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BB0yRJ (November 30, 1999 at 12:00 am)
maths is so confusing.. im 2nd yr hs now.. when i go college.. im not sure if im passing lols..
ghodium (November 30, 1999 at 12:00 am)
yes i agree, these things do make a difference :)
tomdorley (November 30, 1999 at 12:00 am)
i think it makes a huge differnce if your taught by the right people in the right way, and if a lecturer is enthusiastic and has a love for their field
when i try to learn something new, the most important qualitys of a teaching source (books,lectures,etc) for me are, clarity/consistency, large range of "worked" examples and disscusion/contemplation
also making notes is conterproductive to building conections in your brain, you need to think, not think about writing!
ghodium (November 30, 1999 at 12:00 am)
this is quite so, but "the complete level of abstraction that comes during undergraduate math" is something i'm not so sure about, i've seen how so many undergraduates struggle so much and never get their head round it, some of them very ambitious and demanding on lecturers' time
tomdorley (November 30, 1999 at 12:00 am)
quite the opposite, the mental stimulation involved in understanding these concepts has been show to reduce dementia
VeryEvilPettingZoo (November 30, 1999 at 12:00 am)
General Relativity requires manifolds (locally look like n-dim spaces, but global aren't - like 2-dim surfaces, donuts, spheres, etc) and their smooth constructions (tensors, bundles, connections, etc) which generalize vectors, angles and distances, and captures distortions from the global bending of the space.
Quantum Mechanics is usually described using Hilbert Space, which is an infinite-dim vector space with an inner product (so lengths, distances, angles) and good limiting properties.
VeryEvilPettingZoo (November 30, 1999 at 12:00 am)
I'd guess that the biggest math conceptual hurdles between counting and sophisticated math are basic algebra, limits (hence calculus), and the complete level of abstraction that comes during undergraduate math. Numbers get replaced with sets, properties, and the functions that preserve them (linear and abstract algebra). Continuous functions (preserve domain closeness - no jumps or tears) get replaced by maps on arbitrary sets with topologies.
ghodium (November 30, 1999 at 12:00 am)
might not dementia set in for many before they understand it with any real depth, and what of insight?
VeryEvilPettingZoo (November 30, 1999 at 12:00 am)
Yes, that's what I'm saying.
Show me a child of average intelligence and no particular talent for math, but one who is dedicated and willing persevere, and, given enough time, I'll show you someone who understands Einstein's Field Equations for General Relativity well enough to teach the subject.
That's my impression on the matter. Is there research supporting or refuting it? I don't know.
AlboBesi (November 30, 1999 at 12:00 am)
Newton's laws (namely the second and the third) have found vast applications in engineering. huge theories have been developed based off of these laws. continuum mechanics, finite element analysis, elasticity-based solutions are all just some advanced topics that have emerged out of Newtonian physics. |
