Looking to verify my understanding of RSA math
Some random comments:


  RSA's security is based on factoring primes.


Actually, it's based on the hardness of the RSA problem. It is still an open question whether its difficulty is equivalent to that of factoring.


  RSA works as follows. The ciphertext, c, is generated by raising p to the power e modulo n


At this stage, you probably don't want to go into the full details, but you should mention (perhaps in passing) that we never use 'textbook RSA' as you described, but when doing public key encryption, we perform 'padding' before doing the raw RSA operation.

You mentioned that you'll be covering OAEP later; you should give a few words to the effect that 'I'll cover this more fully later; this is a simplified version for now...'


  So encryption then is a matter of multiplying p by itself a certain number of times modulo n.


Not an issue with what you said, but (depending on the time) might want to discuss how we raise p to such enormous powers without taking an enormous amount of time; I believe that your audience should be able to follow that.


  To do this, we can use something called the totient of n, represented by $\Phi(n)$.


Actually, it is more typically represented by a lower case phi, that is, either $\phi(n)$ or $\varphi(n)$.


  To generate the public key (e), find a value of e such that the following is true:


I don't know if you want to go into these sorts of details; however it is more common in practice to select e first, and then select p and q such that $p, q \not\equiv 1 \pmod e$ (which will ensure (for prime e) that $\gcd( \phi(n), e ) = 1$)

Everything else would appear to be reasonable (if simplified...)