# The 2022 Summer Introduction to Mathematical Research

The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

**Summer Introduction to Mathematical Research** (sponsored by CMSA and the Harvard Math Department)

In this course, we will start with an introduction to computer programming, algorithm, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

The program hopes to provide several research mentors from various disciplines who will give some of the course lectures. Students will have the opportunity to work with one of the research mentors offered by the program.

Prerequisites: Basic coding ability in some programming language (C/Python/Matlab or CS50 experience). Some background in calculus and linear algebra is needed too. If you wish to work with a research mentor on differential geometry, more background in geometry such as from Math 132 or 136 will be useful. If you wish to work with a research mentor on computer science, coding experience mentioned above will be very useful. If you wish to work with a medical scientist, some background in life science or basic organic chemistry is recommended.

The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard related perks (such as a place to live if you are in Boston over the summer.)

However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited, so don’t wait too long to apply.