View Full Version : I love mathematics and I think you can too


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.

finallyfound10
08-08-14, 01:14 AM
Interesting. In general, I hate math and it's been the bane of my existence in too many situations to count (Ha!) but I really like to teach math (I was a teacher for a long time) since I have Dyscalculia, I go really slowly and explain every little step. I've had several middle school/high school kids tell me that they didn't understand something until I taught it to them.

You probably don't what Dyscalculia is. I got a degree in Elementary Education in the '90's and never heard of it until 2010! It's Math's Dyslexia more or less.

http://www.dyscalculia.org/

www.dyscalculiaforum.com (http://www.addforums.com/forums/www.dyscalculiaforum.com)

Starskii
08-17-14, 05:24 AM
I want to go into computer science and I've been heavily discouraged that mathematics seems to be so prevalent. Obviously it should be - but still. From what I've learned about programming, the math seems to be relatively primitive. Mostly algebra. However I have recently tried embracing math and got a tutor to help fill in the potholes in my knowledge so I can move on to take calculus 1&2 in college.

I'm really thankful for your post, it's nice knowing that a person suffering from ADHD can actually excel in mathematics -- at least conceptually.

Thanks again - Starskii.

Hathor
08-17-14, 11:37 AM
^^^ A while back I was interested in programing, but since I [have] trouble learning CSS it seemed not for me to take it to the next level.

But I thought most programmers don't really use a lot of math, with the exception of those working in graphics (gaming?)

I do remember one programmer saying traditional algebra can cause confusion when people try to apply it wrongly to programming, but I may be bringing confusion with that here now in this thread.

It seemed to me that perhaps programming is more like learning a language than learning math?

Perhaps an actual programmer can chime in to help with my confusion :confused::)

I think it is easier for me to learn math than to learn languages.

Starskii
08-18-14, 03:38 AM
^^^ A while back I was interested in programing, but since I [have] trouble learning CSS it seemed not for me to take it to the next level.

But I thought most programmers don't really use a lot of math, with the exception of those working in graphics (gaming?)

I do remember one programmer saying traditional algebra can cause confusion when people try to apply it wrongly to programming, but I may be bringing confusion with that here now in this thread.

It seemed to me that perhaps programming is more like learning a language than learning math?

Perhaps an actual programmer can chime in to help with my confusion :confused::)

I think it is easier for me to learn math than to learn languages.

Although I haven't studied Computer Science at a college level yet I feel like I can spread at least a little light on this. Your mathematical problem solving skills are improved by taking Calculus. Also, it helps when programming as an engineer. However the basics of programming only require a firm grip in algebra. For example (using C++):

#include <iostream>
using namespace std;

void clear()
{

system("pause");
system("cls");

}

int main()
{

double a;
double b;
double tax = 1;
double c;

cout << "Predicting annual income...\n\n";
clear();

cout << "Enter monthly income: \n\n";
cin >> a;
clear();

cout << "Enter tax \n IE:0.10 \n\n";
cin >> b;
tax = tax-b;

c = a*tax;

c=c*12;

cout << "Your yearly income is estimated to be: " << c << ".\n\n";

system ("pause");
return 0;
}

In the example program the only knowledge required was a basic understanding of algebra. However, when programming a 3d engine or doing anything in 3d you absolutely need a working knowledge in calculus, geometry, trigonometry, and physics. This knowledge is also helpful when programming something extremely complex that may exceed thousands of lines like: A game, business software, anything with a complex UI. Take everything I've said cautiously as I have not been properly educated, but from my basic understanding the advanced math is more and more helpful as the program gains complexity.

Hathor
08-18-14, 06:46 PM
It seems to me that taking algebra and [possibly] calculus would not help me learn programming, because the way they are taught bore me into a stupor that cannot absorb any information.

I just wonder if it would be better to learn the required math in a holistic way, integrated with programming, or on another tangent physics.

Your mathematical problem solving skills are improved by taking Calculus

This does not fit neatly with the quote below, but it seems to wander in that directon.


I appeal to you, as practical teachers. With good discipline, it is always possible to pump into the minds of a class a certain quantity of inert knowledge. You take a text-book and make them learn it. So far, so good. The child then knows how to solve a quadratic equation. But what is the point of teaching a child to solve a quadratic equation? There is a traditional answer to this question. It runs thus: The mind is an instrument, you first sharpen it, and then use it; the acquisition of the power of solving a quadratic equation is part of the process of sharpening the mind. Now there is just enough truth in this answer to have made it live through the ages. But for all its half-truth, it embodies a radical error which bids fair to stifle the genius of the modern world. I do not know who was first responsible for this analogy of the mind to a dead instrument. For aught I know, it may have been one of the seven wise men of Greece, or a committee of the whole lot of them. Whoever was the originator, there can be no doubt of the authority which it has acquired by the continuous approval bestowed upon it by eminent persons. But whatever its weight of authority, whatever the high approval which it can quote, I have no hesitation in denouncing it as one of the most fatal, erroneous, and dangerous conceptions ever introduced into the theory of education

http://www.anthonyflood.com/whiteheadeducation.htm

Eaaqas
08-18-14, 07:58 PM
I think all full time programmers would agree with me on this point:

Mathematics + rand(n)= Logic
Programming = Logic

Mathematics is not prevalent unless you are using mathematical languages. It takes time to learn programming just due to the fact that you are required to learn a language. I can nail down programming at a conceptual level, but I am required to look up all the nouns to get anywhere, just like when I learn a language.

I've learned about 5 programming languages I'm my 4 years of college. Once you get the initial logic figured out you can hit the rest pretty easily, as long as you know when to google issues.

Math classes ARE so boring ;). What matters is the applications that are relevant to your field. Too bad physisists and engineers need to take these math classes, ornelse it would be a breeze. I have been arguing for years that engineers should have a separate math program like math education.

RobotInDisguise
08-19-14, 08:07 PM
I cant agree more even though I'm pretty quick at mental arithmetic. My problem with that is mostly I get bored with that really fast. Math is as much of an art as drawing cartoons but people rarely teach it that way.

Dysexlia
09-21-14, 05:19 PM
I never appreciated mathematics until I took Logic in the Philosophy dept. Putting formulas in terms of an argument.
For example:
1.(x)(Px then Qx)
2.Pa
3.Qa

In other words: For all x, if x has the property P, then x is Q.

Math doesn't even have to be about numbers imo, it's all about logic and reasoning.

roflwaffle
09-26-14, 12:24 AM
It seems to me that taking algebra and [possibly] calculus would not help me learn programming, because the way they are taught bore me into a stupor that cannot absorb any information.

I just wonder if it would be better to learn the required math in a holistic way, integrated with programming, or on another tangent physics.
Definitely. I ended up getting a degree in math after moving through the college of engineering and social sciences in my university mostly because it was challenging. But... When it wasn't I would tune out and then end up falling really far behind. Still, I think graduate level math is great training for just about anything.

Sekhmet2014
09-26-14, 05:51 PM
I'll take your word for it. My brother is a math professor & someone who strives to enrich and encourage young mathematical minds. He always says that math is beautiful, like art.
I'll take his word and yours for it, but at this point in my life, it's not for me.
Now music and language, that I'll study!

Laserbeak
09-26-14, 08:44 PM
I hated math and did not do well in it in my elementary school days, but once I hit more advanced math and got better teachers (they make all the difference in the world), I started to enjoy it... by my senior year in high school I was taking Advanced Placement Calculus BC (the most advanced math class they taught in high school) and got a 5 (the highest score) on the test!