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Course Information
Identification

CS 740: Mathematics for Visual Computing
 
Description

The syllabus includes a subset of topics from the following list:

1) Multivariate Calculus
* Functions (multi-variable, vector-valued) and their derivatives, Taylor series, matrix calculus, basic vector calculus

2) Numerical Linear Algebra
* Special matrices (e.g., orthogonal, SPD), matrix decompositions (e.g., SVD, eigen analysis)

3) Probability and Statistics
* Distributions, mean, variance, covariance, bounds, likelihood function, Bayes rule, entropy, divergence, mutual information

4) Optimization
* Unconstrained (gradient descent, Newton's method, Levenberg-Marquardt algorithm, quasi-Newton methods), constrained (equality constraints, Lagrange multipliers)

5) Interpolation and regression
* Linear, polynomial, Barycentric coordinates

6) Numerical integration of functions and introductory numerical differential equations

7) Introductory differential geometry

8) Introductory projective geometry
 
References

1.
Title: Numerical Recipes - The Art of Scientific Computing
Authors: William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery
Cambridge University Press 2007

2.
Title: Scientific Computing
Author: Michael T. Heath
McGraw-Hill 2002

3.
Title: Numerical Linear Algebra
Authors: Lloyd N. Trefethen, David Bau III
SIAM 1997

4.
Title: A First Course in Probability
Author: Sheldon Ross
Pearson Education 2012

5.
Title: Probability, Random Variables and Stochastic Processes
Authors: Athanasios Papoulis, S. Unnikrishna Pillai
McGraw-Hill 2002

6.
Title: Numerical Optimization
Authors: Jorge Nocedal, Stephen Wright
Springer 2006

7.
Title: Elements of Information Theory
Authors: Thomas M. Cover, Joy A. Thomas
Wiley-Interscience 2006
 
Home Page

http://www.cse.iitb.ac.in/~sharat/current/cs740
 
Prerequisites

N/A
 
Other Details

Duration : Full Semester Total Credit : 6
Type : Theory
 
Current Semester (Autumn 2017-18)

Status : Not Offered Instructor : ---
 
Next Semester (Spring 2017-18)

Status : Offered Instructor : Prof. Sharat Chandran




Last Modified Date: 09-May-2016

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