Hi David, and thanks a lot for the feedback! I don't find it critical at all - I find it helpful because it helps me to see this project from a new perspective.
On Mar 31, 4:18 pm, David Joyner <wdjoy...@gmail.com> wrote: > In general, I find it hard to comment on this proposal without knowing > how much group theory you know and how well you know it. I have done some > python > programming in group theory, but need to know how much group > theory you know and which algorithms are familiar with. At this stage, it > seems > much more important to say something realistic with a definite useful > product in the end, than to lay out a great plan which might > or might not get completely implemented. > > So: > * Which group theory books have you read and feel you know well? "Algebra", Michael Artin, 2nd edition. This was the book used in Math 55a - the course in abstract and linear algebra I took in the fall. However the problem sets covered a great deal of other material - and in most cases, harder material (if you want to take a look, here they are: http://isites.harvard.edu/icb/icb.do?keyword=k80832). What makes the course unusual is that the instructor has the freedom to choose various topics that are not in the book. So I probably know "parts" of other books as well, I just don't know which they are :). We introduced a lot of group theoretical concepts (normal subgroups, normalizers, commutators, Sylow subgroups, simple groups, group action (orbits, stabilizers, transitivity), Galois groups,...) in the course, and established some major results in group theory, such as the structure theorem for Abelian groups and the three Sylow theorems. The same book is used in Mathematics 123, one of my math courses this term, for Galois theory and (in April) structure theorems for rings and modules. "Linear representations of finite groups", Jean Pierre Serre, Chapters 1,2 "Representation theory", William Fulton & Joe Harris, Lectures 1,2,3 These two books are used in the abstract algebra course I'm taking now (Mathematics 123 http://isites.harvard.edu/icb/icb.do?keyword=k84948&pageid=icb.page489376 ) in its second unit which is about representations. We covered the above chapters and the problem sets used exercises from the same books. If some unknown to me major theoretical concept shows up during the summer (given the background material assumed in the "Handbook", the only such thing will probably be cohomology), I don't think it's going to be a huge obstacle for me to understand it and then apply this understanding in Python. > * Which algorithms do you feel you can implement? A number of > issues arising in abelian groups boil down to a problem in (integer) > lattices. Well I'm now reading the "Handbook of computational group theory" and I find it pretty accessible. I admit I'm not familiar with all the algorithms in the book, but the ones I've seen so far (picking random group elements, computing orbits and stabilizers, testing for the symmetric/ alternating group) seem pretty doable. > * How much linear algebra do you know? How much lattice > theory (which you can regard as "linear algebra over the integers" > or "linear algebra over a finite ring such as ZZ/nZZ") do you know? In the fall we did a bit of that, especially because we needed it for the structure theorem for finite abelian groups. We showed that for example a matrix with entries in ZZ can be simplified by row/column operations to a form in which the only nonzero entries a_1, a_2,..., a_n are on the diagonal with a_1 \mid a_2 \mid ... \mid a_n. We established basic results such as the Chinese Remainder Theorem. I can't say we formally did "lattice" theory but I feel it has a lot to do with number theory which I'm really familiar with from the math olympiads. Also, what do you mean by "something realistic with a definite useful product in the end,"? Do you think that the algorithms in the preliminary version of my proposal would be too difficult to implement (or would not be very useful)? > I hope this doesn't come out sounding critical. I'm trying to be very > encouraging, but I think a good workable plan would have a better > chance of being accepted by the powers that be. It will also be best for > you in the long run. Yep I agree - thanks again! -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
