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**January 2021**

The objective is to understand the theoretical foundations of high dimensional data science. This is an elective course offered to undergraduate and postgraduate students.

- Monday: 5-6.30pm
- Tuesday: 5-6.30pm

- Classroom code: urjfkom
- Link to the live lectures: https://meet.google.com/pek-fimu-pop
- Link to the recorded playlist (Youtube): video lectures

- Algorithm Design
- Probability - video lectures by Prof.John Tsitsiklis
- Linear algebra - video lectures by Prof. Gilbert Strang
- Linear algebra - video lectures by 3blue1brown
- Single variable Calculus - video lecture by Prof. David Jerison

- Foundations of Data science by Blum, Hopcroft and Kannan - online pdf
- Understanding machine learning by Shai Shalev-Shwartz and Shai Ben-David

- NIL

- High Dimensional Space - The geometry of high dimension, properties of unit ball, Random projects and Johnson-Lindenstrauss Lemma, Separating gaussians
- Singular Value Decomposition (SVD) - Introduction to SVD, best k-rank approximations, left singular vectors, power method for SVD, applications of SVD.
- Compressed sensing

We expect every student to follow the highest standards of integrity and academic honesty. Copying/sharing code in exams, homeworks, labs are not allowed. All answers have to be written in your own words. You need to cite any idea you have taken from internet or text book to answer a question. See the IIT Goa policy for academic malpractices.

# | Date | Topic | Video Resources | Other Resources |
---|---|---|---|---|

Introduction to Linear algebra | ||||

1 | 1/2/21 | Vectors: magnitude & direction, linear combination, independence, span, basic, norms, inner product, orthogonal vectors | ||

2 | 2/2/21 | Matrices: column/row vectors, special matrices, matrix addition, matrix times a vector - multiple ways to see this, matrix multiplication, rank of a matrix, special matrices - identity matrix, diagonal matrix, inverse matrix | ||

3 | 8/2/21 | Eigen values and vectors: Computing them, Properties, Special matrices and their eigen values and eigen vectors | Youtube | |

4 | 9/2/21 | Eigen values and vectors: Properties of eigen values and eigen vectors, Diagonalization | Youtube | |

5 | 15/2/21 | Tutorial | google drive 1 google drive 2 | |

7 | 22/2/21 | Discussion on sample linear algebra questions | google drive | |

8 | 23/2/21 | Markov chains and Google matrix | google drive | |

9 | 24/2/21 | Computing the Google page rank | google drive | |

10 | 1/3/21 | Singular Value Decomposition (SVD) | google drive | |

11 | 2/3/21 | Best k-rank approximation | google drive | |

12 | 8/3/21 | Principle component analysis | google drive | |

13 | 10/3/21 | Computing eigen values | google drive | |

14 | Mid semester exam | |||

15 | 22/3/21 | Mid semester answers | google drive | |

16 | 22/3/21 | Introduction to Probability | google drive | |

17 | 5/4/21 | Discrete Probability Review | Youtube | |

18 | 6/4/21 | Normal Distribution Review | Youtube | |

19 | 12/4/21 | Random points in high dimensional space | google drive | |

20 | 17/4/21 | High dimensional volume (CORRECTION: The formula for volume I wrote was correct. But the formula for Gamma function I wrote was wrong.) | google drive | |

21 | 19/4/21 | Introduction and applications of Johnson Lindenstrauss lemma | google drive | |

22 | 20/4/21 | Proof of Johnson Lindenstrauss Lemma (CORRECTION: I said that expectation of the square root of something is the square root of expectation. This claim is not correct. However our proof is not wrong as I had said in the lecture we can assume A = 1/sqrt(k) R and we need not assume my above 'claim'.) | google drive | |

23 | 26/4/21 | Introduction to Randomized algorithms | google drive | |

24 | 27/4/21 | Completing JL lemma proof | google drive | |

25 | 3/5/21 | Applications of JL lemma | google drive | |

25 | 4/5/21 | Applications of JL lemma continued | google drive |