MATH 1241 -- New Course

Wed Feb 22 15:37:55 2012

Approvals Received:
on 02-22-12
by Stephanie Lawson
Approvals Pending: College/Dean  > LE > Catalog > PeopleSoft Manual Entry
Effective Status: Active
Effective Term: 1129 - Fall 2012
Course: MATH 1241
UMNTC - Twin Cities
UMNTC - Twin Cities
Career: UGRD
College: TIOT - College of Science and Engineering
Department: 11133 - Mathematics, Sch of
Course Title Short: Calc & Dyn Sys in Biology
Course Title Long: Calculus and Dynamical Systems in Biology
Max-Min Credits
for Course:
4.0 to 4.0 credit(s)
Differential and integral calculus with biological applications. Discrete and continuous dynamical systems. Models from fields such as ecology and evolution, epidemiology, physiology, genetic networks, neuroscience, and biochemistry.
Print in Catalog?: Yes
CCE Catalog
<no text provided>
Grading Basis: Stdnt Opt
Topics Course: No
Honors Course: No
Delivery Mode(s): Classroom
Contact Hours:
5.0 hours per week
Years most
frequently offered:
Every academic year
Term(s) most
frequently offered:
Fall, Spring
Component 1: DIS (no final exam)
Component 2: LEC (with final exam)
Progress Units:
Not allowed to bypass limits.
4.0 credit(s)
Financial Aid
Progress Units:
Not allowed to bypass limits.
4.0 credit(s)
Repetition of
Repetition not allowed.
for Catalog:
CBS student, 4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155].
No course equivalencies
No required consent
(course-based or
CBS student
Editor Comments: <no text provided>
Proposal Changes: <no text provided>
History Information: <no text provided>
Sponsor Name:
Bryan Mosher (Director of Undergraduate Studies)
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:
MATH Mathematical Thinking
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.

Calculus is one of the pillars of modern mathematics, and it has important applications in science and everyday life.    The course requires students to have a real understanding of the symbolic language of mathematics, giving them ample opportunity to see how mathematics is done by mathematicians and to engage in that same work by solving problems for themselves. In this way, they see how abstract mathematical concepts can find applications in the real world.

An important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia, both for aesthetic reasons and to solve concrete problems.  Calculus was first developed by Newton and Leibniz in the 17th century to solve many types of problems.  For example, using calculus, Newton was able to derive the equations of planetary motion from basic physical laws.  Since that time, calculus has touched virtually every part of modern life, through its use in areas like engineering, the stock market, agriculture, psychology, and all the physical and biological sciences.  While it is beyond the scope of a 1-semester course to cover even a small fraction of all these applications, students will be exposed to a variety of simplified versions of them, preparing them for later advanced study in their fields of interest.  In this way, students experience both the fundamental nature of the questions and the usefulness of abstract reasoning in finding elegant and efficient solutions.

Students meet twice a week in TA recitation sections, where they can ask questions, work problems together, and discuss important points in the material.  The prerequisite for the course is equivalent to 4 years of high school mathematics including trig. The course is taught by a combination of regular faculty and adjunct faculty with on-going appointments, or by experienced grad students or postdocs who act under close supervision by regular faculty.  The final exam is a departmental exam that is given in common to all sections, in order to ensure consistency.
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.

<no text provided>
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.

<no text provided>
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.

<no text provided>
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.

<no text provided>
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.

<no text provided>
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?

<no text provided>
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.

<no text provided>
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.)

Math 1241
Calculus and dynamical systems in biology

Prerequisites: 4 yrs high school math including trig or satisfactory score on placement test or grade of
at least C- in [1151 or 1155]

Credits: 4

Liberal Education:  This course fulfills the Mathematical Thinking component of the Liberal Education requirements at the University of Minnesota.  An important part of any liberal education is learning to use abstract thinking and symbolic language to solve practical problems.  Calculus is one of the pillars of modern mathematical thought, and has diverse applications essential to our complex world.  In this course, students will be exposed to theoretical concepts at the heart of calculus and to numerous examples of real-world applications.

Tentative Text: Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Third
Edition, by Frederick Adler

Catalog description: Differential and integral calculus with biological applications. Discrete and
continuous dynamical systems. Models from fields such as ecology and evolution, epidemiology,
physiology, genetic networks, neuroscience, and biochemistry.

Course objectives:
1. Introduce the connections biological questions and mathematical concepts.
2. Develop the mathematics of calculus and dynamical system 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. One-dimensional discrete dynamical systems
cobwebbing, equilibria, long versus short-time behavior
stability of equilibria
2. Differentiation
continuity and differentiability
tangent line, limit definition of derivative
derivative of basic functions: polynomials, exponentials, sinusoids
brief overview of methods of differentation: product, chain rules
second derivative
partial derivative of function of two variables
3. Optimization and root finding
intermediate and extreme value theorems
4. Integration
indefinite integral as solution to ODE
basic anti-derivatives: polynomials, exponentials, sinusoids
definite integral as change in solution to ODE
definite integral as signed area under curve
fundamental theorem of calculus
Euler's method as approximate solution of ODE and numerical integration
5. 1D Ordinary differential equations
exponential as solution to linear ODE
steady states and stability
6. Linear algebra
matricies and determinants
eigenvectors and eigenvalues
7. Two dimensional dynamical systems
equilibria and stability
phase plane, direction field, nullclines
8. Partial differential equations
recognition of meaning of terms in a PDE

Strategic Objectives & Consultation
Name of Department Chair
<no text provided>
Strategic Objectives -
Curricular Objectives:
How does adding this course improve the overall curricular objectives ofthe unit?

<no text provided>
Strategic Objectives - Core
Does the unit consider this course to be part of its core curriculum?

<no text provided>
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.

<no text provided>