Eaaqas

08-04-14, 01:39 PM

Hi all,

I think that in lieu of another post in this section, I would give some advice about pursuing a mathematics intensive degree. I hope to see something of this sort stickied someday (though please don't sticky this thread.. it is not well written).

I took a lot of time to write this post, so I really do hope it helps some of you feel better. I want everyone to be able to succeed.

I really hope this post helps you. If you have any questions feel free to PM me.

I have separated this into a few unlabeled sections. First, I describe the reasons I hate math in hopes to relate. Second, I explain why I love mathematics at a deeper level. Finally, I explain my personal experience.

I am currently studying Economics with a minor in Mathematics. I'll be heading to graduate school in Econ next year.

As I progressed through mathematics, I noted 3 issues that I hated -- arithmetic was too prevalent, math seemed to be about the "tricks" that I can never remember, and Math does NOT apply to real life.

8+5? I can't do it without my fingers. 13*15? I can't do it without pen and paper.

Prove that x^2+3x+2 is a continuous function? Well, if you let epsilon>0 and take an epsilon ball around x..

You get my point -- I LOVE mathematics. I HATE arithmetic.

The biggest problem that I have with mathematics is how much I will use what I learn later in life. In my adolescence I asked my teachers TOO OFTEN "when am I ever going to use this?" with the oh so common answer, "well, when you are a physicist or engineer!" In college my favorite thing is trying to make a mathematician explain to me how some crazy property applies to economics. They stumble so much it makes me laugh. Luckily I have seen where some things I thought didn't relate actually do in very important ways.

Look, I understand that you REALLY don't care about most of the things that you learn in math. Yes, professors say "you are going to build off of this to something important", but you never see it. My favorite citation is always "you will never have a calculator to carry around to add, subtract, multiply, and divide at the store!!!!" Yeah, right.... My dad is still good friends with one of my mathematics teachers in High School. I call him up sometimes to let him know that I solved a minimization problem with 400 alternatives on my phone when I was at the store trying to figure out how to minimize costs given the constraint that i need to eat all month.

What is absolutely necessary to recognize is that mathematics is NOT solving word problems all day that take some trick that you learned from section 11.3 part A "Finding the height of a tree given that the sun is at X angle and you are X distance away from the tree" (engineers aside :P). Yes, you will need to roll your eyes through calculus I and calculus II while you learn how to find the force that needs to be applied to a spring to pull it a certain distance. As soon as you get past this, you start learning the art of mathematics.

Mathematics is an art! As soon as you get past the artificial problems that professors have created to make sure you understand simple tasks, you start to prove that those formulas you learned work. You begin to see that mathematics takes real skill and, dare I say it, imagination, not just memorization. I have witnessed questions that I have asked that take real skill and imagination to answer. The one I am working on right now involves R&D efficiency -- Does the solution exist, and how many solutions are there (proof using topological compactness and continuity)? What properties does the solution have (examination and proof using countless mathematical methods)? Why have we not reached the efficiency point(empirical analysis)?

Mathematical tools are tools in your toolbox. One of my favorite professors always described two levels of understanding of mathematics. The first involves people saying "ugh, math.. I'm never going to figure this out. I guess I'll have to ask my neighbor the engineer if he has any ideas" The second, higher level, involves interest in new problems. When I have a problem that I have never seen before, I think "Which branch of mathematics applies to this problem? Should I use a topology, dynamic systems, calculus, analysis, geometry, etc?" I have never been able to answer a real mathematics problem with a trick from a book that I memorized. I sit back for a few days and consider what branch I should use, then I open my textbooks to see what properties of the problem I can use to answer the question that I have.

As you can see, my problem with mathematics stems from my field of study -- there are certain fields of mathematics that are VERY important to Economics, but most are not. I don't give a crap how to find the volume of the solid that is formed by rotating the curve x^2+3x+2 around the x-axis. I DO care that the solution exists to a problem regarding general equilibrium in infinite dimensional space.

Now, why do I care about general equilibrium in infinite dimensional space? Well, the number of goods and services for consumption in the world approach infinity, so can we find an efficient allocation of goods? (boring, I KNOW) :P

I learned something important last semester -- though some branch of mathematics may not seem to apply, I bet you can find a way to apply it. One of my professors used Brownian Motion (a physics concept) to answer a question about an equilibrium concept! (lol, the exclamation mark makes me seem like a nerd.. oh wait..)

Understanding mathematics is a prerequisite to understanding physical systems, social systems, statistical systems, computer systems, and tunnel systems (though probably weighted toward the beginning of the list, civil engineers aside). Some mathematicians claim to fame is that they were able to find a mathematical proof that does not apply to ANYTHING in real life, but that is not what mathematics is for as a whole.

PLEASE recognize that the useless stuff you are learning will build up. You CAN be successful.

I think that in lieu of another post in this section, I would give some advice about pursuing a mathematics intensive degree. I hope to see something of this sort stickied someday (though please don't sticky this thread.. it is not well written).

I took a lot of time to write this post, so I really do hope it helps some of you feel better. I want everyone to be able to succeed.

I really hope this post helps you. If you have any questions feel free to PM me.

I have separated this into a few unlabeled sections. First, I describe the reasons I hate math in hopes to relate. Second, I explain why I love mathematics at a deeper level. Finally, I explain my personal experience.

I am currently studying Economics with a minor in Mathematics. I'll be heading to graduate school in Econ next year.

As I progressed through mathematics, I noted 3 issues that I hated -- arithmetic was too prevalent, math seemed to be about the "tricks" that I can never remember, and Math does NOT apply to real life.

8+5? I can't do it without my fingers. 13*15? I can't do it without pen and paper.

Prove that x^2+3x+2 is a continuous function? Well, if you let epsilon>0 and take an epsilon ball around x..

You get my point -- I LOVE mathematics. I HATE arithmetic.

The biggest problem that I have with mathematics is how much I will use what I learn later in life. In my adolescence I asked my teachers TOO OFTEN "when am I ever going to use this?" with the oh so common answer, "well, when you are a physicist or engineer!" In college my favorite thing is trying to make a mathematician explain to me how some crazy property applies to economics. They stumble so much it makes me laugh. Luckily I have seen where some things I thought didn't relate actually do in very important ways.

Look, I understand that you REALLY don't care about most of the things that you learn in math. Yes, professors say "you are going to build off of this to something important", but you never see it. My favorite citation is always "you will never have a calculator to carry around to add, subtract, multiply, and divide at the store!!!!" Yeah, right.... My dad is still good friends with one of my mathematics teachers in High School. I call him up sometimes to let him know that I solved a minimization problem with 400 alternatives on my phone when I was at the store trying to figure out how to minimize costs given the constraint that i need to eat all month.

What is absolutely necessary to recognize is that mathematics is NOT solving word problems all day that take some trick that you learned from section 11.3 part A "Finding the height of a tree given that the sun is at X angle and you are X distance away from the tree" (engineers aside :P). Yes, you will need to roll your eyes through calculus I and calculus II while you learn how to find the force that needs to be applied to a spring to pull it a certain distance. As soon as you get past this, you start learning the art of mathematics.

Mathematics is an art! As soon as you get past the artificial problems that professors have created to make sure you understand simple tasks, you start to prove that those formulas you learned work. You begin to see that mathematics takes real skill and, dare I say it, imagination, not just memorization. I have witnessed questions that I have asked that take real skill and imagination to answer. The one I am working on right now involves R&D efficiency -- Does the solution exist, and how many solutions are there (proof using topological compactness and continuity)? What properties does the solution have (examination and proof using countless mathematical methods)? Why have we not reached the efficiency point(empirical analysis)?

Mathematical tools are tools in your toolbox. One of my favorite professors always described two levels of understanding of mathematics. The first involves people saying "ugh, math.. I'm never going to figure this out. I guess I'll have to ask my neighbor the engineer if he has any ideas" The second, higher level, involves interest in new problems. When I have a problem that I have never seen before, I think "Which branch of mathematics applies to this problem? Should I use a topology, dynamic systems, calculus, analysis, geometry, etc?" I have never been able to answer a real mathematics problem with a trick from a book that I memorized. I sit back for a few days and consider what branch I should use, then I open my textbooks to see what properties of the problem I can use to answer the question that I have.

As you can see, my problem with mathematics stems from my field of study -- there are certain fields of mathematics that are VERY important to Economics, but most are not. I don't give a crap how to find the volume of the solid that is formed by rotating the curve x^2+3x+2 around the x-axis. I DO care that the solution exists to a problem regarding general equilibrium in infinite dimensional space.

Now, why do I care about general equilibrium in infinite dimensional space? Well, the number of goods and services for consumption in the world approach infinity, so can we find an efficient allocation of goods? (boring, I KNOW) :P

I learned something important last semester -- though some branch of mathematics may not seem to apply, I bet you can find a way to apply it. One of my professors used Brownian Motion (a physics concept) to answer a question about an equilibrium concept! (lol, the exclamation mark makes me seem like a nerd.. oh wait..)

Understanding mathematics is a prerequisite to understanding physical systems, social systems, statistical systems, computer systems, and tunnel systems (though probably weighted toward the beginning of the list, civil engineers aside). Some mathematicians claim to fame is that they were able to find a mathematical proof that does not apply to ANYTHING in real life, but that is not what mathematics is for as a whole.

PLEASE recognize that the useless stuff you are learning will build up. You CAN be successful.