jskryn said:
In your original post you mentioned that a student "should" be beyond solving simple derivatives and integrations by the time they reach college and I pose to you a friendly, intellectual challenge: prove it. What axiom do you begin with and what logical deductive process do you use to arrive at the assertion that it is objectively better for an individual to master these skills by a certain time in lieu of mastery of other skills? Or do you have empirical results to back up this claim? I don't intend to sound confrontational, but it's something worth thinking about.
C'mon tehre are no definitions for the problem even. I would have to create a theory from scratch for this. Maybe I can take inspiration of Shannon's Information theory, but stablishing a base line of knowledge si in the end subjective. But in a more discursive sense I would go to before in your own post "I believe the sentiment in most American universities is to allow students to explore their interests for the first year or so and I don't believe this is a bad thing, [...]" (as an addendum nor do I) but here it is. If high schoolls left the basic solving skill covered then colleges could start going into real mathematics at a start (simple set proofs, like de Morgan laws could be enough) in introductory courses to show the student what a mathematician does (the reason I added the question to my OP of what a mathematician does to non mathematiciasn) and why it could be interesitng and fullfiling. The way it is know it does not showcase what you could get into by choosing a Math major.
MysticSlayer said:
I'm up to Calculus 3, which here basically means we start considering more than one variable and move into three or more dimensions (not sure what the equivalent is there). Proofs still aren't used, but at this point, 95% of the people taking the class are engineering students who aren't too concerned with proofs. Given my major, this is essentially the end of pure math for me. After this, it will basically be all about applying the math I've learned to different engineering concepts.
Yes, the disparity of Math level has been adressed before, and it indeed does make sense. About Caluclus 3 here it is also vector calculus, but strictly differentiation. In the carrers of Physics, Math, Actuary and CS there are four Caluclus (I-IV) each concerning the followinf, differentiation (and lmits and series), integration, differentiation inf R^n->R^m functions and integraton in R^n->R^m functions, respectively all in pure form and dedicated to proofs and the such. After that Math and ACtuary still have Mathematical Analysis I and II concerning metrics, compact spaces and finding complete spaces, and theory of measure and Lebesgue integral. The Caluclus course is about 10 hours a week for two years.
Raggedstar said:
I'll assume you're talking about me since I mentioned "university level", "functions", and "trigonometry" in the same post on that thread and seem to be the only one. Not offended, and I apologize if it's not my post you read, but I'll respond to that directly if it was me that you were talking about.
Let me specify in saying that WAS high school.
Well, yes your post indeed was a part of it, but the fact that someone mentioned doing Pre-calc (which are more or less similar to trigonometry, funcitons, etc.) as a college course sparked alos my interest in seeing this as a repeated phenomena. The aclariation though is noted and appriciated.
xshadowscreamx said:
The number is already predetermined. It will always be 6.
Creating a story or art from imagination is creativity.
Ah a huge misconception I find with non-Math studentsm that they are uncreative. Tell me, how many "artists" have imagined worlds in so many dimensions that the human bairn can comprehend them (n-dimensional spaces are quite common after all in math). Or that infinity is not a single thing that is huge, but there are larger infinites than others. Or that donuts and cups are actually ythe same matehmatical object. Or simply how can you know that such a simple equation has an answer? Or even if ti has an answer how can you guarantee it is the only answer? Or that you can wirte a number for it and not a funciton? Those jsutifications are extremely creative, comming form moments of genius. Mathematical proofs can be very creative things.
skywolfblue said:
The highest "Pure" math classes I took were "Differential Equations" and "Linear Algebra". In truth I don't remember which was exactly "higher"?
Because Differential Equations sure look complicated at first, but then you realize there's only a few ways you can solve them (or at least the problems that I deal with in engineering), so it gets kinda easy when you can recognize what "type" each problem is.
Linear Algebra begins as "oh, matrices, boring" and then as time goes on I realize that these simple matrices are describing really interesting N dimensional spaces, then I was like "Cool!".
Electrical Engineering does require a lot of math. Not too much of the theoretical stuff, just that which pertains to the physics of electrical fields.
I would say they are about the same level, but it depends on the focus too and what was covered.
If it was onlu ODE of the first order, it is pretty basic stuff, as if you only kept finding the eigen values of matrcies and not using them. Did you prove the existance of solution for any first order diffrential equation with initial conditions (Cauchy's Problem)? ANd did you go into the nuenances of dimensions and kernels in Linear Algerba? That would determine how high you went.
Also, yeah the equations in engineering tend to be nicer. A huge amount of DE have no simple analytical solution and have to be solve numerically, as those techniques used (variable separation, integratio factor, I guess as the two main ones) are not applicable and the integrals involved can be shown to have no simple primitive.
Danny Ocean said:
Not being a science major does not necessarily mean you only have a high-school level of maths.
Especially if you're a social scientist (stats) or an analytic-school philosopher/philosopher of science/philosopher of maths.
No it doesn't. That is why the Stats centric option exists (although it says science and medicine, it should not be taken as an exhaustive list) and the self-though, as philosphers usually have iffy relation wiht math (several analutic-school and philosphy of science firends that have never taken a higher education math calss).
f1r2a3n4k5 said:
For example, OP, do you have any background in art history? My college offers intro-level art history courses. Presumably, there may be people who went to artistic schools and know this stuff already. I did not. So, I enrolled into an introductory art class. Same basic premise; different field of study.
I personally fall most heavily into the "statistics" category. I took Calc I and Stats I for my degree in Biology/Pre-Medicine. I also took Discrete Math for the hell of it. However, understanding a lot of research has required me to study up on other math on my own. The other day I delved into Principal Components Analysis. Most frustrating thing I've ever tried to understand as I don't have a strong background in matrices.
No formal background, but I've been visitng museums and been very bathed in art history since quite young (family loves art, unlce is an artists, aunt stuided art hisotry). Also, while no being disrepectful, Math is a very central subject in our modern world (we are after all, talking throgh computing machines) and not knowing its real roots seems to me as a huge downfall (in all the world actually), as Math rules the physical world. Alos, those courses are given here in an extra-curricular manner, and they can be at a similar leel to those of the specialized students.
If you are having problem with matrices, read a bit about Linear Algebra, it may help.
Exterminas said:
I have a doctorate in theoretical philosophy and spend my average work day doing math without numbers.
... Should I just pick the "I hate math"-Option then?
What math without numbers does a PdD in philosphy does do if I may ask?
Also, I will edit the OP with a little more explanation on the options, as there seem to be a few complaints about that.
I would love also that the person that chose Phd doing research, would share what resaerch he is doing.
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