Future chapters of this textbook contain exercises as the final section. The exercises are annotated with a difficulty rating:

  • One star [✭]: easy exercises that should take only a minute or two.

  • Two stars [✭✭]: straightforward exercises that should take a few minutes.

  • Three stars [✭✭✭]: exercises that might require anywhere from five to twenty minutes or so.

  • Four [✭✭✭✭] or more stars: challenging or time-consuming exercises provided for students who want to dig deeper into the material.

Some exercises are annotated "advanced" or "optional". It's possible we've misjudged the difficulty of a problem from time to time. Let us know if you think an annotation is off.

Please do not post your solutions to the exercises anywhere, especially not in public repositories where they could be found by search engines. Some of these exercises have been used as homework and exam problems in the past, and some of them may again be used in the future.

A repository of solutions is available to current students in the course. Instructions for how to access it will be provided elsewhere. Instructors from other universities may also request access.

The exercises are a good source of exam questions. A good way to study for an exam is to finish any exercises you haven't already completed, as well as to rework previously completed exercises. You might even discover better solutions when you revisit old exercises.

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