## 1 Numerical Analysis

ðŸš§ *This page will be updated continuously throughout the semester.* ðŸš§

### 1.1 Course information

Course number | MATH-UA 252-005 (NYU), MA-UY.4424-C (Brooklyn) |

Semester | Spring 2022 |

Instructor | Sam Potter (sfp@cims.nyu.edu) |

Office hours | Wed, 2 MTC, 872, 5:00-6:00PM |

Teaching assistant | Mariana Martinez-Aguilar |

Office hours | Tue, Zoom, 7:00-9:00PM (see recitation homepage for info) |

Fri, 2 MTC, Room 858, 1:00-2:00PM | |

Lecture | Mon/Wed, 3:30-4:50PM, RGSH 204 |

Recitation | Fri, 2:00-3:20PM, RGSH 204 |

Recitation homepage (with materials and Zoom info) | |

Links | BrightSpace, syllabus |

### 1.2 Description

This is an introductory course in numerical analysis. Topics include: the solution of linear and nonlinear equations, conditioning, least squares, numerical computation of eigenvalues, interpolation, and quadrature. The focus is on the analysis and implementation of numerical methods.

#### 1.2.1 Materials

Readings will be posted in the schedule below. All material will be accessible either through this website or NYU. You do not need to purchase a textbook for this course.

#### 1.2.2 Homework

There will be written assignments and programming assignments.

Written assignments will consist of short theoretical exercises (proofs) which must be prepared using LaTeX.

Programming assignments will be done using Python along with the numpy, scipy, and matplotlib packages.

#### 1.2.3 Scribing

One person will scribe each class, and each person will be required to scribe at least once. This will count towards 5% of your grade. The scribed notes will be compiled into a shared Overleaf document for you all to use.

Link to the scribed lecture notes on Overleaf (requires access).

Here's our current "scribing workflow":

- write notes by hand (or whatever is most comfortable for you) during class
- after class, re-write them using LaTeX however you prefer (this can be directly in Overleaf or locally on your computer)
- send me the .tex file or share the Overleaf document
- I will edit them lightly and send them back to you for you to make sure I didn't screw them up :-)
- I will merge them into the shared notes

When it comes to scribing, here are a few important things to remember:

- 30 other people will have to read your notes => they must be understandable
- you must include written words to ease the exposition
- you must use LaTeX to typeset the notes properly
- you must include the majority of the content of the lecture

To achieve this, we will go back and forth and edit your notes until I deem them acceptable. Only then will you receive credit for scribing. My goal: you are thoughtful about the process and put effort into it. Please be conscientious and consider your classmates.

Here are some resources on mathematical writing:

- A Guide to Writing Mathematics
- Guidelines for Good Mathematical Writing
- A Brief Introduction to Mathematical Writing
- Practical Suggestions for Mathematical Writing

And some resources on LaTeX:

- Overleaf - Learn LaTeX in 30 minutes
- Overleaf - Aligning equations with
`amsmath`

- Overleaf has a ton of great LaTeX resources—just look at the list of guides on the left-hand side of the previous two pages. In general, if you are stuck on how to do something in LaTeX, try searching Overleaf's docs, or just ask me.

#### 1.2.4 Grading

Scribing | 10% |

Written assignments | 10% |

Programming assignments | 20% |

Midterm | 30% |

Final | 30% |

### 1.3 Schedule

Please note that the date of each topic is tentative.

Week | Date | Scribe | Topics | Materials | Due |
---|---|---|---|---|---|

#1 | Jan 24 | Course intro, Babylonian algorithm | What is NA?, Babylon | ||

Jan 26 | Riya Mokashi | Fixed point iterations | Suli (Ch. 1) | ||

#2 | Jan 31 | Nikhil Isac | Bisection, secant method, Newton's method | Suli (Ch. 1) | |

Feb 2 | Mei Shin Lee | Convergence of the secant method and Newton's method | Suli (Ch. 1) | ||

#3 | Feb 7 | Nigel Shen | Different sources of numerical error | ||

Feb 9 | Cindy Zhang | Representing numbers and floating-point arithmetic | written1.pdf | ||

#4 | Feb 14 | Xinyu Gao | Review of linear algebra | prog1.pdf (prog1_test.py) | |

Feb 16 | Chuanyang Jin | The LU factorization | Golub and Van Loan (Ch. 3) | ||

#5 | Feb 21 |
Presidents' day | |||

Feb 23 | Maosen Tang | More LU factorization | written2.pdf | ||

#6 | Feb 28 | Fatima Mehdi | Least squares and the Cholesky decomposition | ||

Mar 2 | Junyao Chen | The QR decomposition | |||

Mar 4 | Review (during recitation and office hours) |
prog2.pdf | |||

#7 | Mar 7 | ||||

Mar 8 | Review (during Zoom office hours) |
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Mar 9 | Midterm |
Midterm solution | |||

Mar 14–20 |
Spring break | ||||

#8 | Mar 21 | Midterm solutions |
|||

Mar 23 | Zijun Wang | The SVD | |||

Mar 27 (Sunday) | written3.pdf | ||||

#9 | Mar 28 | Lucas Hsu | Eigenvalue algorithms | ||

Mar 30 | Arnav Kanwal | Eigenvalue algorithms (continued) | |||

#10 | Apr 4 | Yishi Wang | Lagrange interpolation | Prenter | |

Apr 6 | Elaine Li | Piecewise Lagrange interpolation | |||

Apr 10 | |||||

#11 | Apr 11 | Jiahao Hui | Function approximation: \(L^\infty\) | ||

Apr 13 | Class canceled |
||||

#12 | Apr 18 | Minghui Xia | Function approximation: \(L^2\) | ||

Apr 20 | Danny Chen | More Vandermonde | |||

Apr 24 (Sunday) | prog3.pdf | ||||

#13 | Apr 25 | Richen Du | Hermite interpolation, divided differences | ||

Apr 27 | Churchill Zhang | Numerical integration: Newton-Cotes | |||

May 1 (Sunday) | written4.pdf | ||||

#14 | May 2 | Panayiotis Christou | Generalized divided differences | ||

May 4 | Hailey Meng | Gaussian quadrature | |||

May 8 (Sunday) | |||||

#15 | May 9 | Saif Azim | Review | ||

May 11–17 |
Final exam period | ||||

Approx. May 17 (Tue) | prog4.pdf | ||||

Approx. May 17 (Tue) | Written extra credit deadline |