Whats It All About?
Why is it computer science?
This is basically a mathematics course: no programming lots of theorems to prove
Continuous mathematicscalculusconsiders objects that vary continuously Discrete mathematics considers discrete obje
RSA: Decryption
If you get an encrypted message C = M e mod n, how do you decrypt Compute C d M ed
ed
Digital Signatures
How can I send you a message in such a way that youre convinced it came from me (and can convince others). Want an analogue o
Methods of Proof
One way of proving things is by induction. What if you cant use induction? Typically youre trying to prove a statement like Given X, prove (or show that) Y . This means you have to prove XY Thats coming next.
Example
Theorem n is o
Theorem: If a1 = k and an = a an = kn for n 1.
n/2
+a
n/2
for n > 1, then
In general, there is no rule for guessing the right inductive hypothesis. However, if you have a sequence of numbers r1, r2, r3, . . . and want to guess a general express
Questions/Complaints About Homework?
Heres the procedure for homework questions/complaints: 1. Read the solutions rst. 2. Talk to the person who graded it (check initials) 3. If (1) and (2) dont work, talk to me. Further comments: Theres no statute
Example of Extended Euclidean Algorithm
Recall that gcd(84, 33) = gcd(33, 18) = gcd(18, 15) = gcd(15, 3) = gcd(3, 0) = 3 We work backwards to write 3 as a linear combination of 84 and 33: 3 = 18 15 [Now 3 is a linear combination of 18 and 15] = 18