Professor when you took the course: Prof. Sukumar Srikant
Course Content: The broad objective of the first part of this course is to introduce to two mathematical structures – groups and vector spaces – with an emphasis on engineering applications. In groups, the focus is on the GL(n, R), SO(3) and SE(3) groups which find large application in the fields of robotics, spacecrafts and vision problems. The notion of the exponential map, restricted to these two groups, is also introduced, thereby bringing in the notions of angular and translational velocities. Vector spaces is then introduced in a more formal setting. After a quick review of the basics, the notions of dual spaces, the dual basis, annihilators, multilinear forms and permutations are stressed. (These ingredients then naturally build up to defining the determinant as a skew-symmetric multilinear form at a later stage.) Linear transformations and matrix representations then follow. Further characterizations like invertible, similarity, projection and adjoint transformations are then presented. The last module is on inner products and normed vector spaces. In inner product spaces, the use of the projection theorem in approximation problems is emphasized.
Pre-requisites: None
Feedback on lectures: Lectures are interactive with the professor not only teaching but also asking the students different methods to derive/solve a particular theorem. Due to low class strength (around 20 come to class), one-to-one interaction with professor is fairly high. Lectures are conducted in LT’s.
The course is more like a pure mathematical course with little introduction to system and control engineering. It is a tough course and might take some time adjusting to the mathematical approach, which can be made easier if one is interactive in class and completes given assignment on his own. Assignments will be from reference texts. All quizzes were open-book tests and required proper understanding of the concepts.
Marks Distribution: Best 3 out of 4 quizzes (80%), assignment+class interaction (20%)
Attendance Policy: No compulsory attendance policy
Difficult level: 3.5/5
Grading: Grading was decent with 4 AA’s, 9AB’s, 5BB’s, 7BC’s, 6CC’s, 2CD’s, 3 W’s out of 36 students
Study Material:
- Finite Dimensional Vector Spaces – P. R. Halmos, Springer 1984
- Elementary Topics in Differential Geometry – J. A. Thorpe, Springer 2004
- Lecture notes by the instructors
We thank “Rajat Daga” for the course review.
Department Academic Mentorship Program 