Quote:
Originally Posted by diddy!
Yea, that just wasn't the bargain I signed up for. I was a physics major, so math was just the language that we used. Where math lacked an analogue or could be used to explain something in physics, my curiosity and interest waned. I'm not saying I couldn't do it, just that unlike most math it didn't come natural and I didn't feel like putting in the time to get better. I'm also bitter, because the class that advanced these concepts to me is the only one I have ever failed in my entire life, so yea it is possible I am just not smart enough to understand it which kind of sucks.
Here is the description, and the class that is responsible for me dropping a math major to a math minor and picking up a history minor which eventually led me to law school and my current path:
MATH 201 TRANSITION TO ADVANCED CONCEPTS
An examination of the introductory concepts which pervade most upper level mathematics courses with an emphasis on proving techniques. Topics include logic and proving, sets, functions, cardinality and the properties of integers.
Offered each spring.
Here is a list of upper-level math courses which these concepts didn't pervade and which I had no problem getting a high passing grade in. It is also pretty easy to see the applicability of these topics to physics, which was my primary reason for learning them.
303. MULTIVARIABLE CALCULUS
307. DIFFERENTIAL EQUATIONS
323. MATHEMATICAL METHODS OF PHYSICS AND ENGINEERING
404. VECTOR ANALYSIS
hmm, like gusjohnsongoat said the 201 course sounds a bit like a discrete math class (did you guys do combinatorics?). the listed concepts pop up all over the place, so it's correct to say said concepts pervade upper level math. still, it's possible that the treatment of the topics obscured the connection, or that it was taught in such a way that the previous course wasn't actually necessary. . .
even at the multivariable level many people learn calc in a way that appears unrelated to sets and the like, but still makes meaningful use derviatives and what not. similarly, i am not surprised that the 201 course wasn't useful for the the methods course appeared unrelated-- it's a methods course after all. i'm a little surprised by your inclusion of the vector analysis course, but analysis means different things to different people. what did you do in the class? but yeah all these topics often emphasize computations/operations, esp if you are interested in the applications, in which case foundations tend to fall by the wayside.
i'd guess a lot of the 201 course's value comes via direct exposure to mathematical reasoning that many people, including good math students, don't get before college and reasoning that isn't always exercised in classes that are heavy on computations and what not. so the payoff of the course may not strictly be in the form of procedural knowledge (e.g. learning to integrate/differentiate), but also in the form of "proper thought."
this type of mathematical reasoning is essential as courses in the foundation/analysis of math are naturally more abstract and proof heavy. it's natural to math, but not natural to the way most people learn math, and thus many people--predictably--stagnate. that's troublesome, but such struggles are to be expected to some extent. there's a learning curve, not to mention that a lot of the content is more difficult. at least as troublesome is the inability to draw the connections b/t the abstractions and their applications, which is an indictment of the math education system. it's not a wonder that many people find the rigorous math to be unimportant, as it seemingly bears no resemblance to any of the math they have learned.
i'm rambling/ranting at this point and wrote a fair amount so
cliffs:
i think there's a good reason that the course description is stated the way it is. it's meant to prepare you for higher level stuff, but in particular for analyzing the foundations. i wouldn't say everyone needs to learn this stuff by any means but someone does need to know it (e.g. you want to differentiate/integrate, but do you know the function behaves nicely?), hence my comment about someone needing to know how the tool was created/how it works.