How to model "Courses prerequisites" for a university?
You have some Courses:

COURSES
-------
course_id
course_number
course_name


You need to combine one or more of these Courses with a logical operator:

COMBINATIONS
------------
combination_id
logical_operator (AND, OR or NOT)

COMBINATION_COURSES
-------------------
combination_id
course_id


You may also need to combine some of these combinations (so changing the COMBINATION_COURSES table):

COMBINATION_COURSES
-------------------
combination_id
course_id
sub_combination_id


where one and only one of course_id and sub_combination_id is not null.

A Course may have one of the combinations as a prerequisite (so changing the COMBINATIONS table):

COURSES
-------
course_id
course_number
course_name
prerequisite_combination_id


EDIT

So, given your original examples your tables would be populated:

COURSES
=======
course_id course_name                    prerequisite_combination_id
--------- ------------------------------ ---------------------------
        1 Artificial Intelligence                                 12
        2 Data Structures
        3 Introduction to Logic
        4 Mathematical Logic and Proofs 
        5 Calculus 1
        6 Calculus 2                                              13
        7 Analytical Geometry

COMBINATIONS
============
combination_id logical_operator
-------------- ----------------
            11 OR
            12 AND
            13 AND

COMBINATION_COURSES
===================
combination_id course_id sub_combination_id
-------------- --------- ------------------
            11         3
            11         4
            12         2
            12                           11
            13         7
            13         5


Course 1 - Artificial Intelligence has a prerequisite of the Combination 12. Combination 12 is Course 2 - Data Structures AND Combination 11. Combination 11 is Course 3 - Introduction to Logic OR Course 4 - Mathematical Logic and Proofs. 

Hence, the prerequisite of Course 1 - Artificial Intelligence is Course 2 - Data Structures AND (Course 3 - Introduction to Logic OR Course 4 - Mathematical Logic and Proofs).

This structure should allow you to store any prerequisite that is the any logical combination of any number of courses.