Math 2241 Syllabus, Spring 2017
General information
Instructors: Duane Nykamp (Mathematics)
Prerequisites: Math 1241 or 1271 or 1371 or equivalent
Credits: 3
Summary: Development, analysis and simulation of models for the dynamics of biological systems. Mathematical topics include discrete and continuous dynamical systems, linear algebra, and probability. Examples will be drawn from fields such as ecology, epidemiology, physiology, genetics, neuroscience, biophysics, microbiology and biochemistry.
Course Overview
This course provides an introduction for developing, analyzing, and interpreting mathematical models of biological systems. We will cover a variety of different mathematical approaches and draw on examples from biological systems. Throughout this course, our general goal is to use mathematics as a tool for gaining a deeper understanding of biological systems and their dynamics.
The specific learning goals of this course are:
- Introduce the connections between biological questions and mathematical concepts.
- Develop the mathematics of dynamical systems, linear algebra, and probability through modeling biological systems.
- Explore the utility of using mathematical tools to understand the properties and behavior of biological systems.
- Develop facility in interpreting mathematical models and the conclusions based on the models.
Class Format
To help students achieve these learning goals, Math 2241 will use an active learning format for class instruction. The lecture material will be posted online in the form of videos and text that will be watched and read at home. In class time will be spent working through problems and projects in groups.
Course Topics
- Class-structured models (3 weeks)
- multi-dimensional linear discrete dynamical systems
- matrix equations and eigenvalues of matrices
- age-structured models for population dynamics
- biological examples: sea turtle conservation, gut microbiota
- Two-dimensional continuous dynamical systems (3 weeks)
- equilibria and nullclines
- phase plane analysis
- stability of equilibria
- partial derivatives
- biological examples: infectious disease and vaccination, interspecific competition, neuron spike generation, predator-prey
- Probabilistic modeling (3 weeks)
- probability distributions, independence, conditional probability, random variables
- probabilistic inference
- biological examples: population growth, genetics, disease testing, cancer
- Spatial modeling (3 weeks)
- two-patch models with dispersal
- metapopulation models, occupancy
- random walks and the diffusion equation
- interpretation of partial differential equations
- biological examples: habitat loss, molecular diffusion, macrophage movement
- Modeling philosophy (2 weeks)
- development of a mathematical model
- appropriate use and limitations of mathematical models
Course Materials
Math Insight
Lecture videos, additional expository material, interactive applets, quizzes, and exercises will be posted on the Math Insight website.
Textbooks
We will use material from the following textbooks, which are available online for University of Minnesota students.
- Mathematics for the Life Sciences by Glenn Ledder
- A Primer of Ecology with R by M. Henry H. Stevens
- Population Biology by Alan Hastings
Assessment
Your grade will be determined by
- your scores on exams, problem sets, and quizzes
- obtaining full credit on projects,
- completing reflection assignments.
The criteria for each grade are as follows. To earn a grade, you must meet all the criteria in the corresponding column.
| D | C | B | A | ||
|---|---|---|---|---|---|
| Reflection papers (out of 10 possible) | 4 | 6 | 6 | 6 | |
| Average score on problem sets (you can drop two scores) | 80% | 90% | 90% | 90% | |
| Average score on online quizzes (you can drop one score) | 80% | 90% | 90% | 90% | |
Total points out of 900 on
|
550 | 600 | 650 | 700 | |
| Module 1-4 projects | Total | 3 | 4 | 6 | 7 |
| Module 1 | 0-1 | 1 | 1-2 | 1-2 | |
| Module 2 | 0-1 | 1 | 1-2 | 1-2 | |
| Module 3 | 0-1 | 1 | 1-2 | 1-2 | |
| Module 4 | 0-1 | 1 | 1-2 | 1-2 | |
| Communicating models project | ✔ | ✔ | |||
| Synthesis project | ✔ | ||||
Reflection papers
Each week, you will have the opportunity to submit a short paper (100-200 words) reflecting on what you learned that week or an another topic announced in class. If you submit a paper on the requested topic of a least 100 words, you will receive credit.
Exams
The course is divided into five modules. The first three have an associated exam.
The last two modules will not have separate exams, but the exams for the last modules will be combined with the comprehensive final exam. The final exam will be from 1:30-4:30 PM on Monday, May 8.
Quizzes
Quizzes will be taken online. Each quiz can be taken repeatedly up to the deadline.
Problem sets
Problem sets will be worked on in groups during class. Answers to problem set will entered online for grading.
Projects
Students will complete up to ten projects (two per module) where they apply math skills to different biological scenarios. Students will work in groups of up to three students and submit one write-up per group.
Each project will be on a credit/no credit basis. If your work meets the requirements specified by appropriate rubric, you will earn full credit. If your work does not meet the requirements, you will earn no credit. There will be no partial credit.
In general, there will not be an opportunity to redo work that resulted in now credit. However, you will have the opportunity to redo one project and resubmit it for full credit.
To receive credit for a project, all other members of your group must attest that you made a substantial contribution to the majority of the project. (Simply completing a section of the project yourself doesn't suffice.) Each group is responsible for ensuring all contribute and may remove members who are not contributing.
The following is a list of projects that are currently available.
- Class-structured models
- Sea turtle conservation
- Gut microbiota
- Two-dimensional continuous dynamical systems
- Influenza
- Short-term memory
- Probabilistic modeling
- Neuronal decoding and mind reading
- Tumor growth
- Spatial modeling
- Metapopulations and habitat loss
- Molecular diffusion
- Modeling philosophy
- Communicating models
- Synthesis
Policies
Make-ups
Students must make arrangements in advance if they will not be handing in homework on time or will miss an exam. Exam absences due to recognized University related activities, religious holidays, verifiable illness, and family/medical emergencies will be dealt with on an individual basis. See official University Policy on Makeup Examinations for Legitimate Absences.
Scholastic conduct
We expect the highest standards of conduct from members of this class. Cases of academic dishonesty will be treated with utmost seriousness. See Student Conduct Code.
Student privacy and course website
In this class, our use of technology will sometimes make students' names and U of M Internet IDs visible within the course website, but only to other students in the same class. Since we are using a secure, password-protected course website, this will not increase the risk of identity theft or spamming for anyone in the class. If you have concerns about the visibility of your Internet ID, please contact your instructor for further information.
Incompletes
A final grade of incomplete is given only if you have successfully completed all but a small portion of the work of the course, and have a very compelling, well documented excuse from completing the course. Simply being behind in your work does not qualify you for an incomplete.
Drop dates
You may drop the course without permission by the end of the eighth week of the semester. If you drop before the end of the second week, no mention of the course will appear on your transcript. Otherwise, you receive a "W" for the course.
Equity and Equal Opportunity
The University provides equal access to and opportunity in its programs and facilities, without regard to race, color, creed, religion, national origin, gender, age, marital status, disability, public assistance status, veteran status, sexual orientation, gender identity, or gender expression. For more information, see the Board of Regents Policy.
Accessability
The University of Minnesota is committed to providing equitable access to learning opportunities for all students. The Disability Resource Center (DRC) is the campus office that collaborates with students who have disabilities to provide and/or arrange reasonable accommodations. If you have, or think you may have, a disability (e.g., mental health, attentional, learning, chronic health, sensory, or physical), please contact the DRC at 612-626-1333 to arrange a confidential discussion regarding equitable access and reasonable accommodations. If you are registered with the DRC and have a current letter requesting reasonable accommodations, please contact your instructor as early in the semester as possible to discuss how the accommodations will be applied in the course. For more information, please see the DRC website.
Mental Health and Stress Management
As a student you may experience a range of issues that can cause barriers to learning, such as strained relationships, increased anxiety, alcohol/drug problems, feeling down, difficulty concentrating and/or lack of motivation. These mental health concerns or stressful events may lead to diminished academic performance and may reduce your ability to participate in daily activities. University of Minnesota services are available to assist you. You can learn more about the broad range of confidential mental health services available on campus via the Student Mental Health Website.
Sexual Harassment
Sexual harassment interferes with academic performance and creates a hostile academic environment. Such behavior is not acceptable in the University setting. For additional information, see the Board of Regents Policy.
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