cantormath’s Comments (group member since Sep 06, 2010)

cantormath’s comments from the Mathematics Students group.

I have noticed there is only one discussion topic in this group. If anyone wishes to post another discussion topic related to mathematics or books on mathematics, feel free. If the Goodreads does not let you post a new discussion topic for this Goodreads group, let me know. Feel free to post new topics here and I will post them if you cannot. Please, no publisher solicitations for calculus books etc, this group is for mathematicians and mathematicians in training. With that, feel free to discuss calculus or lower levels subjects; all math is good math here ::grin::

@Ronald, nice description and comment.

I am currently studying topology in grad school (knot theory). At the undergrad level you will probably find yourself studying point set topology. Munkres and/or McCleary are the best books for point set topology, IMO. Think of this course as doing mathematics without the concept of distance (i.e., a metric). Without distance, how do you differentiate two objects mathematically? Do the objects have holes? how many? is it smooth, rough(resp), is there a boundary or is it locally round like a sphere? Basic (point set) topology looks to compare mathematical objects upto homeomorphisms. After point set topology things get really fun with subjects like knot/braid theory, homology and other algebraic topology, differential geometry and/or 4 manifolds, combinatorial topology, tqft's, Dessin D'enfant, just to name a few.

Regardless of your field of study in grad school, I find that Linear Algebra is one of the most used subjects on a regular basis.

Topology, knot theory mostly. Just got done with Skein Module theory in the spring'11. I also receive a pretty good dose of Algebraic Geometry (pain to learn but very important). Nice to meet you all.