There is a perceived barrier to mathematics: proofs. In this course we will try to convince you that this barrier is more frightening than prohibitive: most proofs are easy to understand if explained correctly, and often they are even fun. We provide an accompanied excursion in the “proof zoo” showing you examples of techniques of different kind applied to different topics.
We use some puzzles as examples, not because they are “practical”, but because discussing them we learn important reasoning and problem solving techniques that are useful. We hope you enjoy playing with the puzzles and inventing/understandings the proofs.
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

从本节课中

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.