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Week 1 Update

I finally made it to Canada and just finished my first full week at the Fields Institute! St. George Street One of the campus dining halls Fields is housed on the University of Toronto's campus, and the participants of the program are given accommodations at one of the university's residence halls. Over the past week and a half, in addition to my research, I've been exploring the campus and neighborhood. I'm really enjoying getting to live in Toronto for the summer (especially because it's not as hot and humid as Atlanta right now)! Bloor Street West Thomas Fisher Rare Books Library As part of the research program, I have an office at the Fields Institute that I share with the two other members of my group the Project 8 group. Fields is great; for one, I don't think there are any whiteboards in the building - only blackboards.  There are also conferences and talks that are going on many of the days, so that means there's also free coffe...
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Update

Happy Tau ( τ)  Day! For those of you who may not be familiar with  τ , it's equivalent to 2 π , a constant extensively used in mathematics. I prefer   τ to  2 π because it's simpler (and because it's one number instead of two, so I'm less likely to make some sort of algebra or arithmetic mistake).  Read about some of the advantages of tau over pi here :  Let’s Use Tau—It’s Easier Than Pi . (Yes, that is a math book in my jacket pocket.  The wonders of pockets on men's jackets!) Now the update: I'm leaving for Toronto very soon, and the program at Fields starts on July 3rd. I don't have much more information on the research this summer, but our PI (principal investigator) sent an email with a few details. We'll be looking at hybrid symplectic integrators, which are numerical ODE (ordinary differential equation) solvers. I don't know much about them beyond that, but part of the goal for the research is to determine how they work and how...
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Introduction

Welcome to the blog I'll be keeping while participating in the  2018 Fields Undergraduate Summer Research Program .  The program is through the Fields Institute for Research in Mathematical Sciences, which is on the campus of the University of Toronto in Ontario, Canada. I will be participating in Project 5 along with other students from around the world. From the above website: "This project is about the methods used for numerical simulations of both exo-planetary systems and our own Solar System. Having fast and accurate numerical tools to perform such simulations is crucial if we want to understand the dynamical architecture of these systems." My understanding of the project is as follows: we'll be working on a project that involves solving complicated equations (higher-order differential equations, specifically). These equations are complicated enough that we can't solve them using our nice standard techniques. Because of these complexities, we turn...
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