On Wednesday, March 31st, Dalhousie University hosted its latest virtual Math Circles evening. Dr. Asmita Sodhi (Dalhousie Mathematics Department) led the seminar, providing interactive opportunities and the mathematical motivation to make the event a great success. The topic itself, Exploding Dots, had our curiosity piqued, and the ensuing mathematical connection did not disappoint. The hour-long presentation was an uplifting mathematical experience. Time itself seemed to “explode”. First, participants were introduced to a ”2 to 1” exploding dot machine, where they introduced numbers into the furthermost right block of a series of attached boxes, and watched as pairs of dots exploded into one dot in the adjacent box to the left. This pattern continued in adjacent boxes until participants discovered that they were actually expressing numbers in base 2, or binary form.
Topics: Academics at KES
March is Fraud Prevention Month. The stats are fascinating: according to internet security experts, it takes a hacker only a fraction of a millisecond to crack a simple password like “abcdefg”. Add just one more character and the time increases to five hours. Nine-character passwords typically take five days to break, and ten characters, four months to crack. The timing was right last Wednesday, February 24th for Dalhousie’s Virtual Math Circles event that explored Cryptography, the science of encryption and security behind applications like banking transaction cards, computer passwords, and e-commerce transactions. The presenter was Dr. Frank Fu, a postdoctoral researcher who showed us encryption methods used to safeguard the digital world. The presentation began by discussing how checks can be made to ensure communication is secure online and that websites are legitimate. Next, encryption and decryption were defined, and specific encoding methods were explored. Caesar encryption, a shift cipher, was one of the easiest encryption techniques to learn. Each letter of the message is “shifted” a fixed number of positions (key) down the alphabet. For example, if the key is “2”, the word “MAGIC” would be encrypted to “OCIKE”. Dr. Fu pointed out that when trying to break a code, a frequency analysis of letters is beneficial. A bar graph demonstrated that the letter “e” occurs most frequently, and much more so than the letter “q”. With this in mind, participants were challenged to decrypt “ALIIP”. Substituting a probable double “e” for the double “I”, leads to an encryption key of “-4”. Moving four letters back from the original letters results in the word “WHEEL”. Did you get it? The seminar continued to explore more complicated encryption protocols. I commend Lillian Blois, Hunter Hood, Will Larder, Anthony Wheeler and Owen Xu for their participation and contributions. The next opportunity to attend Dalhousie Math Circles will be on March 31st. It is a great form of Math enrichment for students of all grades.