2007 Quantitative Biology Workshop: Abstracts
Cansius College
Not Available
Case Western Reserve Univ.
Robin Snyder
CWRU has recently approved a B.S. program in Systems Biology and is in its first year of an NSF-funded program to support mixed teams of biology and mathematics majors to work on research at the interface of mathmatics, statistics, and biology.
City College of City University of New York
Not Available
Clemson University
Robert J. Kosinski, (Biological Sciences)
James K. Peterson, (Mathematical Sciences)
The Present Situation. Kosinski teaches the introductory biology sequence for biology majors. These two courses have labs on constructing simple difference models of biochemical reactions and human weight regulation using Stella software, simple statistical analysis using the chi-square median test, and two laboratories on bioinformatics.
Since 2004, Peterson has taught a biology-oriented section of the second calculus course in a required two-semester sequence. This new course uses biological examples, introduces matrix algebra, and uses Matlab for numerical solutions of differential equations.
Several upper-division biology courses continue a modeling emphasis. Evolutionary Biology uses population genetics simulations and phylogenetic software. Ecology students model several kinds of populations and island biogeography. Systems Physiology uses Stella to simulate metabolic clearance of drugs and the dynamics of gases in the alveoli.
Future Plans. Kosinski plans to expand his use of modeling and statistics in the introductory course through the use of Excel spreadsheets, which are well-accepted by the students. Peterson plans to create biology-oriented sections of the first calculus course in the sequence and introduce a new course on modeling using partial differential equations.
At the curriculum level, Biological Sciences is debating whether it should require more mathematics for all its majors, or create a Quantitative Biology emphasis area with more intense mathematics exposure for a smaller number of students.
College of William and Mary
George W. Gilchrist, (Biology)
Paul J. Tian, (Mathematics)
The departments of Biology, Mathematics, and Applied Science actively promote quantitative biology at the College of William and Mary. Funding initiatives from HHMI and NSF support faculty and students both in terms of coursework and in enhancing research experiences. We offer a series of courses including a two semester Calculus for the Life Sciences, a 300 level Introduction to Mathematical Biology and an advanced seminar course on topics in Mathematical Biology. Applied Sciences sponsors a new Quantitative Biology minor, incorporating several existing and new courses from Mathematics, Biology, and Applied Science. We have made some progress in incorporating more math in general biology and more biology in general mathematics courses, however this is an ongoing challenge. In terms of undergraduate research, we have mentored more than 20 William and Mary undergraduates and 10 local Community College students (many from underrepresented groups) in BioMath-related research projects over the last three years. Several of these projects have or will result in peer-reviewed publications or presentations at national and international conferences. Our graduates have gone on to research positions with NIH and other agencies or have entered graduate or professional schools in BioMath and the Life Sciences.
Cornell University
Not Available
Dartmouth College
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Davidson College
Not Available
Emory University
Dwight Duffus, (Math and Computer Science)
Mathematical, computational and statistical methods are of ever growing importance in the life sciences. We introduce the basic quantitative tools required in modern life science research, adhering to the recommendations of BIO 2010 [NRC] and Math & Bio 2010 [MAA]. Courses emphasize modeling change in biological systems via discrete dynamics, continuous differential equations, and stochastic processes, and organizing and analyzing data in information-intensive application areas such as molecular evolution and genetics. Researchers in the biological sciences and health science professionals must be discerning readers of the research literature. In particular, critical evaluation of the construction of, and conclusions drawn from, statistical studies is indispensable. This requires an understanding of probability theory, as the underpinning of inferential statistics, and exposure to a variety of statistical methods used to establish confidence and test hypotheses. Over the last six years we have designed and taught a two course sequence designed to address these needs. We address the challenges of finding appropriate resources and adapting the course to students with diverse preparation. We also present some examples from the two course sequence. Poster and handout available at: http://www.mathcs.emory.edu/math4bio
P. A. Marsteller, (Biology and Center for Science Education)
Emory’s Science 2020 plan calls for the integration of quantitative skills in the undergraduate science curriculum. Our HHMI grant has already supported the development of a Life Science Calculus series and a Probability and Statistics course, specifically designed for life science majors. We have also supported the integration of problems and cases that are quantitative into numerous biology and chemistry courses. We have a University wide strategic theme to develop computational and life sciences research programs.
We are using HHMI funds to support graduate students or postdocs to work with faculty on the development and teaching of new courses with high quantitative content. This poster briefly outlines some of the recent course developments, strategies for collaborating across disciplines to create these initiatives and future plans. We are developing a website, Best Practices in Teaching Undergraduate Sciences and Math, that could serve as the host for this conference.
East Tennessee State University
Anant Godbole; Amiee Govett; Michel Helfgott; Karl Joplin; Istvan Karsai; Jeff Knisley; Ken McDonald; Hugh Miller; Darrell Moore, Justin Peyton, Susan Reynolds, and Edith Seier.
We are developing an inquiry-based, active-learning curriculum in which math and biology are integrated into a coordinated, mutually beneficial relationship, beginning at the freshman level. This curriculum consists of three courses; Integrative Biology and Statistics, Integrative Biology and Calculus, and Integrative Biology and Discrete Mathematics. Each course is being developed in a modular fashion, integrating biological concepts with math and/or statistics. The first course will cover the scientific method, cellular and molecular biology, Mendelian genetics, and an introduction to evolution while developing concepts and skills from probability and statistics. The second course includes concepts related to population genetics, ecology, behavior, and energy & metabolism while developing calculus. The third course includes topics such as membranes and neuroscience, development and gene expression, genomics, advanced evolution, and bioinformatics. The math required to develop quantitative approaches to these topics will also be covered. Each course will consist of 5 hours of lecture and 2 hours of laboratory each week (6 credit hours). Each module will take on average, two weeks, which will allow students to spend one lab period collecting data and the second lab period using various software to analyze and model the data collected. Students completing the first two courses will receive general education credit for introductory biology, probability and statistics, and calculus I.
Haverford College
Rob Manning, (Mathematics)
Phil Meneely, (Biology)
The collaboration between mathematics and biology rests primarily on informal yet intentional relationships between faculty members of the two departments. The strength of the collaboration is that nearly all faculty members in each department have been involved in a research, outreach, or curricular activity with faculty in the other department. The most established and successful efforts include a summer journal club, student and faculty/student research projects, and outreach activities to local schools and to admitted students perceived to be under-prepared. An annual HHMI-funded faculty development program, begun in 2002, has included topics that link math and biology, such as computing across the sciences, bioinformatics, statistics, and imaging (planned for 2007-08). Two new courses, one in biology and one in computer science, arose directly from this program; new laboratory exercises, lectures, and examples have been added to existing courses in both biology and mathematics. Several of the curricular innovations benefited from a structural redesign of the calculus sequence that introduced material from probability as a bridge from Calculus II to Calculus III. A new tenure-track faculty member in statistics has been hired with the expectation that she will bring a focus on statistical analysis to courses in many departments, including biology. Much remains to be done, particularly at the curricular level. We are particularly interested in developing a small set of core mathematical and computational concepts that all biology students should master, as well as some stronger curricular ties between the departments in upper level courses.
Kenyon College
Not Available
Louisiana State University
Not Available
Point Loma Nazarene University
Greg Crow (Mathematics)
Rob Elson (Biology)
Point Loma Nazarene University has roughly 3500 students of whom 2400 are undergraduates at the main campus on Point Loma in San Diego. Of the 500+ undergraduate degrees awarded each year, about 15 are in Biology, 10 are in Biology and Chemistry, 7 are in Mathematics, and 3-4 are in Computer Science. Mathematics, Computer Science and Biology have a slowly evolving interrelationship at Point Loma Nazarene University.
Topics in Biology are integral parts of a few Mathematics courses. Biology and Bio-Chem Students typically take a four hour Calculus with Applications course in the Spring of their Freshmen year. This calculus class uses examples drawn from Biology and Chemistry throughout. This computational facility is put to use in the back to back two hour courses Calculus Based Statistics and Bio-Informatics which are required of Biology majors. The distinctive of this Statistics course is that the examples are mainly taken from Biology. For instance, in hypothesis testing, Type I and Type II errors are cast as sequence inclusion or exclusion errors when searching a protein database for a known sequence.
Quantitative topics are integral parts of a few Biology courses. Basic data gathering, descriptive statistics, graphing and curve fitting are used in many introductory courses for majors and non-majors. Issues of sample size and random noise are addressed. Based on the data, explanations are required at a conceptual level. Typical courses of an introductory nature include Human Biology and Bioethics, Introduction to Biology, and Human Anatomy and Physiology. In upper level courses, probability, hypothesis testing, and various equation based analyses are employed. Model building and estimation are used. Students use Excel, Maple, and the Biology Workbench site of the San Diego Supercomputer Center in their work. In addition, the resources available at the NCBI website and others are used. We are beginning to use GPS units coupled with GIS software in Field Biology.
In order to work more collaboratively, faculty members have suggested having lunch discussions of questions on Bio-Informatics and the pedagogical implications for our classrooms. A mathematician and a Biologist have team taught the Bio-informatics course for seven years.
Princeton University
Not Available
Swarthmore College
Not Available
University of Arizona
Not Available
University of California-San Diego
Not Available
University of Delaware
Hal White (Chemistry and Biochemistry)
David Usher (Biological Sciences)
John Pelesko (Mathematical Sciences)
Since 1992, the University of Delaware has received four Undergraduate Science Education Grants from the Howard Hughes Medical Institute. The most recent grant continues to support the University of Delaware’s national leadership in the implementation of problem-based learning, undergraduate research, and science career access to underrepresented students in the sciences. It also supports a major new effort in curricular change to reflect the importance of mathematics and the physical sciences in contemporary biology. The curricular changes revolve around embedded activities in introductory calculus and biology courses, the development of math modules for advanced biology laboratories and the creation of a new major in quantitative biology.
University of Florida
R. Duran (Chemistry)
S. Hagen (Physics)
G. Jones (College of Education)
D. Julian (Zoology)
R. Machhar (Biochemistry & Molecular Biology)
S. Pilyugin (Mathematics)
At the University of Florida we have recognized the disconnect between the mathematical background of most undergraduate students and the mathematical knowledge that these students will need if they are to get the most out of their teaching laboratories or participate in original research. There is no room in our traditional calculus sequence to teach all the practical tools - data representation and analysis, probability, and modeling – that are essential for handling data in quantitative laboratory work. As part of the HHMI-funded Science-for-Life interdisciplinary program at UF, we have therefore designed a new math course for Fall 2007 that will address the gap. The course aims to provide the early undergraduate with a core set of mathematical tools that will be most useful in the laboratory, both in lab courses and in actual research. The course is also aligned to two other goals of Science for Life: getting our most talented early undergraduates placed in active research groups with multi-year projects, and developing an integrated laboratory curriculum for freshmen physics, chemistry, and biology in the new HHMI Science for Life Core Laboratory.
The Science for Life Core Laboratory is a sequence of advanced early-undergraduate laboratory courses that integrates physics, chemistry, and biology. The math course, MAC4930 is a calculus-level, MATLAB-based introduction to mathematical modeling and quantitative/statistical analysis of data. It adds a fourth discipline – mathematics – to the Core Laboratory.
University of Louisiana at Monroe
A. M. Findley
J. Bhattacharjee
S. Saydam
D. Magoun
(Departments of Biology and Mathematics & Physics)
Integrating Mathematical Concepts Across the Biology Curriculum - Remediation, Introductory Biology, Biostatistics, and Bioinformatics Initiatives
Faculty members at ULM have formed a working group to devise a concerted plan to integrate mathematics into a variety of biology curricular offerings. To date our efforts have centered on:
1. the redesign of the college algebra/trigonometry sequence and the life sciences calculus courses to include modular content and hybrid delivery methods to facilitate the remediation of the quantitative skills of ill-prepared beginning students;
2. a team-taught module on probability and statistics as an integral part of the discussion of genetics in the introductory biology sequence;
3. upper-division courses in biostatistics that include Bayesian inferences, estimation techniques, hypothesis testing, goodness of fit, analysis of variance, linear and multiple regression techniques, longitudinal data analysis, nonparametric methods, and principle component techniques;
4. incorporation of these statistical methods into ecology-based courses to assist in the quantitative treatment of species-area relationships, the disturbance-diversity hypothesis, modeling of ecosystem productivity and restoration models, and design of refuges and refuge complexes (SLOSS hypothesis); and,
5. a new course in genome annotation and bioinformatics.
Further development efforts include the initiation of a quantitative biology seminar series, hiring of faculty with mathematical biology expertise, and the development of an interdisciplinary mathematical biology concentration within the Department of Mathematics and Physics. Joint departmental sponsorship of HHMI-supported undergraduate research projects in biomathematics is also anticipated. Finally, an interdisciplinary, team-taught capstone course in mathematical biology is currently being developed.
University of Maryland
Karen Nelson
William Fagan
Kaci Thompson
Gili Marbach-Ad
MathBench Biology Modules: Using interactive web-based modules to infuse mathematics into the undergraduate biology curriculum
This poster demonstrates one approach to bridging the gap between math and biology for all undergraduate biology majors, using online interactive activities which enhance mathematical education. Even when students have mastered both biology and mathematics, the bridge between the two is problematic. The MathBench Biology Modules team is developing a series of interactive web-based modules that introduce the mathematical underpinnings of the biological content being taught in lecture. The modules cover a variety of topics but focus repeatedly on a core set of skills and concepts. Each module steps the students through a set of mathematical tools, using highly intuitive explanations, and then provides a mathematically-informed discussion of biological applications. Undergraduate biology majors at the University of Maryland encounter more than 25 such modules spread over their first 5 fundamental biology courses. Initial feedback indicates that the students feel that the modules are clear, interesting, and non-threatening. Students felt that the ability to practice mathematically-based problems at their own pace helped them master content more easily. Finally, instructors who have used the modules were pleased that lecture time spent on mathematical foundations was reduced.
University of Massachusetts
Not Available
University of Miami
Our overarching goal is to incorporate more mathematics into the biology curriculum. As a first step, we are writing modules that ask students to complete a sequence of exercises in an area of mathematical biology. These modules are designed for first year general biology courses and will be implemented in our peer- led team learning (PLTL) biology workshops. In the PLTL model students work cooperatively in small groups outside of class on material related to lecture. Inquiry-based learning is facilitated by an advanced undergraduate who has previously excelled in the course.
We have developed modules integrating mathematics and biology for population dynamics, evolution, genetics, and epidemiology. Each module consists of take-home and workshop activities. The take-home activities consist of reading material and a series of exercises that prepare the student for the mathematics needed in the workshop. The reading material contains step-by-step examples to help lead and instruct the student through the exercises. The workshop activities consist of a series of exercises that require computer programming, mathematical analysis, and critical thinking to complete. Students will program in MATLAB and are given a general MATLAB guide designed specifically to complement the modules.
University of Minnesota
Not Available
University of Montana
Not Available
University of Richmond
Lester Caudill (Mathematics)
Scott Knight (Biology)
Barry Lawson (Computer Science)
Kathy Hoke (Mathematics)
At the University of Richmond, the mathematics program created a new two-semester calculus sequence for science students, and an upper-division follow-up course in mathematical modeling. These courses are:
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Math 231 Scientific Calculus I
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Math 232 Scientific Calculus II
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Math 395 Mathematical Models in Biology and Medicine
From the science perspective, our primary goal with Scientific Calculus was to rethink the content of traditional calculus courses, so their relevance to the sciences would be enhanced, in realistic and practical ways. Simultaneously, we seek to help the science students better understand and appreciate, and begin to utilize, the important role that mathematical modeling can play in scientific investigation. The main goal in the modeling course is to teach math-inclined science students how to construct and analyze mathematical models of scientific processes.
After consultation with our science faculty, we identified important mathematical topics that have been absent or underrepresented in standard calculus courses. These topics include
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multivariate calculus (Currently, most science students see quantities that depend on two or more independent variables much earlier in their science courses than they do in mathematics.)
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more emphasis (than is typical in calculus courses) on worst-case error estimates and practical estimation
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responsible data set management, including regression techniques
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discrete probability
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linear algebra, as it relates to dynamical systems models
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modern and relevant examples and applications
To make room for these new topics, while keeping Scientific Calculus to two semesters, we did two things:
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Omitted some less-relevant (to the sciences and to modern applied mathematicians) math topics, such as endpoint tests for Taylor series, and the old traditional physics/geometry applications of integrals.
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Opened the course only to those students who already have a good calculus background (typically, a good calculus course in high school). This way, we can relegate some simpler (review) topics ( e.g., Function and other pre-calculus review, derivative shortcut formulas, vector basics, single-variable optimization) to outside readings and assignments.
This course was offered for the first time during the 2005-6 academic year, and a substantially revised version was offered during 2006-7.
The course developed to follow the new calculus sequence, Mathematical Models in Biology and Medicine, was developed during the Spring and Summer of 2006, and offered for the first time in Fall 2006. The main goals in this course are to teach math-inclined science students how to construct and analyze mathematical models, using difference and differential equations, of scientific processes. The strategy is to teach the students some modeling principles, then study models in various areas of biology and medicine. The topics and their sequencing were carefully planned to introduce successively higher-level model-building situations and analysis skills. The bio-medical topics for the course are, in sequence:
University of Texas at El Paso
Not Available
Virginia Commonwealth University
Not Available
Wesleyan University
Quantitative Biology initiatives at Wesleyan University
As part of our Hughes Program, we are developing collaboratively taught courses that bring together faculty in the life sciences with faculty in Mathematics and Computer Science. These courses include:
Bioinformatics and Functional Genomics; M. Weir (Biology), M. Rice (Mathematics and Computer Science) Evolutionary and Ecological Informatics; F. Cohan (Biology), D. Krizanc (Mathematics and Computer Science) Calculus and its Applications to Life Sciences; C. Wood (Mathematics and Computer Science), I. Russu (Chemistry) T
he sessions in these courses are often co-presented by both faculty, providing for rich discussions. We have found that students appreciate hearing complementing perspectives and expertise of two faculty. We find that collaborative teaching provides a powerful and efficient way to build bridges between disciplines in our curriculum. And these teaching collaborations have led to research collaborations.
We have also developed genomic scale relational databases for use in our bioinformatics classes. We have built web interfaces allowing students without programming background to work in the database environment (http://igs.wesleyan.edu > Databases and Tools). The web interface also allows more advanced students to program in SQL. We find that relational databases provide an excellent framework for introducing students to thinking informatically (Cell Biology Education 3: 241-252).
We have also developed downloadable teaching demonstrations to illustrate K-means and Self Organizing Map clustering algorithms (http://igs.wesleyan.edu > Teaching Demos). These interactive demonstrations provide a visual way to conceptualize these clustering algorithms.
Xavier University
Not Available
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