1 Numerical Analysis

🚧 This page will be updated continuously throughout the semester. 🚧

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":

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

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

  1. 30 other people will have to read your notes => they must be understandable
  2. you must include written words to ease the exposition
  3. you must use LaTeX to typeset the notes properly
  4. 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:

  1. A Guide to Writing Mathematics
  2. Guidelines for Good Mathematical Writing
  3. A Brief Introduction to Mathematical Writing
  4. Practical Suggestions for Mathematical Writing

And some resources on LaTeX:

  1. Overleaf - Learn LaTeX in 30 minutes
  2. Overleaf - Aligning equations with amsmath
  3. 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)    
  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