Jul
9
answered How to intuitively convince the students that a strip with two full twists is homeomorphic to the standard annulus?
Apr
29
awarded  Caucus
Mar
13
awarded  Yearling
2018
Dec
9
revised Word for the dimension of the vector space in which a vector lives?
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Dec
9
asked Word for the dimension of the vector space in which a vector lives?
Oct
30
awarded  Nice Answer
Mar
13
awarded  Yearling
2017
Jul
14
revised Teaching strong induction instead of induction
added 11 characters in body
May
18
comment Do “gateway tests” work?
I teach at Michigan, including I taught Applied Linear Algebra which instituted a Gateway on row reduction and other matrix operations while I was there. My post-gateway syllabus has an extra week of material in it, because I spend so much less time on these basics. But I don't have the sort of formal data you want.
Mar
13
awarded  Yearling
Jan
20
revised Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?
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2016
Oct
24
awarded  Nice Answer
Jul
26
revised Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?
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May
3
comment How to get students in a under-graduate linear algebra course interested in determinants?
@LoopSpace How about: Given two $n \times n$ matrices $A$ and $B$, find all $t$ for which $t^2 \mathrm{Id} + t A + B$ is singular? For $t \mathrm{Id} + A$, you can use specialized methods for computing eigenvalues but, as far as I know, you need to fall back on determinants once the polynomial is higher degree in $t$.
Mar
24
revised How can one motivate the adjugate matrix?
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Mar
24
answered How can one motivate the adjugate matrix?
Mar
13
awarded  Yearling
Jan
21
comment How to motivate the surface element
I wonder whether it might be useful to spell out the $k=2$ case: $\det \left( \begin{smallmatrix} \vec{u} \cdot \vec{u} & \vec{u} \cdot \vec{v} \\ \vec{v} \cdot \vec{u} & \vec{v} \cdot \vec{v} \end{smallmatrix} \right) = |u|^2 |v|^2 - |u|^2 |v|^2 \cos^2 \theta = |u|^2 |v|^2 \sin^2 \theta$. Sometimes I find that students whose eyes are glazing over in linear algebra wake up when I remind them of high school geometry/trig. (And sometimes I learn that they never had high school geometry, which is a different problem.)
Jan
21
revised How to motivate the surface element
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Jan
21
comment How to motivate the surface element
For someone who really understands QR decomposition, this is the same as Dirk's answer, but I claim it is more friendly to those who don't.