Overview:

One of the most beautiful ideas generated by modern science in the past few decades is the concept of neural nets, a computational framework that imitates the workings of the human brain. These networks have been used to understand the outcome of scientific experiments, make weather prediction and political forecasts and even aid mathematical research. In this program, we are going to take a comprehensive approach to neural nets, with focus on both the theoretical and applied aspects of this beautiful emerging discipline. To this end, we are going to develop the basic theory of neural nets in the mornings, followed by intensive programming sessions in the afternoons. We are looking for participants who are equally excited about the pure and applied aspects of data science- those who are just as willing to delve into the mathematical intricacies as they are to write complex code to implement the resulting ideas.

The program is particularly focused on recruiting participants who are women and members of underrepresented groups.

In addition to the research aspects, the program will also have an outreach component. A small group of middle school students from the inner city Rochester schools will be exposed to mathematical explorations using python. The participants in the program will be asked to assist in this wonderful and rewarding process.

The basic structure of the REU is the following. The participants are going to be selected in the last week of February 2022. They will be asked to learn the background material prior to the start of the program. To this end, they will be provided with notes, videos and computer code that will give them the necessary skills for the research phase of the program. Regular (hybrid) meetings will be held starting in March 2022, to reinforce the material. Early in May 2022, the participants will be given a description of the research projects, and they will be asked to make a preliminary selection within a few weeks, at which point they will begin hybrid meetings with their research group. The composition of the research groups will remain in flux until the first few days of the program in July 2022, to give the participants an opportunity to explore several different groups and get a better feel for the projects.

The program is going to run for four weeks, July 18-August 12, 2022. The program will run in person in Rochester, NY. Fifteen (15) Tripods NSF participants will be accepted and each is going to receive a $1600 stipend for successfully completing the program. The application procedure is described below. The application deadline is February 21, 2022.

Once the preliminary phase of the program starts in late April, 2022, after the selection process is finalized, a variety of study materials will be placed on the following website: Tripods2022 Study Materials.

Mini-courses (July 18-22):

Instructor:

i) The applicant must be a U.S. Citizen or a permanent resident. If you are not a U.S. Citizen or a permanent resident, you can still apply to this program under the auspices of STEM FOR ALL 2022 (see below)

ii) The applicant must be an undergraduate student at the University of Rochester, Cornell University, or a college or university in the Rochester area

ii)i Good knowledge of linear algebra and multi-variable calculus

iv) Good knowledge of mathematical analysis at the level of Rudin's "Principles of Mathematical Analysis" book or equivalent

v) Good knowledge of elementary probability, including moment generating functions, central limit theorem and related concepts

vi) Proficiency in python programming, including knowledge of numpy and other computational packages

vii) Willingness to prepare for the program diligently by reading the introductory materials and carefully going over the python code depository that will be prepared ahead of the program

i) Official college transcript

ii) One letter of recommendation from a mathematics instructor, preferably from an upper division course, and one from a computer programming instructor. The letters should be emailed by the letter writers directly to urstemforall2022@gmail.com.

iii) A page-long statement describing your interest in the program and future plans.