Sometimes expressed as ... "No repeating columns"

 create table{
         bookTitle    
        ,author1   
        ,author2   
        ,author3 
        .....
      }

2NF and 3NF are all about being dependent on the primary key. 

Realize(recall) that a primary key can be made up of multiple columns. 


"The data depends on the key [1NF], 
                           
 the whole key [2NF] and nothing 
                           
 but the key [3NF]"


----  2NF  -----
Suppose Sewanee's CS program gets really really big.  Takes over the campus really!
And we have a table containing courses offered with the following data:



      (Primary Key) 
     
  
 CourseID
Semester
#Students
CourseName 
InstructorName
InstructorOffice
 157 
  2029-A  
100     
Programming  
  Dalero     
  Woods 130
 157 
  2029-B  
100     
Programming  
  SP Carl    
  Woods 136
 284 
  2029-A  
200     
Databases    
  HM Walker 
  Woods 128
 284 
  2030-B  
150     
Databases    
  Dalero   
  Woods 130
 320 
  2029-A  
120     
Algorithms 
  SV Smith   
  Spencer 008



The table as it is already satisfies 1NF but what about 2NF?  

Consider the first few columns.



      (Primary Key) 
     
 uh-oh...
 CourseID
Semester
#Students
CourseName 
 157 
  2029-A  
100     
Programming  
 157 
  2029-B  
100     
Programming  
 284 
  2029-A  
200     
Databases    
 284 
  2030-B  
150     
Databases    
 320 
  2029-A  
120     
Algorithms


This is not in 2NF, because the fourth column does not rely upon the entire 
key - but only a part of it. The course name is dependent on the Course's ID, 
but has nothing to do with which semester it's been taken in. Thus, as you can see, 
we have duplicate information - several rows telling us that 157 is 
programming, and 284 is Databases. So we fix that by putting the course name 
into another table, where CourseID is the ENTIRE key.



    
(Primary Key) 
   
CourseID    
  Course Name 
157         
 Programming 
284         
 Databases   
320         
 Algorithms  


No redundancy!

----  3NF  -----
Okay, so let's say add the name of the instructor of the course, 
and some details about them back into the table of sample data.

This one _is_ in 2NF even with those extra columns. 
The instructor depends on both course & semester and the instructor's office
depends on the instructor.  So... indirectly the office DOES depend
on ENTIRE primary key.  



      (Primary Key) 
  
   
 uh-oh...
 CourseID
Semester
#Students
InstructorName
InstructorOffice
 157 
  2029-A        
  100       
  Dalero     
  Woods 130        
 157 
  2029-B        
  100       
  SP Carl    
  Woods 136        
 284 
  2029-A        
  200       
  CV Jones 
  Woods 128        
 284 
  2030-B        
  150       
  Dalero   
  Woods 130        
 320 
  2029-A        
  120       
  SV Smith   
  Spencer 008        


BUT... 3NF says the dependency CANNOT be indirect.  So, as usual, to fix this, 
we do much the same as we did in 2NF - take InstructorName out of this table, 
and put it in its own, which has InstructorID as the key.



    
(Primary Key) 
   
InstructorID 
InstructorName 
InstructorOffice
  332        
  Dalero             
Woods 130
  599        
  SP Carl             
Woods 136
  495        
  CV Jones         
Woods 128
  242        
  SV Smith            
Spencer 008


No redundancy!!

Yes, the dependency in both cases is on a single field.

    CourseName on CourseID          (and not both CourseID,Semester)

    InstructorName on InstructorID  (and only indirectly on CourseID,Semester)



However, in non-2NF example:

    dependency is on part of the primary key



while in non-3NF example (which _is_ in 2NF):

   dependency is on a field that is not a part of the primary key (and also notice 
   that in that example it does satisfy 2NF; this is to show that even if you check for 
   2NF you should also check for 3NF)



In both cases to normalize, the solution is another table which does not exhibit 
update anomalies (example of update anomaly: in 2NF example, what happens if you 
update CourseName for ( 157,2029-A ), but not for ( 157,2029-B )?
You get inconsistent=meaningless=unusable data).

If the distinction between 2NF and 3NF seems subtle -- well, it is -- get over it.

But if you memorize "the key, the whole key and nothing but the key", 
you have mnemonics for 1NF, 2NF and 3NF.  Hope that helps!