Lecture No. 1. Introduction

1. Database management systems

Database management systems (DBMS) are specialized software products that allow:

1) permanently store arbitrarily large (but not infinite) amounts of data;

2) extract and modify these stored data in one way or another, using so-called queries;

3) create new databases, i.e. describe logical data structures and set their structure, i.e. provide a programming interface;

4) access stored data by several users at the same time (i.e. provide access to the transaction management mechanism).

Accordingly, the Database are datasets under the control of management systems.

Now database management systems are the most complex software products on the market and form its basis. In the future, it is planned to conduct developments on a combination of conventional database management systems with object-oriented programming (OOP) and Internet technologies.

Initially, DBMS were based on hierarchical и network data models, i.e. allowed to work only with tree and graph structures. In the process of development in 1970, there were database management systems proposed by Codd (Codd), based on relational data model.

2. Relational databases

The term "relational" comes from the English word "relation" - "relationship".

In the most general mathematical sense (as can be remembered from the classical set algebra course) respect - it's a set

R = {(x₁,..., x_n) | x₁ ∈ A₁, ..., x_n ∈ A_n},

where A₁,...,A_n are the sets forming the Cartesian product. In this way, ratio R is a subset of the Cartesian product of sets: A₁ x... x A_n :

R ⊆ A ₁ x... x A_n.

For example, consider the binary relations of the strict order "greater than" and "less than" on the set of ordered pairs of numbers A ₁ = A2 = {3, 4, 5}:

R_> = {(3, 4), (4, 5), (3, 5)} ⊂ A₁ xA₂;

R_< = {(5, 4), (4, 3), (5, 3)} ⊂ A₁ xA₂.

These relationships can be presented in the form of tables.

Ratio "greater than"_>:

Ratio "less than" R_<:

Thus, we see that in relational databases, a wide variety of data is organized in the form of relationships and can be presented in the form of tables.

It should be noted that these two relations R_> and R_< are not equivalent to each other, in other words, the tables corresponding to these relationships are not equal to each other.

So, the forms of data representation in relational databases can be different. How does this possibility of different representation manifest itself in our case? Relations R_> and R_< - these are sets, and a set is an unordered structure, which means that in tables corresponding to these relationships, rows can be interchanged. But at the same time, the elements of these sets are ordered sets, in our case - ordered pairs of numbers 3, 4, 5, which means that the columns cannot be interchanged. Thus, we have shown that the representation of a relation (in the mathematical sense) as a table with an arbitrary order of rows and a fixed number of columns is an acceptable, correct form of representation of relations.

But if we consider the relations R_> and R_< from the point of view of the information embedded in them, it is clear that they are equivalent. Therefore, in relational databases, the concept of "relationship" has a slightly different meaning than a relation in general mathematics. Namely, it is not related to the ordering by columns in a tabular form of presentation. Instead, so-called "row - column heading" relationship schemes are introduced, i.e., each column is given a heading, after which they can be freely swapped.

This is what our R relationships will look like_> and R_< in a relational database.

A strict order relation (instead of the relation R_>):

A strict order relation (instead of the relation R_<):

Both tables-relationships get a new one (in this case, the same, since by introducing additional headers we have erased the differences between the relations R_> and R_<) title.

So, we see that with the help of such a simple trick as adding the necessary headers to the tables, we come to the fact that the relations R_> and R_< become equivalent to each other.

Thus, we conclude that the concept of "relationship" in the general mathematical and relational sense does not completely coincide, they are not identical.

Currently, relational database management systems form the basis of the information technology market. Further research is being carried out in the direction of combining varying degrees of the relational model.

>> Forward: Missing data (Empty values. Null values. Null values ​​and the general rule for evaluating expressions. Null values ​​and logical operations. Null values ​​and testing conditions)

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