Advanced Mathematics Program (AMP) 2019 in Analysis
Welcome to the Real Analysis section of the Advanced Mathematics Program! This session meets Monday–Thursday July 1-11 in Skye 268 with your organizers Savanna Gee and Jonathan Dugan. There will also be an algebra session running Monday–Thursday July 15-25, as well as invited speakers on the Fridays of the weeks AMP is running. See below for a schedule of speakers.
Day One: Mon July 1–Metric Spaces
Day Two: Tue July 2–Ordered Sets and Bounds
Day Three: Wed July 3–Sequences and Subsequences
Thur July 4–Independence Day
No meeting today. Enjoy your holiday!
Day Four: Mon July 8–More on Sequences
Day Five: Tue July 9–Cauchy Sequences and Series
Day Six: Wed July 10–More on Series and Continuity
Day Seven: Thur July 11–More on Continuity and Review
Miscellaneous Bonus Content
Here is a good writeup on a rigourous construction of the real numbers, written by Todd Kemp from UCSD. This construction is called the Cauchy completion of the rational numbers, and comes from looking at what are called “equivalence classes” of Cauchy sequences of rational numbers. We wanted to touch on this in AMP, but ran out of time. Take a look if you wish! It’s available at http://www.math.ucsd.edu/~tkemp/140A/Construction.of.R.pdf.
July 5: Tim McEldowney, a PhD candidate at UCR and founder of AMP, will defend his dissertation at 10am in Skye Hall 284. The defense is not mandatory for you to attend, but if you’d like to see what a PhD defense looks like, you are welcome to join.
Afterwards (around 11am) there will be a social event with some attendees, which include Edray Goins of Pomona College and the undergraduates from his REU, PRiME. This is the part which is meant for you guys. It will be a good networking opportunity to make some friends and meet some people outside of the UCR bubble. Light refreshments will be provided.
July 12: Cory Colbert of Washington & Lee University will be visiting and will give a talk around 11am with a Q&A session afterwards. His research interests are in Commutative Algebra. We plan to get lunch afterwards and everyone is invited.
July 19: John Rock of Cal Poly Pomona will be giving a talk at 11am. He will give a two part talk: the first part will be about fractals and the second part will be more about mentoring type things. Fun fact: John Rock got his PhD from UCR under Michel Lapidus. The plan is to get lunch afterwards and everyone is invited.
July 26: Alissa Crans of Loyola Marymount University will be giving a talk with a Q&A session afterwards. Her research interests include quantum algebra and quantum topology. Fun Fact: Alissa Crans also get her PhD from UCR, under John Baez. Time: TBA
It is highly encouraged that you attend the Friday events even if you aren’t registered for the session it will take place during. These Friday meetings were many of the past participants favorite parts of AMP.