Final Summary

Throughout this summer, I have gained valuable insight into mathematics research. Coming in with little knowledge of dynamical systems, I began by reading and learning all about the topic. Participating in a reading group helped me understand the material quickly and in depth, since other students and I tackled and solved practice problems together.

[Read more…]

Time Series and Partitions

My project took a new direction after my presentation. I had the idea to implement partitions along the time series points instead of using uniform partitions. The reason behind this new approach is that the finite representation given by it would be true to the time series. This approach would also improve the quality of the finite representation, bringing it closer to an outer approximation. Since every time series point is on a partition, every interval and their image gets picked up by the finite representation.

[Read more…]

Time Series Analysis: Update

As I have mentioned before, I am part of a group of research students, each with their own individual projects, mentored by Professor Day and/or Professor LaMar. We all meet once a ¬†week to hear a talk on someone’s research. In preparing for my talk, I read various articles on giving talks, most of which included the following,

[Read more…]

Finite Representation

The next phase in my research was to learn about Conley Index Theory, with the intention of applying it to time series analysis. In my research, I approach time series as an incomplete map. “Maps” are deterministic, discrete-time dynamical systems of the form, [Read more…]

Week One- Time Series

Most of the time, it can be difficult to find direction in mathematics research. Trying to phrase a meaningful question that could lead to meaningful answers is a great challenge in initiating research. To accomplish this step, I spent my first week of research reading various books on Chaos and time-series. I became familiar with terminology that pervades the area of interest. I found it helpful to write a list of definitions, which will be useful when I write about my research.

[Read more…]