$2$b$1.$ ER Model

To create an ER model for the given university environment, we need to identify entities, relationships, and attributes. Here is a detailed breakdown:

Entities and Attributes:

Department

Attributes: DepartmentID $($PK$),$ Name

Relationships: Has a Chairperson $(1$:$1),$ Offers Courses $(1$:M$),$ Has Faculty Members $(1$:M$)$

Chairperson

Attributes: ChairpersonID $($PK$),$ Name, DepartmentID $($FK$)$

Course

Attributes: CourseID $($PK$),$ Title, Description, PrerequisiteCourseID $($FK$,$ nullable$)$

Relationships: Offered by Department $($M:$1),$ Has Classes $(1$:M$)$

Class $($Section$)$

Attributes: ClassID $($PK$),$ SectionNumber, MeetingTime, Location, IsLab $($Boolean$)$

Relationships: Taught by Professor $($M:$1),$ Enrolled by Students $($M:N$),$ Is a Section of Course $($M:$1)$

Professor

Attributes: ProfessorID $($PK$),$ Name, Rank, DepartmentID $($FK$)$

Relationships: Teaches Classes $(1$:M$),$ Advises Graduate Students $($M:N$)$

Student

Attributes: StudentID $($PK$),$ Name, AcademicStatus $($undergraduate$,$ graduate, non$-$degree$),$ FinancialAid

Relationships: Enrolled in Classes $($M:N$),$ Has Advisor $($Graduate Students$)($M:$1),$ Joins Clubs $($M:N$)$

Club

Attributes: ClubID $($PK$),$ Title, Description, ContactName, ContactEmail

Relationships: Joined by Students $($M:N$)$

LabManagement

Attributes: StaffID $($PK$),$ Name

Relationships: Manages Labs $(1$:M$)$

Weak Entity:

Class $($Section$)$ is a weak entity dependent on Course.

Supertype$-$Subtype Entity:

Student can be a supertype with subtypes UndergraduateStudent and GraduateStudent.

Recursive Relationship:

Course has a recursive relationship for prerequisites.

ER Diagram

Below is a textual representation of the ER diagram:

Department $($DepartmentID$,$ Name$)$

$1$:$1$ with Chairperson $($ChairpersonID$,$ Name, DepartmentID$)$

$1$:M with Course $($CourseID$,$ Title, Description, PrerequisiteCourseID$)$

$1$:M with Professor $($ProfessorID$,$ Name, Rank, DepartmentID$)$

Course $($CourseID$,$ Title, Description, PrerequisiteCourseID$)$

M:$1$ with Department

$1$:M with Class $($ClassID$,$ SectionNumber, MeetingTime, Location, IsLab$)$

Recursive relationship for PrerequisiteCourseID

Class $($ClassID$,$ SectionNumber, MeetingTime, Location, IsLab$)$

M:$1$ with Course

M:$1$ with Professor

M:N with Student

Professor $($ProfessorID$,$ Name, Rank, DepartmentID$)$

$1$:M with Class

M:N with GraduateStudent $($Advisor relationship$)$

Student $($StudentID$,$ Name, AcademicStatus, FinancialAid$)$

Supertype with subtypes UndergraduateStudent and GraduateStudent

M:N with Class

M:N with Club

M:$1$ with Professor $($Advisor relationship for Graduate Students$)$

Club $($ClubID$,$ Title, Description, ContactName, ContactEmail$)$

M:N with Student

LabManagement $($StaffID$,$ Name$)$

$1$:M with Class $($for lab classes$)$

$2$b$2.$ Information Not Modeled in ER Diagram

The following information from the narrative cannot be directly modeled using an ER diagram:

Performance and Hard Work of Students: The narrative mentions that some students perform better because they are hard$-$working. This qualitative information about student performance and effort is not typically captured in an ER diagram.

Summer Courses: The narrative states that not all departments offer summer courses. This temporal aspect of course offerings is not explicitly modeled in the ER diagram.

Financial Aid Dependency on Performance: While financial aid is mentioned, the specific dependency on academic performance is not detailed in the ER diagram.

Double Majors: The concept of students having double majors is not explicitly modeled. This would require additional relationships or entities to represent multiple majors for a single student.

These aspects would require additional business rules or constraints that are typically handled at the application or database management system level.