1.1.1.1. 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.

1.1.1.2. What we will do¶

During this course, we will talk about problems and algorithms that are probably new to you. But that is not really the focus for the course. A lot of the time we will be working to understand new techniques for analyzing algorithms and problems. So we get a lot of cases where we see an “obvious” algorithm, and work hard to prove that it is “best”. Many of the problems and algorithms picked to study are choosen deliberately to expose new ways to do analysis.

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.

• Some graph algorithms.