MATH 485: syllabus

University of Arizona | Department of Mathematics | Ildar Gabitov | MATH 485 | Syllabus

MATH 485
Mathematical Modeling

Classroom:

Section 002: Education 337, TR, 2:00–3:15pm

Instructor:

Ildar Gabitov

office:	MATH 722
e-mail:	gabitov[at]math.arizona.edu
phone:	☎ (520) 626-8853

Office Hours:

Tuesday 4:00–5:00pm, Wednesday 2:00–3:00pm, Thursday 4:00–5:00pm (subject to change) and by appointment

Text:

my lecture notes

Course description: This course is concerned with the development, analysis, and evaluation of mathematical models for physical, biological, social, and engineering problems; both analytical and numerical solution techniques are discussed. The course contributes to the Discovery and Professionalism UA 100% Engagement Competencies. It is also a Writing Emphasis Course.

Course Format and Teaching Methods: The course consists of regular lectures with in-class discussions, group-work, presentations, written reports and labs, as well as out-of-class group activities. Course Objectives Using examples from physics, chemistry, engineering, biology, and social sciences, the course will cover the following topics:

Basics of mathematical modeling
Modeling deterministic phenomena including deterministic chaos by means of ordinary differential equations.
Modeling phenomena with random parameters
Spatial effects and partial differential equations.
Data processing and machine learning
Single- and two-species models

Expected Learning Outcomes: After taking this course, you should be able to do the following.

Critically evaluate and extend mathematical models described in the scientific literature.
Apply computational methods and concepts from prerequisite mathematical content to analyze scientific problems.
Work together in small groups to read, understand, discuss and reproduce work from articles in the current scientific literature.
Effectively communicate results to non-specialized audiences in written and verbal form.

Course Communications: Please consult the D2L site for announcements. If needed, additional email announcements to the entire class will be sent from the class roster to your official UA email address.

Please use my UA Mathematics email address (Gabitov@math.arizona.edu) for general course questions and communications. Please also ensure that you write from your official UA email address when you contact me.

Required Texts or Readings: The class notes and supplemental materials will be available at the D2L site.

Required or Special Materials: You may bring a laptop or tablet to class to take notes and work on labs. It is strongly recommended you install MATLAB on your device.

Required Extracurricular Activities: You are required to meet weekly as a group with your mentor.

Assignments and Examinations: Schedule/Due Dates
Students will work in teams on a semester-long project, worth 340 points. Each team will give two oral progress reports on its project, will turn in a midterm and a final written report, and will present in a poster session at the end of the semester (in lieu of a final exam). The written part of the project will be worth 160 points and the oral and poster presentations will count for a total of 180 points.

The midterm report is due on Thursday 2/27 (just before Spring Break)
The midterm oral presentations will take place on Thursday 3/26, Tuesday 3/31, and/or Thursday 4/02
The poster is due in final form on Thursday 4/23
The final report and the end-of-term reflection are due on Monday 5/12 by 6 pm

Homework problems will be assigned regularly. Either I will collect your homework, or I will give a quiz based on the homework assignment, or you will work on an in-class lab.

If you miss an oral presentation for a valid reason, please inform me as soon as possible and within 2 days of your absence. Please also make an appointment to discuss how your contribution to the project will be evaluated.

Final Examination or Project: Your team's final report is due by 6 pm on Tuesday May 12, 2020. The poster session is organized by the Department of Mathematics. It will most likely be held on Thursday May 7 (Reading Day) at a time to be determined. The date, time, and location of the poster session will be confirmed in due course. For final exams schedule and regulations, please consult the following sites:

Final Exam Regulations: https://www.registrar.arizona.edu/courses/final- examination-regulations-and-information.
Final Exam Schedule: http://www.registrar.arizona.edu/schedules/finals.htm.

Grading Scale and Policies: The UA policy regarding grades and grading systems is available at http://catalog.arizona.edu/policy/grades-and-grading-system. The project will count for 340 points:

Midterm report: 70 points
Midterm oral presentation: 50 points
Final presentation: 50 points
Poster presentation: 80 points
Final report: 90 points

The quiz/homework/lab score will be out of 120 points and based on 6 quizzes (each worth 50% of homework; only the 4 best scores will be kept), 4 homework assessments.

Group and in-class participation will count for 25 points and the end-of-term reflection 15 points.

The total number of points available is therefore 500. Grades will be no lower than set forth in the following table:

450 ≤ points ≤ 500	90% to 100%	A
400 ≤ points ≤ 449	80% to 90%	B
350 ≤ points ≤ 399	70% to 80%	C
300 ≤ points ≤ 349	60% to 70%	D
0 ≤ points ≤ 299	0% to 60%	E

Withdrawing from the course: If you withdraw from the course by , the course will be deleted from your enrollment record. If you withdraw from the course by , you will receive a grade of W. The University allows withdraws after , but only with the Dean's signature. Late withdraws will be dealt with on a case by case basis, and requests for late withdraw with a W without a valid reason may or may not be honored.

Incompletes: The grade of I will be awarded if all of the following conditions are met:

The student has completed all but a small portion of the required work.
The student has scored at least 50% on the work completed.
The student has a valid reason for not completing the course on time.
The student agrees to make up the material in a short period of time.
The student asks for the incomplete before grades are due, 48 hours after the final exam.

Grades Policies o f the University of Arizona.

Scheduled Topics/Activities: Below is a tentative syllabus. Topics covered on a given day may change but due dates will not be modified.

1/16:	Welcome; course syllabus and policies; projects and working groups, basics of mathematical modeling.
1/21:	Models from classical mechanics.
1/23:	Models from classical mechanics.
1/28:	Models from classical mechanics.	HW #1 due.
1/30:	Models from classical mechanics.	Quiz #1.
2/04:	Concept of critical phenomena: switching, bistability, catastrophe.
2/06:	Classical mechanics Lab.
2/11:	Classical mechanics Lab.	Quiz #2.
2/13:	Population Dynamics and Epidemiology.
2/18:	Population Dynamics and Epidemiology.
2/20:	Population Dynamics and Epidemiology.
2/25:	Population Dynamics and Epidemiology.	HW #2 due.
2/27:	Population Dynamics and Epidemiology.
3/03:	Midterm oral presentations.	Project presentations:
3/05:	Midterm oral presentations.	Project presentations:
3/10:	Spring break — no classes.
3/12:	Spring break — no classes.
3/17:	Random walks and diffusion.
3/19:	Effects of randomness.	HW #3 due.
3/24:	Effects of randomness.
3/26:	Effects of randomness.
3/31:	Spatial effects.
4/02:	Spatial effects.	Quiz # 3.
4/07:	Spatial effects.	Midterm report due, Quiz # 4.
4/09:	Spatial effects.
4/14:	Machine learning.	Quiz # 5, HW #4 due
4/16:	Machine learning.
4/21:	Machine learning.	Quiz # 6.
4/23:	Machine learning.	Final version of poster due.
4/28:	Final Presentations.
4/30:	Final Presentations.
5/07:	Poster Session.
5/12:	Final report due by 6 pm.

Accessibility and accommodations: It is the University's goal 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.

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.

Attendance and Protocol: You are expected to be familiar with the University Class Attendance policy. It is your responsibility to stay informed of any announcements, syllabus adjustments, or policy changes.

The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable. Absences pre-approved by the UA Dean of Students (or Dean's designee) will be honored.

You are expected to behave in accordance with the Student Code of Conduct and the Code of Academic Integrity. The University is committed to creating and maintaining an environment free of discrimination.

The information contained in this syllabus, other than the grade and absence policies, may be subject to change with reasonable advance notice, as deemed appropriate by the instructor.