The official prerequisite courses for CS 555 are

CS 251  Data structures
CS 381  Analysis of algorithms
CS 426  Introduction to computer security
MA 351  Linear algebra

If you are an undergraduate student at Purdue, then you may
enroll in CS 555 if and only if you have taken these 4 courses
(and passed them).

If you are a graduate student, these prerequisites are not enforced.

If you are a graduate student in Computer Science, then you have the
proper background for CS 555 (but keep reading).

If you are a graduate student in some other department or program,
please consider the following "real prerequisites" to determine
whether you are ready to take CS 555.

To succeed in CS 555 you will need the following knowledge and skills:

Calculus: Can integrate and differentiate polynomials, e^x and log x.
Can find extreme values of functions.  Can graph functions and find
lines of symmetry.  Have seen the epsilon-delta definition of limit.
Know simple approximations, such as e^x is approximately 1 + x when
x is near 0.  Have seen implicit differentiation.

Probability: Understand equally likely events, mutually exclusive
events, conditional probability, coin tossing, dice, the standard
deck of playing cards, random variables, probability distribution
functions, mean, median, uniform distribution, factorial, binomial
coefficients.

Arithmetic:  Know what even and odd integers are.  Understand
the mod function and greatest common divisor.  Understand
divisibility (of integers) and the division algorithm with
quotient and remainder.  Know about prime and composite numbers
and factoring (small) integers.  Know about positional number
systems: binary and decimal, at least, and arithmetic with such
numbers.

Data structures: Understand trees, traversals, Huffman codes
and logical bit operations: AND, OR, NOT, EXCLUSIVE-OR.

Networks: Have seen the network protocol layers in some model
of peer-to-peer correspondence.  Understand some network
addressing and routing scheme, network topologies and network
vulnerabilities.  Know what routers and name servers do.

Operating systems: Understand protection of files, memory and
general objects.  Understand user authentication via passwords.

Linear algebra: Can multiply matrices.  Can solve n linear
equations in n unknowns by an efficient algorithm.  Understand
vectors: addition, scalar and dot products.  Know what groups
and fields are.  Have heard of the field with 2 elements.

Analysis of algorithms: Know big-Oh, big-Theta and big-Omega
notations for asymptotic time and space complexity as a function
of input size.  Know how to sort n things in O(n log n) time.
Understand deterministic versus probabilistic algorithms.  Have
heard of polynomial time (P) algorithms, NP-hard and NP-complete
problems.  Can easily see what this function does and find its
time complexity:

     real f(real x, positive integer n) {
          real y, z; integer m;
          y = 1.0;
          z = x;
          m = n;
          while (m > 0) {
               if ((m AND 1) == 1) y = y*z;
               z = z*z;
               m = floor(m/2);
               }
          return y;
          }