The second lecture of the season provided lessons in both applied mathematics and number theory. Dr. Bennette Harris began with an easy to follow introduction to binary and computer operations including XOR. He then defined the terms “encoding” and “encryption” and gave several examples of early encryption methods.
Dr. Harris described the difference between “strong” and “weak” encryption methods. This led to a deep dive into the popular RSA encryption method which depends on extremely large prime numbers. Dr. Harris used this as an opportunity to give the students a sense for mind-boggling large numbers and some of the very creative and efficient ways of determining whether or not a given number is a prime.
In this part of the discussion, Dr. Harris taught the students various techniques in modular arithmetic. Modular arithmetic is a tool that is not just useful in encryption but is critical for success in math contests and other pursuits.
Dr. Harris used several techniques to engage students including a series of 10 problems that he worked into the lecture for the students to solve. He also demonstrated the UBASIC program which very quickly found tremendously large prime numbers.
Dr. Harris has provided his slides from the lecture and answers to the problems. Members of the Metroplex Math Circle e-mail group can download these files from the group site. To join the e-mail group simply click below.