Sintu
Jan8-11, 08:57 AM
In my math career, I have been exposed to topics such as real analysis, topololgy, metric spaces, lattice and order theory, group theory, rings and fields, linear algebra, differential equations, vector calculus and other topics. I pass my exams and tests and believe that with enough studying I could pass anything. My challenge is research. I did a supervised research project on topology: I had to investigate function spaces which did not go too well. I only understood the basic concepts which extended my understanding of metric spaces and lattice theory. None of it was very insightful and none of it was investigating the compact-open topology and such things.
I believe that it was because some topics were too advanced for my consumption back then. I have time now to find a topic that is possibly more readily consumable and I would like help with such a topic. I really enjoyed group theory and lattice theory which is why I approached my topology project in that way. I did not understand the problems of cardinality: in fact, I still cannot explain away the problems of large cardinals and why a product of Hausdorff spaces, each with at least two points, is separable if and only if each factor is separable and the factors number fewer than or equal to the continuum.
A great answer to my question would be one that gave me a really good paper to review that applies group theory and lattice theory. I would like to investigate applications of representations of difficult lattices in simpler forms. I also majored in economics so game theoretic applications of math would also be easier for me to understand, if they existed. And of course the cardinals may come back to haunt me again.
Hopeless isn't it? That's why I need help. Please help me.
I believe that it was because some topics were too advanced for my consumption back then. I have time now to find a topic that is possibly more readily consumable and I would like help with such a topic. I really enjoyed group theory and lattice theory which is why I approached my topology project in that way. I did not understand the problems of cardinality: in fact, I still cannot explain away the problems of large cardinals and why a product of Hausdorff spaces, each with at least two points, is separable if and only if each factor is separable and the factors number fewer than or equal to the continuum.
A great answer to my question would be one that gave me a really good paper to review that applies group theory and lattice theory. I would like to investigate applications of representations of difficult lattices in simpler forms. I also majored in economics so game theoretic applications of math would also be easier for me to understand, if they existed. And of course the cardinals may come back to haunt me again.
Hopeless isn't it? That's why I need help. Please help me.