## Math and Science Popular With Students Until They Realize They're Hard 580

First time accepted submitter HonorPoncaCityDotCom writes

*"Khadeeja Safdar reports in the WSJ that researchers who surveyed 655 incoming college students found that while math and science majors drew the most interest initially, not many students finished with degrees in those subjects. Students who dropped out didn't do so because they discovered an unexpected amount of the work and because they were dissatisfied with their grades. "Students knew science was hard to begin with, but for a lot of them it turned out to be much worse than what they expected," says Todd R. Stinebrickner, one of the paper's authors. "What they didn't expect is that even if they work hard, they still won't do well." The authors add that the substantial overoptimism about completing a degree in science can be attributed largely to students beginning school with misperceptions about their ability to perform well academically in science. ""If more science graduates are desired, the findings suggest the importance of policies at younger ages that lead students to enter college better prepared (PDF) to study science.""*
## Don't ignore the study itself (Score:5, Informative)

Not that I entirely disagree with the premise, but I think a study at a school with a broader academic base would provide more worthwhile results.

## Re:like anything else.. (Score:4, Informative)

## Re:like anything else.. (Score:5, Informative)

> I am still not sure I understand using 4x4 matrices to do transforms in three space. I can write the code though (slowly).

That's just proof that you had a bad/crappy teacher. :-( Here is one explanation:

In 3D computer graphics we use a 4x4 matrix to conveniently and compactly represent _two_ things:

a) orientation, and

b) location (or position) within a single variable.

Where:

R = 3x3 orientation matrix, and

T = 3-dimensional position vector.

To understand how this comes about let us start with something a little more basic: 2D Affine Transformations. Namely: Rotations, Translations, Scaling.

Given a point P = we can write it in matrix form as either [ x y ], or

[ x ]

[ y ]

How would we write the equation for a point that is rotated around the origin (or z-axis.)? We will eventually want to write a matrix equation where the matrix represents a change in orientation. That is by definition:

x = R * cos(A), and

y = R * sin(A)

x' = R * cos(A+B), and

y' = R * cos(A+B)

Where:

R = radius of the angle,

A = initial angle,

B = the

relativechange in the angle,A+B = the

absolutefinal angleWe don't always know R, so let us rewriting these in terms without R:

x' = R * cos(A+B)

= R * {cos(A)*cos(B) - sin(A)*sin(B)}

= {R*cos(A)} * cos(B) - {R*sin(A)} * sin(B)

= x * cos(B) - y * sin(B)

Similarly we do the same for y.

Now, we would also like to write the equation for the Translation of a 2D point:

x' = x + dx

y' = y + dy

Likewise Scaling is pretty straightforward:

x' = x * sx

y' = y * sy

These 3 different operations require 3 different functions and order of operations! This sucks. It sure would be nice if we could

unifythese operations into one equation! We actually havetwochoices for how we could write/calculate this:a) Pre-multiply the column vector (ignore the '.' it is whitespace due to /. being lame.)

b) Post-multiply the row vector

At the end of the day it doesn't matter which convention you pick just as long as you are consistent.

Since /. is lame and doesn't like an _informative_ MATH post I'm breaking it into two parts...