Course Topics
Below is a tentative list of topics to be covered, divided into four modules at roughly three weeks each. It will, of course, be adjusted as needed as the course progresses.- Module 1: Reasoning common to mathematics, computer science, and statistics. The power of pure reason—proofs. Functions as basic building blocks of mathematical models. Growth and decay models as examples of abstraction. Limitations of models.
- Module 2: Elements of computational thinking. Computer science asks not only what the result is, but also how to compute it. Foundations of computation: modeling information via digital representation, universality of basic operations, what can and cannot be computed. Measuring computational efficiency. Impossible computation as a foundation for cryptography.
- Module 3: Elements of statistical thinking. Modeling and predicting with incomplete information. Sampling. Describing available data through quantitative and visual summaries. Statistical inference. Evaluating statistical conclusions and not getting taken by lies masquerading as statistics.
- Module 4: Putting it all together. How do the simple, beautiful, and elegant concepts in Mathematics, Statistics, and Computer Science help us understand, reason about, and build complex and seemingly impenetrable systems such as the Internet? Building upon all previous modules, this one helps tame a complex system.