way, my math load was never too much "material," it's just getting through it the first time that can be intimidating if you can't stay calm.</p>
<p>If you want to know, the natural progression would be to learn some linear algebra (because the structures you deal with are simplest to work with, and give you good practice so you won't find the ones in modern algebra as scary), multivariable calculus (which I actually think seemed LESS intimidating to me than single variable calculus did, since the ideas aren't all terribly new), and some differential equations (certainly will be friendly, just more complex techniques to solve them). Then you'll get to the stuff I went on about earlier. </p>
<p>Hey, a good exercise if you haven't seen them much before is to practice a few epsilon-delta proofs. Proofs about limits from the definition of limit. I think it's more important to break the ice with this sort of stuff than to get yourself too deep into any material. Toying around with a few exercises is often less annoying anyway! </p>
<p>Good luck.</p>
<p>Well,i did have calculus. But the way I saw it, I thought it was just another branch of math which consists of some relatively easy formulas! Back then I didn't need to bother with the basic behind those formulas, just used it for calculation of differentiation and integration. Few months ago I actually understood that calculus is needed to measure the slope/tangent line of a curve line . We can easily measure the slope of a straight line but we need calculus to find the slope for curve line.And it also has lots of other uses. And I was really happy when I realized this concept.So I guess I'm waiting for more discoveries!</p>
<p>OK then, if you think you could use some brushing up on the actual theory behind calculus, going back and looking at what the real definition of a limit is will actually help you. I actually really wish calculus courses taught some of the theory, because a lot of the proofs are simple enough that they actually get you comfortable remembering the basic theorems.</p>
<p>mathboy98, that brings up an interesting topic. How do you explain a non-math-person what abstract math is about? I have had my own problems explaining younger math majors what abstract algebra is in a non-intimidating way. I have tried using modular arithmetic to get to the idea of an algebraic structure, but maybe the vector space approach works better because students are already familiar with it. The problem is that our linear algebra course does not really go into the abstraction of a vector space. It feels more like a course on matrix arithmetic. Maybe use matrices as an example of a group or a ring? Or on an even lower level, the integers vs the rationals?</p>
<p>If you know a good way of explaining abstract algebra that makes students actually want to take it, please let me now :)</p>
<p>mathboy98 - Your short summary of college math is excellent, and I will point people to it in the future instead of trying to replicate it.</p>
<p>b@rium - depending on your audience, talking about symmetry groups (or even, more concretely, Rubik's cube) may be a good illustration of abstract algebra.</p>
<p>Thanks johnshade, I hope it is somewhat welcoming =]</p>
<p>The Rubik's cube looks like it'd be really fun and exciting! I think I even have a principle, aside from any specific examples, of how to get someone excited about math. It's by showing that it's POWERFUL. I.e., I think you could walk someone through the proof of Fermat's Little Theorem (OR my problem about the Euler-phi function, listed on another thread) using group theory and the theorems, without actually proving the theorems themselves. </p>
<p>You could prove the Brouer (YIKES, no idea how to spell) Fixed Point Theorem in all dimensions using homology groups, but without actually showing how to compute the homology groups or the fundamental group. </p>
<p>The general principle of mine is to forget the technical details and show how a natural flow of logic can yield unobvious conclusions. It's had some success with people I talked to at least!</p>
<p>BROUWER!!!!!!!!!!!!!!!!!!!!!!!!!!</p>
<p>Anyway, a prof. of mine actually did that to get us excited on the first day of topology.</p>
<p>See because if you ONLY introduce modular arithmetic, you run the risk of them thinking it's boring! You have to show them that abstract algebra packs a punch!!! The most inspiring thing about math to me is seeing that it's so powerful, and concludes such unobvious things in such mysterious ways.</p>
<p>Geez, OK my "edit" function is giving trouble - I always get readers mad because my posts are in fragments. SORRY!</p>
<p>Anyway, I should address that you wanted also, beyond exciting students about abstract algebra, to get them to realize what it's like. Well, I'd sort of explain for instance the magic behind figuring out Fermat's Little Theorem. I'd say that abstract algebra tells you to forget about all the structure of an object EXCEPT what matters for our problem. And lets you solve problems about different objects (like the integers) using their structure. Then, perform your magic and give some examples -- POOF, here's a proof of a cool fact. </p>
<p>The point is, I believe one can show how abstract algebra is a refined theory without delving into messy details, and get a layman to want to take it!</p>