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What is a mathematical model in a database system?
The description of data model includes three parts: data structure, data operation and data constraint.

1) data structure: The data structure in the data model mainly describes the types, contents, attributes and relationships of data. Data structure is the basis of data model, and data operations and constraints are based on data structure. Different data structures have different operations and constraints.

2) Data operation: The data operation in the data model mainly describes the operation type and operation mode on the corresponding data structure.

3) Data constraints: Data constraints in the data model mainly describe the syntax, semantic relations, constraints and dependencies between data in the data structure, as well as the rules of data dynamic change, so as to ensure the correctness, validity and compatibility of data.

According to different application levels, data models can be divided into three types: conceptual data model, logical data model and physical data model.

1. Conceptual data model: referred to as conceptual model, it is a model for database users to know the world. It is mainly used to describe the conceptual structure of the world. It enables database designers to get rid of the specific technical problems of computer system and DBMS at the initial stage of design and concentrate on analyzing the relationship between data, which has nothing to do with the specific database management system (DBMS). Conceptual data model must be replaced by logical data model in order to be realized in DBMS.

2. Logical Data Model: referred to as data model for short, this is the model that users see from the database and the data model supported by a specific DBMS, such as network data model and hierarchical data model. The model should be user-oriented and system-oriented, mainly used for the implementation of database management system (DBMS).

3. Physical Data Model: referred to as physical model for short, it is a model for computer physical representation, describing the organizational structure of data on storage media, which is not only related to the specific DBMS, but also related to the operating system and hardware. Each logical data model has a corresponding physical data model when it is implemented. In order to ensure the independence and portability of DBMS, most physical data models are automatically implemented, while designers only design special structures such as index and aggregation.

The most commonly used conceptual data models are E-R model, extended E-R model, object-oriented model and predicate model. The most commonly used logical data types are hierarchical model, grid model and relational model.