This is the 6575th most frequent Spanish word.
carlos
"Carlos" is a proper noun, a Spanish given name equivalent to "Charles" in English.
Here, 'Carlos' is used as a proper noun referring to a specific person named Carlos, the subject of the sentence, who is performing the action of studying.
Carlos está estudiando matemáticas.
Carlos is studying mathematics.
In this instance, 'Carlos' indicates possession, as 'de Carlos' means 'Carlos's,' showing ownership of the book.
El libro de Carlos está en la mesa.
Carlos's book is on the table.
Here, 'Carlos' is again used as a proper noun to indicate the person with whom the subject intends to converse.