Syllabus: Numerical Analysis (Spring 2023)

Basic Info

Welcome to Numerical Analysis (MATH-UA.0252, MATH-UY.4424)! This syllabus contains important information regarding course policies and procedures.

Course goals

• Demonstrate an general understanding of key concepts in numerical analysis such as: stability and conditioning, techniques for solving linear systems and least squares problems, matrix factorizations, and polynomial approximation and quadrature
• Gain basic proficiency with numerical computing in numpy or a similar language
• Build confidence communicating about advanced mathematical subjects using natural language

Accommodations and Accessibility

While participation in and engagement with the course is necessary, I recognize that not everyone has the same learning needs. I am happy to work with you directly, or with you in conjunction with the Center for Student Accessibility (CSA) to accommodate your individual needs. This includes accommodations for religious/cultural holidays, learning needs, sickness, etc. Please reach out to me with any concerns.

Absenses which can be forseen must be planned for in advance.

Textbook

There is no required textbook. In addition to the course notes, it is recommended that you read the relevant topics in:

• Numerical methods: design, analysis, and computer implementation of algorithms by Anne Greenbaum and Tim Chartier [link]
• An Introduction to Numerical Analysis by Endre Süli and David Mayers [link]

Both of these texts are available online for free with an NYU netID.

Grading

Grading is broken down as follows:

• 15% Participation
• 30% Homework
• 35% Quizzes
• 20% Final Project

Numerical grades will be converted to letter grades using the following thresholds:

Cutoff	95%	93%	90%	85%	80%	76%	70%	65%
Grade	A	A-	B+	B	B-	C+	C	D

These thresholds may be adjusted based on the final grades, but they will only be moved down; i.e. any changes can only bennefit your final grade.

Participation

Active participation in the course is expected. This will be evaluated through participation points. If you earn between 20-30 points, you particpation grade will be min(#points/2,15)%. If you earn 10-19.99 points you will receive 5%. Less than 10 points will receive 0%.

There are many ways in which you can participate to earn you participation points.

• (20pts, max 20pts) Actively engage in breakout groups throughout semester
  • Repeated unexcused absenses will result in a zero for this category. Please talk to me if you have any questions/concerns.
• (1pts, max 10pts) Attend office hours/recitation
• (.5pts, max 5pts) Ask/answer a question on the discussion board
  • Questions/answers must be high quality and related to the course materials. Thus, a question like “what is the difference between a definite and indefinite integral?” would get a point, but a question like “is there a quiz today?” would not.
• (.5pts, max 3pts) Find a mistake in the course notes, and suggest a fix on the thread on Ed.

It is your responsibility to make sure that the attendence to worksheets, office hours, and recitation is correct. Corrections to the Gradescope assignment will not be made for activities more than 2 weeks in the past.

If you have 98% or higher in the rest of the categories at the end of the class, I will give you an “A” regardless of your participation score. However, if you miss this threshold and did not participate at all, the best final score you could get would be a “B-”.

Homework

You are highly encouraged to work with peers on the homework, but you must write up the solutions on your own. See the section on Academic Integrity for more information.

• Homework problems will be a combination of problems from the textbook as well additional problems
• Homework will be due Thursdays at 11:59pm, unless noted otherwise
• You will always have at least 1 week between the release of a homework assignment and the due date
• You can use any language you like, even if the homework specifies a particular langauge.

While subject to change, it is planned that we will have 7 homeworks.

Submission policy (Gradescope)

• Write the names of anyone you work with on the top of your assignment
• Homework should be turned in on Gradescope
  • One problem per page
  • Do not put the solutions to multiple problems on the same page.
  • Tag your responses on gradescope. Each page should have a single problem tag. Improperly tagged responses will not receive credit.
  • Scans of homeworks must be high resolution and cropped to the page (i.e. no random stuff in the background). Make sure that the nothing from the back side of the page bleeds through
• Include all code you use as copyable text in the PDF (i.e. not as a screenshot)
• Typesetting with a program such as LaTeX is highly encouraged
• Late homework will not be accepted

Quizzes

• In general, every other Monday there will be an in-person quiz lasting about 15 minutes
• Quizzes will contain straightforward questions similar to previous homework problems
• The goal of quizzes is to serve as a self-check that you understand the important concepts
• The lowest quiz grade will be dropped if you fill out intro survey, mid-quarter check-in, and exit survey.

While subject to change, it is planned that we will have 7 quizzes.

Final project

• The last few weeks of the course will be spent on final projects meant to apply the knowledge gained during the course to a real-world problem.
• Grading will be based on effort and a project proposal, report, in-class poster presentation, and reviews of your peer’s posters
• More details will be given later in the semester

Academic Integrity

Please see the general NYU policy: https://www.nyu.edu/about/policies-guidelines-compliance/policies-and-guidelines/academic-integrity-for-students-at-nyu.html

Any violations of the NYU or course policy on academic integrity may result in punishment. Depending on severity, this could include receiving a zero on the homework, quiz, or project, failure of the course, or being reported to the University.

Homework policy

The general rule of thumb is that you must write up the solutions yourself and you should be able to explain anything you turn in. This is particularly important because the quiz problems will be very similar to the homework problems. Working with friends/classmates

You are encouraged to work together with peers. This not only helps to cut down on the workload, but strengthens your own understanding of the topics. This is because explaining concepts forces you to engage with them in a deeper way, thereby building a better understanding of the material.

However, you must still write up your solutions on your own, and you should understand everything you write. For each assignment, you must include who you worked with (first name+last name). Failure to do this is plagiarism and may be penalized.

• okay: You are stuck on a problem, so you ask a friend how they did it. The friend provides a high level description of their approach.
• not okay: You are stuck on a problem, so you ask a friend how they did it. The friend sends you their solution and you copy it down.
• okay: You are stuck on a problem, so you ask a friend how they did it. You meet with your friend and they walk you through each step.
• not okay: You send someone your code.

Internet or other external sources

Figuring out how to effectively search for information on the internet is an extremely useful skill. At the same time, you will eventually come across problems without solutions, and without having developed the proper problem solving skills, it will be much harder to come up with a solution. To balance these two possibilities, you are allowed to use the internet to search for solution to a problem after (i) you have been to office hours or used the discussion board to ask about this problem, and (ii) you have spent at least 24hr on the problem after office hours/receiving a response on the discussion board.

If you use the internet or other external sources, you must cite the source and include a description of how you used the source. Failure to do this is plagiarism and will be penalized.

• okay: It’s always fine (even without going to office hours) to search for generic information (e.g. definition of a word/phrase, coding syntax, etc.).
• not okay: You find the answer on the internet and copy it down.
• okay: You have gone to office hours or posted on the discussion board and after a day are still confused. You then find the answer on the internet and later, on your own, you reproduce the solution.
• not okay: the use of Chegg or any other paid services.
• not okay: asking/posting any of the homework questions on stackoverflow or similar websites