MA3352 Probability and Linear Algebra Syllabus:
MA3352 Probability and Linear Algebra Syllabus – Anna University Regulation 2021
COURSE OBJECTIVES:
• To introduce the basic notions of vector spaces which will then be used to solve related problems.
• To understand the concepts of vector space, linear transformations and diagonalization.
• To apply the concept of inner product spaces in orthogonalization.
• To provide necessary basics in probability and random processes that are relevant in applications such as random signals, linear systems in communication engineering.
• To understand the basic concepts of probability, one and two dimensional random variables and to introduce some standard distributions applicable to engineering which can describe real life phenomenon.
UNIT I PROBABILITY AND RANDOM VARIABLES
Axioms of probability – Conditional probability – Baye’s theorem – Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions – Functions of a random variable.
UNIT II TWO- DIMENSIONAL RANDOM VARIABLES
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).
UNIT III VECTOR SPACES
Vector spaces – Subspaces – Linear combinations and linear system of equations – Linear independence and linear dependence – Bases and dimensions.
UNIT IV LINEAR TRANSFORMATION AND DIAGONALIZATION
Linear transformation – Null spaces and ranges – Dimension theorem – Matrix representation of a linear transformations – Eigenvalues and eigenvectors –Diagonalization.
UNIT V INNER PRODUCT SPACES
Inner product, norms – Gram Schmidt orthogonalization process – Adjoint of linear operations – Least square approximation.
TOTAL: 60 PERIODS
COURSE OUTCOMES:
Upon successful completion of the course, students should be able to:
CO1:Explain the fundamental concepts of advanced algebra and their role in modern mathematics and applied contexts.
CO2: Demonstrate accurate and efficient use of advanced algebraic techniques.
CO3: Demonstrate their mastery by solving non-trivial problems related to the concepts and by proving simple theorems about the statements proven by the text.
CO4: Understand the fundamental concepts of probability with a thorough knowledge of standard distributions that can describe certain real-life phenomenon.
CO5: Understand the basic concepts of one and two dimensional random variables and apply them to model engineering problems.
TEXT BOOKS
1. Johnson. R.A., Miller. I and Freund. J., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 9th Edition, 2016.
2. Milton. J. S. and Arnold. J.C., “Introduction to Probability and Statistics”, Tata McGraw Hill, 4th Edition, 2007.
3. Friedberg. A.H., Insel. A.J. and Spence. L., “Linear Algebra”, Prentice Hall of India, New Delhi, 4th Edition, 2004.
REFERENCE BOOKS
1. Devore. J.L., “Probability and Statistics for Engineering and the Sciences”, Cengage Learning, New Delhi, 8th Edition, 2014.
2. Ross. S.M., “Introduction to Probability and Statistics for Engineers and Scientists”, 5th Edition, Elsevier, 2014.
3. Spiegel. M.R., Schiller. J. and Srinivasan . R.A., “Schaum’s Outline of Theory and Problems of Probability and Statistics”, Tata McGraw Hill Edition, 4th Edition, 2012.
4. Kolman. B. Hill. D.R., “Introductory Linear Algebra”, Pearson Education, New Delhi, First Reprint, 2009.
5. Kumaresan. S., “Linear Algebra – A Geometric Approach”, Prentice – Hall of India, New Delhi, Reprint, 2010.
6. Strang. G., “Linear Algebra and its applications”, Thomson (Brooks/Cole), New Delhi, 2005.