## John McCarthy, Ph.D.

Operator Theory, One and Several Complex Variables, and Their Interaction

# Math 139A, Fall 2021Applications of Mathematics

Instructor                   John E. McCarthy
Class                           Tu 11.00-11.50 in Lopata 103

No class October 12 (Fall Break); we will have class November 23

JM Office                  105 Cupples I
JM Office Hours       M 4.00-4.50, Tu 10.00-10.50,  Th. 2.30-3.20, and by appointment
In office and via Zoom: Meeting ID: 932 2571 1839

Prerequisites

Math 131, preferably taken concurrently

Description

Mathematics can often seem intimidatingly abstract.
“Why do we need to know this?” and “What is this good for?” are common
It is all very well to say that mathematics is needed for cell-phone design, or
to make ultrasound images, or for Google to calculate page-rank; but explaining
exactly how it is used in any of these applications takes a great deal ot time.

The purpose of this course is to give examples of how mathematics can be used to
understand real world problems. It is aimed at students who are also enrolled in Calculus I, Math 131,
so we will start with problems that only need pre-calculus to solve, and work up to ones that use
calculus.

Do I need to be a math wiz to take this course?
No. The course is for students who are curious about how mathematics is used,
and want some inkling of its scope.

Content

Here is a tentative schedule. The first seven do not use calculus, the next six do.
We may change some of these topics.

1. Dimensional Analysis. How to guess plausible formulas.
2. The mathematics of convoys. Are they a good idea? What are the pros and cons? Reading for class on Sep 6
3. Fibonacci Numbers. See this site for pictures
4. The golden ratio
5. Fractals I :  Coastlines
6. Fractals II : what is dimension?
7. Linear regression I. Application: the Gutenberg-Richter law of earthquake magnitudes. How can we speak of a twenty thousand year event? Earthquakes
8. Linear Regression II: How to find the best line. Regression to the mean Application: Metabolic rate versus animal size Metabolic Rates
9. Network capacities. Braess’s paradox – building extra roads can increase congestion.
10. Fractals III: Blood flow.
11. Should we all have the same mitochondrial DNA? Galton’s approach to surnames.
12. How genes spread through populations.
13. Sigmoid curves for populations, and the logistic equation.
14. SIR model of infectious diseases.

Grading will be based on classrooom participation, and a term paper.
The topic of the term paper should be chosen in consultation with the Instructor.
A preliminary draft should be handed in October 26th. This will be graded and returned,
and a final version should be handed in December 7th.

Classroom Participation (contribution to discussion): 20%

Attendance is mandatory, unless you need to miss class due to illness or COVID exposure. In this event, please send me confirmation of the need to miss class from Habif.

Term Paper – first draft: 30%
Term Paper – final draft: 50%

Class

You must come to class every day, and participate in class discussions, unless you are ill or quarantining.
I expect you to read the corresponding section in Korner’s book. I may call on you at
any time to answer a question.

Texts           The Pleasures of Counting, by T.W. Korner  (Cambridge, 1996).
This is a lovely book. If you get bogged down in some section, it is okay to move on.

COVID-19 Health and Safety Protocols                 Exceptions to course attendance policies, expectations, and requirements because of a COVID-19 diagnosis, symptoms consistent with COVID-19, or exposure to a person with a confirmed or suspected COVID-19 diagnosis that requires quarantine or isolation will be made in collaboration between the student and instructor. In these cases, please notify your instructor as soon as possible to discuss appropriate accommodations. While on campus, it is imperative that students follow all public health guidelines established to reduce the risk of COVID-19 transmission within our community. The full set of University protocols can be found at https://covid19.wustl.edu/health-safety/. This includes:

• Completing a self-screening using the WashU COVID-19 Screening app every day before coming to campus or leaving your residence hall room. If you do not receive a green check and pass the screening, you are not permitted to come to campus or leave your residence hall room. You must contact the COVID Call Center (314-362-5056) or the Habif Health and Wellness Center (314 935-6666) immediately. Note: In addition to the symptoms listed in the screening tool, everyone also should pay attention to symptoms that are new or different for you, including things like headache and congestion, particularly in combination with diarrhea. These can also be signs of COVID-19. Call the COVID Call Center or Habif to report these symptoms.

• Complying with universal masking. All individuals on campus must wear disposable masks or cloth face coverings while occupying indoor public settings, including: multi-person offices, hallways, stairwells, elevators, meeting rooms, classrooms and restrooms. Masks are encouraged but not required for outdoor activities, particularly at large events or in crowded settings. Students with disabilities for whom masked instructors or classmates create a communication barrier are encouraged to contact Disability Resources (www.disability.wustl.edu) or talk to their instructor for assistance in determining reasonable adjustments. Adjustments may involve amplification devices, captioning, or clear masks but will not allow for the disregard of mask policies.

• Maintaining physical distancing as needed. While distancing requirements have been removed for vaccinated students, those who are not fully vaccinated are strongly encouraged, for their own health, to maintain a distance of 6 ft from others in the classroom. If you are not able to be vaccinated or have conditions that may put you at increased risk of failed immunity and classroom activities would bring you in frequent proximity to other students, contact your instructor to discuss alternatives.

• Practicing healthy personal hygiene, including frequent handwashing with soap and warm water for at least 20 seconds and/or using hand sanitizer with at least 60% alcohol.

University-Wide Policies

Reporting Sexual Harassment If a student discusses or discloses an instance of sexual assault, sex discrimination, sexual harassment, dating violence, domestic violence or stalking, or if a faculty member otherwise observes or becomes aware of such an allegation, the faculty member will keep the information as private as possible, but as a faculty member of Washington University, they are required to immediately report it to the Department Chair or Dean or directly to Ms. Cynthia Copeland, the University’s Associate Title IX Coordinator, at (314) 935-3411, cmcopeland@wustl.edu. Additionally, you can report incidents or complaints to the Office of Student Conduct and Community Standards or by contacting WUPD at (314) 935-5555 or your local law enforcement agency. See: Title IX

Reasonable Accommodations for Disabled Students. Washington University in St. Louis supports the rights of enrolled students to a full and equal educational opportunity and, in compliance with federal, state, and local requirements, is committed to reasonable accommodations for individuals with documented disabilities. Disabled students for whom accommodations may be necessary must be registered with, and provide their instructors official notification through, WUSTL’s Disability Resources (www.disability.wustl.edu). Once established, responsibility for disability-related accommodations and access is shared by DR, faculty, and the student. Please contact Disability Resources at 314.935.5970 or disabilityresources@wustl.edu.

Statement on Military Service Leave Washington University recognizes that students serving in the U.S. Armed Forces and their family members may encounter situations where military service forces them to withdraw from a course of study, sometimes with little notice. Students may contact the Office of Military and Veteran Services at (314) 935-2609 or veterans@wustl.edu and their academic dean for guidance and assistance. See: https://veterans.wustl.edu/policies/policy-for-military-students/.

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To report an emergency: Danforth Campus: (314) 935-5555 School of Medicine Campus: (314) 362-4357 North/West/South and Off Campus: 911 then (314) 935-5555

Academic Integrity Effective learning, teaching and research all depend upon the ability of members of the academic community to trust one another and to trust the integrity of work that is submitted for academic credit or conducted in the wider arena of scholarly research. Such an atmosphere of mutual trust fosters the free exchange of ideas and enables all members of the community to achieve their highest potential.

In all academic work, the ideas and contributions of others must be appropriately acknowledged and work that is presented as original must be, in fact, original. Faculty, students and administrative staff all share the responsibility of ensuring the honesty and fairness of the intellectual environment at Washington University in St. Louis.

Resources for Students:

Bias Reporting and Support System (BRSS) The University has a process through which students, faculty, staff, and community members who have experienced or witnessed incidents of bias, prejudice, or discrimination against a student can report their experiences to the University’s Bias Report and Support System (BRSS) team. See: brss.wustl.edu.

Mental Health Services Mental Health Services’ professional staff members work with students to resolve personal and interpersonal difficulties, many of which can affect a student’s academic experience. These include conflicts with or worry about friends or family, concerns about eating or drinking patterns, and feelings of anxiety, depression, and thoughts of suicide. See: https://students.wustl.edu/mentalhealth-services/. Additionally, see the mental health services offered through the RSVP Center listed above.

WashU Cares WashU Cares specializes is connecting students to mental, medical, financial and academic resources by using supportive case management. We seek to empower students to be successful through life’s challenges and to have ownership of their own experiences. Our services are designed to support Danforth Campus students. If you feel concerned about a student who may need help connecting to resources we accept referrals from all students, faculty, and staff. If you are concerned about a student, you can file a report here: https://washucares.wustl.edu/ and a WashU Cares Case Manager will reach out to you to get more information about your concern.

The Writing Center The Writing Center, located in Olin Library, offers free one-on-one writing tutorials to WashU students, as well as workshops designed to help students become better writers. The Writing Center staff can assist by providing feedback on the strength of an argument, clarity, and organization. Contact them at 935-4981 or writing@wustl.edu. Visit them at: https://writingcenter.wustl.edu/.

The Learning Center The Learning Center works collaboratively with University partners to provide undergraduate students key resources, like academic peer mentoring, to enhance their academic progress. Contact them at https://ctl.wustl.edu/learningcenter/ to find out what support they may offer for your classes.

Center for Diversity and Inclusion (CDI) The Center for Diversity and Inclusion (CDI) supports and advocates for undergraduate, graduate, and professional school students from underrepresented and/or marginalized populations, collaborates with campus and community partners, and promotes dialogue and social change to cultivate and foster a supportive campus climate for students of all backgrounds, cultures, and identities. See: https://diversityinclusion.wustl.edu/.

Gephardt Institute State and local elections can have direct and immediate impacts on our communities and will be happening here in St. Louis and around the country this year. Make sure you stay current on upcoming elections at all levels by registering as a voter, requesting an absentee ballot, or getting election day reminders. You can do all this at http://wustl.turbovote.org for any of the 50 states and Washington D.C. If you are ineligible to vote, you can still participate by referring your friends who are eligible to the TurboVote link to register and by engaging your peers in local issues. If you have any questions about the voting process in the United States, please visit http://washuvotes.wustl.edu.