[SalesForce] getting error “System.NullPointerException: Attempt to de-reference a null object”

There are two objects student_details__c and department__c. department__c – contains name and no_of_students__c; student_details__c contains name, department(lookup to department object).

when a student is inserted in a department, that respective department needs to increment the no_of_students__field,similarly when department is changed of a student from one dept to other then no_of_students__c needs to be incremented in the new department and decremented from the old department field. no_of_student__c is the total count of students in respect to the department the belong to in each department object.

There maybe other ways to accomplish this,but need to create a trigger for this at the moment.

I dont know why it is giving me error,it is

Trigger

trigger Deptnumberupdate on Student_Details__c (after insert, after update,after delete) {

    studentchangeshandler studobj = new studentchangeshandler();
    if(trigger.isinsert)
    {
    studobj.afterinsert(trigger.new);
    }

    if(trigger.isupdate)
    {
    studobj.afterupdate(trigger.new );
    }    
}

Trigger Handler

public class studentchangeshandler{



         public void afterupdate(student_details__c[] newstudList , map<id,sobject> oldstudlist) {

         set<id> Deptids = new set<id>();

         for(student_Details__c record: newstudlist){

            Deptids.add(record.Department__c);
            }


        list<department__c> deptlist = [select id,name,no_of_students__c,(select id from student_details__r) from department__c where id in:Deptids];


     for(department__c dept : deptlist){

               if (dept.Name == 'CSE')
                   {
                   dept.no_of_students__c = dept.no_of_students__c +1;
                    }

                else if (dept.Name == 'ECE')
                {
                   dept.no_of_students__c = dept.no_of_students__c +1;
                   }
                else if (dept.Name == 'IT')
                   {
                   dept.no_of_students__c = dept.no_of_students__c +1;
                   }

                else if (dept.Name == 'EEE')
                {
                   dept.no_of_students__c = dept.no_of_students__c +1;
                   }

            }       

            for(department__c dept : deptlist){       
                  for(Student_details__c student : dept.student_details__r){
        Student_details__c oldStud = (student_details__c)Trigger.oldMap.get(student.ID);





             //student_details__c oldstud = (student_details__c)oldstudlist.get(dept.ID);
                       if (oldstud.department__c == 'CSE')
                   {
                   dept.no_of_students__c = dept.no_of_students__c -1;


                   }

                else if (dept.Name == 'ECE')
                {
                   dept.no_of_students__c = dept.no_of_students__c -1;
                   }
                else if (dept.Name == 'IT')
                   {
                   dept.no_of_students__c = dept.no_of_students__c -1;
                   }

                else if (dept.Name == 'EEE')
                {
                   dept.no_of_students__c = dept.no_of_students__c -1;
                   }

            }       


  update deptlist;   

 }



}
}

getting error

Error: Invalid Data. Review all error messages below to correct your
data. Apex trigger Deptnumberupdate caused an unexpected exception,
contact your administrator: Deptnumberupdate: execution of AfterUpdate
caused by: System.NullPointerException: Attempt to de-reference a null
object: Class.studentchangeshandler.afterupdate: line 89, column 1 at line
student_details__c oldstud = (student_details__c)Trigger.oldMap.get(dept.ID);