Fall 2018

CENGAGE Learning. ISBN-13: 978-1-133-18779-0, ISBN-10: 1-133-18779-X.

In your journey through computation, you likely have noticed that many problems can be solved
with the same solution through a skill you have honed called abstraction. Through this process,
you may have noticed more nuanced connections between problems. Some problems require
some translation before being solved using the solution to another problem. Some problems are
immune this sort of transformation and feel fundamentally more difficult than others. Some
problems feel downright impossible: are they actually impossible?

In this course, we study the theory of computation where we use mathematics to model problems
of increasing complexity and study their relationships with each other. Although some
applications may be discussed from time to time, this course will emphasize the formal
underpinnings and theory of computer science.

By going through this modeling process, we can:

- Deeply understand a problem and its potential corner cases.
- Prove properties of a problem, e.g., the correctness of potential solutions or whether said problem has a solution at all.
- Reduce one problem to others of similar complexity.
- Categorize this problem as easier or harder than other problems in a precise way.

- Are there problems that are intractable in practice?
- Are there problems that can provably never have a solution?

- Manipulate and reason about mathematical definitions like computer programs.
- Model problems using mathematics and use these models to perform the techniques described above.
- Understand when a problem is intractable or undecidable.