COURSE SUMMARY
Course Title: 
Mathematics for Intelligent System 1
Course Code: 
19MAT105
Year Taught: 
2019
Semester: 
1
Type: 
Subject Core
Degree: 
Undergraduate (UG)
School: 
School of Engineering
Campus: 
Bengaluru
Coimbatore
Amritapuri

'Mathematics for Intelligent System 1' is a course offered in the first semester of  B. Tech. in Computer Science and Engineering (Artificial Intelligence) program at the School of Engineering, Amrita Vishwa Vidyapeetham.

Course Objectives

The course will lay down the basic concepts and techniques of linear algebras applied to signal processing. It will explore the concepts initially through computational experiments and then try to understand the concepts/theory behind it. At the same time, it will provide an appreciation of the wide application of these disciplines within the scientific field. Another goal of the course is to provide connection between the concepts of linear algebra, differential equation and probability theory.

Course Outcomes

CO1 To develop an understanding of the basic concepts and techniques of linear algebra as applied to signal processing.
CO2 To provide an appreciation of these disciplines within the scientific field.
CO3 To provide connection between the concepts of linear algebra, differential equation and probability theory.
CO4 To develop an insight into the applicability of linear algebra in business and scientific domains.
CO5 To enable the students to understand the use of calculus and Linear algebra in modelling electrical and mechanical elements.
CO6 To equip the students to understand the role of probability theory in providing data sets for computational experiments in data science.

 

  PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
CO1 3 3 2 2 3       3 2 3 3
CO2 3 3 3 3 3 2     3 2 3 3
CO3 3 2 3 3 3       3 2 3 3
CO4 3 3 3 2 3       3 2 3 3
CO5 3 2 3 3 3       3 2 3 3
CO6 3 3 3 3 3 2     3 2 3 3

Course Evaluation Pattern:

Internal – 75%

  • Assignments – 50% (20 assignments with equal credit)
  • Quiz- 25% (5 Quizzes with equal credit)

External – 25%

  • Project – 25%

Basics of Linear Algebra - Linear Dependence and independence of vectors - Gaussian Elimination - Rank of set of vectors forming a matrix - Vector space and Basis set for a Vector space - Dot product and Orthogonality - Rotation matrices - Eigenvalues and Eigenvectors and its interpretation - Projection matrix and Regression – Singular Value Decomposition.

Convolution sum, Convolution Integral, Ordinary Linear differential equations, formulation, analytical and Numerical solutions, Impulse Response Computations, formulating state space models of Physical systems.

Examples of ODE modelling in falling objects, satellite and planetary motion, Electrical and mechanical systems. Multivariate calculus, Taylor series, Introduction to Optimization.

Introduction to Probability Distributions and Monte Carlo Simulations.

  1. Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019.
  2. William Flannery, Mathematical Modelling and Computational Calculus, Vol-1, Berkeley Science Books, 2013.