MATH 2241 -- New Course

Mon Jun 15 10:15:13 2015

Approvals Received:
on 06-04-15
by Stephanie Lawson
Approvals Pending: College/Dean  > Provost > Catalog
Effective Status: Active
Effective Term: 1159 - Fall 2015
Course: MATH 2241
UMNTC - Twin Cities/Rochester
UMNTC - Twin Cities
Career: UGRD
College: TIOT - College of Science and Engineering
Department: 11133 - Mathematics, Sch of
Course Title Short: Math Model Biological Systems
Course Title Long: Mathematical Modeling of Biological Systems
Max-Min Credits
for Course:
3.0 to 3.0 credit(s)
Development, analysis and simulation of models for the dynamics of biological systems.  Mathematical topics include discrete and continuous dynamical systems, linear algebra, and probability. Models from fields such as ecology, epidemiology, physiology, genetics, neuroscience, and biochemistry.

prereq: [1241 or 1271 or 1371] w/grade of at least C-,CBS student
Print in Catalog?: Yes
CCE Catalog
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Grading Basis: Stdnt Opt
Topics Course: No
Honors Course: No
Online Course: No
Contact Hours:
5.0 hours per week
Course Typically Offered: Every Fall & Spring
Component 1 : DIS (no final exam)
Component 2 : LEC (with final exam)
Progress Units:
Not allowed to bypass limits.
3.0 credit(s)
Financial Aid
Progress Units:
Not allowed to bypass limits.
3.0 credit(s)
Repetition of
Repetition not allowed.
for Catalog:
<no text provided>
No course equivalencies
Add Consent
No required consent
Drop Consent
No required consent
(course-based or
000056 - CBS students
Editor Comments: <no text provided>
Proposal Changes: <no text provided>
History Information: <no text provided>
Sponsor Name:
Duane Nykamp
Sponsor E-mail Address:
Student Learning Outcomes
Student Learning Outcomes: * Student in the course:

- Can identify, define, and solve problems

Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome.

Problem solving is at the heart of any mathematics course. In this course some problems would involve purely mathematical issues, like finding the derivative of a polynomial or determining the features of the graph of a rational function. Other problems involve taking a real world situation like predicting the trajectory of a projectile or analyzing population growth and decline, requiring students to first identify the mathematically relevant aspects, then define appropriate mathematical variables and relations, and finally solve the resulting mathematics problem.

How will you assess the students' learning related to this outcome? Give brief examples of how class work related to the outcome will be evaluated.

Practically every homework assignment, quiz, and exam requires students to solve problems. Students receive ample feedback about this learning outcome during the semester.

Liberal Education
this course fulfills:
Other requirement
this course fulfills:
Criteria for
Core Courses:
Describe how the course meets the specific bullet points for the proposed core requirement. Give concrete and detailed examples for the course syllabus, detailed outline, laboratory material, student projects, or other instructional materials or method.

Core courses must meet the following requirements:

  • They explicitly help students understand what liberal education is, how the content and the substance of this course enhance a liberal education, and what this means for them as students and as citizens.
  • They employ teaching and learning strategies that engage students with doing the work of the field, not just reading about it.
  • They include small group experiences (such as discussion sections or labs) and use writing as appropriate to the discipline to help students learn and reflect on their learning.
  • They do not (except in rare and clearly justified cases) have prerequisites beyond the University's entrance requirements.
  • They are offered on a regular schedule.
  • They are taught by regular faculty or under exceptional circumstances by instructors on continuing appointments. Departments proposing instructors other than regular faculty must provide documentation of how such instructors will be trained and supervised to ensure consistency and continuity in courses.

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Criteria for
Theme Courses:
Describe how the course meets the specific bullet points for the proposed theme requirement. Give concrete and detailed examples for the course syllabus, detailed outline, laboratory material, student projects, or other instructional materials or methods.

Theme courses have the common goal of cultivating in students a number of habits of mind:
  • thinking ethically about important challenges facing our society and world;
  • reflecting on the shared sense of responsibility required to build and maintain community;
  • connecting knowledge and practice;
  • fostering a stronger sense of our roles as historical agents.

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LE Recertification-Reflection Statement:
(for LE courses being re-certified only)
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Statement of Certification: This course is certified for a Core, effective as of 
This course is certified for a Theme, effective as of 
Writing Intensive
Propose this course
as Writing Intensive
Question 1 (see CWB Requirement 1): How do writing assignments and writing instruction further the learning objectives of this course and how is writing integrated into the course? Note that the syllabus must reflect the critical role that writing plays in the course.

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Question 2 (see CWB Requirement 2): What types of writing (e.g., research papers, problem sets, presentations, technical documents, lab reports, essays, journaling etc.) will be assigned? Explain how these assignments meet the requirement that writing be a significant part of the course work, including details about multi-authored assignments, if any. Include the required length for each writing assignment and demonstrate how the minimum word count (or its equivalent) for finished writing will be met.

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Question 3 (see CWB Requirement 3): How will students' final course grade depend on their writing performance? What percentage of the course grade will depend on the quality and level of the student's writing compared to the percentage of the grade that depends on the course content? Note that this information must also be on the syllabus.

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Question 4 (see CWB Requirement 4): Indicate which assignment(s) students will be required to revise and resubmit after feedback from the instructor. Indicate who will be providing the feedback. Include an example of the assignment instructions you are likely to use for this assignment or assignments.

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Question 5 (see CWB Requirement 5): What types of writing instruction will be experienced by students? How much class time will be devoted to explicit writing instruction and at what points in the semester? What types of writing support and resources will be provided to students?

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Question 6 (see CWB Requirement 6): If teaching assistants will participate in writing assessment and writing instruction, explain how will they be trained (e.g. in how to review, grade and respond to student writing) and how will they be supervised. If the course is taught in multiple sections with multiple faculty (e.g. a capstone directed studies course), explain how every faculty mentor will ensure that their students will receive a writing intensive experience.

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Statement of Certification: This course is certified as Writing Internsive effective  as of 
Course Syllabus
Course Syllabus: For new courses and courses in which changes in content and/or description and/or credits are proposed, please provide a syllabus that includes the following information: course goals and description; format;structure of the course (proposed number of instructor contact hours per week, student workload effort per week, etc.); topics to be covered; scope and nature of assigned readings (text, authors, frequency, amount per week); required course assignments; nature of any student projects; and how students will be evaluated. The University "Syllabi Policy" can be found here

The University policy on credits is found under Section 4A of "Standards for Semester Conversion" found here. Course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification. This course syllabus information may not correspond to the course as offered in a particular semester.

(Please limit text to about 12 pages. Text copied and pasted from other sources will not retain formatting and special characters might not copy properly.)

Mathematical Modeling of Biological Systems

Prerequisites: Math 1241 or 1271 or 1371 with grade of C- or better

Credits: 3

Catalog description: Development, analysis and simulation of models for the dynamics of biological systems.  Mathematical topics include discrete and continuous dynamical systems, linear algebra, and probability. Models from fields such as ecology, epidemiology, physiology, genetics, neuroscience, and biochemistry.

Course objectives:

1.        Introduce the connections between biological questions and mathematical concepts.
2.        Develop the mathematics of dynamical systems, linear algebra, and probability through modeling biological systems.
3.        Explore the utility of using mathematical tools to understand the properties and behavior of biological systems.
4.        Develop facility in interpreting mathematical models and the conclusions based on the models.

Course topics:

1. Class-structured models
multi-dimensional linear discrete dynamical systems
matrix equations and eigenvalues of matrices
age-structured models for population dynamics

2. Two-dimensional continuous dynamical systems
equilibria and nullclines
phase plane analysis
stability of equilibria
partial derivatives
models of infectious diseases, neurons, competition and predation

3. Diffusive processes
interpretation of partial differential equations
the diffusion equation
models of dispersal

4. Networks
metabolic networks or genetic networks

5. Probabilistic modeling
probability distributions, independence, conditional probability, random variables
probabilistic inference
population genetics

6. Modeling philosophy
development of a mathematical model
appropriate use and limitations of mathematical models
Strategic Objectives & Consultation
Name of Department Chair
Peter Olver
Strategic Objectives -
Curricular Objectives:
How does adding this course improve the overall curricular objectives ofthe unit?

This course will help deepen the mathematical facility of the scientific and medical community.
Strategic Objectives - Core
Does the unit consider this course to be part of its core curriculum?

Strategic Objectives -
Consultation with Other
In order to prevent course overlap and to inform other departments of new curriculum, circulate proposal to chairs in relevant units and follow-up with direct consultation. Please summarize response from units consulted and include correspondence. By consultation with other units, the information about a new course is more widely disseminated and can have a positive impact on enrollments. The consultation can be as simple as an email to the department chair informing them of the course and asking for any feedback from the faculty.

We consulted with both CBS and CFANS, and they stated they did not have overlapping courses.