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Section 0.3 Examples, Problems, and Checkpoints

Definitions sometimes are quite abstract. We illustrate the objects or properties or operations defined by giving concrete examples. Similarly we demonstrate what the statement of a theorem does in examples. The examples are formulated as examples or as problems with solutions. In addition we also give checkpoints in which you can verify your understanding of the material by doing exercises that are embedded in the text. While, some of the examples are instructional, in general, what is done in the examples and problems is close to what you are expected to do in the assignments and on exams. Some of the examples allow you to explore the material interactively.

The definitions and theorems in this text often build on other definitions and theorems. Also in other places you will find that we refer to statements that were previously presented in the text. We reference algorithms, definitions, examples, problems, and theorems by their number. All these are hyperlinks that let you easily jump to the location in the text that was referenced.