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comment How to show that a polynomial does not have real roots
(A minor remark: The constant term is nonzero, so that $0$ is also not a root.)
Jul
8
revised Modeling, Measuring, and Maximizing “Mixedness”
Added keywords from the responses by post and comment.
Jul
7
comment What are the formal terms for the intersection points of the geometric representation of the extended trigonometric functions?
Since you mention Spherical Trigonometry: This was a part of the NY Regents Exams 14 times between 1890 and 1964; unfortunately, not all of them have been uploaded to the archives. (The first linked ones are from 1924; the oldest is from 1891!)
Jul
5
comment Modeling, Measuring, and Maximizing “Mixedness”
@Tad Though you refer to them as standard combinatorial optimization techniques, I have no familiarity with simulated annealing or genetic algorithms. A similar post analysis here, if you have the time and energy, would be great! (As far as the number at each table: It would be best if the students who were at the 4-table changed a fair amount, too...)
Jul
5
revised Modeling, Measuring, and Maximizing “Mixedness”
deleted 2 characters in body; edited title
Jul
1
revised Modeling, Measuring, and Maximizing “Mixedness”
altered title slightly, and clarified where the actual Question is
Jul
1
comment Is there an alternative intuition for solving the probability of having one ace card in every bridge player's hand?
@GTonyJacobs Agreed; see, in particular, Chapter 4 Problem 21 here in Grinstead and Snell's Introduction to Probability.
Jul
1
comment Cardinality of the set of all field automorphisms of $\mathbb C$
See MSE 412010...
Jul
1
comment Is there an alternative intuition for solving the probability of having one ace card in every bridge player's hand?
(Clearly "ace of space" is a typo for ace of spades, $A \spadesuit$!)
Jul
1
answered Is there an alternative intuition for solving the probability of having one ace card in every bridge player's hand?
Jul
1
asked Modeling, Measuring, and Maximizing “Mixedness”
Jun
18
revised Probability that a stick randomly broken in five places can form a tetrahedron
Updated MSE to correspond with updated MO
Jun
12
comment Maximum number of Sylow subgroups
Possibly the problem can be traced back one [small] step to AoPS. You may have to ask there to find out its original source.
May
27
revised Self Teaching Theory for Olympiad. Need advice for books.
xp
May
27
comment What branch of Mathematics does the study of Algebraic/Transcendental Numbers lie in?
You may wish to check the wikipage on transcendence theory, which begins: "Transcendence theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways."
May
2
comment Probability that a stick randomly broken in five places can form a tetrahedron
... Still running???
Apr
18
revised Advice on finding counterexamples
Alternative counterexamples briefly expanded upon in a final comment
Apr
3
comment Advice on finding counterexamples
The only thing I might add is that, at least for me, I try to contradict set size or closure. In this case, you can union any two $2$-element subgroups of the Klein $4$-group, multiply the non-identity elements together, and show that closure fails for the set. (Your answer, quite reasonably, took the set size route instead...)
Apr
2
comment Advice on finding counterexamples
Very nice answer!
Apr
2
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