According to the catalogue:
As determined by the GIDP Program in Applied Mathematics Graduate Student Handbook.
Browse to Core Courses for addition information.
Information | Data |
---|---|
Instructor | Professor Marek Rychlik |
Office | Mathematics 605 |
Telephone | 1-520-621-6865 |
rychlik@arizona.edu | |
Instructor Homepage/Web Server | http://alamos.math.arizona.edu |
Course Homepage | http://alamos.math.arizona.edu/math589 |
Course Homepage (Mirror) | http://marekrychlik.com/math589 |
Personnel | Day of the Week | Hour | Room | Comment |
---|---|---|---|---|
Marek Rychlik | Tuesday | 11:00am-12:00am | Upper Division Tutoring via Teams (Zoom) | Upper Division Tutoring |
Novel Dey, Math 589 Super-TA | Tuesday | 3:30pm-4:30pm | ENR2 - N270HH | Math 589 Super-TA office hours (in person) |
Marek Rychlik | Wednesday | 5:00pm-6:00pm | Math 464 Zoom Link | Regular office hours (Zoom, Math 464) |
Bella Salter, Math 464 TA | Thursday | 12:30pm-1:30pm | ENR2 - N270HH | Math 464 TA office hours (in person) |
Novel Dey, Math 589 Super-TA | Tuesday | 1:30pm-2:30pm | TBA | Math 589 Super-TA office hours (in person) |
Marek Rychlik | Friday | 3:00pm-4:00pm | Math 589 Zoom Link | Regular office hours (Zoom, Math 589) |
Office hours by appointment are welcome. Please contact me by e-mail first, so that I can activate a Zoom link for the meeting.
The course format is that of a conventional lecture, with in-class discussion and additional web-delivered content. All lectures will be recorded and available on Zoom and Panopto.
Written homework will be assigned regularly and graded using Gradescope.
In addition, the course incorporates required programming assignments. Numerical experimentation is essential to understanding and using the course subject matter. The assignments will be graded by an autograder implemented in Gradescope.
In this course you are welcome and expected to use generative artificial intelligence/large language model tools, e.g. ChatGPT, Dall-e, Bard, Perplexity. Using these tools aligns with the course learning goals such as developing writing and programming skills, and ability to effectively use available information. Be aware that many AI companies collect information; do not enter confidential information as part of a prompt. LLMs may make up or hallucinate information. These tools may reflect misconceptions and biases of the data they were trained on and the human-written prompts used to steer them. You are responsible for checking facts, finding reliable sources for, and making a careful, critical examination of any work that you submit. Your use of AI tools or content must be acknowledged or cited. If you do not acknowledge or cite your use of an AI tool, what you submit will be considered a form of cheating or plagiarism. Please use the following guidelines for acknowledging/citing generative AI in your assignments:
Students are expected to be present for all exams. If a verifiable emergency arises which prevents you from taking an in-class exam at the regularly scheduled time, the instructor must be notified as soon as possible, and in any case, prior to the next regularly scheduled class. Make-up exams and quizzes will be administered only at the discretion of the instructor and only under extreme circumstances. If a student is allowed to make up a missed exam, (s)he must take it at a mutually arranged time. No further opportunities will be extended. Failure to contact your instructor as stated above or inability to produce sufficient evidence of a real emergency will result in a grade of zero on the exam. Other remedies, such as adjusting credit for other exams, may be considered.
Advanced Numerical Methods and High-Performance Computing By Marek Rychlik (the instructor). A lecture note style booklet prepared especially for this course.
See Background reading for a list of texts worth studying along with taking the course.
All examinations are planned to be administered during the class time, either in person or on Zoom.
If, due to unforseen circumstances, they cannot be held in person, they are held on Zoom using the "gallery view" mode.The exam papers for not in-person tests will be distributed on-line by D2L and collected electronically using D2L "dropbox" feature.
Exam or Assignment | Date | Grade contribution |
---|---|---|
Midterm 1 | TBA | 20% |
Midterm 2 | TBA | 20% |
Final Examination | December 18, Wednesday, 10:30am - 12:30pm | 30% |
Homework | Written and Programming, administered via Gradescope | 30% |
Written and programming homework consists of approximately twelve assignments equally contributing to the grade, each worth 30/12 = 2.5% of the grade. Written assignments are downloaded from Gradescope. The programming assignments are posted on line at this link: Homework. The assignment papers are collected via Gradescope, which is cloud-based software for semi-automatic grading. Programming assignments will be graded using autograders - programs written by the instructor that run the code and verify the results. Things to keep in mind:
Using Gradescope for grading differs from other grading systems. Mainly, it uses AI to allow the instructor to accurately grade a larger number of problems than it would be possible otherwise. Some grading is completely automated (e.g., solutions to problems with a numerical answer). More comples answers may be grouped automatically by using Machine Learning, OCR and image analysis. However, it is possible to completely confuse the system by improperly structuring the submitted document. Therefore, please read the instructions below carefully and re-visit them as needed. Note that Gradescope supports automatic regrade requests which you can use if all fails.
The solutions must be structured in such a way that Gradescope can read them and that its 'AI' can interpret them. Your homework must be submitted as a PDF document, even if you use scanner or phone to capture images. Two typical workflows will be as follows:
Programming in Python and MATLAB is an important part of the course. Programming assignments in the first parts of the course will be in Python, and later in the course they will approximately alternate between MATLAB and Python.
Additionally, for illustrating some aspects of the course, I will be using these programs (easy to download and free to use):
The University of Arizona has vast computing resources for projects of all sorts of sizes. In the course of your studies you will most likely need to use these resources. Some of the activities in this class will utilize HPC resources. The students in the class will be provided access through a class group associated with this class. The resources available to each student are described here:
The final examination is scheduled for: December 18, Wednesday, 10:30am - 12:30pm.
The time, data and general exam rules are set by the University and can be found at these links:
The student in the class normally receives a letter grade A, B, C, D or E.
The cut-offs for the grades are:
Grade | % Range |
---|---|
A | 90%+ |
B | 80-90% |
C | 70-80% |
D | 60-70% |
E | 0-60% |
Normally, individual tests and assignments will not be "curved". However, grade cut-offs may be lowered at the end of the semester (but not raised!) to reflect the difficulty of the assignments and other factors that may cause abnormal grade distribution.
The grade will be computed by D2L and the partial grade will be updated automatically by the system as soon as the individual grades are recorded.
General UA policy regarding grades and grading systems is available at https://catalog.arizona.edu/policy-type/grade-policiesFor a list of emergency procedures for all types of incidents, please visit the website of the Critical Incident Response Team (CIRT):
Our goal in this classroom is that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact Disability Resources (520-621-3268) to establish reasonable accommodations. For additional information on Disability Resources and reasonable accommodations, please visit http://drc.arizona.edu/ .
If you have reasonable accommodations, please plan to meet with me by appointment or during office hours to discuss accommodations and how my course requirements and activities may impact your ability to fully participate. Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable. Code of Academic Integrity Required language: Students are encouraged to share intellectual views and discuss freely the principles and applications of course materials. However, graded work/exercises must be the product of independent effort unless otherwise instructed. Students are expected to adhere to the UA Code of Academic Integrity as described in the UA General Catalog. See: http://deanofstudents.arizona.edu/academic-integrity/students/academic-integrity http://deanofstudents.arizona.edu/codeofacademicintegrity .
Week | Date | Topic | Notes |
---|---|---|---|
1 | Aug 26 | Introduction | |
Aug 28 | Floating Point Arithmetic | ||
Aug 30 | Floating Point Arithmetic | ||
2 | Sep 2 | No Class | Labor Day |
Sep 4 | Floating Point Arithmetic | ||
Sep 6 | Numerical Linear Algebra: SVD | ||
3 | Sep 9 | Numerical Linear Algebra: SVD | |
Sep 11 | Numerical Linear Algebra: SVD | ||
Sep 13 | Numerical Linear Algebra: SVD | ||
4 | Sep 16 | Numerical Linear Algebra: QR and LU Factorizations | |
Sep 18 | Numerical Linear Algebra: QR and LU Factorizations | ||
Sep 20 | Numerical Linear Algebra: QR and LU Factorizations | ||
5 | Sep 23 | Numerical Linear Algebra: QR and LU Factorizations | |
Sep 25 | Numerical Linear Algebra: QR and LU Factorizations | ||
Sep 27 | Numerical Linear Algebra: QR and LU Factorizations | ||
6 | Sep 30 | Eigenvalues and Eigenvectors | |
Oct 2 | Eigenvalues and Eigenvectors | ||
Oct 4 | Eigenvalues and Eigenvectors | ||
7 | Oct 7 | Systems of Non-Linear Equations: Functional Iteration | |
Oct 9 | Systems of Non-Linear Equations: Functional Iteration | ||
Oct 11 | Systems of Non-Linear Equations: Functional Iteration | ||
8 | Oct 14 | Systems of Non-Linear Equations: Newton's Method | |
Oct 16 | Systems of Non-Linear Equations: Newton's Method | ||
Oct 18 | Systems of Non-Linear Equations: Newton's Method | ||
9 | Oct 21 | Numerical Differential Equations: Basic Integration Schemes, Order of Accuracy | |
Oct 23 | Numerical Differential Equations: Basic Integration Schemes, Order of Accuracy | ||
Oct 25 | Numerical Differential Equations: Basic Integration Schemes, Order of Accuracy | ||
10 | Oct 28 | Initial Value Problem: Euler Method, Explicit-Implicit Methods | |
Oct 30 | Initial Value Problem: Euler Method, Explicit-Implicit Methods | ||
Nov 1 | Initial Value Problem: Euler Method, Explicit-Implicit Methods | ||
11 | Nov 4 | Initial Value Problem: Stability, Runge-Kutta Methods | |
Nov 6 | Initial Value Problem: Stability, Runge-Kutta Methods | ||
Nov 8 | Initial Value Problem: Stability, Runge-Kutta Methods | ||
12 | Nov 11 | No Class | Veterans Day |
Nov 13 | Initial Value Problem: Adaptive Step Size | ||
Nov 15 | Initial Value Problem: Adaptive Step Size | ||
13 | Nov 18 | Boundary Value Problem: Shooting Method | |
Nov 20 | Boundary Value Problem: Shooting Method | ||
Nov 22 | Boundary Value Problem: Shooting Method | ||
14 | Nov 25 | Boundary Value Problem: Quasi-Linearization | |
Nov 27 | Boundary Value Problem: Quasi-Linearization | ||
Nov 29 | No Class | Thanksgiving | |
15 | Dec 2 | Other Topics | |
Dec 4 | Other Topics | ||
Dec 6 | Other Topics | ||
16 | Dec 9 | Review and Final Discussions | |
Dec 11 | Review and Final Discussions | Last Day of Class |