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ENGINEERING MATHEMATICS IV
MAT 2228
Syllabus
- 01Probability and Distributions: Construction of a Probability Space, Discrete and Continuous Probabilities, Sum Rule, Product Rule, and Bayes' Theorem, Summary Statistics and Independence, Distributions: Binomial, Poisson, uniform, normal, Chi-square and exponential distributions
- 02Multivariate Random variables and Stochastic Process: Two and higher dimensional random variables, covariance, correlation coefficient, Moment generating function, functions of one dimensional and two dimensional random variables
- 03Static probabilities: review and prerequisites generating functions, difference equations
- 04Dynamic probability: definition and description with examples, Markov chains, transition probabilities
- 05Vector Calculus: Differentiation of Univariate Functions, Partial Differentiation and Gradients, Gradients of Vector-Valued Functions, Gradients of Matrices, Useful Identities for Computing Gradients, Backpropagation and Automatic Differentiation, Higher-Order Derivatives, Linearization and Multivariate Taylor Series
- 06Optimization: Basic solution, Convex sets and function, Simplex Method, Optimization Using Gradient Descent, Constrained Optimization and Lagrange Multipliers
References
- Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, Mathematics for Machine Learning, Cambridge University Press, 2020
- P L Meyer, Introductory Probability and Statistical Applications, Addison Wiley
- Medhi. J. Stochastic Processes, Wiley Eastern
- Murray R. Spiegel, Vector Analysis Theory and Problems, Schaum's Outline Series, 2019
- Hamdy A. Taha, “Operations Research: An Introduction”, 8th Edn., Pearson Education, (2008)
- Sheldon M. Ross, Introduction to Probability Models Eleventh Edition Elsevier
- E. S. Page, L. B. Wilson, An Introduction to Computational Combinatorics, Cambridge, University Press
- Bhat U R, Elements of Applied Stochastic Processes, John Wiley
Credits Structure
2Lecture
1Tutorial
0Practical
3Total