1 INTRODUCTION  
2 BACKGROUND MATHEMATICS  
2.1 Algebraic Definitions  
2.2 Algebra in Context  
2.3 Computational Factors  
3 APPLICATIONS  
3.1 Dual-Quaternion Applications in Computer Vision  
3.2 Dual-Quaternion Applications in Kinematics  
3.3 Dual-Quaternion Applications in Graphics and Other Areas  
4 TAKING DUAL-QUATERNIONS TO THE EDGE (FUTURE DIRECTIONS)  
4.1 Security  
5 CONCLUSION AND DISCUSSION