Title: MA607 Probability Theory and Linear Algebra

Semester: First Semester M Tech (VLSI)

3-0-0,  3 Credits

Prerequisites:  None

Vector Spaces:

General Vector Spaces, Subspaces, Linear Independence, Basis and Dimension, Span, Some Fundamental Theorems, Row Space, Column Space, Nullspace,  Rank and Nullity, Four Fundamental Spaces,

Inner Product Spaces:

General Inner Products, Euclidean and Weighted Inner Product, Length, Distance, Norm, Angle and Orthogonality in Inner Product Spaces, Caucy-Schwarz Inequality, Orthogonal Complement, Orthonormal Bases, Gram-Schmidt Procedure, QR-decomposition.

Linear Transformations:

General Liner Transformations, Linear operators, Composition of operators and linear transformations, Kernel and Range, Dimension theorm for Linear Transformation, Inverse Linear Transformations, Matrices of General Linear Transformations, Matrices of Compositions and Linear Transformations,

Probability Theory:

Basics of Probability theory, Discrete Random Variables and Probability Distributions, Mean and Variance, Moments of a Discrete Random Variable, Uniform Distribution, Binomial Distribution, Poisson Distribution, Functions of Random Variables, Continuous Random Variables and Probability Distributions

Text Books/References:

1. Howard Anton and Chris Rorres, "Elementary Linear Algebra", John Wiley and Sons, 9th Edition, 2008.

2. Douglas C. Montgomery and George C. Runger, "Applied Statistics and Probability for Engineers", John Wiley and Sons,  3rd Edition, 2003.