Final answer:
Reference systems are frameworks used to describe the position and orientation of objects in mathematics. Mathematical models are descriptions of phenomena using mathematical concepts like equations and inequalities. They help us understand relationships and predict changes in variables.
Step-by-step explanation:
In mathematics, reference systems are frameworks or coordinate systems used to describe the position and orientation of objects. They provide a set of rules and measurements that allow us to locate and quantify physical phenomena. Examples of reference systems include Cartesian coordinates, polar coordinates, and spherical coordinates.
Mathematical models, on the other hand, are descriptions of phenomena using mathematical concepts such as equations, inequalities, and distributions. They help us understand and predict how variables are related and how they change over time or space.
When creating a mathematical model, it is important to test and validate it to ensure its accuracy and reliability. This involves using appropriate scientific and mathematical principles to evaluate the model's performance. Mathematical models are particularly useful in fields like relativity and quantum mechanics, where conditions may be beyond human perception and understanding.