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Course Detail

Course Name Mathematics for Intelligent Systems 3
Course Code 23MAT204
Program B.Tech in Artificial Intelligence and Data Science
Semester 3
Credits 3
Campus Coimbatore , Amritapuri ,Faridabad , Bangaluru, Amaravati

Syllabus

Unit 1

Direct methods for convex functions – sparsity inducing penalty functions- Constrained Convex Optimization problems – Krylov subspace -Conjugate gradient method – formulating problems as LP and QP – Lagrangian multiplier method-KKT conditions – support vector machines- solving by packages (CVXOPT) – Introduction to RKS – Introduction to DMD-Tensor and HoSVD- Linear algebra for AI.

Unit 2

Introduction to PDEs – Formulation and numerical solution methods (Finite difference and Fourier) for PDEs in Physics and Engineering- Computational experiments using Matlab/Excel/Simulink.

Unit 3

Multivariate Gaussian and weighted least squares – Markov chains – Markov decision Process

Unit 4

Introduction to quantum computing-Bells inequality-Quantum gates

Objectives and Outcomes

Course Objectives

  • To provide students with advanced knowledge and skills in optimization, PDEs, probability and statistics, and quantum computing.
  • To develop students proficiency in solving real-world problems in various domains, including physics, engineering, and computer science using the concepts of optimization, PDEs, and probability.
  • To apply the concepts and techniques learned in the course to solve complex problems and communicate their solutions effectively to both technical and non-technical audiences.
  • To equip students with advanced mathematical knowledge and problem-solving skills highly valued in various industries and research fields.

Course Outcomes

After completing this course, students will be able to

CO1

Apply the fundamental techniques of optimization theory to solve data science problems.

CO2

Analyse and solve computationally, physical systems using the formalism of partial differential equations.

CO3

Apply Markovian concepts in stochastic sequential systems.

CO4

Explain Bells Inequality and Quantum gates.

CO-PO Mapping

PO/PSO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

PSO1

PSO2

PSO3

CO

CO1

3

3

3

2

3

–

–

–

3

2

–

3

3

–

3

CO2

3

3

3

2

3

–

–

–

3

2

–

3

3

–

3

CO3

3

3

3

2

3

–

–

–

3

2

–

3

3

–

–

CO4

3

–

–

–

–

–

–

–

3

2

–

3

2

–

3

Evaluation Pattern

Evaluation Pattern

Assessment

Internal/External

Weightage (%)

Assignments (minimum 2)

Internal

30

Quizzes (minimum 2)

Internal

20

Mid-Term Examination

Internal

20

Term Project/ End Semester Examination

External

30

Text Books / References

Text Books / References

Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019.

Gilbert Strang, “Differential Equations and Linear Algebra Wellesley”, Cambridge press, 2018.

Stephen Boyd and Lieven Vandenberghe, Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares, 2018.

Bernhardt, Chris.?Quantum computing for everyone. Mit Press, 2019. (From pages 71 to 140).

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