urstemforall2021@gmail.com

Application Deadline: April 15, 2021 (see application instructions below)

PLEASE NOTE THAT THE APPLICATION DEADLINE HAS BEEN EXTENDED

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 the neural- 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 program is the following. During the first two weeks of the program, lectures on the basics of the neural networks theory will be delivered in the mornings. In the afternoons, the participants will be broken up into small study/recitation groups for the purpose of working out the assigned problems meant to cement the material from the lectures. In the evenings, the students will be broken up into python groups with the aim of coding as much of the material presented in the lectures as possible. During the second half of the program, the participants will be introduced to several possible research projects related to the neural networks, and they will begin working on those projects under the guidance of the TripodsREU2021/StemForAll2021 team.

The program is going to run for four weeks, July 19-August 13, 2021. It will either run in person, or by zoom, depending on the degree of forbearance of the CoronaZombies and other cataclysms that we may be able to model using the aforementioned neural networks. The final decision will be made, based on circumstances, in the coming months. Fifteen (15) Tripods NSF participants will be accepted and each is going to receive a $1600 stipend for successfully completing the program. Another ten (10) STEM FOR ALL students will be accepted, but there is no funding currently available for the STEM FOR ALL participants, though we are hoping to secure such funding before the program begins. The application procedure is described below. The application deadline is March 26, 2021.

9.00-10:00 a.m. Lecture # 1

11:00 a.m.- noon Lecture # 2

2.00-3.00 p.m. Crash course on basic inequalities, Part I

4.00-5.00 p.m. Crash Course on Probability, Part I

7.00-8.30 p.m. Discussion of the material from the morning lectures

9.00-10:00 a.m. Lecture # 3

11:00 a.m.- noon Lecture # 4

2.00-3.00 p.m. Crash course on basic inequalities, Part II

4.00-5.00 p.m. Crash Course on Probability, Part II

7.00-8.30 p.m. Homework problem session

9.00-10:00 a.m. Lecture # 5

11:00 a.m.- noon Lecture # 6

2.00-4.00 p.m. Python jam session

7.00-8.30 p.m. Discussion of the material from the morning lectures

9.00-10:00 a.m. Lecture # 7

11:00 a.m.- noon Lecture # 8

2.00-3.00 p.m. Guest Lecture

3.00-3.30 p.m. Discussion with the guest lecturer

4.00-5.00 Participants meeting in small groups to discuss the morning lecture material

7.00-8.30 p.m. Homework problem session

9.00-10:00 a.m. Lecture # 9

11:00 a.m.- noon Lecture # 10

2.00-4.00 p.m. Python jam session

7.00-8.30 p.m. Discussion of the material from the morning lectures

A tour of the Rochester City Cemetery!

Meetings with mentors (time to be arranged)

3.00-5.00 p.m. Discussion of the material from the week's lectures

9.00-10:00 a.m. Lecture # 11

11:00 a.m.- noon Lecture # 12

2.00-4.00 p.m. Python jam session

7.00-8.30 p.m. Homework problem session

9.00-10:00 a.m. Lecture # 13

11:00 a.m.- noon Lecture # 14

2.00-4.00 p.m. Discussion of possible research projects, I

7.00-8.30 p.m. Discussion of the material from the lectures

9.00-10:00 a.m. Lecture # 15

11:00 a.m.- noon Lecture # 16

2.00-3.00 p.m. Guest lecture

3.00-3.30 p.m. Discussion with the guest lecturer

4.00-5.00 p.m. Participants meeting in small groups to discuss the morning lecture material

7.00-8.30 p.m. Homework problem session

9.00-10:00 a.m. Lecture # 17

11:00 a.m.- noon Lecture # 18

2.00-4.00 p.m. Python jam session

7.00-8.30 p.m. Discussion of the material from the lectures

9.00-10:00 a.m. Lecture # 19

11:00 a.m.- noon Lecture # 20

2.00-4.00 p.m. Discussion of possible research projects, II

7.00-8.30 p.m. Homework problem session

REST DAY!

Meeting with the mentors (to be arranged)

Informal meetings of the research groups

The research groups are going to establish a coherent schedule and approach to the projects.

The coordinator is going to meet with each research group, at least briefly, every day at 9 a.m.

Coordinator:

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 2021 (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 urstemforall2021@gmail.com.

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