I think it'd be more appropriate to put the research I'm interested in first so as to provide a bit of information into my background.
2)
Research Interests:
I spent 3 years in Kinesiology attempting to 'double major' in Kinesiology and Mathematics. When I was told this was not possible, I was faced with a difficult decision regarding which direction to choose...Ultimately, I always had to struggle to study the Kinesiology information while Math came naturally...and it seems as though fewer people go into Pure (Abstract) Math and since I feel confident and capable in this field, I decided to give it my all, and in my 4th year took 12 Math courses.
In Kinesiology, I loved Biomechanics, particularly Spinal Stability (how much your spine 'reverberates' if you will, when you do various actions like standing up, or throwing a baseball), as well as Ergonomics, particularly the analysis and repair of employee workspaces, relating to lifts, loads and spinal damage.
As for Math, I'm very interested in Pure Math. I'm not as fond of 'applied' Math fields, like solving equations or modelling natural phenomena, and instead like the bare essentials which have no roots in the real world (but still have applications to the real world).
In particular my interests lie in Mathematical Logic, Differential Geometry, (which is the Mathematical language of Cosmology and Astrophysics(, as well as Point Set Topology and Algebraic Topology. Topology is sometimes called the "Geometry of Rubber sheets." Usually when I say Geometry people know what I'm refering to, shapes, various objects which you can measure. Topology is a generalization of Geometry, where lengths and angles are immeasurable. Basically this means, you can stretch, compress and bend objects and they are the exact same object!
To a geometer, a circle and a square are different structures...but to a topologist, they are they same! (Namely, they both have no holes, and I can squish a square so that it is round and becomes a circle). In a similar manner, a donut and a coffee mug both have exactly one hole...and so to a Topologist they are the same "Topological Space" or structure!
1)
Research Conducted:
a) KINESIOLOGY:
-I did an ergonomics project on the LCBO's workspace for my ergonomics course. This may not seem like research, but I (along with my 3 colleagues) successfully redesigned the workplace! We used some methods of analysis, such as the Snook/MITAL tables, and Biomechanical Lifting Analyses. The paper is fairly official looking, and I'm pretty proud of it. (:
-I had two proposed research projects for a 4th year thesis, but I haven't conducted either project. One would be a quantitative assessment of spinal stability in mining truck drivers (not my idea, I would have been assisting a PhD student with their research).
-The other would be a qualitative assesment of the ergonomics of purses...sounds fruity doesn't it? I wanted to compare the incidence of poor posture, scoliosis, etc. in female populations based on what type of purses they use (long straps, short straps, backpack style, etc.) and how frequently they 'switched arms.'
b) MATHEMATICS:
I've currently been working on a problem in Point-Set Topology. Namely, I am trying to solve the question: Is |R^∞ Normal in the Box Topology?
This question is currently unsolved, and my attempts to answer it have been fruitless...but I'm trying nonetheless!
If anyone is interested, the following are the technical details of the project (Sorry if it's a bit too technical...but it has to be precise! Please skip it if you don't really care haha):
Definition: We say a Topological Space is
Normal if any two closed sets (of 'points') can be separated by disjoint ("Non-touching") open sets.
Definition: We call
|R^∞ ("The Real numbers to the exponent infinity") the collection of all possible infinite sequences. Such as {1,2,...}, {1,11,111,...} etc. Even though it's very hard to visualize 'an object' this
is a Topological Space!
Definition: If X is a Topological Space that is the 'cartesian product' of some number of Topological Spaces (
|R^∞ is an infinite number of 'copies' of the Real Numbers), then we define a topology on X called the
Box Topology by designating that open sets are the arbitrary cartesian product of open sets in each smaller Topological space. (I know this is very technical but I'm sorry ): )
-I've discovered, and proven, a very elegant construction of what is called Circular Inversion. To the layman, this can be explained as "Ok, I have a circle, and I have a point inside the circle. How do I "Mirror" this point to the outside of the circle?"
This is also a very important method for contructing multiplicative inverses. That is, if I have line segment of length n, I can construct the length 1/n, without using a ruler.
-I've also used Fourier Analysis to sum a series...but after the rigorous details I've posted above, I don't want to bore anyone, haha.
3)
Other Interests:
I have a few, but I'm pretty occupied at the moment with the research I've posted above.