Point of theroretical math?

[Mr Shifty]

Something to lighten up the tone of this thread (ref: XKCD):

I've had this one posted on the door of my office for several months:)

[Jim DiGriz]

[Beowolf]

I had a similar problem in high school with being unable to connect algebra to my real life. In later decades I realized the connections were there, only they're two steps away instead of one, and so harder to see: Measuring things yields numbers. Numbers have some simple uses by themselves, but most of their value comes from manipulating them with tools like ratios and equations. Math is what we call that toolkit, and the more you learn, the more specialized tools you have available when you need them.

When my son hit this same issue my advice was to treat it as a strategy game. He and I both enjoy those. When starting out with a completely new one, there are all these completely arbitrary-seeming rules to learn about strengths, weaknesses, resources, income and such. They don't seem to fit together in a logical way for a while, but after you've learned a dozen of the rules, you can start using them as tools to build simple tactics. And you keep adding more as you work your way deeper into the game.

So that's my advice to you: Accept that you just have to memorize a set of 50 arbitrary rules for manipulating numbers and learn them. Learn them your way, whatever works best for you, but learn them thoroughly. The repeat-practice drills schools use work for many people, but not me and perhaps not you. Fifty might sound like a lot, but I had to memorize at least twice that many just to play last year's XCOM game. Trust that by the end of that group, you'll have a large enough toolkit to play the game...meaning you'll start automatically seeing places to use these mathematical tools to improve your own life.

It can also be really helpful to pick up a non-traditional textbook, so you can get a completely different perspective on the topics that confuse you. Something like an "Algebra for Dummies". I remember I was out sick when the teacher covered what a function is. My textbook's explanation was just gibberish to me, and so I ended up not learning that until almost a year later. Having a differently-written book around sure would have been useful then. Later on, when I did learn about functions, would you believe they changed my life? When the new math teacher explained them, she mentioned something about computers and my eyes must have lit up. She noticed that and gave me a cardboard computer trainer called CARDIAC

and I've been working with computers ever since.

Best of luck!

[DaveofDefeat]

I know an engineer who just barely passed his math classes and is doing just fine now. You really should get to understanding it though, sometimes it just takes a little while for you to get it, I failed my college algebra class and then went on to get a B in calculus, so its not that bad.

[Camacha]

To sum up my question, why do I need to worry about theoretical math I will never use after these classes and not the "practical" math I use on an almost daily basis?

I thought the same. Now that I am playing around with robotics, I find that my knowledge is lacking in some respects. I know there is a pretty, clean and efficiënt way to do and calculate things, but because I can't get the equations to work, I am stuck with some dirty old fashioned brute forcing. Of course, you can intelligently reduce the calculative load of brute forcing with some tricks, but I would really rather use the proper calculations.

I have started picking up the books again. If you would have told me 10 years ago I would voluntarily do equations in my own spare time, I would have simply laughed. Now I want to know how this works, so I can do things properly and efficiently. And it is fun too, I am discovering now. Mathmatics are a construct, but one with which you can play and have fun, but only if you are opening up to it. It's a tool, a very powerful tool, and a toy. Sure, I am just doing stupid find x questions, but each time I learn a new trick, I can do not-so-stupid stuff too.

Edited November 21, 2013 by Camacha

[Camacha]

I know an engineer who just barely passed his math classes and is doing just fine now. You really should get to understanding it though, sometimes it just takes a little while for you to get it, I failed my college algebra class and then went on to get a B in calculus, so its not that bad.

I heard a teacher tell his students not to cheat or slack. Not because it is immoral, but because it could get people killed. Be the best engineer you can be, or do not do it at all. Anything in between is a liability.

Edited November 21, 2013 by Camacha

[drakesdoom]

I hear a teacher tell his students not to cheat or slack. Not because it is immoral, but because it could get people killed. Be the best engineer you can be, or do not do it at all. Anything in between is a liability.

I would go further and say that doing anything other than your best at anything is a failure to the human race. If you don't want to do it don't, if you fail try to learn something, if you were wrong stop. If you keep the proper mind set you can only ever have been wrong you will never be wrong.

[Camacha]

I would go further and say that doing anything other than your best at anything is a failure to the human race. If you don't want to do it don't, if you fail try to learn something, if you were wrong stop. If you keep the proper mind set you can only ever have been wrong you will never be wrong.

Yeah, on one hand I would agree, on the other hand I know the world does not work that way. You can not do everything a 100% and even if some people can, the majority will not. Working with any other idea is not very realistic. However, engineers are one of those groups of people that can not afford to accept half work (just like pilots, doctors, you name it).

[Mmmmyum]

Did you not do complex numbers and all that in high school? I'm in grade 11 and the most complex maths I've done is complex numbers and partial fractions (that's under IEB AP maths) and I'm aiming to move onto A levels next year. Are things done differently in America or? (don't mean to derail the thread at all, just surprised at the difference in education)

Whoops this thread is a few days old... I need sleep

Edited November 23, 2013 by Mmmmyum

[NGTOne]

Did you not do complex numbers and all that in high school? I'm in grade 11 and the most complex maths I've done is complex numbers and partial fractions (that's under IEB AP maths) and I'm aiming to move onto A levels next year. Are things done differently in America or? (don't mean to derail the thread at all, just surprised at the difference in education)

Whoops this thread is a few days old... I need sleep

In Canada, we don't hit complex numbers in high school (unless you're in an advanced class). In the States, I don't know if anything beyond algebra and trigonometry is covered in high school (though this is dependent on the district).

[Nuke]

my math classes were horrible. sometimes we were spending months on elementary stuff, like fractions and exponents. i took two algebra classes, where the books were 2 grades below us, and a trig class that didnt actually teach any trig because the school district screwed up ordering books and we didnt get em till the last month of the semester, and we just ended up reviewing fractions. the only redeeming thing was an electronics class elective that was math heavy. though it was more about learning how to use formulas for electronic design and troubleshooting, than learning the math concepts behind them (there was some linear algebra and calculus in it, but i didnt realize until i learned those on my own sometime later).

[Mmmmyum]

Ah okay. I only did complex numbers and partial fractions (worst things ever) because I do the higher level extra maths courses

[architeuthis]

In Canada, we don't hit complex numbers in high school (unless you're in an advanced class). In the States, I don't know if anything beyond algebra and trigonometry is covered in high school (though this is dependent on the district).

I think it is normal for math classes in the US to cover complex numbers in Algebra 2 which is usually taken in the junior year. Math beyond that isn't required to graduate at least where I went to high school (in Washington state). Of course their standards may have changed in the time since I was in high school, which was a while ago in my case.

I'll agree with many of the posters here though, speaking from my own perspective as a mechanical engineering undergraduate you should try to learn to love math for it's own sake because you'll be using a lot of it in any engineering career. Calculus, linear algebra or differential equations are definitely not "theoretical math", they are just as practical as algebra or geometry. Equations describing many physical principles are derived using calculus of varying complexity, and unless you can follow these derivations you don't really fundamentally understand the physical concepts. And in my case at least, getting to learn about the way the world works was what drew me to the engineering degree. Also as you get to higher level continuum mechanics type classes such as heat transfer, vibrations, fluid mechanics and so on, you find many cases where the simplifying assumptions made earlier to whittle down the equations into things you can solve using simple algebra no longer apply. Also control theory and statistics make heavy use of calculus. Depending on the route you take even more "theoretical" kinds of math may be helpful to your career, such as tensor algebra or group theory.

You may find that your dislike of math will change as you grow more comfortable with it. Learning math is kind of like learning a new language: you will grow more fluent in it with practice. But don't negatively prejudice your potential for success by telling yourself that you "hate" math. That is counterproductive.

Edited November 25, 2013 by architeuthis

[Nuke]

hating math class is entirely different though

dont blame math for crappy teachers and/or the asinine way that math is taught in public schools.

[gjay822]

You know in Math's field there are always having an equation and regarding on your post there are having the REAL NUMBERs on it and since you have the book of your father then you will have the advantages to solve it all. Just read,study and learn from a trusted references.

[CaptainKipard]

I will never run across a variable without a REAL number in the REAL world.

Don't quaternions used in gimbals use imaginary numbers? This seems relevant to your field of study.

[*Aqua*]

I would guess gimbals are controlled by some kind of fuzzy logic. At least that's what is controlling automatic transmissions in cars.

I study applied computer science and all I yet have to do is to write my master thesis. My teachers always said 'Take pity on those poor engineers. They have to calculate derivations all day long while you only have to pick an intelligent algorithm to let it do it for you.'

[K^2]

Don't quaternions used in gimbals use imaginary numbers? This seems relevant to your field of study.

Erm, sort of, but not exactly.

Group of unit quaternions is homomorphic to SO(3). In layman's terms, every unit quaternion can have a rotation assigned to it. Taking a product of these quaternions is like applying rotations one after another. That's the connection to real world.

But you don't have to go this far. Group of unit complex numbers is isomorphic to the SO(2) group. In other words, every rotation in 2D can be described with just a complex number. And we know that you can combine 3 2D rotations to form a 3D rotation via Euler's Angles. That's your connection between complex numbers and quaternions. (I'm oversimplifying that last bit a hell of a lot, but it illustrates the point, I hope.)

I would guess gimbals are controlled by some kind of fuzzy logic. At least that's what is controlling automatic transmissions in cars.

Completely unrelated topics.

[Sillychris]

If you're failing algebra... a mathy program like engineering might not be a good path for you.

Just like a person who has poor reading comprehension probably wouldn't do a degree in literature.

An aerospace engineer doesn't plug numbers into formulas. That's what the technicians and high school students do.

An engineer MAKES the formulas. The engineer is the one breaking ground and trying to optimize and improve what was before him. The days of wood and canvas planes are over. The low hanging fruit has been picked. If you want to engineer something new in the 21st century, you are going to need a math-rich arsenal at your disposal.

Furthermore, you are going to need to utilize computational methods, probably more often than pen and paper methods. For this, you need to be math literate so you can converse with a computer and get it to do the impossible calculations.

Unrelated to work, strong math skills can make you win at board games, poker, and even hockey.

I also utilize math heavily in my outdoor pursuits, particularly rock climbing.

[TheGatesofLogic]

AC circuitry always requires complex numbers by necessity. Imaginary numbers are extremely important. Also: if you want to be an aerospace engineer and you are failing algebra, please don't. I don't trust you in such a case with my life. Aerodynamics and mechanic requires high levels of calculus for simplification (I think of calculus as a simplified way of doing EXTREMELY complex math despite the fact that many people consider calculus as complex). Also, how did you get an A in Physics in high school if you can hardly do trig? Highschool Physics courses are like 50% vector analysis nowadays aren't they? Btw Calculus isn't the study of math as variables get exponentially smaller, only part of calculus is the study of functions as they approach continuums or in other words as variables become infinitely small yet still not zero and number as infinitely many, these are called infinetisimals, and one way to envision them is a .000... and infinitely on with a 1 at the end. the calculations of Riemann sums and complex volumes wuld be nearly impossible without calculus, and aerodynamics HEAVILY relies on the curvature of these volumes which can be described much more easily using calculus. I honestly can't think of a single branch of math that is PURELY theoretical nowadays.

When I originally wanted to major in Nuclear Physics and Engineering I had to take 3-4 calculus courses IIRC and had to learn 3 computer languages to be able to poperly model systems, and if trig and algebra is hard for you, those types of classes will kill you, end of story.

Edited March 16, 2014 by TheGatesofLogic

[K^2]

AC circuitry always requires complex numbers by necessity.

That's not strictly true. Looking at thing like impedance and conductivity as complex values helps, of course, but you can do everything in electricity and electrodynamics using real values only.

This might be what you were going for, but it seemed to require clarification.