Math 589A - Algorithms of Applied Mathematics I
Syllabus for Math 589, Section 001, Fall 2025
Location and Times
Math 589A, Section 001, meets in ENR2, S395, MWF 12:00PM - 1:00PM.Course Description
According to the catalogue:
Part A (Fall)
Part B (Spring)
Course Prerequisites or Co-requisites
As determined by the GIDP Program in Applied Mathematics Graduate Student Handbook.
In particular, successful completion of Math 589A is required to take Math 589B.
Browse to Core Courses for addition information.
Instructor and Contact 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 |
Office Hours
Semester: Fall, 2025| Personnel | Day of the Week | Hour | Room | Comment |
|---|---|---|---|---|
| Marek Rychlik | Monday | 5:30pm-6:30pm | Math 589A Zoom Link | Regular office hours |
| Marek Rychlik | Tuesday | 1:00pm-1:50pm | Teams or Zoom (Launched from "Teams plugin" in D2L) | Upper Division Tutoring |
| Novel Dey, Math 589 Super-TA | Tuesday | 2:00pm-3:00pm | Math 410 (Old Math Bldg, not ENR2) | Math 589 Super-TA office hours |
| Marek Rychlik | Wednesday | 5:00pm-6:00pm | Math 464 Zoom Link | Regular office hours |
| Novel Dey, Math 589 Super-TA | Friday | 1:00pm-2:00pm | Math 410 (Old Math Bldg, not ENR2) | Math 589 Super-TA office hours |
Office hours by appointment are welcome. Please contact me by e-mail first, so that I can activate a Zoom link for the meeting.
Course Format and Teaching Methods
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.
Course Objectives - Math 589A
- Gain Understand floating point arithmetic.
- Gain Understanding of numerical linear algebra, including solving dense and sparse linear systems, SVD, QR and LU factorizations.
- Aquire the ability to solve systems of non-linear equations.
- Gain the ability to solve basic linear ODE and PDE numerically
- Become familiar with the HPC resources of the University of Arizona.
- Gain working knownledge of Python and MATLAB.
- Learn basics of parallel, distributed and GPU programming.
- Gain the ability to apply acquired knowledge to "real-life" problems.
Course Objectives - Math 589B
- Gain understanding of of numerical methods for unconstrained and constrained optimization, including gradient descent BFGS and gradient projection methods.
- Gain understanding of polynomial interpolation and approximation.
- Gain understanding of numerical differentiation and integration.
- Gain in-depth understanding of numerical ODE solvers for initial and boundary value problems.
- Gain understanding of theory and numerical implementation of optimal control.
- Gain understanding of Monte-Carlo algorithms and their applications in inference and learning.
- Gain understanding of neural network algorithms and their implementation in modern programming frameworks with emphasis on automatic differentiation.
- Develop the skills necessary to address large scale numerical calculations using parallel processing and GPU.
Generative AI use IS permitted or encouraged
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:
Absence and Class Participation Policy
Importance of attendance and class participation
Participating in course and attending lectures and other course events are vital to the learning process. As such, attendance is required at all lectures and discussion section meetings. Students who miss class due to illness or emergency are required to bring documentation from their healthcare provider or other relevant, professional third parties. Failure to submit third-party documentation will result in unexcused absences.Missed Exams
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.
COVID-19 related policies
As we enter the new semester, the health and wellbeing of everyone in this class is the highest priority. Accordingly, we are all required to follow the university guidelines on COVID-19 mitigation. Please visit http://www.covid19.arizona.edu for the latest guidance.UA policies
The UA"s policy concerning Class Attendance, Participation, and Administrative Drops is available at: http://catalog.arizona.edu/2015-16/policies/classatten.htm The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable, http://policy.arizona.edu/human-resources/religious-accommodation-policy . Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: http://uhap.web.arizona.edu/policy/appointed-personnel/7.04.02Required Texts or Readings
Required Textbook
Advanced Numerical Methods and High-Performance Computing By Marek Rychlik (the instructor). A lecture note style booklet prepared especially for this course.
Additional reading
See Background reading for a list of texts worth studying along with taking the course.
Assignments and Examinations
Notes on exam administration
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/assignment listing with date and grade contribution
| Exam or Assignment | Date | Grade contribution |
|---|---|---|
| Midterm 1 | October 15, Wednesday | 20% |
| Midterm 2 | November 12, Wednesday | 20% |
| Final Examination | December 17, Monday, 10:30am - 12:30pm | 30% |
| Homework | Written and Programming, administered via Gradescope | 30% |
Homework Assignments
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:
- The student will submit all graded work through Gradescope. Gradescope assignments, by their nature, are answer-oriented. The opportunity for partial credit on written assignments is somewhat limited.
-
The programming assignments shall be maintained in a GitHub repository.
A read/write link to the repository will be shared with the instructor
via the "collaborator" mechanism of GitHub. The repository will
include all code necessary to test the code. Python test code must be
runnable via 'pytest' program and preferrably use the 'unittest' package.
A good way to start with this system is to clone
the Assignment 0 repository:
https://github.com/Arizona-Math/Math589Assignment0 - Homework may not be submitted through e-mail, no exceptions.
- Due dates will be adjusted in Gradescope only as needed and the student is expected to check regularly for those adjustments. Due dates in D2L will not be updated.
Homework submission requirements
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:
- Download the blank assignment (also called a 'template') from Gradescope.
- Read and understand exactly what answers you need to provide. The space to enter the answer is a blue box, and marked with a label such as 'Q1.1' ("Question 1, part 1").
- Work out the problem on "paper" (real or virtual), to obtain the answers. They must fit in the designated boxes in the 'template'. The size of the box is a hint from the instructor about the size of the answer (typically a number or a math formula) when entered by hand, using regular character size.
- The recommended way to fill out the 'template' is paperless, by using suitable software and hardware (digital pen or tablet). I use a free program Xournal for this and it works great. You need to use it in combination with a digital pen or a tablet. It can produce a PDF easily, ready for submission to Gradescope.
- You can also print the assignment on (real) paper, fill out the answers and scan the marked up document back to PDF format. However, the position of the boxes must be exactly (to a fraction of an inch) as in the original. Also, you may encounter a variety of "quality control" issues, especially if you are using a digital camera to scan the paper solution. All issues can be solved by a mix of the right hardware and software, but may not be the best time investment. The least troublesome way to scan is to use a real, flatbed scanner, e.g. in the library.
- Upload the resulting document (a PDF of the 'template' marked up with your answers) to Gradescope. Your PDF must contain your name and student id in designated spaces. The Gradescope 'AI' will look for your name and student id, to properly associate it with your account.
- After grading, the grade will be transmitted to D2L (Brightspace) and will be added to your 'Final Calculated Grade' automatically.
-
Do not reduce handwriting size! Reduce the size of your
answer using
- closed form expressions;
- appropriate math functions, e.g., absolute value, min and max.
- Under no circumstances write outside the provided space (boxes). Gradescope, and the grader only considers the content of the designated boxes.
- IMPORTANT! Do not insert pages in the solution template. This will confuse Gradescope, and will result in reduced score and/or will require re-submission. However, you are encouraged to submit scratchwork. You should create pages at the end of the document. Similarly, if you run out of space in the template for your solution, you can continue the solution on a newly created page at the end of the document, adding a note in the template: "Solution continued on page 13" where page 13 will contain the continuation.
- CRITICALLY IMPORTANT! You may insert handwritten solutions into the template using "electronic ink" (such as xournal), as long as you achieve similar legibility to typed text. You may also use a high-quality digital scanner capable of producing quality comparable to printed document, as long as you write very legibly. You may not insert pictures of handwritten or typed pages taken with a cell phone camera! If your work does not meet the legibility criterion, the instructor will ask you to move to a different system.
Programming and Software
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):
- A computer algebra system (CAS) called Maxima.
- The maxima GUI wxMaxima is a separate program and this is the preferred way to use Maxima if you are a beginner. During the previous semester students successfully applied Maxima to doing their homework, and I will provide examples of Maxima calculations in class.
-
Automatic Row Reduction Generator (ARRG) -
a program I wrote in Common Lisp for training students in various flavors of Gaussian elimination.
It simulates row reduction, as it would be performed on paper by hand, featuring:
- various pivoting strategies
- row echelon and reduced row echelon forms
- rational arithmetic with exact answers
- Floating-point and rational complex numbers
The use of High-Performance Computing (HPC)
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:
- Supercomputers with thousands of CPUs
- Vast storage
- Hundreds of GPUs (Graphical Processing Units)
Final Examination
The final examination is scheduled for: December 17, Monday, 10:30am - 12:30pm.
The time, data and general exam rules are set by the University and can be found at these links:
Grading Scale and Policies
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-policiesSafety on Campus and in the Classroom
For a list of emergency procedures for all types of incidents, please visit the website of the Critical Incident Response Team (CIRT):
Classroom Behavior Policy
To foster a positive learning environment, students and instructors have a shared responsibility. We want a safe, welcoming and inclusive environment where all of us feel comfortable with each other and where we can challenge ourselves to succeed. To that end, our focus is on the tasks at hand and not on extraneous activities (i.e. texting, chatting, reading a newspaper, making phone calls, web surfing, etc).Threatening Behavior Policy
The UA Threatening Behavior by Students Policy prohibits threats of physical harm to any member of the University community, including to one's self. See: http://policy.arizona.edu/education-and-student-affairs/threatening-behavior-students .Accessibility and Accommodations
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 .