Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the
most important tools used in discrete mathematics: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements?
In the course, we use a try-this-before-we-explain-everything approach: you will be solving many interactive (and mobile friendly) puzzles that were carefully designed to allow you to invent many of the important ideas and concepts yourself.
Prerequisites:
1. We assume only basic math (e.g., we expect you to know what is a square or how to add fractions), common sense and curiosity.
2. Basic programming knowledge is necessary as some quizzes require programming in Python.

Na lição

How to Find an Example?

One example is enough to prove an existential statement, but how to find an example? In many cases the search space is enormous. A computer may help, but some reasoning that narrows the search space, is important both for computer search and for "bare hands" work — how can this be done? What do we need to prove if we claim that our solution is optimal? As usual, we'll practice solving many interactive puzzles. We'll show also some computer programs that help us to construct an example.