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Results tagged with teaching
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user 3106
For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.
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Elementary applications of linear algebra over finite fields
Rubik's Clock and Its Solution by Dénes and Mullen (Math. Mag. 68 (1995), 378–381) uses linear algebra modulo 12 to solve the Rubik's clock puzzle.
2
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Elementary applications of linear algebra over finite fields
There is a Martin Gardner problem, reprinted in his Unexpected Hanging collection, that goes like this:
Miranda beat Rosemary in a set of tennis, winning 6–3. There were five service breaks. Who …
8
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Readings for an honors liberal art math course
In my opinion, one of the most important concepts to discuss in a liberal arts math course is the notion of mathematical proof—what it is, why mathematicians put so much emphasis on it, whether it is …
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How to teach generalizing the induction hypothesis?
The following observation about your question 2 might be too obvious, but one simple way to recognize when you need to strengthen the induction hypothesis is to notice that when you try to prove your …
- 82.7k
14
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Interesting examples of systems of linear differential equations with constant coefficients
There is some indication of what Rota had in mind in the book Ordinary Differential Equations by Birkhoff and Rota. I don't have a copy handy, but the preview on Amazon has this to say in the Introduc …
- 82.7k
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Interesting examples of systems of linear differential equations with constant coefficients
There has been some discussion of rigid-body dynamics in the comments. It's a little hard for me to imagine that there was a newly (1967+) "discovered" system of linear differential equations with con …
- 82.7k
7
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Hard problems with an easy-to-understand answer
Lomonosov's theorem that a bounded operator on a complex (infinite-dimensional) Banach space that commutes with a nontrivial compact operator has a nontrivial invariant subspace had a surprisingly sim …
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Important open exposition problems?
I'd nominate the theory of Macdonald polynomials (and associated topics). This is an extremely important area of algebraic combinatorics. Even if we restrict to type A, there are certain features of …
23
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Accepted
Does seeing beyond the course you teach matter? The case of linear algebra and matrices
These examples may not translate directly into useful material for your teaching. However, I do believe that they give a good taste of how mathematicians think about linear algebra. …
45
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Not especially famous, long-open problems which anyone can understand
The Kneser–Poulsen conjecture in dimension 3: An arrangement of (possibly overlapping) unit balls in space is tighter than a second arrangement of the same balls if, for all $i$ and $j$, the distance …
69
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Not especially famous, long-open problems which anyone can understand
There are infinitely many primes $p$ such that the repeating part of the decimal expansion of $1/p$ has length $p-1$.
First explicitly asked by Gauss, now generally thought of as a corollary of Artin …
131
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Not especially famous, long-open problems which anyone can understand
The lonely runner conjecture. As Wikipedia puts it:
Consider $k + 1$ runners on a circular track of unit length. At $t = 0$, all runners are at the same position and start to run; the runners' sp …
121
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Not especially famous, long-open problems which anyone can understand
Gourevitch's conjecture1:
$$\sum_{n=0}^\infty \frac{1+14n+76n^2+168n^3}{2^{20n}}\binom{2n}{n}^7 = \frac{32}{\pi^3}.$$
1Jesús Guillera: About a New Kind of Ramanujan-Type Series; Experimental Mathemati …
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Demystifying complex numbers
I noticed this old question because it got bumped recently, and am surprised that the original, historical motivation for complex numbers—namely, a formula for solving a cubic equation—does not seem t …
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"Homotopy-first" courses in algebraic topology
As an undergraduate, I took a semester of point-set topology that used Munkres's book Topology, and we studied the fundamental group towards the end of the course. Following that, I took a semester o …