| 1 | Defines the fundamental concepts related to the ring of dual numbers and proves and interprets theorems related to the ring of dual numbers. |
| 2 | Compare the dual number system with the real and complex number systems |
| 3 | Define the fundamental concepts of D-modules and be able to prove and interpret the fundamental theorems of D-modules |
| 4 | Define dual variables in a manner similar to the theory of complex variable functions |
| 5 | Define the basic concepts related to real quaternions and compare the real quaternions with the real number system |
| 6 | Compare real and dual quaternions |
| 7 | Define and formulate the quaternion operator and other operators similar to the complex number operator |