478 reputation
28
bio website abundantmichael.com
location Cusco Peru
age 50
visits member for 2 years, 2 months
seen Jun 18 at 3:15

I am interested in many areas of math including topology (point-set, algebraic), functional analysis, Banach spaces and algebras, real analysis, complex analysis, measures and distributions, group theory, rings, fields, Galois theory, number theory, graph theory, numeric analysis, special relativity, matrices, non-standard analysis, foundations of mathematics, logic, categories and probably some others I am not thinking about right now!

I love to question basic assumptions and also like to create new connections between different areas. I have been playing with math since I was about 4 years old (my father was a mathematician too) and also grew up playing with computers too.

My favorite math book right now is the Princeton Companion to Mathematics which contains hundreds of interesting articles and has given me many new insights into topics I thought I already knew. :-)

I have bachelor and masters degrees in math from Cambridge University. I started a software company a few years after that, which is still one of my sources of income. I have lived in UK, Holland, USA and now Permanently Traveling in South America. As part of the PT life I sold and gave away 95% of the contents of my house and stored the rest in 2011. I also sold my car. Less is more!

I have many other interests including language learning (currently Spanish!), dance, painting, improv, 2012 changes, honest communication, energy healing, teaching Kundalini yoga, EFT, gender, futurology, history (especially of WWI and WWII), alternative history, reading science fiction and mystery books. Just like in my math investigations I follow the joy!


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.
Jun
3
comment How can we find and categorize the subgroups of R?
I am thinking that the structure of the subgroups of R might be clearer if we look at the generators of them. For example Z = [1], nZ = [n], aZ = [a], Dyadic =[1/2^n n in N], Q = [1/p p prime] etc. Then it is clearer which subgroups are subgroups or supergroups of others. Perhaps this idea can be extended to infinite (uncountable?) sets of irrational generating elements...
Jun
3
revised How can we find and categorize the subgroups of R?
added 28 characters in body
Jun
3
comment How can we find and categorize the subgroups of R?
@benmachine Oh, thanks for that example! That is interesting - we have a set that spans the subgroup but no subset is linearly independent! In fact we can remove any number of elements (finite or infinite) from this spanning set and so long as an infinite number of elements remain the subset still spans the subgroup... However I am not clear how to prove that no basis exists for dyadic subgroups of Q. I tried to get a contradiction from expressing 1/2^n as Z linear combination of basis elements but don't see that yet.
Jun
3
awarded  Commentator
Jun
3
comment How can we find and categorize the subgroups of R?
I am probably missing something here but is not the infinite set { 1/2<sup>n</sup> where n in N} a basis for the dyadic rationals of binary form ( 1/2<sup>a</sup> )? Thanks for the idea on Z-modules too!
Jun
3
comment How can we find and categorize the subgroups of R?
@benmachine - thanks for clarifying, I will look into those more and I found a proof of the classification of subgroups of Q at answers.yahoo.com/question/index?qid=20080425160119AA19f8E which shows that they are all either finitely generated or of the type of the dyadic rationals.
Jun
3
revised How can we find and categorize the subgroups of R?
added 19 characters in body
Jun
2
comment How can we find and categorize the subgroups of R?
That is a useful way to look at the problem. I know that R has a Hamel basis over Q and also any subgroup H that contains Q would also have a Hamel basis. Then we can make other subgroups by picking arbitrary subsets of these bases. I did some google searching on submodules of infinite power modules without any luck so you have any links for articles on that I would appreciate it.