Undergraduate Mathematics for the Life Sciences

Undergraduate Mathematics for the Life Sciences: Models, Processes, and Directions

Glenn Ledder
Jenna P. Carpenter
Timothy D. Comar
Series: MAA Notes
Volume: 81
Copyright Date: 2013
Edition: 1
Pages: 227
https://www.jstor.org/stable/10.4169/j.ctt5hh880
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  • Book Info
    Undergraduate Mathematics for the Life Sciences
    Book Description:

    There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind. In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.

    eISBN: 978-1-61444-316-2
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Foreword: Looking Backward and Moving Forward in Undergraduate Life Science Quantitative Education
    (pp. vii-viii)
    Louis J. Gross

    It is a pleasure to read the contributions in this book, particularly since the importance of mathematics in biology has only slowly been realized over the past several decades by the biological research and education community. When I organized a Quantitative Sciences Curriculum for the Life Sciences Students workshop in 1992 for leading practitioners of mathematical biology, there were few mathematics courses designed specifically for life science students and many bench biologists were unconvinced of a need for quantitative education. Although I did not know it at the time, several of the issues addressed in the 1992 and later workshops...

  3. Foreword: An Invitation to BIO SIGMAA
    (pp. ix-x)
    Eric Marland

    Although the history of mathematics and computation in biology began a long time ago, the history of this volume begins with the formation of BIO SIGMAA. In January of 2006, Carl Cowan and Michael Pearson spoke with me about the SIGMAAs of the MAA at the Joint Mathematics Meetings in San Antonio. Carl was President of the MAA at the time and saw mathematical biology as an important growing area in mathematics and one that might benefit from the SIGMAA program of the MAA. I had helped run several successful MAA PREP workshops related to mathematical and computational biology and...

  4. Table of Contents
    (pp. xi-xiv)
  5. Preface
    (pp. xv-xvi)
    Glenn Ledder
  6. General Introduction
    (pp. xvii-xviii)
    Glenn Ledder

    The mathematics curriculum as we know it grew out of the mathematical needs of physical science. We start with a full course in calculus, which requires three semesters at most institutions. This is followed by courses in linear algebra, differential equations, and calculus-based probability and statistics in some order. The latter subjects are the ones with the broadest applications in biology, along with several discrete topics that do not occupy a place in the physics-based mathematics curriculum. Biological applications in these courses have been rare until recently, but many authors are now incorporating biological examples. There are some books in...

  7. I Models

    • [I Introduction]
      (pp. 1-4)

      One reason for the diversity of curriculum ideas for biology is that there are only a small number of slots, perhaps only two or three, available in the packed curriculum of biology majors. A second reason is the lack of uniformity in the biology curriculum that the mathematics curriculum is supposed to support. Physicists are generally in agreement about what constitutes introductory learning in physics, which has led to a mathematics curriculum that varies little among institutions, with no issues more serious than the order of linear algebra and differential equations. Biologists, in contrast, have not yet reached a consensus...

    • 1 BioCalc at Illinois
      (pp. 5-16)
      J. Jerry Uhl and Judy Holdener

      Weeks per term: 15-week semester

      Classes per week/type/length: One or two 1-hour lecture periods

      Labs per week/length: Three or four 1-hour laboratory periods

      Average class size: Sections are capped at 20.

      Enrollment requirements: First-year students in the biological sciences. Students cannot enroll unless they are life science majors.

      Faculty/dept per class, TAs: Typically taught by a graduate TA in mathematics or sometimes a faculty member. There is also one undergraduate class assistant.

      Next course: Life science majors must take two of Calculus I, Calculus II, and Statistics, so some continue on to Calculus II.

      Website:http://www-cm.math.uiuc.edu/

      In the late 1980s...

    • 2 Biocalculus at Benedictine University
      (pp. 17-24)
      Timothy D. Comar

      Weeks per term: 15 weeks

      Classes per week/type/length: Biocalculus I: 4 50 minute lecture periods per week; Biocalculus II: 3 50 minute lecture periods per week

      Labs per week/length: Calculus with Analytics I Lab/Biocalculus II Lab: 1 2 hour period per week

      Average class size: Biocalculus I: about 15 students in each of two sections; Biocalculus II/Biocalculus II Lab: 5–10 students in one section; Calculus with Analytics Lab: up to 20 students

      Enrollment requirements: Biocalculus I: placement exam; Biocalculus II: a grade of C in Biocalculus I or Calculus with Analytics I

      Faculty/dept per class, TAs: One mathematics structure...

    • 3 Implementation of First Year Biomath Courses at the Ohio State University
      (pp. 25-32)
      Laura Kubatko, Janet Best, Tony Nance and Yuan Lou

      Weeks per term: 10 weeks (will convert to semesters in 2012)

      Classes per week/type/length: three 48-min lectures, two 48-min recitations

      Average class size: Calc I = up to 120; Calc II = up to 60; Stats = up to 40

      Enrollment requirements: Calc = standard; Stats = Calc II prerequisite

      Faculty per class, TAs: each course has 1 faculty and 2, 1, 1 TA respectively

      The Ohio State University (OSU) is one of the largest schools in the nation, with over 50,000 students on the main campus in Columbus, Ohio, approximately 38,000 of whom are undergraduates. The administrative structure of...

    • 4 Teaching Calculus, Probability, and Statistics to Undergraduate Life Science Majors: A Unified Approach
      (pp. 33-38)
      Frederick R. Adler

      Weeks per term: Two semesters, about 30 weeks

      Classes per week: Three 1-hour lectures

      Labs per week: One 1-hour lab

      Average class size: 25–50 students

      Enrollment requirements: For freshman, students should have passed college algebra and trigonometry, or have Math SAT score of at least 630, Math ACT score of at least 28, or AP Calculus AB score of at least 3

      Faculty/dept per class, TAs: One math instructor with one graduate student TA to handle the computer labs

      Next course: The purpose of this course is to prepare students for the quantitative aspects of the biology curriculum

      Current...

    • 5 The First Year of Calculus and Statistics at Macalester College
      (pp. 39-44)
      Dan Flath, Tom Halverson, Danny Kaplan and Karen Saxe

      Weeks per term: 14-week semester

      Classes per week/type/length: three 1-hour lecture periods each week

      Labs per week/length: none required, but AC meets frequently in lab; ISM meets every day in lab

      Average class size: AC has 30–40 students in 5–6 sections per year; ISM has 30 in 3–4 sections per year

      Enrollment requirements: AC—Macalester admission; ISM—either AC, or Multivariable Calculus, or Linear Algebra

      Faculty/dept per class, TAs: One department faculty member per section, plus one undergraduate assigned to help with grading, and to help in lab, as instructor sees fit

      Next course: After AC either...

    • 6 Biology in Mathematics at the University of Richmond
      (pp. 45-50)
      Lester Caudill

      Weeks per term: 15

      Classes per week/type/length: three 50-minute class meetings each week

      Average class size: 17–20 students

      Enrollment requirements: For freshmen with previous calculus experience.

      Faculty/dept per class, TAs: Taught by one mathematics faculty member.

      Next course: Mathematical Models in Biology and Medicine (see below)

      Weeks per term: 15

      Classes per week/type/length: three 50-minute class meetings each week

      Average class size: 8–12 students

      Enrollment requirements: Completion of Scientific Calculus sequence. Alternatively: completion of regular calculus sequence, along with linear algebra.

      Faculty/dept per class, TAs: Taught by one mathematics faculty member.

      Next course: There is currently no course...

    • 7 A Terminal Post-Calculus-I Mathematics Course for Biology Students
      (pp. 51-60)
      Glenn Ledder

      Weeks per term: 15

      Classes per week/type/length: five 1-hour lecture/lab/recitation periods each week

      Labs per week/length (if any): 1-hour laboratory periods as needed

      Average class size: 5–10 students, but could accomodate 30

      Enrollment requirements: One calculus course

      Faculty/dept per class, TAs: Taught by one mathematics instructor, with a TA for grading.

      Next course: This course gives students the necessary background to take more advanced interdisciplinary courses in mathematical biology. Both the Department of Mathematics and the School of Biological Sciences have such a course.

      The need for a new mathematics curriculum for biology students has been well documented (National...

    • 8 Modeling Nature and the Nature of Modeling—an Integrative Modeling Approach
      (pp. 61-64)
      Claudia Neuhauser

      Weeks per term: 15

      Classes per week/type/length: two 75-minute integrated lecture/computer lab each week

      Labs per week/length: integrated with lecture

      Average class size: 15–20 students in one section

      Enrollment requirements: some familiarity with calculus (one semester)

      Faculty/dept per class, TAs: Taught by one instructor

      Next course: This course gives students an introduction to modeling that can serve as the basis for graduate level research in the biological sciences or prepare students for interdisciplinary mathematics courses with a biology focus that are available in the School of Mathematics

      Website:http://bioquest.org/numberscount/courses/bshs-calculus-2/

      The course Modeling Nature and the Nature of Modeling was...

    • 9 Mathematical Biology and Computational Algebra at the Sophomore Level
      (pp. 65-68)
      Rohan Attele and Dan Hrozencik

      Weeks per term: 16 weeks.

      Classes per week: Two 100 minutes sessions.

      Labs per week: No specific time set aside for labs; computer or experiment assignments done as needed.

      Average class size: Three in the pilot; 15–20 can be accommodated.

      Faculty/dept per class, TAs: Team-taught by one mathematics instructor and one biology instructor. No TAs.

      Next course: Not yet approved. It will be a course in computational algebra.

      Chicago State University has consistently led Illinois public universities in the conferring of baccalaureate and master’s degrees to African American students. CSU graduates more African Americans with a master’s degree in...

    • 10 An Interdisciplinary Research Course in Theoretical Ecology for Young Undergraduates
      (pp. 69-82)
      Glenn Ledder, Brigitte Tenhumberg and G. Travis Adams

      Weeks per term: 5-week summer session

      Classes per week/type/length: five 1-hour lecture periods each week

      Labs per week/length: five 1-hour laboratory periods each week

      Average class size: 8–14 students in one section

      Enrollment requirements: For high school students and university freshmen. Students had to apply for the program and get a recommendation from a teacher.

      Faculty/dept per class, TAs: Team-taught by one mathematics instructor and one biology instructor, with the mathematics instructor doing the quantitative portion of the lecture.

      Next course: The purpose of this course was to teach research skills. There were no related courses, but many of...

    • 11 An Interdisciplinary Course, Textbook, and Laboratory Manual in Biomathematics with Emphasis on Current Biomedical Research
      (pp. 83-88)
      Raina Robeva, Robin Davies and Michael L. Johnson

      Weeks per term: 14-week semester

      Classes per week/type/length: three 1-hour lecture periods each week

      Labs per week/length: one 3-hour laboratory periods each week

      Average class size: 7–10 students

      Enrollment requirements: One semester of calculus, one semester of biology, and one semester of statistics.

      Faculty/dept per class, TAs: Team-taught by one mathematics professor and one biology professor, with both doing portions of the lectures and supervising the laboratory periods.

      Next course: The purpose of this course is to introduce students to the field of biomathematics. There are no specific follow-up courses, but some students will choose biomathematics related projects to...

    • 12 Teaching Bioinformatics in a Mathematics Department
      (pp. 89-96)
      Steven Deckelman

      Weeks per term: 16 week semester

      Classes per week/type/length: Three fifty-five minutes classes each week.

      Labs per week/length: One fifty-five minute lab per week in bioinformatics capstone. Required science courses will have science labs.

      Average class size: 20 Students; 10 or fewer students the bioinformatics capstone.

      Enrollment requirements: Students should be in the bioinformatics concentration within the Applied Mathematics and Computer Science major.

      Faculty/dept per class, TAs: Taught by a single faculty member.

      Next course: Students in bioinformatics may want to take related courses in biology.

      Web pages: UW Stout, 2012a; UW Stout, 2012b.

      The terminformaticshas sometimes been...

    • 13 SYMBIOSIS: An Integration of Biology, Math and Statistics at the Freshman Level: Walking Together Instead of on Opposite Sides of the Street
      (pp. 97-104)
      Karl H. Joplin, Istvan Karsai, Darrell Moore, Hugh A. Miller III, Edith Seier, Anant Godbole and Michel Helfgott

      Weeks per term: 15 weeks

      Classes per week/type/length: M (Lec-2 hrs), T (Lab-2 hrs), W (Lec-2 hrs), Th (Lec-2 hrs), F (Lec-2 hrs)

      Labs per week/length: one 2-hr lab/wk

      Average class size: 16 students in one section

      Enrollment requirements: Students supported by our NSF STEP grant

      Faculty/dept per class, TAs: One biology and one mathematics instructor, two TAs

      Next course: IBMS 1200, Integrated Biology and Calculus

      Website:http://www.etsu.edu/cas/symbiosis/default.aspx

      Picture a busy thoroughfare through a city with cars speeding by and people standing on the sidewalk. Viewpoints of the people on the sidewalk depend on which side of the street they...

  8. II Processes

    • [II Introduction]
      (pp. 105-108)

      There is a wide variety of wonderful projects described in the Models section of this book. However, as the authors of those projects will tell you, successful curriculum development in mathematics for biology requires more than an exciting course built on sound pedagogical ideas. An academic system based on standard courses distributed among standard departments is resistant to innovation and interdisciplinary teaching. The enthusiasm that accompanies new pedagogical ideas are often dampened by difficulties encountered in the implementation. In the hope of encouraging readers who are interested in emulating the projects in this volume or developing different ones, our goal...

    • 14 Science One: Integrating Mathematical Biology into a First-Year Program
      (pp. 109-114)
      Mark Mac Lean

      Weeks per term: 26 weeks over two terms plus two exam periods in December and April

      Classes per week/type/length: 12 1-hour lecture periods each week; 4 1-hour tutorials each week

      Labs per week/length: 3 3-hour laboratory periods each week

      Average class size: 75 students in one section broken down into three tutorial/lab groups of 25 students each

      Enrollment requirements: For students entering first-year sciences; students must apply for the program; admission based on an essay, list of science-related activities, and high school grades

      Faculty/dept per class, TAs: Team-taught by eight instructors, two for each discipline

      Next course: Prepares students for...

    • 15 Planning for the Long Term
      (pp. 115-120)
      Meredith L. Greer

      Weeks per term: 12-week semester

      Classes per week/type/length: Three 55-minute or two 80-minute lecture periods each week

      Average class size: 25–30 students in one section

      Enrollment requirements: There is a Calculus 1 prerequisite

      Faculty/dept per class, TAs: One mathematics instructor

      Next course: None !!

      Many mathematics faculty members are extremely enthusiastic these days. We are working together with our colleagues in biology, and perhaps other sciences, to create and teach new mathematical biology courses. What will result from our efforts after five years go by? Ten? More? Will our mathematical biology courses remain vital, current, cross-disciplinary, engaging? Many aspects...

    • 16 Some Lessons form Fifteen Years of Educational Initiatives at the Interface between Mathematics and Biology: The Entry-Level Course
      (pp. 121-126)
      Louis J. Gross

      Weeks per term: 15-week semester

      Classes per week/type/length: two 50-minute periods and one 75-minute lab

      Labs per week/length: one 75-minute lab/recitation

      Average class size: 150 students with 35–40 students per section

      Enrollment requirements: Placement exam evaluation based upon high school algebra and trigonometry.

      Faculty/dept per class, TAs: One math/biology faculty member with several TAs teaching the labs/recitations.

      Next course: Calculus-based statistics or Models in Biology.

      Website:http://www.tiem.utk.edu/?gross/math151.html

      The history of courses in mathematics in the U.S. designed specifically for undergraduate students with interests in the biological sciences dates back at least to the early 1970s with the text by...

    • 17 A “Wet-Lab” Calculus for the Life Sciences
      (pp. 127-132)
      James L. Cornette, Gail B. Johnston, Ralph A. Ackerman and Brin A. Keller

      Weeks per term: Two 15-week semesters

      Classes per week/type/length: Four 50-minute lectures per week

      Labs per week/length: Seven 2-hour laboratories per semester

      Average class size: 34 students

      Enrollment requirements: Competence in high school algebra, geometry and trigonometry

      Faculty/dept per class, TA’s: Mathematics faculty teach the lectures; Biology teaching assistants teach the laboratory with biology faculty supervision

      Next Course: This course and possibly a semester of statistics constitute the mathematics taken by these students

      Website: The textbook for the course is posted onhttp://cornette.public.iastate.edu/CLS.html

      A black and white print version of the text is now available from CreateSpace, a subsidiary of...

    • 18 Creating an Interdisciplinary Research Course in Mathematical Biology
      (pp. 133-138)
      Glenn Ledder and Brigitte Tenhumberg

      Weeks per term: 5-week summer session

      Classes per week/type/length: five 1-hour lecture periods each week

      Labs per week/length: five 1-hour laboratory periods each week

      Average class size: 8–14 students in one section

      Enrollment requirements: For high school students and university freshmen. Students must apply for the program and get a recommendation from a teacher.

      Faculty/dept per class, TAs: Team-taught by one mathematics instructor and one biology instructor, with the mathematics instructor doing the quantitative portion of the lectures.

      Next course: The purpose of the course is to teach research skills. There are no related courses, but many of the...

    • 19 Bioinformatics: An Example of a Cooperative Learning Course
      (pp. 139-142)
      Namyong Lee and Ernest Boyd

      Weeks per term: 15-week regular semester course

      Classes per week/type/length: Two 75 minute lecture/computer lab (hybrid) per week

      Labs per week/length: Two 75 minute lecture/computer lab (hybrid) per week

      Average class size: 12–20 students

      Enrollment requirements: Each student must interview one of the three instructors to enroll in the course

      Faculty/dept per class, TAs: Team-taught by three instructors, one from each of the mathematics, biology, and computer science departments

      Next course: Students are encouraged to take Mathematical Models in Biology (Math 490/ Biol 490). Both Bioinformatics and Math Models in Biology courses focus on interdisciplinary undergraduate research

      Website:https://d2l.mnsu.edu/...

    • 20 Integrating Statistics and General Biology I in a Learning Community
      (pp. 143-148)
      William Ardis and Sukanya Subramanian

      Weeks per term: 16-week semester

      Classes per week/type/length: two 2-hour, 30-minute lecture class meetings per week

      Labs per week/length: one three-hour lab each week

      Average class size: 24 students

      Enrollment requirements: students must assess into a college level mathematics course, or pass MATH 0310—Intermediate Algebra for the statistics class, no requirement for the biology class

      Faculty/dept per class, TA’s: Lecture section team taught by one math professor and one biology professor, lab section taught by one of the lab instructors or an associate faculty member in the biology department

      Next Course: after completing this biology course, students are eligible...

    • 21 Constructing an Undergraduate Biomath Curriculum at a Large University: Developing First Year Biomath Courses at The Ohio State University
      (pp. 149-154)
      Tony Nance and Laura Kubatko

      Weeks per term: 10 weeks (will convert to semesters in 2012)

      Classes per week/type/length: three 48-minute lectures, two 48-minute recitations

      Average class size: Calculus I = up to 120; Calculus II = up to 60; Statistics = up to 40

      Enrollment requirements: standard for 1st-year Calculus; Statistics = Integral Calculus prerequisite

      Faculty per class, TAs: 1 faculty; 2 TAs for Calculus I; 1 TA for Calculus II; 1 TA for Statistics

      Development and revision of a curriculum to meet the educational needs of students is one of the most important and most difficult jobs of faculty and administrators at the...

    • 22 Initial Steps Towards an Integration of Quantitative Thinking into the Teaching of Biology at a Large Public University
      (pp. 155-164)
      Carole L. Hom, Eric V. Leaver and Martin Wilson

      Weeks per term: ten-week quarter

      Classes per week/type/length: one lecture per week in lower division course, with computer-based tutorial in all courses

      Labs: one hour computer lab per week, optional

      Average class size: up to 50 per section

      Enrollment requirements: lower division course: integral calculus (may be taken concurrently); upper division courses: any prerequisites that correspond to the accompanying lecture course

      Faculty/dept per class, TA’s: coordinating faculty member plus one TA

      Next Courses: students who satisfy appropriate prerequisites may elect upper division courses on modeling in biology taught in life sciences, mathematics, or engineering departments

      Website:http://biosci3.ucdavis.edu/qcourses/

      All aspects of...

  9. III Directions

    • [III Introduction]
      (pp. 165-168)

      Each of the papers in the Directions section addresses some perceived, but largely unmet, need in curricular development for undergraduate mathematical biology. Of course the question of what developments ought to occur is a matter of opinion. Each of these papers lays out a strong case and offers insights on how to introduce and develop the topics. As editors, we endorse these calls for a change in emphasis.

      The section begins with the paperIntegrating Statistics into College Algebra to Meet the Needs of Biology Students, by Sheldon Gordon of Farmingdale State University and Florence Gordon of the New York...

    • 23 Integrating Statistics into College Algebra to Meet the Needs of Biology Students
      (pp. 169-176)
      Sheldon P. Gordon and Florence S. Gordon

      Weeks per term: 15

      Classes per week/type/length: two 75-minute and one 50-minute class each week

      Labs per week/length: none

      Average class size: 30 students per section

      Enrollment requirements: For high school students and freshmen, though many postpone taking the mathematics course as long as possible.

      Faculty/dept per class, TAs: Taught by one mathematics instructor (usually a full-time instructor).

      Next course: The purpose of the course is to teach the mathematical ideas and methods needed by students who plan to major in biology or who want a mathematical approach that reflects the needs of biology and other laboratory sciences. It is...

    • 24 Motivating Calculus with Biology
      (pp. 177-188)
      Sebastian J. Schreiber

      Weeks per term: 10-week quarter

      Classes per week/type/length: three 50-minute lecture class meetings per week

      Labs per week/length (if any): one 50-minute lab each week

      Average class size: 250 students

      Enrollment requirements: Entering students

      Faculty/dept per class, TAs: One mathematics faculty and 4 TAs.

      Next Course: N/A

      As Leo Breiman said, calculus has a right hand and a left hand.² On the right hand is the rigorous foundation of limits and infinitesimals. The left hand thinks physically in terms of rates of change and accumulated change. In the historical development of calculus, the left hand came first, driven by applications...

    • 25 Computational Systems Biology: Discrete Models of Gene Regulation Networks
      (pp. 189-200)
      Ana Martins, Paola Vera-Licona and Reinhard Laubenbacher

      2–3 days

      Average audience size: 5–15 participants

      Enrollment requirements: High school algebra and biology.

      Team-taught by one mathematics instructor and one biology instructor

      Web site:http://admg.vbi.vt.edu/home/Outreach/Workshops/2

      Mathematical biology uses theoretical and computational tools from mathematics to describe or analyze biological systems (Murray 1993). Biological problems are considered mathematically (such as effective drug targeting (Caplan and Rosca 2005) or inferring cancer-inducing genes (Ribba et al. 2006)). Mathematical models provide a language in which to encode the key features of a biological system, which can then be analyzed with mathematical tools to obtain insight into its structure and properties. Mathematical...

    • 26 Creating Quantitative Biologists: The Immediate Future of SYMBIOSIS
      (pp. 201-206)
      Darrell Moore, Karl H. Joplin, Istvan Karsai, Hugh A. Miller III, Michel Helfgott, Anant Godbole and Edith Seier

      Weeks per term: 15 weeks

      Classes per week/type/length: M (Lec-2 hrs), T (Lab-2 hrs), W (Lec-2 hrs), Th (Lec-2 hrs), F (Lec-2 hrs)

      Labs per week/length: one 2-hr lab/wk

      Average class size: 16 students in one section

      Enrollment requirements: Students supported by our NSF STEP grant

      Faculty/dept per class, TAs: One biology and one math instructor, two TAs

      Next course: IBMS 1200, Integrated Biology and Calculus

      Website:http://www.etsu.edu/cas/symbiosis/default.aspx

      Biological research is undergoing a major transformation, but biological education is not keeping up. Biology is becoming much more quantitative and computational, incorporating concepts and methods that integrate the biological sciences with...

  10. About the Editors
    (pp. 207-208)