Contents

This course will cover important concepts from computability theory; techniques for designing efficient algorithms for combinatorial, algebraic, and number-theoretic problems; and basic concepts such as NP-Completeness from computational complexity theory

Students are expected to have a solid grasp of the basics of discrete mathematics. Discrete Mathematics and Its Applications by Ken Rosen provides an excellent background for this course.

If you answer “no” to any of the following questions, it may be beneficial to acquire background knowledge concurrently or prior to taking the course.

- Can you show that the sum of the first n numbers is n(n+1)/2? Can you give the proof as an induction on n?
- Can you give an O(n log n) algorithm for sorting n numbers?
- Can you describe the difference between breadth-first and depth-first search?
- Given an nxn matrix A and an n-dimensional vector b, can you give a polynomial-time algorithm to find a vector x such that Ax=b?

The course is intended to be self-contained. Nevertheless, for their reference, we recommend that students acquire copies of

- Introduction to the Theory of Computation by Sipser and
- Introduction to Algorithms, Cormen, Leiserson, Rivest, and Stein.

Similar texts may be substituted if they are more readily available to the student.

- Computability
- Complexity
- Algorithms