Groups and Linear Algebra-SC220
Instructor: Jaideep Mulherkar
Fall 2018
DA-IICT, Gandhinagar
Course description: The course introduces second year undergraduate students to abstract mathematical structures such as groups, vector spaces etc. Here the student builds on his/her mathematical intuition and is able to connect the abstract ideas that are part of this course with concrete ideas that he/she learns in other engineering courses such as signals and systems. The course consists of two parts. The first part is on groups and group actions with emphasis on symmetries and applications to counting problems. The second part is linear algebra. Here unlike his/her earlier exposure to matrices emphasis is on the abstract vector spaces and operators on them. Inner products are introduced with emphasis on geometric and analytical ideas such as closet point theorem, Gram-Schmidt orthogonalization and adjoints. Student will also learn to systematically solve a system of linear equations and a system of coupled linear differential equations. Ideas of least square and discrete Fourier transform are introduced.
Prerequisites: None
Textbooks:
Groups and Symmetry, M.A. Armstrong, Springer, Undergraduate texts in mathematics.
A first course in abstract algebra, J. Fraleigh, Pearson.
Linear Algebra, J.H. Kwak, S. Hong, Springer
Linear Algebra, S. Friedberg, A. Insel, L. Spence, Prentice Hall.
Course Notes:
Grading:
30% each for 2 midterms, 40 % for final.