Syllabus and Course Policy for

Mathematical Modeling (MATH 485)

Spring 2021

Last updated on January 11, 2021

Instructor

Prof. Calvin Zhang-Molina, Ph.D.

Email: [email protected]

Office hours (on Zoom): To be announced in class and posted on course website.

Project Mentors

To be announced soon.

Course Website 

http://math.arizona.edu/~calvinz/math485_s21.html

Lecture Hours

Tuesdays and Thursdays: 2:00–3:15pm (meet on Zoom)

Zoom

https://arizona.zoom.us/j/85217996682 (connection restricted to UA accounts)

Gradescope

https://www.gradescope.com/courses/225931 (contact instructor for enrollment) You are required to have a Gradescope account and enroll into our class on Gradescope. This is needed because you are required to submit all your assignments digitally. See Submitting Your Work Digitally on page 2 for more details.

Textbook

Mathematical Modeling, by Joceline Lega, available at: https://press.rebus.community/mathmodeling/ (ask Instructor for password) Textbook and additional course materials are provided at no cost to the students.

Required Equipments

Laptop or web-enabled device with webcam and microphone; regular access to reliable internet signal; ability to scan documents into a single and legible PDF file (see Submitting Your Work Digitally on page 2 for more details). Students can borrow technology from the UA Library on a first come, first served basis. See https://new.library.arizona.edu/tech/borrow.

Prerequisites

In addition to Calculus I, Calculus II, and Vector Calculus, this course also requires completion of (1) at least one 400-level MATH course (422, 454, 456, or 475A), (2) Linear Algebra, (3) Differential Equations, and (4) a programming course.

Course Objective

(1) Understand what is mathematical modeling, its merits, and limits;

(2) learn the theory and techniques needed to construct a simple mathematical model using differential equations, probability theory, and/or statistical theory;

(3) learn how to analyze your mathematical model analytically (using mathematical theories and techniques) and numerically (using numerical methods and computer simulations);

(4) learn how to test and refine your mathematical model using existing data and knowledge;

(5) learn how to interpret the results of your mathematical model in the context of the problem;

(6) learn how to work with peers in a collaborative environment; and

(7) learn how to communicate effectively your results, in both written format and through oral presentations, to not only the academic audience but also the general public.

Expected Learning Outcomes

(1) Be able to read, understand, and summarize main results from interdisciplinary literatures involving mathematical models;

(2) be able to work collaboratively and positively in a team environment;

(3) be able to construct, analyze, and simulate simple mathematical models with deterministic and/or stochastic elements;

(4) understand the basic theories and techniques in

(i) dynamical systems theory (bifurcation analysis and numerical methods),

(ii) simple probabilistic models and their computer simulation,

(iii) basic line search methods, conjugate gradient methods, KKT condition, least square problems, linear programming (the simplex method) in continuous optimization;

(iv) integer programming, shortest paths problem;

(v) linear regression, logistic regression, and nonlinear transforms;

(5) be able to summarize findings from your mathematical model in a clear and organized written report; and

(6) be able to speak clearly, effectively, and efficiently about your mathematical findings to a general audience.

MATLAB Access

You will need access to MATLAB software (free of charge through UA). More information on how you can obtain MATLAB will be provided later in the semester; it will not be needed immediately. If you prefer using a different programming language, such as Java, Python or Swift, please talk to the instructor for further advice.

Submitting Your Work Digitally

You are required to submit all your graded assignments (including weekly homework, initial essay, midterm written report, final poster file, and final written report) digitally by uploading your work in the form of a single and legible PDF file to our Gradescope website. Unless you choose to type up your math solutions using a LaTeX compiler or an equation editor, you will need to scan your written solutions into a single and legible PDF file (or take clear pictures of each page of your handwritten work and then merge those pictures into a single and legible PDF file), and then upload the PDF file to Gradescope to officially record your assignment submission. Please keep the PDF file size below 10 MB while ensuring legibility. All UA students have access to Adobe Creative Cloud, which includes the Adobe Scan app. (For additional remote learning tools, see https://student.it.arizona.edu.)

If you need help, please don’t hesitate to ask the instructor or university’s IT support office for advice. You are strongly advised to learn and get familiar with document scanning at the beginning of the semester before any assignment becomes due. Having a last-minute technical issue is not an acceptable excuse for late submission.

Information contained in the course syllabus, other than the grade and absence policy, may be subject to change with advance notice, as deemed appropriate by the instructor. Changes will be announced in class and posted on the course website.

Homework

There are approximately 9 homework sets. Homework will be posted on Thursdays on Gradescope. You are required to upload your solutions to Gradescope by noon (12:00pm) on the following Thursday. To ensure fairness, late homework is not accepted unless you have extreme hardship of long duration. Note, however, your lowest two homework scores will be dropped in your course grade calculation. This policy is designed to provide flexibility while ensuring fairness to everyone.

Unlike your Team Project, you are required to work on homework independently. You are welcome to discuss homework with your classmates, but you need to write your own solutions and computer code independently. All types of plagiarism, including through online means (such as copying solutions or computer code directly from the Internet), are strictly prohibited.

You are expected to express your ideas completely, clearly, and legibly. This means you could lose points for incomplete, ambiguous, or sloppy answers.

Request for Regrade

A request for regrade will be accepted if a written request is submitted online through the Gradescope website within five calendar days after graded work are released online. In your written request, please explain: (1) what part of the homework should be regraded; and (2) why it should be regraded.

Team Projects

You will work in a team on a semester-long project. Each team will give two oral presentations, an initial presentation in the first half of the semester and a midterm presentation in the second half of the semester. In addition, each team will turn in a midterm written report and a final written report, and will present a poster in a poster session held in a public venue. Here is a list of projects for this semester:

Project A:   Control Theory - Glycolytic Oscillation

Project B:   Neurophysiology - Coordination of Limbs

Project C:   Stochastic Processes - Neurotransmitter Release

Project D:   Data Analysis - Instant Decision for Credit Card Applications

Project E:   Probability Theory - Investment Portfolio Selection

Project F:   Dynamical Systems - Cancer Cell Growth and Treatment

         Each team will be assigned a Project Mentor. Project Mentors are math graduate students, postdoctoral researchers, or the instructor himself, who have volunteered to provide you with guidance and advice on your project throughout the semester. More details on these projects are available on the course website.

Schedule of Topics and Activities

Jan 14 – Feb 2      Continuous, deterministic models and their computer simulation

Feb 4                   In-class team activity

Feb 9                   Initial Team Project Oral Presentation

Feb 11 – Mar 4     Stochastic models and their computer simulation

Feb 25                 no class (in lieu of spring break)

Mar 9                   no class (in lieu of spring break)

Mar 11                 In-class team activity

Mar 16 & 18          Midterm Team Project Oral Presentation

                            (Midterm written report due at noon on Thursday, March 25)

Mar 23 – Apr 1      Continuous and discrete optimization and numerical methods

Apr 6                    In-class team activity

Apr 8 – 29             Machine learning methods

May 4                   In-class team activity

May 6                   Final Poster Presentation

                            (Final written report due at 5:30pm on Monday, May 10)

Grading Policy 

The course grade will be determined by an absolute scale with a slight modification if appropriate. An approximate guideline is: 90% - 100% = A; 80% - 89% = B; 70% - 79% = C; 60% - 69% = D; Less than 60% = E. Each component of your graded work will be counted into your course grade with the following weight factors:

Homework*:                                                      50%

Initial Reading and Essay:                                   5%

Team Project Initial Presentation (oral):                5%

Team Project Midterm Report (written + oral):      20%

Team Project Final Report (written + poster):        20%

(* The lowest two scored homework items will be dropped from course grade calculation. This policy is designed to accommodate unexpected situations with no excuse needed.) University policy regarding grades and grading systems is available at catalog.arizona.edu/policy/grades-and-grading-system

A student may withdraw from the course with a deletion from record through January 26, 2021, using UAccess. A student may withdraw with a grade of ”W” through March 30, 2021, using UAccess. It is suggested that students consult his/her academic advisor before withdrawal from any course. Requests for incomplete (I) or withdrawal (W) must be made in accordance with University policies, which are available at http://catalog.arizona.edu/policy/grades-and-grading-system

Veteran Students

This instructor is a Vet Ally. Veterans Education and Transition Services (VETS) provides the tools and assistance necessary for veteran students to achieve academic success while fostering camaraderie and engagement. VETS is an on-campus organization run by veterans, spouses, dependents, and current service members who through their shared experiences endeavor to maintain a dynamic and effective program responsive to the needs of our community. VETS recognizes the military-to-academic shift is not always a straightforward process and is committed to providing a safe and supportive environment that makes this transition as smooth as possible. If you have questions, please feel free to talk to the instructor directly, contact VETS directly at 520-626-8380 or [email protected], or visit one of the two VETS Centers on campus.

Drop-in Tutoring

The mathematics department provides free drop-in tutoring service for upperdivision math classes, including this class. For hours and locations, please click this link: https://www.math.arizona.edu/academics/tutoring

Emailing the Instructor

Due to the large volume of emails the instructor receives, he may not be able to respond to your emails quickly. For a quick response, please use the time after class for a short communication. You are most welcome to talk to him during office hours.

Accessibility

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 the instructor know immediately so that we can discuss options. You are also welcome to contact the Disability Resource Center 520-621-3268 to establish reasonable accommodations. For additional information on the Disability Resource Center and reasonable accommodations, please visit http://drc.arizona.edu

If you have reasonable accommodations, please plan to meet with the instructor by appointment or during office hours to discuss accommodations and how the 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.

Student Code of Conduct

Students at The University of Arizona are expected to conform to the standards of conduct established in the Student Code of Conduct. Some essential aspects of the Student Code as they pertain to our class are discussed below. Students found to be in violation of the Student Code of Conduct are subject to disciplinary action. For more information about the Student Code of Conduct, including a complete list of prohibited conduct, see https://deanofstudents.arizona.edu/student-rights-responsibilities/student-code-conduct

Academic Integrity. 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 Code of Academic Integrity as described in the UA General Catalog. See https://deanofstudents.arizona.edu/policies/code-academic-integrity

Threatening Behavior. The University seeks to promote a safe environment where students and employees may participate in the educational process without compromising their health, safety, or welfare. The Student Code of Conduct prohibits threats of physical harm to any member of the University community, including to one’s self. Threatening behavior can harm and disrupt the University, its community, and its families. See http://policy.arizona.edu/education-and-student-affairs/threatening-behavior-students

Harassment and Discrimination. The University of Arizona is committed to creating and maintaining an environment free of discrimination. In support of this commitment, the University prohibits discrimination, including harassment and retaliation, based on a protected classification, including race, color, religion, sex, national origin, age, disability, veteran status, sexual orientation, gender identity, or genetic information. The University encourages anyone who believes he or she has been the subject of discrimination to report the matter immediately. All members of the University community are responsible for participating in creating a campus environment free from all forms of prohibited discrimination and for cooperating with University officials who investigate allegations of policy violations. See http://policy.arizona.edu/human-resources/nondiscrimination-and-anti-harassment-policy

Absence from Class. Students are expected to be regular and punctual in class attendance and to fully participate in the course. The University believes that students themselves are primarily responsible for attendance and class participation. Students who need to miss more than one week of classes in any one semester must provide a doctor’s note of explanation to [email protected]. Excessive or extended absence from class is sufficient reason for the instructor to administratively drop the student from the course. See http://catalog.arizona.edu/policy/class-attendance-participation-and-administrative-drop. Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored; see: https://deanofstudents.arizona.edu/absences. Absences for any sincerely held religious belief, observance, or practice will be accommodated where reasonable; see http://policy.arizona.edu/human-resources/religious-accommodation-policy.