Tasks on the topic «Artificial Intelligence» in School Informatics

Lialin Andrei Vasilevich Senior Lecturer of Applied Mathematics and Computer Science Department, Vyatka State University 610000, Russia, Kirov region, Kirov, Moskovskaya str., 36 lialinandrei@rambler.ru

IntroductionArtificial intelligence is one of the most promising areas of computer science.

Here they create programs that recognize text and speech, translate from one language to another, identify plagiarism, recommend movies, books or music, search for information on the Internet, control robots, predict stock prices, prove theorems, play chess, make a medical diagnosis, and so on and so forth. And in a few words, here they study "how to make computers do things that people are currently doing better" ^{[1, p.3]}.

Intelligent systems are a mandatory and fundamental area in the recommendations for teaching computer science compiled by the joint Commission of the ACM and IEEE Computer Science ^[2]. They teach students of many American and European higher educational institutions.

However, in Russian school textbooks on computer science, the topic of artificial intelligence has been touched upon for a long time and only twice. This is a textbook by V. A. Kaimin in 1989 ^[3] and a textbook by I. G. Semakin in 1998 ^[4]. Both provide a general overview and talk about the Prolog programming language.

Currently, except for the only elective course of L. N. Yasnitsky ^[5], issues related to artificial intelligence are not considered in general computer science. Although they could become a source of real, meaningful, natural, feasible and interesting tasks for schoolchildren. Their examples are given below.

Example 1. ClusteringClustering is the division of objects into groups.

Each group should consist of similar objects, and objects from different groups differ significantly.

Clustering is used, for example, in recommendation systems. Users are divided into groups and everyone is recommended those products, movies, music, books that his "classmates" buy, watch, listen to, read.

Let's say the ratings of several users for two films are known (Fig. 1). The figure shows that they can easily be divided into three groups.

Figure 1. User ratings for two films.

Of course, when there are more users and movies, there is no visual splitting to do. For this, many clustering algorithms have been invented.

For example, a clustering algorithm using a minimal spanning tree. We build a minimal spanning tree on the points. Let them be divided into k clusters. Then we remove (k-1) of the longest edges from the tree. It splits into exactly k subtrees, which will be clusters.

Task1. Define the minimum spanning tree.

You must understand all the words that are found in the definitions.

2. Formulate the well-known Kruskal algorithm for constructing a minimal spanning tree.

3. Perform the Kruskal algorithm manually for the points from the figure. Namely, draw all the edges and indicate in what order they appeared. Remove the two longest edges from the resulting tree. Users will be divided into three groups.

Example 2. ClassificationClassification is the assignment of a new object to one of these classes.

One of the simplest classification algorithms is called the k nearest neighbors algorithm.

For example, we want to build a system that decides whether to give a person a loan or not, whether he belongs to the class of "good" or to the class of "bad" customers.

We know the history of the bank (Fig. 2). Customers marked with green circles have returned money in the past, and red ones have not returned it.

Figure 2. The history of the bank.

A new client arrives – a yellow circle. What should I do with it? We find k of its nearest neighbors. Let k=3. If there are more green ones among them, then we approve the loan, and if there are more red ones, we refuse.

Of course, real systems include thousands of customers and look not only at their expenses and income.

Task1. Let the new client have an income of 14, and an expense of 2.

In the algorithm of k nearest neighbors, the parameter k=5. What answer will the algorithm give for this client and why?

2. Why is it better to take the parameter k odd?

3. The user enters the client's income and expense. The program, using the algorithm of k nearest neighbors at k = 3, tells whether to give him a loan or not. Solve the problem in MS Excel. Take the data from the drawing. Save them on a sheet.

 Example 3. Recognition

A "picture" of black and white cells is stored in a text file (Fig. 3). Black cells are designated 1. White cells are 0. We read it into a two–dimensional array.

Figure 3. An example of a "picture" and a text file for it.

TaskOn the "picture" there is a figure.

Come up with an algorithm and write a program that recognizes exactly which digit it is. Both their size and location can be any. But they are drawn only in vertical and horizontal solid segments with a thickness of one cell (Fig. 4).

Figure 4. Examples of writing numbers.

Example 4. ManagementLet the bully have three detectors.

The force detector is triggered if a passerby can protect himself. People detector – if there is someone else on the street besides a passerby. Money detector – if you run out of money. The detector that triggered gives out a signal 1. Otherwise - 0.

A bully attacks a passerby if he cannot defend himself, there is no one around and the money has run out.  In other cases, he just watches.

TaskBuild and train "manually" a neural network that will control such behavior of a bully.

There are three detectors at its entrance. There is one command signal at the output. It is equal to 1 if the bully attacks, and 0 if not.

Hint. Here it is enough to take a neural network consisting of only one layer and one neuron.

ConclusionsThe non-text problem has already been formulated in the language of the field of knowledge by which it can be solved, and the text problem requires the translation of its conditions into this language ^{[6, p. 10]}.

For example, the following problem from a school textbook on computer science under the authorship of K.Y. Polyakov and E.A. Eremin is non-textual. "Fill the array with random numbers in the range 20..100 and count separately the number of elements with even and odd values" ^{[7, p.170]}.

In his work ^[8], the Polish teacher V. Okon voiced and justified the following thesis.

The more successful education is and the more intelligence develops, the more the student gets on the path that the scientist follows in the course of research (Fig.5).

Figure 5. The full cycle of scientific knowledge

What happens if students are offered only non-text tasks?They will be turned off from the very first, important and interesting step on this path.

They will not have "the conditions and opportunities to learn to pose problems and formulate special questions themselves – there is a clear deficiency in the development of a thinking culture" ^[9].

The above tasks from the field of artificial intelligence are just textual. In addition to getting acquainted with the "inner kitchen" of artificial intelligence, they bring learning closer to the activity of a scientist, which means they contribute to the intellectual development of students.