MATH 463 Topics in Biomathematics

Spring 2024

Course Syllabus

Welcome to MATH 463 Topics in Biomathematics for Spring 2024! This page contains the syllabus for the course. We begin with a brief description of Biomathematics, followed by information about the instructor, course materials, and course policies.

What is Biomathematics?

Biomathematics is concerned with the use of mathematical methods (e.g., linear algebra, differential equations, dynamical systems, and probability theory) to understand phenomenon in the life sciences, it is part of the larger field of mathematical and theoretical biology. Mathematical and theoretical biology provide a solid foundation for computational and quantitative approaches to investigations in biology and medicine.

Instructor Information

  • Instructor: Jason M. Graham

  • Office Location: LSC 319A

  • Office Hours for Students: Students are welcome and encouraged to visit my office Mondays 1:30 - 2:30; Wednesdays 10:30 - 11:30 and 1:30 - 2:30. You may also make an appointment via email to meet with me outside of these scheduled office hours, view my general schedule. Appointments are not necessary for regularly scheduled student office hours.

Course Materials

Required Course Materials

All students in MATH 463 from Spring, 2024 will be expected to have access to the following required textbook:

Additionally, we will often refer to the following journal articles:

Suggestions for Further Reading

To go deeper into the topics covered in this course, the following books are recommended. These books are not required for the course and students are not expected to purchase them. However, these may be valuable sources for topics for a final project or for further study.

  • Dynamics of cancer by Natalia Komarova and Dominik Woodarz, ISBN: 978-981-4566-36-0

  • Dynamics of cancer aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools.

Use of Digital Technology

Work and research in Biomathematics requires students and professionals in the field to make use of computing and digital technology. The primary uses of digital technology in Biomathematics is for producing and importing data, scientific computing, visualization of data and model-based simulations, and preparing written documents to present scientific results. Students in this course will be expected to make some use of computing and technical writing. Two commonly used technological tools are R for scientific computing and LATEX for technical writing. This course will emphasize the use of R which can be installed to any platform via the downloads available here. R is best used with the integrative development environment RStudio which can be installed from here. Further, RStudio facilitates the integration of code and technical writing in LATEX via the Quarto system. The progamming languages Julia and Python are also commonly used in scientific computing and are also available for free.

The course website contains reference pages for scientific computing for Biomathematics using R, Julia, and Python.

Course Information

Course Description

A study of discrete and continuous mathematical models in biology. Topics include: population dynamics of single species and interacting species, infectious diseases, population genetics, and cell populations with tumor modeling.

Prerequisites

The prerequisites for this course is MATH 341 Differential Equations and MATH 351 Linear Algebra. Specifically, the students are expected to have a solid foundation in calculus, and a working knowledge of elementary linear algebra and basic ordinary differential equations (ODEs). Some topics from probability and statistics will be used, but these will be reviewed as needed. Additionally, some topics from linear algebra and differential equations may be reviewed or presented from a different perspective than MATH 341 or MATH 351. No background in programming is assumed.

Student Learning Objectives and Assessment

Table 1: Course objectives and assessment.
After taking this course, the student should be able to: Methods of assessment
Use mathematical tools from calculus, differential equations, and linear algebra to analyze foundational mathematical models arising in the life sciences. Homework assignments and in-class written exams.
Interpret the meaning of mathematical equations or models representing various biological processes. Homework assignments, model reports, and final project.
Utilize computing tools such as R to analyze and interpret data-driven mathematical models. Homework assignments, model reports, and final project.
Communicate effectively in writing their work in applying the techniques of applied mathematics to problems arising in the life sciences. Homework, model reports, and final project consisting of a written paper.

Course Policies and Procedures

Attendance

Class attendance and active participation in class discussion is strongly encouraged. If absence is necessary, please inform the instructor and develop a plan to make up for missing content as soon as possible.

Grading

Grade Policy

The course grade will be based on two in-class exams (totaling 50% and evenly distributed), approximately ten weekly homework assignments (15%), one model report (10%), and a final project (25%).

Grade Scale

Letter grades will be assigned based on the following scale:

Table 2: Letter grade scale.
Grade Range Letter Grade
94-100 A
90-93 A-
87-89 B+
83-86 B
80-82 B-
76-79 C+
72-75 C
69-71 C-
65-68 D+
60-64 D
<60 F

Use of AI

Artificial intelligence (AI) can be an effective tool in science. For example, AI-based programming assistants like GitHub Copilot or generative model platforms like ChatGPT now help programmers to write better code in less time. Learning to use AI effectively and responsibly is quickly becoming a basic skill for the modern scientist. Because of this, I do not want to completely discourage the use of AI assistance.

However, I ask that you avoid using AI platforms or tools in a manner that is inappropriate in the context of this course. This course teaches a variety of concepts, skills, and critical thinking. Using AI in such a way as to avoid learning, developing skills, or critical thinking is not appropriate. If you find yourself using AI to look up answers, search for complete solutions to problems, or things like this, then your use of AI is not acceptable. It might be helpful to think of AI as an analog to a calculator. If the goal of an assignment is for you to demonstrate that you can do a certain calculation, then using a calculator is not appropriate. On the other hand, if the goal of an assignment is for you to demonstrate that you can solve a problem for which a minor step involves doing a calculation, then using a calculator is okay. AI use in the context of this course should be treated analogously.

In particular, it is expected that students will be able to explain independently and in detail any work or ideas on assignments this semester. Also, it is expected that students can explain independently and in detail the solution to any problem submitted as part of an assignment this semester.

If you have any doubts about your use of AI, then either ask the instructor if your use of AI is acceptable or just don’t use AI.

Assignments

Homework

There will be weekly homework assignments. Assignments will be posted on the course learning management system and made up of problems relating to or extending the material covered in class discussions. Working problems is essential to learning the material and doing well on exams.

Do not underestimate the value (and joy) of carefully working through homework problems.

Exams

The in-class exams are meant to assess 1) students’ understanding of the material covered in class and in homework assignments, 2) students’ understanding of the core concepts, 3) students’ problem solving abilities, and 4) students’ ability to think independently. Exam 1 is scheduled for March 6, and Exam 2 is scheduled for May 1. In writing the tests, I assume that you have been studying the material at least 6 hours per week outside of class.

Model Report

As part of the required coursework for Topics in Biomathematics, students are asked to submit a model report. The goal of this assignment is for students to read, understand, assess, and explain modeling results from a recently published paper in theoretical or quantitative biology or biomathematics. The model report will make up 10% of the course grade. Students must submit at least two drafts of a model report. A model report should be four to five typed pages and prepared using LATEX or R Markdown. The first draft is due March 25 and the final draft is due May 3. A set of guidelines for the model report can be found on the course learning management system.

Final Project

It should be recognized that the mathematical techniques developed in class are applicable in broader situations than can be covered in lectures and homework. Thus, students are asked to individually explore a topic in biomathematics beyond what is covered in lecture by means of a final project. Final projects should be an 8-12 page manuscript prepared using LATEX or R Markdown, and students must submit at least two drafts of their written final projects. The final draft is due no later than 5:00pm on Wednesday May 15. All written and presented work must be original, explained in your own words, and use proper citation for works referenced.

A set of guidelines for the final project is posted on the course learning management system. You must choose a topic for your final project and submit a one to two paragraph description of your proposed project along with at least two scholarly references to me no later than 5:00pm on March 1.

Course Timeline

Weekly Schedule

  • Week 1 (01/22-01/26): Introduction to Biomathematics

  • Week 2 (01/29-02/02): Dimensional Analysis and Scaling

  • Week 3 (02/05-02/09): One-Dimensional Dynamics and Introduction to Population Dynamics

  • Week 4 (02/12-02/16): Bifurcation Theory and Compartment Models

  • Week 5 (02/19-02/23): SIR Type Models and The Chemostat Bio-reactor

  • Week 6 (02/26-03/01): Functional Forms

  • Week 7 (03/04-03/08): Exam 1

  • Week 8 (03/11-03/15): Spring Break

  • Week 9 (03/18-03/22): Two-Dimensional Dynamics and Phase Plane Analysis

  • Week 10 (03/25-03/29): Mass Action and Reaction Kinetics/ Easter Break; Model Report Draft 1 Due

  • Week 11 (04/01-04/05): Easter Break/ Mass Action and Reaction Kinetics

  • Week 12 (04/08-04/12): Mathematical Physiology

  • Week 13 (04/15-04/19): Perturbation Methods

  • Week 14 (04/22-04/26): Additional Topics

  • Week 15 (04/29-05/03): Exam 2; Model Report Final Draft Due

  • Week 16 (05/06-05/10): Dead Week

  • Week 17 (05/13-05/17): Final Exams; Final Project Due

Important Dates

Table 3: Important Dates
Event Date
Classes begin Wednesday, January 24
Last day to add classes Tuesday, January 30
Last day for 100% tution refund Friday, February 2
Last day to drop with no grade Friday, February 23
Exam 1 Wednesday, March 6
Last day of class before spring break Friday, March 8
Classes resume after spring break Monday, March 18
Semester Midpoint Wednesday, March 20
Last day of class before Easter break Wednesday, March 27
Classes resume after Easter Tuesday, April 2
Last day to withdraw with W grade Friday, April 12
Exam 2 Wednesday, May 1
Last day of class Friday, May 10
Final exams begin Monday, May 13
Final exams end Friday, May 17

University Resources for Students and Academic Honesty

Students with Disabilities

Reasonable academic accommodations may be provided to students who submit relevant and current documentation of their disability. Students are encouraged to contact the Center for Teaching and Learning Excellence (CTLE) at or (570) 941-4038 if they have or think they may have a disability and wish to determine eligibility for any accommodations. For more information, please visit http://www.scranton.edu/disabilities.

Writing Center Services

The Writing Center focuses on helping students become better writers. Consultants will work one-on-one with students to discuss students’ work and provide feedback at any stage of the writing process. Scheduling appointments early in the writing progress is encouraged.

To meet with a writing consultant, call (570) 941-6147 to schedule an appointment, or send an email with your available meeting times, the course for which you need assistance, and your phone number to: . The Writing Center does offer online appointments for our distance learning students.

Academic Honesty and Integrity

Each student is expected to do their own work. It is also expected that each student respect and abide by the Academic Code of Honesty as set forth in the University of Scranton student handbook. Conduct that violates the Academic Code of Honesty includes plagiarism, duplicate submission of the same work, collusion, providing false information, unauthorized use of computers, theft and destruction of property, and unauthorized possession of tests and other materials. Steps taken in response to suspected violations may include a discussion with the instructor, an informal meeting with the dean of the college, and a hearing before the Academic Dishonesty Hearing Board. Students who are found to have violated the Code will ordinarily be assigned the grade F by the instructor and may face other sanctions. The complete Academic Code of Honesty is located on the University website at https://www.scranton.edu/academics/wml/acad-integ/acad-code-honesty.shtml.

My Reporting Obligation as a Responsible Employee

As a faculty member, I am deeply invested in the well-being of each student I teach. I am here to assist you with your work in this course. Additionally, if you come to me with other non-course-related concerns, I will do my best to help. It is important for you to know that all faculty members are required to report incidents of sexual harassment or sexual misconduct involving students. This means that I cannot keep information about sexual harassment, sexual assault, sexual exploitation, intimate partner violence or stalking confidential if you share that information with me. I will keep the information as private as I can but am required to bring it to the attention of the University’s Title IX Coordinator, Elizabeth M. Garcia, or Deputy Title IX Coordinator, Diana M. Collins, who, in conversation with you, will explain available support, resources, and options. I will not report anything to anybody without first letting you know and discussing choices as to how to proceed. The University’s Counseling Center (570-941-7620) is available to you as a confidential resource; counselors (in the counseling center) do not have an obligation to report to the Title IX Coordinator.

Non-discrimination Statement

The University is committed to providing an educational, residential, and working environment that is free from harassment and discrimination. Members of the University community, applicants for employment or admissions, guests, and visitors have the right to be free from harassment or discrimination based on race, color, religion, ancestry, gender, sex, pregnancy, sexual orientation, gender identity or expression, age, disability, genetic information, national origin, veteran status, or any other status protected by applicable law.

Students who believe they have been subject to harassment or discrimination based on any of the above class of characteristics, or experience sexual harassment, sexual misconduct or gender discrimination should contact Elizabeth M. Garcia, Title IX Coordinator, (570) 941-6645 , Deputy Title IX Coordinators Diana M. Collins (570) 941-6645 , or Ms. Lauren Rivera, AVP for Student Life and Dean of Students, at (570)941-7680 . The United States Department of Education’s Office for Civil Rights (OCR) enforces Title IX. Information regarding OCR may be found at <www.ed.gov/about/offices/list/ocr/index.html>

The University of Scranton Sexual Harassment and Sexual Misconduct Policy can be found online at https://www.scranton.edu/diversity. All reporting options and resources are available at https://www.scranton.edu/CARE.

About Pronouns

It is easy to make assumptions about an individual’s pronouns, but we try not to! Please tell us in class or via a private email if you would like to let us know what your pronouns are, if/when you would like us (and others) to use them, and certainly feel free to correct us or others if we make a mistake. Using the pronouns that a person has indicated they prefer is considered both professional and polite, and as such we ask that all members of our class use the appropriate pronouns.

If you have questions about this, please feel free to look up more information here (https://www.mypronouns.org/) or email with any questions.

Student Mental Health: Suggestions and Resources

Many students experience mental health challenges at some point in college. Struggles vary and might be related to academics, anxiety, depression, relationships, grief/loss, substance abuse, and other challenges. There are resources to help you and getting help is the smart and courageous thing to do.

  • Counseling Center (6th Floor O’Hara Hall; 570-941-7620) – Free, confidential individual and group counseling is available on campus.

  • Teletherapy – For students who wish to access therapy via video, phone, and/or chat, the University offers a teletherapy resource. Please contact the Counseling Center (570-941-7620) to inquire about teletherapy.

  • Mental Health Screenings – Confidential, online “check up from your neck up” to help you determine if you should connect with a mental health professional.

  • Dean of Students Office (201 DeNaples Center; 570-941-7680) – Private support and guidance for students navigating personal challenges that may impact success at the University

Final Note

The instructor reserves the right to modify this syllabus; students will immediately be notified of any such changes and an updated syllabus will be made available to the class via the course learning management system.

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