Syllabus and References
| Event | Date | Description | References | |
|---|---|---|---|---|
| Introductory Lecture | Aug 1 | Course Introduction | NA | |
| Lecture 1 | Aug 2 | Countable and uncountable sets, Axioms of probability, Conditional probability, Independent events | [HOS] | |
| Lecture 2 | Aug 8 | Independent events (contd.), Law of total probability, Bayes theorem, Conditional independence | [HOS] | |
| Lecture 3 | Aug 9 | Random variables, Probability distribution, Some special parametric probability distributions | [HOS] | |
| Lecture 4 | Aug 10 | Some special parametric probability distributions (contd.) | [HOS] | |
| Lecture 5 | Aug 16 | Discrete random variables, Probability mass function, Cumulative distribution function | [HOS] | |
| Lecture 6 | Aug 17 | Continuous random variables, Probability density function, Function of random variables | [HOS] | |
| Quiz 1 | Aug 22 | Syllabus: lecture 1-2 | [ Solutions ] | |
| Lecture 7 | Aug 23 | Probability bounds: Markov and Chebyshev's inequalitites, Chernoff bound | [HOS] | |
| Lecture 8 | Aug 24 | Probability bounds (contd.): Cauchy–Schwarz inequality, Jensen's inequality; Multiple random variables: Joint distribution, Marginal distribution, Conditional distribution | [HOS] | |
| Lecture 9 | Sep 12 | Conditional Expectation and Variance | [HOS] | |
| Lecture 10-11 |
Sep 13 | Conditional Variance (contd.), Covariance, Correlation coefficient, Moment generating functions | [HOS] | |
| Lecture 12 | Sep 14 | Law of large numbers, Limit theorems | [HOS] | |
| Lectures 13 | Sep 15 | Limit theorems (contd.), Sample problem discussion for the Mid sem | [HOS] | |
| Mid Sem | Sep 20 | Syllabus: lecture 1-11 | NA | |
| Lecture 14 | Sep 26 | Discussion of the Mid sem problems | NA | |
| Lecture 15 | Sep 27 | Discussion of the Mid sem problems (contd.) | NA | |
| Lecture 16 | Sep 28 | Random walks | [GRI] | |
| Lecture 17 | Oct 3 | Ballot problem, Returns and first returns | [FEL] Chapter III: Section 1 (also recommended: Sections 2, 3 and 4) [GRI] 12.1 | |
| Lecture 18 | Oct 4 | Gambler's ruin problem | [GRI] Sec 12.2 | |
| Lecture 19 | Oct 5 | Markov chains: Absorbing, Ergodic/Irreducible, Regular | [GRI] Chap 11 | |
| Quiz 2 [2Hrs] | Oct 6 | NA | ||
| Lecture 20 | Oct 17 | Introduction to Linear Algebra | [STR] Chap 1, [LAN] Chap 1 | |
| Lecture 21 | Oct 18 | Linear system of equations: Algebraic and Geometric interpretation | [STR] Chap 1 | |
| Lecture 22 | Oct 19 | Matrix way of solving linear system of equations: Elimination matrix, permutation matrix, pathological cases, inverse of a matrix, A = LU and A = LDU decomposition | [STR] Chap 2 | |
| Lecture 23 | Oct 24 | Underdetermined System of Eq/Inverse of Matrix/Vector Space/Subspace | [STR] Chap 2 and 3, [LAN] III [For vector space] | |
| Lecture 24 | Oct 25 | Linear Independence/Basis | [LAN] III | |
| Lecture 25 | Oct 26 | Rank of Matrix/Subspaces related to Matrix and relation among them | [LAN] III | |
| Lecture 26 | Oct 31 | Linear Transformation/Linear Map | [LAN] IV | |
| Lecture 27 | Nov 1 | Kernel and Image of Linear Map, Rank and Systems of Linear Equations Again | [LAN] IV | |
| Lecture 28 | Nov 2 | Problem Solving Session | NA | |
| Quiz 3 [1Hr] | Nov 2 | [ Solutions ] | ||
| Lecture 29-30 |
Nov 5 | Matrices associated with Linear Map, change of Bases | [LAN] IV | |
Text and Reference Book(s)
- HOS: Hossein Pishro-Nik. Introduction to Probability, Statistics, and Random Processes. 2014. Companion Website
- FEL: William Feller. An Introduction to Probability Theory and its Applications. Volume 1.
- GRI: Charles M. Grinstead and J. Laurie Snell. Introduction to Probability. Companion Website
- LAN: Serge Lang. Introduction To Linear Algebra.
- STR: Gilbert Strang. Introduction to Linear Algebra. Companion Website
- HOF: Kenneth M Hoffman and Ray Kunze. Linear Algebra.