Michael Smith
Reputation
633
Top tag
Next privilege 1,000 Rep.
Create new tags
 Dec 5 comment Difference of differentiation under integral sign between Lebesgue and Riemann In your right hand side is it supposed to be df/dx(x,t)dt evaluated at x = x0 and not df/dx(x0,t)? Nov 22 answered Show that $\mathbb{Q}$ is dense in the real numbers. (Using Supremum) Nov 20 comment What do we lose passing from the reals to the complex numbers? Does losing ordering define the complex numbers? Ie is there only one field (strictly) containing the reals that can not be ordered but is complete? Nov 15 answered Complete course of self-study Oct 9 awarded Supporter Oct 3 comment Permutating dance partners with least distance moved Thanks that is useful link and solve all the parts except minimizing how far the people have to move to swap partners and what this problem is called in graph theory Oct 3 revised Permutating dance partners with least distance moved improved title and added some combinatorics tags Oct 3 comment Permutating dance partners with least distance moved I looked up Maximal independent set here en.wikipedia.org/wiki/Maximal_independent_set but it doesn't seem to capture the same idea Oct 3 comment Permutating dance partners with least distance moved @Ross - that does seem to solve the first part and the rotating lines part. It does not address what this is called in graph theory (Qiaochu Yuan commented: I think he means counting the number of maximal sets of disjoint edges in a complete graph on n vertices but did not give a reference at the time). And it also does not address how we minimize the amount of movement required by the people. Oct 3 asked Permutating dance partners with least distance moved Sep 12 answered Historical textbook on group theory/algebra Sep 12 answered What are some good math specific study habits? Aug 28 comment On the Math Mindset I got "A survey of modern algebra" by Birkhoff and Mclane while I was in grade 12 and while I enjoy it now I did find it a bit abstract at the time. When I am getting into a subject I like to have more motivation and history in a math book. If you are into Algebra then "Rings, Fields and Groups" by RBJT Allenby is a much easier read that still covers most of the same ground. And the author's enthusiasm for math really shines through. Given that you are not finding your current teaching method motivating I think finding books that explain why the material is interesting are useful. Aug 11 comment How to tell $i$ from $-i$? That is an interesting question - is there an algebraic definition of orientation in the (complex) plane. For the question that was asked for an elementary explanation of difference between i and -i and I think it is reasonable to use the complex plane and the natural notions of geometry that students usually already know. Here is my attempt at describing clockwise in words - if you multiply a complex number by another complex number of length 1 that is close to 1 then if the y coordinate increases it is an anti-clockwise rotation and if it decreases it is clockwise. Aug 11 comment How to tell $i$ from $-i$? Yes there is an automorphism (a mirror reflection of the complex plane) that swaps i to -i and changes clockwise to anti-clockwise. I don't think that affects the above way to explain the difference between i and -i Aug 11 answered How to tell $i$ from $-i$? Aug 1 awarded Teacher Jul 31 answered How to make notes when learning a new topic Jun 3 comment How can we find and categorize the subgroups of R? Yes that is true. And the point I am trying to make is that I think there is a infinite hierarchy of dense subgroups between Q or these other non-Q subgroups and the full group R. And I am wondering how to classify those... My intuition says that this is somehow related to the diagonal proof of the uncountablity of the reals and the point that @rschwieb made on the related question math.stackexchange.com/questions/152263/… about stripping away leading digits doesn't matter. Jun 3 comment How can we find and categorize the subgroups of R? @benmachine - thanks for correction of definition of dyadic rationals - I updated the question text to reflect this.