MATH 551 TRANSFORMATIONAL GEOMETRY

Course Syllabus

1. Review of Linear Algebra and Intro to Mathematica software
1. Matrices and their operations
2. Elementary row operations
3. Linear transformations
4. Eigenvalues and eigenvectors
5. Quadratic and bilinear forms
2. Extended Euclidean Plane (EEP) and Space (EES)
1. Homogeneous coordinates
2. Horizon points, line(s) and plane
3. Analytical Euclidean Plane (AEEP) and Space (AEES)
3. Linear Transformations of AEEP and AEES
1. Coordinate Transformations
2. Euclidean Transformations
1. Translation
2. Rotations About points About axes About lines
3. Reflections in points in lines in planes
4. Products of the above
5. Similarity Transformations
6. Affine Transformations
4. Applications to Computer Graphics

Prerequisites: B.S. in Mathematics

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