1.1. Prerequisites¶

This course assumes that you already have sufficient background in a number of Computer Science topics

You should have had a course in Discrete Math, covering at least the following:

• Basic proof techniques like proof by contradition and induction.

• Basic techniques for solving summations and recurrence relations

• Set theory and relations

You should have had a course in Data Structures to cover at least the following:

• Basic algorithm analysis, including big-oh, big-Omega, and \(\Theta\) notations.

• Basic data structures and algorithms including lists, search structures such as BSTs, sorting algorithms, heaps, hashing, and basic graph algorithms.

1.2. What we will do¶

Major topics/goals for this course include:

• Getting a good understanding of upper and (especially) lower bounds for an algorithm or problem.

• Lower bounds proofs.

• Analysis techniques, including solving a lot of summations and recurrence relations.

• Reductions, most importantly NP-completeness theory.

• A little bit of computability theory as a bonus.

1.3. Process¶

The primary work in this course will come from the weekly homework sets. They will typically consist of three problems. You should expect that a lot of them will be fairly hard.

The intention of the course design is that you will work with a partner on the homework. Understanding this course content is hard. Figuring out the problem solutions is intended to be hard. This works best if you can bounce ideas off of someone else, and actively work together toward a final solution. If nothing else, being a skeptical reviewer is a key contribution. Recognizing that an answer is no good, or incomplete, is crucial to succeeding in this class.