| ÖÇ1 | Defines the fundamental concepts related to the dual number ring and proves and interprets theorems related to the dual number ring |
| ÖÇ2 | Compares the dual number system with the real and complex number systems |
| ÖÇ3 | Defines the fundamental concepts in D-modules and proves and interprets the fundamental theorems in D-modules |
| ÖÇ4 | Defines dual variables functions in a manner similar to the theory of complex variable functions |
| ÖÇ5 | Defines the basic concepts related to real quaternions and compares the real quaternions with the real number system |
| ÖÇ6 | Compares real and dual quaternions |
| ÖÇ7 | Defines and formulates the quaternion operator and other operators similar to the complex number operator |