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Mathematics of Data Science and Statistics - Part 1
Course Objective: This course aims to give an introduction to mathematical statistics with applications. Prerequisites include calculus, linear algebra, and probability at the undergraduate level.
Instructor: Shuyang LING (sl3635@nyu.edu)
Time/Location: 1:15PM - 2:30PM on Mondays and Wednesdays, PDNG 211
Office hours: Room 1162-3
Textbook:
All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman. It is available free of charge on Springerlink if you are connected to the NYU wireless networks.
Statistical Inference, 2nd Edition by George Casella and Roger L. Berger. It is available on Amazon.com. This is a classic textbook on statistical inference, covering essential parts of statistical inference in depth.
Homework
Late homework will not be accepted. Only a subset of problems will be graded.
Course schedule:
The slides will be updated after each lecture.
| Date | Topics | Slides |
| Sep 2 | Review of probability, Chapter 1-2 | Lecture 1 |
| Sep 4 | Review of probability, Chapter 2 | Lecture 2 |
| Sep 9 | Review of probability, Chapter 3 | Lecture 3 |
| Sep 11 | Review of probability, Chapter 3 | Lecture 4 |
| Sep 16 | Review of probability, Chapter 4-5 | Lecture 5 |
| Sep 18 | Basics of statistics, Chapter 6 | Lecture 6 |
| Sep 23 | Basics of statistics, Chapter 6 | Lecture 7 |
| Sep 25 | Method of moments, Chapter 9 | Lecture 8 |
| Oct 7 | Maximal likelihood estimation, Chapter 9 | Lecture 9 |
| Oct 9 | Equivalence and consistency of MLE, Chapter 9 | Lecture 10 |
| Oct 14 | Asymptotic normality of MLE, Chapter 9 | Lecture 11 |
| Oct 16 | Multiparameter MLE, Chapter 9 | Lecture 12 |
| Oct 21 | Delta method and Cramer-Rao bound, Chapter 9 | Lecture 13 |
| Oct 23 | Hypothesis testing, Chapter 10 | Lecture 14 |
| Oct 25(F) | Midterm, 1:15pm-2:30pm | |
| Nov 4 | Hypothesis testing, Chapter 10 | Lecture 15 |
| Nov 6 | Hypothesis testing, Chapter 10 | Lecture 16 |
| Nov 8(F) | Hypothesis testing, Chapter 10 | Lecture 17 |
| Nov 11 | Hypothesis testing, Chapter 10 | Lecture 18 |
| Nov 13 | Linear regression, Chapter 13 | Lecture 19 |
| Nov 18 | Linear regression, Chapter 13 | Lecture 20 |
| Nov 20 | Linear regression, Chapter 13 | Lecture 21 |
| Nov 25 | Linear regression, Chapter 13 | Lecture 22 |
| Nov 27 | Linear regression, Chapter 13 | Lecture 23 |
| Dec 2 | Linear regression, Chapter 13 | Lecture 24 |
| Dec 4 | Logistic regression, Chapter 13 | Lecture 25 |
| Dec 9 | Logistic regression, Chapter 13 | Lecture 26 |
| Dec 11 | Logistic regression, Chapter 13 | Lecture 27 |
| Dec 18 | Final exam, 9am-11am, Rm 211 |
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