Discrete Math - Day 38

Today's focus was working on problems created by students.

The first question posed proved to be difficult for students. What is φ(90)? The difficulty came in students just started to calculate the value directly rather than recalling properties of φ(n), specifically that φ(nm) = φ(n)φ(m) when gcd(n,m)=1. So φ(90) = φ(9 x 10) = φ(9)φ(10)= 6 x 4 = 24.

Another number theory problem asked to find the gcd(88, 160).

Two problems presented then dealt with ciphering. These were relatively straightforward problems. For example, encode and cipher the word "towel" using C(x) = x + 3.

Next came a couple of counting problems. One dealt with how many toppings did a pizzeria have if they offered 66 different two topping pizzas? Another asked how many 8 character passwords could be created if you were required to use one number and any number of upper-case letters, lower-case letters, and digits for the remainder of the password?

Overall, the problems provided students an opportunity to revisit some problems that they may not have worked on recently.

Next class will be the mid-term.

Visit the class summary for a student's perspective and to view the lesson slides.