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. Do you have technical problems? Write to us: coursera@hse.ru
The Rules of 15-Puzzle
배우게 될 기술
Mathematical Induction, Proof Theory, Discrete Mathematics, Mathematical Logic
검토
KL
Nov 29, 2018
The course is excellent and most stuff is being taught in a nicely presented way. The main disappointment is 15-puzzle, because it's too difficult to understand without proper material.
DG
Jun 30, 2018
Love the quality of thought that goes into each lesson. The professors speak with acute clarity and really demonstrate and empathy for the student to truly understand the topics!
In this module, we consider a well known 15-puzzle where one needs to restore order among 15 square pieces in a square box. It turns out that the behavior of this puzzle is determined by mathematics: it is solvable if and only if the corresponding permutation is even. We will learn the basic properties of even and odd permutations. The task is to write a program that determines whether a permutation is even or odd. There is also a more difficult bonus task: to write a program that actually computes a solution (sequence of moves) for a given position assuming that this position is solvable.
강사:
Alexander S. Kulikov
Visiting Professor
Michael Levin
Lecturer
Vladimir Podolskii
Associate Professor