|
On November 02 2009 12:52 Shivaz wrote:Show nested quote +On November 02 2009 12:45 Sadist wrote:
B) the ridiculously easy example problem that allows you to only do like 2 of the homework problems before getting stuck because theres absolutely no reference for how to do the problem you are now because its far more involved than the example problem.
I fucking hate that shit.
Okay, the usual problem as to why this problem arises is because most people don't fully understand the concept AND don't remember that they have so many other tools in their toolbox. I currently tutor calculus at my college and i see SO many people not doing well because they don't remember jack shit from pre-calculus and algebra and WHAT THEY MEAN.. which leads me to believe that if you don't understand what's going on in the mathematics, as far as:
1. Elementary Limits
2. Derivatives
3. Word problems using derivatives (related rates/ minmax problems)
goes, people don't seem to remember their math sooooo often, which leads me to believe that if they don't REALLY understand it, they never will really remember it for future courses and will never really *care* about the pure logical beauty that goes into creating some of these ideas.
So as far as simple examples go, there's always almost NO difference at all between simple and complex, different numbers, and maybe different steps. The reason why my professors do this is so these problems really make you think before trying solve the problems.
|
Aotearoa39261 Posts
LOL Dave you are so right. People just forget everything and anything they've learned from other courses and they get destroyed haha
|
You are right about not "fully" understanding the stuff, but i still hate it  . Also I am taking calc 3 not having trouble on calc 1 lol.
|
While I agree that most people including myself dont understand math enough to remember it I dont believe its through any fault of my own.
Calculus is the biggest bullshit the way its taught IMO more specifically than math in general.
Heres how calculus is taught....learn to take derivatives, chain rules, integrals, la place transforms, etc.....
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related.
|
On November 02 2009 12:45 Sadist wrote:Show nested quote +On November 02 2009 11:01 Cloud wrote:
Dude I've had my series of shitty teachers. People who would have no clue at all on the subject or would just come in, ask "any question" and since obviously no one ever studied and had no doubts, then he would just walk away.
You cant go in school with the mentality that you're gonna receive in a silver platter everything that you're ever gonna need, especially considering that you sound like you're not in a rich kid's school and (I hope) you're mature enough.
Study by yourself for yourself. In my opinion this is almost impossible in math unless you have some type of awesome math background and have been teaching yourself for a long time. Some math books are horrendously shitty....the longs proofs that make little or no sense with absolutely no indication of why the assumptions were made. The example problems that are either A) made up so poorly it takes an incredibly long time just trying to decipher what/why its asking or B) the ridiculously easy example problem that allows you to only do like 2 of the homework problems before getting stuck because theres absolutely no reference for how to do the problem you are now because its far more involved than the example problem. I hate math or at least the way math is taught. This is coming from Junior Mechanical Engineering student too. Proofs are ridiculous.
but don't kick a cat :/
are you black?
|
Baa?21242 Posts
I love calculus, and I don't see a problem with the way it's taught :3
|
On November 02 2009 13:44 Carnivorous Sheep wrote:
I love calculus, and I don't see a problem with the way it's taught :3
do you not have problems doing physics problems like say a current density that varies with location along both the x and y axis so that you must decide how you want to vary dA in your equations? I understand it a hell of a lot more now because of physics than I ever did when I took Calculus. All i learned was how to do brainless operations with little knowledge of what I was doing so I have little or no recall of what ive "learned".
I wish i could be like
"Oh hey ya thats partial fractions...I remember that from all those spring problems we did....thats really easy look"
no its like "Fuck partial fractions? Ill plug it into my Ti89" because if I try to look it up in the math book i probably wont get much out of it or spend an inconvenient amount of time trying to figure out why the book did what it did.
|
On November 02 2009 13:23 Plexa wrote:Show nested quote +On November 02 2009 12:39 illu wrote:On November 02 2009 11:06 Archaic wrote:On November 02 2009 11:01 Cloud wrote:
Dude I've had my series of shitty teachers. People who would have no clue at all on the subject or would just come in, ask "any question" and since obviously no one ever studied and had no doubts, then he would just walk away.
You cant go in school with the mentality that you're gonna receive in a silver platter everything that you're ever gonna need, especially considering that you sound like you're not in a rich kid's school and (I hope) you're mature enough.
Study by yourself for yourself. I'd agree with this. Honestly, math is straight-forward, very linear. Study the process, and repeat the memorized instructions. Whether it makes sense or not, you should be able to come upon the answer that your teacher wants. Just remember certain rules (which are usually minor changes). Examples include coefficients and constants before variables, rationalized fractions, etc. Just remember what your teacher wants, remember the rules that you studied, and that is really all there is to it. What is the most advanced mathematics course you've done? I'm a math major, and I agree with what he said. Any math at undergrad level is exactly what he described (and if you don't see that then just think really hard about all the math you've done). It's not until you start doing higher level stuff and research that its not just a mechanical process anymore.
It was like this in high school, but ever since I got to college, it has been the complete opposite. Our first term math course, Ma001a, which is supposed to be single-variable calculus, is entirely proof-based. Our problem sets are just pages upon pages of text. Next trimester is linear algebra, and 3rd term is multivariable calculus. Needless to say, I hate math now.
|
On November 02 2009 13:34 Sadist wrote:
While I agree that most people including myself dont understand math enough .....
Wrong. TL is full of people well-versed in mathematics. evanthebouncy's math puzzles showed that.
On November 02 2009 13:34 Sadist wrote:
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related.
That is from your perspective. For me, for example, I do not want any, and I mean ANY, other subjects mixed into my mathematics courses. When I take a math course, I want it to be just math and nothing else; if I want to learn something that is not math (say physics), I will go take a course at the physics department.
By the way, the way physicists do mathematics is absolutely despicable.
|
On November 02 2009 13:50 Saracen wrote:Show nested quote +On November 02 2009 13:23 Plexa wrote:On November 02 2009 12:39 illu wrote:On November 02 2009 11:06 Archaic wrote:On November 02 2009 11:01 Cloud wrote:
Dude I've had my series of shitty teachers. People who would have no clue at all on the subject or would just come in, ask "any question" and since obviously no one ever studied and had no doubts, then he would just walk away.
You cant go in school with the mentality that you're gonna receive in a silver platter everything that you're ever gonna need, especially considering that you sound like you're not in a rich kid's school and (I hope) you're mature enough.
Study by yourself for yourself. I'd agree with this. Honestly, math is straight-forward, very linear. Study the process, and repeat the memorized instructions. Whether it makes sense or not, you should be able to come upon the answer that your teacher wants. Just remember certain rules (which are usually minor changes). Examples include coefficients and constants before variables, rationalized fractions, etc. Just remember what your teacher wants, remember the rules that you studied, and that is really all there is to it. What is the most advanced mathematics course you've done? I'm a math major, and I agree with what he said. Any math at undergrad level is exactly what he described (and if you don't see that then just think really hard about all the math you've done). It's not until you start doing higher level stuff and research that its not just a mechanical process anymore. It was like this in high school, but ever since I got to college, it has been the complete opposite. Our first term math course, Ma001a, which is supposed to be single-variable calculus, is entirely proof-based. Our problem sets are just pages upon pages of text. Next trimester is linear algebra, and 3rd term is multivariable calculus. Needless to say, I hate math now.
I wish I had a calculus course like yours in my first year... one that is just proofs.
|
On November 02 2009 13:52 illu wrote:Show nested quote +On November 02 2009 13:34 Sadist wrote:
While I agree that most people including myself dont understand math enough ..... Wrong. TL is full of people well-versed in mathematics. evanthebouncy's math puzzles showed that. Show nested quote +On November 02 2009 13:34 Sadist wrote:
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related. That is from your perspective. For me, for example, I do not want any, and I mean ANY, other subjects mixed into my mathematics courses. When I take a math course, I want it to be just math and nothing else; if I want to learn something that is not math (say physics), I will go take a course at the physics department. By the way, the way physicists do mathematics is absolutely despicable.
I meant most people as in the general population of students. Math Majors and people with strong math backgrounds were obviously not meant to be included.
As for Physics and Math beef. Ok whatever, I understand that they have a problem with each other but Math is FOR physics. Its supposed to be applicable to the real world is it not? Why the hell else would we have math? If you think physicists disgrace math you'd hate engineers =(
I, and many people who ive talked to in school (note these are almost entirely engineering majors and not math majors) do not remember much if anything from math. Some people are dishonest and try to lie and say they do but if you really push them on it and give them a difficult problem its obvious they are bullshitting. I am shocked that you would not want other subjects interfering with your math. Do you not like math in practical applications?
|
Aotearoa39261 Posts
On November 02 2009 13:50 Saracen wrote:Show nested quote +On November 02 2009 13:23 Plexa wrote:On November 02 2009 12:39 illu wrote:On November 02 2009 11:06 Archaic wrote:On November 02 2009 11:01 Cloud wrote:
Dude I've had my series of shitty teachers. People who would have no clue at all on the subject or would just come in, ask "any question" and since obviously no one ever studied and had no doubts, then he would just walk away.
You cant go in school with the mentality that you're gonna receive in a silver platter everything that you're ever gonna need, especially considering that you sound like you're not in a rich kid's school and (I hope) you're mature enough.
Study by yourself for yourself. I'd agree with this. Honestly, math is straight-forward, very linear. Study the process, and repeat the memorized instructions. Whether it makes sense or not, you should be able to come upon the answer that your teacher wants. Just remember certain rules (which are usually minor changes). Examples include coefficients and constants before variables, rationalized fractions, etc. Just remember what your teacher wants, remember the rules that you studied, and that is really all there is to it. What is the most advanced mathematics course you've done? I'm a math major, and I agree with what he said. Any math at undergrad level is exactly what he described (and if you don't see that then just think really hard about all the math you've done). It's not until you start doing higher level stuff and research that its not just a mechanical process anymore. It was like this in high school, but ever since I got to college, it has been the complete opposite. Our first term math course, Ma001a, which is supposed to be single-variable calculus, is entirely proof-based. Our problem sets are just pages upon pages of text. Next trimester is linear algebra, and 3rd term is multivariable calculus. Needless to say, I hate math now.
Just because it's proof based doesn't mean it's not mechanical. Think about the arguments you employ in your assignments/tests.
|
Aotearoa39261 Posts
On November 02 2009 13:59 Sadist wrote:Show nested quote +On November 02 2009 13:52 illu wrote:On November 02 2009 13:34 Sadist wrote:
While I agree that most people including myself dont understand math enough ..... Wrong. TL is full of people well-versed in mathematics. evanthebouncy's math puzzles showed that. On November 02 2009 13:34 Sadist wrote:
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related. That is from your perspective. For me, for example, I do not want any, and I mean ANY, other subjects mixed into my mathematics courses. When I take a math course, I want it to be just math and nothing else; if I want to learn something that is not math (say physics), I will go take a course at the physics department. By the way, the way physicists do mathematics is absolutely despicable. I meant most people as in the general population of students. Math Majors and people with strong math backgrounds were obviously not meant to be included. As for Physics and Math beef. Ok whatever, I understand that they have a problem with each other but Math is FOR physics. Its supposed to be applicable to the real world is it not? Why the hell else would we have math? If you think physicists disgrace math you'd hate engineers =( I, and many people who ive talked to in school (note these are almost entirely engineering majors and not math majors) do not remember much if anything from math. Some people are dishonest and try to lie and say they do but if you really push them on it and give them a difficult problem its obvious they are bullshitting. I am shocked that you would not want other subjects interfering with your math. Do you not like math in practical applications? Sadist has a point. Although Physicists do brutally mutilate math =[. High school math is so much more rooted in applications of techniques to solve problems rather than real math. Whether or not it would be better to teach in a more physics context at highschool is actually a pretty interesting debate.
In NZ our school calculus course is designed to lead onto engineering, which is nothing like studying math at university. It's a pretty effective way of teaching people I think, although many people still cannot grasp how to turn real life problems into mathematics (e.g. D.Es or Optimisation problems)
|
United States24650 Posts
On November 02 2009 14:04 Plexa wrote:Show nested quote +On November 02 2009 13:59 Sadist wrote:On November 02 2009 13:52 illu wrote:On November 02 2009 13:34 Sadist wrote:
While I agree that most people including myself dont understand math enough ..... Wrong. TL is full of people well-versed in mathematics. evanthebouncy's math puzzles showed that. On November 02 2009 13:34 Sadist wrote:
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related. That is from your perspective. For me, for example, I do not want any, and I mean ANY, other subjects mixed into my mathematics courses. When I take a math course, I want it to be just math and nothing else; if I want to learn something that is not math (say physics), I will go take a course at the physics department. By the way, the way physicists do mathematics is absolutely despicable. I meant most people as in the general population of students. Math Majors and people with strong math backgrounds were obviously not meant to be included. As for Physics and Math beef. Ok whatever, I understand that they have a problem with each other but Math is FOR physics. Its supposed to be applicable to the real world is it not? Why the hell else would we have math? If you think physicists disgrace math you'd hate engineers =( I, and many people who ive talked to in school (note these are almost entirely engineering majors and not math majors) do not remember much if anything from math. Some people are dishonest and try to lie and say they do but if you really push them on it and give them a difficult problem its obvious they are bullshitting. I am shocked that you would not want other subjects interfering with your math. Do you not like math in practical applications? Sadist has a point. Although Physicists do brutally mutilate math =[. High school math is so much more rooted in applications of techniques to solve problems rather than real math. Whether or not it would be better to teach in a more physics context at highschool is actually a pretty interesting debate. In NZ our school calculus course is designed to lead onto engineering, which is nothing like studying math at university. It's a pretty effective way of teaching people I think, although many people still cannot grasp how to turn real life problems into mathematics (e.g. D.Es or Optimisation problems)
Can you or someone explain to me how physicists brutalize math?
|
On November 02 2009 13:59 Sadist wrote:Show nested quote +On November 02 2009 13:52 illu wrote:On November 02 2009 13:34 Sadist wrote:
While I agree that most people including myself dont understand math enough ..... Wrong. TL is full of people well-versed in mathematics. evanthebouncy's math puzzles showed that. On November 02 2009 13:34 Sadist wrote:
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related. That is from your perspective. For me, for example, I do not want any, and I mean ANY, other subjects mixed into my mathematics courses. When I take a math course, I want it to be just math and nothing else; if I want to learn something that is not math (say physics), I will go take a course at the physics department. By the way, the way physicists do mathematics is absolutely despicable. I meant most people as in the general population of students. Math Majors and people with strong math backgrounds were obviously not meant to be included. As for Physics and Math beef. Ok whatever, I understand that they have a problem with each other but Math is FOR physics. Its supposed to be applicable to the real world is it not? Why the hell else would we have math? If you think physicists disgrace math you'd hate engineers =( I, and many people who ive talked to in school (note these are almost entirely engineering majors and not math majors) do not remember much if anything from math. Some people are dishonest and try to lie and say they do but if you really push them on it and give them a difficult problem its obvious they are bullshitting. I am shocked that you would not want other subjects interfering with your math. Do you not like math in practical applications?
Despite what I said, my focus is applied analysis and probability theory - I am definitely not a theoretical mathematician. I do like mathematics in practical applications. However, the problem is that to use mathematics to solve practical applications you need a solid foundation in theoretical mathematics, and a calculus course that is half physics will not teach you that solid foundation.
This might also be a good point to tell you there physics is not the only field where mathematics is applied. There is probability+statistics, computer science, economics+finance, chemistry, and to lesser degrees, biology, social sciences, philosophy, etc. So doing mathematics only with application on physics is definitely narrow-minded.
Also, to the perfectly honest I don't remember everything I did in undergraduate mathematics either. For example if you ask me questions on, say.... extension fields, I honestly do not remember what it is. I do know where to look for answers, however wikipedia.
|
On November 02 2009 14:09 micronesia wrote:Show nested quote +On November 02 2009 14:04 Plexa wrote:On November 02 2009 13:59 Sadist wrote:On November 02 2009 13:52 illu wrote:On November 02 2009 13:34 Sadist wrote:
While I agree that most people including myself dont understand math enough ..... Wrong. TL is full of people well-versed in mathematics. evanthebouncy's math puzzles showed that. On November 02 2009 13:34 Sadist wrote:
Ok but what the fuck you dont understand what any of that shit applies to or actually means until you take physics courses. So WHY not teach math through practical applications instead of mindless mechanical operations? Sure I can take integrals but that doesnt help me one fucking bit when Im trying to take differentials of areas and to solve a magnetic field problem.
The problem is math is taught mechanically and most if not all people have no real idea what the general concept is or means.
Math should be taught more like physics. Instead its taught like spelling is to english. Sure you can recognize the word...you can probably say the word.....and you can damn sure spell the word. But you have no idea what the hell it means or the context in which it can be used. The reason people dont remember it is because they have nothing to remember it by....math is broken up way too much (at least the way its taught) to where you dont know things are related. That is from your perspective. For me, for example, I do not want any, and I mean ANY, other subjects mixed into my mathematics courses. When I take a math course, I want it to be just math and nothing else; if I want to learn something that is not math (say physics), I will go take a course at the physics department. By the way, the way physicists do mathematics is absolutely despicable. I meant most people as in the general population of students. Math Majors and people with strong math backgrounds were obviously not meant to be included. As for Physics and Math beef. Ok whatever, I understand that they have a problem with each other but Math is FOR physics. Its supposed to be applicable to the real world is it not? Why the hell else would we have math? If you think physicists disgrace math you'd hate engineers =( I, and many people who ive talked to in school (note these are almost entirely engineering majors and not math majors) do not remember much if anything from math. Some people are dishonest and try to lie and say they do but if you really push them on it and give them a difficult problem its obvious they are bullshitting. I am shocked that you would not want other subjects interfering with your math. Do you not like math in practical applications? Sadist has a point. Although Physicists do brutally mutilate math =[. High school math is so much more rooted in applications of techniques to solve problems rather than real math. Whether or not it would be better to teach in a more physics context at highschool is actually a pretty interesting debate. In NZ our school calculus course is designed to lead onto engineering, which is nothing like studying math at university. It's a pretty effective way of teaching people I think, although many people still cannot grasp how to turn real life problems into mathematics (e.g. D.Es or Optimisation problems) Can you or someone explain to me how physicists brutalize math?
A lot of math and physics people joke about this or exaggerate this. I have two explanations.
1) As illu posted above this, math is not truly FOR physics, it is used in many other fields. In each field, some assumptions are applied to simplify the math involved. And of course, these assumptions vary field to field. As a result, sometimes physics professors choose to oversimplify their explanations to their students at the cost of theoretical math (I've seen this firsthand myself).
2) My pure math professor told me this was another reason: In physics, a lot of new fields are emerging that math haven't provided all the tools for yet. So physicists would create their own temporary shorthand math which are burdened by numerous assumptions specific to their field, and then try to extrapolate the math to make predictions. The resulting mess leads to them consulting with mathematicians to refine their ideas.
As for Sadist's and illu's dialog, I can see where both are coming from. The math from high school up through to the math that engineers are required to take heavily go hand in hand with physics and it's easy to see why one who doesn't major in math would be frustrated that math isn't taught by emphasizing this fact more. But this math is an *extremely* small tip of the iceberg. And this tip of the iceberg is not general enough for all fields of science. And this is where illu's perspective is coming from.
-below this line is a long but hopefully enjoyable post-
If you wander into pure math (which is theoretical math, the most general form of math), it would blow your mind at first about how general math really is and how the things you've learned in high school math and prerequisite math for engineers/physics/chemists/etc. are actually very narrow. Because of this, a lot of people claim pure math is useless. But this is not true.
First off, math is indeed a human construct in a sense. There is an underlying truth that math describes. But there are many angles of looking at this with all angles being "correct enough" depending on the field in question. The problem is that some angles are more roundabout, less efficient, and less general than others. An example is calculus. Most of you know that Leibniz and Newton both "discovered" calculus. But what they did is based most of their math on intuitions from the physical world rather than prove it with mathematical rigor. With the Age of Reason's influence, some scholars sought to distinguish science and math apart from faith-based religion. And one of the main tasks was to define and prove the concepts of calculus with mathematical rigor. A big question during the 1800s was, "What is space?" A high school level teacher named Green (or Greene?, not the one from Green's Theorem) and Hamilton (the math genius) each came up with a different answers. Hamilton's answer was obviously taken more seriously given his prestige. And mathematicians used his viewpoint to further advance calculus to what it is today. What you learn in high school, undergraduate college, and standard graduate college is all based on Hamilton's interpretation of space. My professor told me that it takes an additional 8 years of studying calculus (beyond prerequisite calculus most hard sciences undergraduate majors learn) to see the big picture behind calculus. And this is not due to the difficulty of the material, but rather due to the poor interpretation by Hamilton that requires a sort of "unlearning" of the habits students have picked up. Green's interpretation was not forgotten, rather it went underground and a few elite mathematicians furthered it to develop an even more elegant interpretation of calculus (able to generalize all of calculus' big theorems as special occurrences of a single simple mapping).
Also, Newton's notation was notoriously inefficient and supposedly held the English back compared to the Germans and French.
Anyways, the point of all this was to illustrate that pure math is not useless. If no one did it, then each field of science would advance math in their own way. Because their math would have biases and constraints from their fields, transitive laws from two different fields would not be fluid and the discovery rate of unifying theories between fields would slow down. Oh yeah, number theory/encryption and algorithm efficiency/computer science are also why pure math is good.
|
Regarding the mechanical debate:
I taught college math for three years, and I've tutored much longer than that. My university wanted me to stay and get a Ph.D. and teach because they needed "more teachers like me." (Instead, I took my M.S. and got a damn job =p). The short answer is YES, you can teach an algorithm, have them practice, and then it becomes mechanical. It's just like practicing a b.o. in SC. Eventually it becomes second nature. However, if you don't teach them the WHY, then they're not going to be able to adapt, even to simple situations where two ideas are combined, each of which they know individually.
My advice is learn the 'algorithms' you're taught, but understand the reason behind each step. Having a bad teacher is going to make this hard, but pin them down in office hours, or ask a TA. (Professors who intentionally refuse to hold office hours are usually doing something wrong and can get in trouble). Work in groups. Don't just do the work to get it done... study until you can pick up a new (but related) problem you haven't seen before and
1) classify what type of problem it is
2) identify what tools you'll need and -why-
3) perform your algorithm(s)
all without looking back at your old work or notes. That's what you're going to have to do in an exam, so you might as well practice that way.
If your professor wants you to explain everything in words, he might be a prick, or he might be trying to help you. If you have to explain it, you -have- to know the "whys" of the steps. Does he have a policy that if you don't explain, he won't grade the problem? If so, maybe you're just not following directions :/
|
i think the main problem with how math is taught is that they tend to assume that you know much more than you do when it comes to math. More importantly, the main issue is how utterly useless the textbooks are when it comes to proof. Ninety-nine percent of the time, proofs are either "left as exercise" or so hopelessly annotated that it's next to impossible for students that learn "AP" calculus to get to that point.
as an econ major, at a school where "econ" is really "take shitloads of partial derivatives of abstract economic concepts," even though i did terrible in pure math, i can now start to see where they're coming from (because in econ, while we don't use epsilon and all that stuff, we do use notations and yet are still able to prove and derive things.
I still hate math though. Stupid epsilon delta.
|
On November 02 2009 13:32 Plexa wrote:
LOL Dave you are so right. People just forget everything and anything they've learned from other courses and they get destroyed haha
I'm an engineer so naturally i do a shitload of math almost every day. I used to be terrible at math, not because it was "too hard" and "stupid" but because I was not putting in the effort to learn it and fully understand the concepts. Math builds on itself almost from day 1. What this means is that everything you learn in math will be used again later (ESPECIALLY algebra through trig). If you do not take the time to be able to do algebra and trig effortlessly then calculus/linear algebra/proofs etc are going to be almost impossible because it will take twice as long to understand every little thing.
I find the best way to learn math is go to every class and then spend roughly 5-6 hours a week doing math problems that relate to the section you are in. Re-write all the formulas over and over every time you need to use one. You CANNOT, i repeat CANNOT learn math by watching.. You have to do it yourself and learn it yourself. Do not blame a teacher for being "shitty" because math is concrete and it's your fault if you did not learn it.
@Op: do not attempt physics.
|
Aotearoa39261 Posts
On November 03 2009 00:36 Caller wrote:
i think the main problem with how math is taught is that they tend to assume that you know much more than you do when it comes to math. More importantly, the main issue is how utterly useless the textbooks are when it comes to proof. Ninety-nine percent of the time, proofs are either "left as exercise" or so hopelessly annotated that it's next to impossible for students that learn "AP" calculus to get to that point.
as an econ major, at a school where "econ" is really "take shitloads of partial derivatives of abstract economic concepts," even though i did terrible in pure math, i can now start to see where they're coming from (because in econ, while we don't use epsilon and all that stuff, we do use notations and yet are still able to prove and derive things.
I still hate math though. Stupid epsilon delta. If you have ever read Ruden then you would have the opposite problem to the one you had. The proofs are so elegant and streamlined that working out where the fuck that argument came from and understand each step is a serious mission lol
|
|
|
|
|
|
EPT
