On Sunday March 24, 2013, I gave a talk on the History of Cryptography [PDF], at the University of Toronto (Scarborough) for the parents of students writing the Kangaroo Contest. I had many questions after my talk, so here are some answers to the questions I received.
My child is interested in codes, what are some resources for them to learn more?
Here is a great introduction to modular arithmetic which serves as the foundation for learning about the math of cryptography. Modular arithmetic is like “clock math”, where 4 hours after 10 o’clock is 2 o’clock.
Codecademy is a very good way to start learning computer programming. It is a very fun website and is very motivating, and fun!
Earlier on this month my dad turned 50, and my brother and I drove down to his house in rural Saskatchewan to surprise him. He was so surprised and happy that he started crying. It was very sweet. My dad is a very sweet guy in general. He lives close to my Baba (grandmother) and makes his living doing odd jobs around the town.
Now my dad is no mathematician, but he observed a cool thing with birthdays and his siblings. First, my dad (born in 1962) has 4 siblings: Zandy (1956), Pat (1951), Phillip (1949) and Perry (1953). In 2011, when he turned 49, his brother Phillip turned 62. I.e. they each were as old as the other’s year of birth (well not counting the 1900 part). Even more, in 2013, when my dad turns 51, his sister Pat turns 62. This will continue on when he turns 53 (Perry will be 62) and 56 (Perry will turn 62). Neat!
(After writing some posts directed at other mathematicians, here is one for everybody.)
I was sifting through some old issues of Crux Mathematicorum last Friday. For those of you who don’t know, this is a wonderful magazine that contains tons of math questions generally like those you would see in a math contest or olympiad, and the difficulty ranges from elementary school to undergraduate. In the September 2009 issue, I stumbled upon the following nice problem originally from the 2005 Brazilian Mathematical Olympiad. It is one of those problems that is mathematical in flavour and doesn’t need any previous math knowledge to begin thinking about the problem. For me, a nice problem is one that rewards you for thinking about it and can be attacked from many different angles.
So here’s the problem as stated:
We have four charged batteries, four uncharged batteries, and a flashlight which needs two charged batteries to work. We do not know which batteries are charged and which ones are uncharged. What is the least number of attempts that suffices to make sure the flashlight will work? (An attempt consists of putting two batteries in the flashlight and checking if the flashlight works or not.)