Consider a database schema with the following tables:

CREATE TABLE Students $($

StudentID INT PRIMARY KEY,

Name VARCHAR$(50),$

Age INT,

GPA FLOAT $)$;

CREATE TABLE Courses $($

CourseID INT PRIMARY KEY,

CourseName VARCHAR$(50))$;

CREATE TABLE Enrollments $($

EnrollmentID INT PRIMARY KEY,

StudentID INT,

CourseID INT,

Grade FLOAT,

FOREIGN KEY $($StudentID$)$ REFERENCES Students$($StudentID$),$

FOREIGN KEY $($CourseID$)$ REFERENCES Courses$($CourseID$))$;

Solve the following SQL problems by nesting queries.

$1.$ Write an SQL query to find the names of students who are enrolled in the course 'Mathematics' and have a GPA greater than $3\mathrm{.}5.$

$2.$ Assuming the same database schema, write an SQL query to find the average GPA of students who have enrolled in the course 'Physics'.

$3.$ Extend the previous query to find the average GPA of students who have enrolled in the course 'Physics' and whose age is less than $25.$