Are you good at math?

Grell

Grell

I have spent my whole life avoiding math. I learned to program at a young age and only really needed the basic math skills. Now I am in college at an engineering school and I have to learn all the stuff I avoided years ago. To be honest I am starting to enjoy it. The theory and thought process behind it is quite similar to the thought process of computer science. It is a tough learning curve though. Just curious, if you are good at math, were you always? If not, do you have any pointers to someone trying to learn all this stuff for the first time, trigonometry, calculus, etc...?
 
For one thing, curiosity is good. As an engineering student you might be tempted to look at math mostly algorithmically ("I just want to know how to do this-and-that"), but I often find it enlightening to ask myself questions and then just try to find out. In other words: thinking along the lines of "I suspect something, can I (dis)prove it?", "What would happen if I try this?", "Would that be possible?", that sort of thing. Basically, just "play" with math.
 
When you get to its core, all math is just addition and subtraction.
So don't look at a problem or subject as "calculus". Look at it as a method to solve a problem.
For me, it's a lot easier to understand how it all works if someone would just tell me how the method/formula is used in a practical situation. The why.
All those math symbols only represent a formula or method. 'x' represents adding a bunch of times. The curvy 'f' sort of does the same thing.
 
Having an understanding of arithmetic is the foundation to build from, addition, subtraction, multiplication and division. That tends to be followed by algebraic manipulation of those mechanics. Algebra gives an abstract layer to the literal numbers, and designs formulas for the execution of arithmetic. From there you can learn fields that specialize toward your studies.

Spatial math: geometry, topology, trigonometry, will describe physical space and objects. Useful for design in almost all engineering.

Mathematical logic presents the logical operators(AND, OR, NOT, etc.), and truth tables. It's useful for programming and electronic engineering. Programmers use logic for things like comparing two values and if they are equal then do this, or not equal do that. Electronic engineers use logic similarly in circuit design. Logic gates can be made to define logic operations in circuits.

Differential calculus deals with rates of change and derivatives. It applies toward physical sciences. Look up the relationships between distance, velocity, and acceleration to get a better idea. Integral calculus has definite and indefinite integrals. Definite integrals describe areas below curves, and indefinite integrals look at reversing derivatives.

Statistics looks at large sets of data and applies distribution formulas to derive probability information from that data. Its used for analysis to try and create normal or standard patterns.

As far as tips, I would say try and apply the programming knowledge you have to help you learn. Try to write simple programs that apply the formulas and ideas you're learning about. Even some simple scripting languages could work well for this. Use the internet it helps solve problems sometimes. I have recommend buying a dictionary of mathematical terms and good slide rule but those might not be as helpful anymore.

I wasn't always good at math and I still might not be, but proficiency comes with practice. Good luck.
 
Naught0 said:
Having an understanding of arithmetic is the foundation to build from, addition, subtraction, multiplication and division.
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Algebraic operations also include powers and surds (n-th roots) ;) Depending on the kind of math you do, knowledge of complex numbers may be quite helpful as well, even if it's just the basics.
 
It is a bit like programming, I feel you get good at it as you need it.

I would say I suck at maths in general but since I work (almost entirely) with 3D and OpenGL, I am getting pretty good at linear algebra.

What is a little bit annoying is when academics much smarter than me put up a slide filled with one massive equation. I mean, I tend not to just put up code listings when I give presentations. I wish they would demonstrate the same courtesy ;)
 
kpedersen said:
What is a little bit annoying is when academics much smarter than me put up a slide filled with one massive equation. I mean, I tend not to just put up code listings when I give presentations. I wish they would demonstrate the same courtesy ;)
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You may want to chalk that up to occupational hazard. Mathematicians are an interesting species, but they often seem to have difficulty assessing the mathematical ability of common humans ;) I remember from my days as a physics student that for the math courses we were just dumped at math courses given by mathematicians for mathematicians. Needless to say I bailed; I'm not bad at math (if I may say so myself), but if I were good enough at it to understand math classes for mathematicians I probably would have been one...
 
b]
fonz said:
You may want to chalk that up to occupational hazard. Mathematicians are an interesting species, but they often seem to have difficulty assessing the mathematical ability of common humans ;) I remember from my days as a physics student that for the math courses we were just dumped at math courses given by mathematicians for mathematicians. Needless to say I bailed; I'm not bad at math (if I may say so myself), but if I were good enough at it to understand math classes for mathematicians I probably would have been one...
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The problem relies on teachers. Almost all of them believe that everything is trivial, and if not, you're a dumb. Most of them are talented guys. Talented guys never think about "normal" people.
 
Pardon me for the essay :r.

drhowarddrfine said:
When you get to its core, all math is just addition and subtraction.
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I have to disagree with you. Maybe it is so in the engineering waters, but it's not like that in general. To me the high enough level of mathematical abstraction with time becomes more like philosophy than merely '+' and '-'. What you're talking about is computing (e.g. applied mathematics, and crunching the numbers by hand), and not math (which is theoretical mathematics). Mathematics was also the last "science" that diverged from metaphysics with Georg Cantor and his classification of different "infinities" (see cardinal and ordinal numbers... it's amazing).

This philosophical view especially becomes apparent when you're dealing with "bleeding edge" physics, like Quantum Field Theory. You're introducing spaces that have a fraction or even real number of dimensions and you integrate over surfaces within them. How can you accept it in your heart that such a thing exists? Purists need more than just a physical proof. And if such objects do exist abstractly, how do we interpret its existence in the real world? Where does such an object exist? Does it exist in the world of ideas, or does it exist in the real world. Or maybe it's just an imperfect approximation of perfect abstract objects, that carry no such ambiguities. People have literally gone mad because of such questions! This isn't a joke! Read the excellent Greek comic book Logicomix. Just think of the complex plane for a while and really really try to justify it in your mind.

fonz said:
In other words: thinking along the lines of "I suspect something, can I (dis)prove it?", "What would happen if I try this?", "Would that be possible?", that sort of thing. Basically, just "play" with math.
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Yeah, that's how we're taught in our university -- every problem must be dealt with this hacker mentality. From physics to programming or whatever. And in my opinion this is the best approach. Let your own passion guide you.

However, I noticed that many great computer scientists have been great mathematicians as well (and vice-versa). Take Knuth for example, he made a contribution for example in tetration function and power towers (and other things). Or John von Neumann -- a genius in fields of physics, mathematics and computer science. Feynman, awesome as he was, was wrong when he said that studying computers isn't a science, but still pushed on with quantum computers.

My skill at math fluctuated. Some things were really not my forte in primary school (like fractions, I actually failed an exam because of them... damn!) but now I am a fraction "guru" :p (but compared to most mathematicians I suck big time! :r). So even if you sucked big time before, you might come to love the subject. I have friend from Germany, who used to be such a lazy person (and still is) and wanted to study economy or something, and failed the entry exams, so he had to enroll in physics, because there was no limit to students (or the criteria were very low at least) and there he found love in pure theoretical mathematics. He's done string theory, quantum gravitation and all those things. And all his life before it he was avoiding math too.
 
One of the last chapters in my first semester Calculus text described how to successively approximate an integral, each approximation being closer to the integral than the prior approximation. Such a process is tailor made for a computer algorithm. The programmer who conceived of the algorithm had to have a basic understanding of an integral.

I also do not think that it is a coincidence that the FermiLab devotes some of it effort to Scientific Linux.

That being said I think most of the commercial demand for code is based on lower level math.
 
I'm not that great in math and I'm doing a PhD in statistics. With my mediocre abilities I still feel I am making worthwhile contributions.
 
Math is also some kind of language, and you can not learn a language without starting to think in it. Even a little. Then you can start with a dialog, changing sentences. Let the problem talk to you, but first you need to know the language it talks in.

Most people who are really good at math or programming do not really think about it but with it. They do not describe a function in terms they use verbally but take the function "as is", it has become part of their mental vocabulary. Otherwise, you would loose track of what you do. And it would take too much time to do that. When programming, you think "loop", not "now I need some fancy method to repeat this untill something happens". And once this vocabulary, this thinking in some new terms, worms its way trough into your subconcious - you get new ideas, new inspirations. Then you no longer control it, but invite it to the party - so to speak.
 
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