Recent content by Tom Gilroy

Thank you, those are both excellent ideas.

Actually no, it doesn't have to be technical at all, and that's a pretty good idea. The motivations for the formulation of Vertex Operator Algebras is quite an interesting story, and they've been a tremendously important tool in mathematics and physics in the last 25 years. My only concern is...

Hi everybody, I'm a first year Ph.D student in mathematics and I've been asked to give an hour long talk for the university maths society. Speakers have the choice to talk about just about anything maths related, however the focus of most talks is usually the discussion of a classic maths...

R and R x R have the same cardinality, there's certainly an injective function f:R x R->R. I don't however, have an example of one offhand. I'll try to think of one.

I officially began as a Ph.D student almost 2 months ago, studying vertex operator algebras. Typically, I get into the university at 9am and study until about 7pm, granted with about an hour of a break inbetween. So that's 9 hours. I often might spend another hour to an hour an a half studying...

Well, what happens when we multiply any non-constant polynomial in R[x] by any non-zero polynomial in R[x]?

I was aware of this, and reconsidering my post, I probably should have said that the definition of a category on Baez's page isn't accepted universally, and given the class based definition as an alternate option. My intention was merely to point out that the set based definition does not...

I'd first like to mention that the definition of a category that appears on Baez's page is incorrect. A category does not consist of "a set of objects and a set of morphisms." A category consists of a class of objects and a class of morphisms (any set is a class, but not all classes are sets)...

Several, the most relevant definition that would encompass mathematics would be a body of knowledge attained through sytematic study, this particular definition being broad enough to include the natural sciences and mathematics. http://dictionary.reference.com/browse/science Certainly if...

Here you have given the definition of natural science, however the word "science" itself has other meanings, which do encompass mathematics. Moreover, the concepts of right and wrong aren't evenly slightly relevant in mathematics, mathematics is about what is consistent and provable with respect...

Actually, this reminds me of a situation when I worked in a hardware store several years ago. We had a certain terracotta plant pot that was quite a reasonable price (which I forget, but let's say €5, for the sake of the story), but was being sold as "buy one, get one free." Quite quickly, we...

I would consider mathematics a science, though perhaps not a natural science. It's certainly a science to at least the same degree that computer science is a science. Most mathematicians I've met seem to subscribe to the platonist veiwpoint, including myself to some degree. I wouldn't accept...

Well, that depends on the specific courses I suppose (that could be said about real/complex analysis too). I had to take a two semester course in group theory as an undergraduate which was very deep and advanced, and a two semester course in ring theory and field theory which was also quite...

Just curious, you haven't mentioned courses in group theory, or ring theory or field theory, or other algebraic topics. Are they not available at undergraduate level where you studied, or do you not feel they're as important? Abstract algebra was emphasised hugely in my university.

Thanks. I'll just dive right in I guess!