Canisius College has a number of component activities in Mathematical Biology and Quantitative Science, supported by a series of HHMI grants, as well as by the institution and the NSF. We present a series of both ongoing and planned activities, in both teaching and research in these areas, as points of discussion. Interdisciplinary Faculty and student research areas in computational ecology, bioinformatics, biophysics and the application of Differential Geometry and cellular structure are discussed. Interdisciplinary courses and modules in scientific modeling and genomics are presented, as well as activities developed to support the integration of mathematics and biology at the introductory level. Our undergraduate institution is in the process of developing closer ties with the rapidly developing life-sciences initiatives in the Buffalo area, as evidenced by our Bioinformatics program, and placement of students in various laboratory and computational settings locally. Our efforts are still in an early stage, and are expected to expand as we develop plans for a new interdisciplinary science center.

Case Western Reserve University

B.S. in Systems Biology: CWRU has recently approved a B.S. in Systems Biology, essentially an undergraduate major in mathematical and computational biology. Students take 4 semesters of calculus and two modeling classes (BIOL 300, 306, described below) in addition to courses in computer science and statistics. They are then able to specialize in a subfield of biology, such as theoretical ecology or computational neuroscience. See http://www.case.edu/artsci/sysbio/sysbio.html for more information.

UBM grant: We are also in the first year of our UBM grant, an NSF-sponsored program that funds mixed teams of math/stats majors and biology majors to work on problems at the interface of the biological and mathematical sciences. Students work intensively over the summer, then continue their work over the course of the following school year. Teams are co-mentored by biology and math/stats faculty. This year, we have two teams of two, one working on a computational neuroscience project on behavioral plasticity in Aplysia and the other working on modeling and genotypic analysis of malaria. For more information, see http://www.case.edu/artsci/ribms/ribms.html

Mathematical biology in the regular curriculum: Students who are not interested or able to participate in the systems biology or UBM programs can still study biological dynamics. “The Dynamics of Biological Systems” (BIOL 300) is an introductory, Mathematica-based course which has become hugely popular — it may soon be necessary to add a second section. Some of these students then go on to take “The Dynamics of Biological Systems II” (BIOL 306), a more analytical course which reviews the material in BIOL 300 and goes on to cover matrix modeling and an introduction to reaction-diffusion systems and pattern formation. A third course covering the use of stochastic processes in biology (MATH/BIOL 319) was first offered this past spring

Clemson University

Clemson’s Departments of Biological Sciences and Mathematical Sciences have begun a multi-year collaboration to strengthen quantitative biology.

The Present Situation–Strengths: Clemson’s Biological Sciences curriculum has 650 majors. Freshmen take two semesters of Calculus of One Variable. Since 2004 Mathematical Sciences has taught a biology-oriented section of the second calculus course, MTHSC 108. This new course covers traditional topics such as integration techniques, but it uses biological examples such as exponential and logistic population growth, predator-prey models, and epidemiological models. It introduces matrix algebra topics such as eigenvalues and eigenvectors, and uses Matlab for numerical solutions of differential equations. Finally, it discusses qualitative solution techniques like phase-plane analysis.

The introductory Biology sequence, BIOL 110/111, has labs on modeling biochemical reactions and human weight regulation using Stella modeling software. Other quantitative topics include the action of buffers, Hardy-Weinberg equilibrium, and stochastic modeling of genetic drift. BIOL 110 and 111 also introduce the students to simple statistical analysis (the chi-square median test). Finally, each introductory semester has a laboratory on bioinformatics. The first of these gives the students a “mystery protein,” and they discover all they can about it using BLAST, the NCBI sites, Swiss-Prot, and several other resources. The second uses ClustalW analysis of mitochondrial DNA to study human evolution.

We have several upper-division Biology courses with a modeling emphasis. Evolutionary Biology uses population genetics simulations such as Populus and phylogenetic software such as PAUP. Ecology students model population growth in a population with discrete generations, competition, predator-prey dynamics, human demographics (using data derived from cemeteries), and island biogeography. Ecology also uses RAMAS software to investigate population dynamics. Systems Physiology uses Stella to simulate metabolic clearance of drugs and the dynamics of gases in the alveoli.

The Present Situation–Problems: Because of transfers in and out, Biological Sciences has a 60% turnover rate of its majors between freshman and senior years. Also, upper-division courses have many majors in them aside from Biological Sciences. This means that many upper-division students have not had MTHSC 108 or BIOL 110/111. Also, MTHSC 106 (the first calculus course) is still traditional. There is no statistics requirement and no bioinformatics requirement for BIOSC students, although they get some bioinformatics in introductory genetics courses. Most of all, we are concerned about a gap in mathematical application courses between the first year and the third or fourth year.

The Future: Mathematical Sciences may orient a section of the Calculus I course towards modeling, which will free up more time in the Calculus II course for additional modeling topics. In Fall 2007, Mathematical Sciences will teach a follow-up course to MTHSC 108. This course will emphasize partial derivatives and partial differential equations, will extend the use of Matlab, and will use these techniques to model diffusion, heat flow, and chemical reactions.

The introductory biology course plans to use Excel spreadsheets for modeling and statisticial analysis. Students seem to accept Excel as a common tool, and this may increase acceptance of mathematical applications.

Biological Sciences is debating some curriculum decisions. First, how can it increase the mathematical experience of its majors? It might require an additional course in mathematical biology, but the curriculum is full now. Clemson requires that students complete an e-portfolio, and one approach is to establish a departmental requirement that mathematical competency be demonstrated by one or more artifacts in this portfolio. This could be done most easily as students were taking courses like MTHSC 108.

Another approach, which might be done in addition to or instead of a broad increase in math exposure, is to create a Quantitative Biology emphasis area within the Biological Sciences degree. These students would take several quantitative biology courses beyond the present requirements. This emphasis area approach would avoid much resistance by those uninterested in more mathematics, but it would also only impact a small number of students.

College of William and Mary

Curriculum development

Research mentoring

Faculty contributing to quantitative biology:

Emory University

Emory Undergraduate Curriculum Development

As part of our interdisciplinary initiatives, we are simultaneously integrating mathematics and problem solving into our introductory biology and chemistry courses, developing math and computer science courses with biological applications and planning mathematically intensive minors. The minors include:

Recent Math courses with biological applications

Life Science Calculus Series

MATH 115 Life Science Calculus I

MATH 116 Life Science Calculus II

MATH 215 Probability and Statistics with Applications

Freshman Seminar: Bioinformatics

CS 153 Computing for Bioinformatics

Recent Biology courses with significant math focus

Bio/Chem 330:

Introductory biology series

Strategic Planning theme for the whole University

East Tennessee State University University

SYMBIOSIS : An Integrated Math-Biology Introductory Curriculum at East Tennessee State University

East Tennessee State University (ETSU) is a regional state university with approximately 10,000 undergraduate and 2000 graduate students. The Department of Mathematics and the Department of Biological Sciences have Masters programs, and both are intensively committed to undergraduate education and research. The Institute for Quantitative Biology (IQB) was created by faculty within the two departments and was approved by the Tennessee Board of Regents to facilitate interdisciplinary research and education.

The faculty of the departments involved in the IQB were awarded an HHMI grant with the objective to establish an inquiry-based and active-learning curriculum in which math and biology are integrated into a coordinated, mutually beneficial relationship we have called SYMBIOSIS (HHMI #52005872), beginning at the earliest stages of a student’s college career. Such an innovative melding of math and biology will introduce and reinforce aspects of the modern approaches to quantitative biological research and instruction, including collaboration, creativity, and rigorous analytical thinking. Our integrative course sequence will address topics in the same manner in which a researcher would address them – through hypothesis testing, modeling, exploration, and analysis.

The project will integrate five courses (three in biology, one in calculus, and one in statistics) plus selected elements from other math courses, into a sequence of three highly coordinated, interdisciplinary courses (SYMBIOSIS I, II, and III) offered at the beginning of the student’s college career. Lectures and exercises will be followed by wet- and dry-labs so that students will generate their own data and develop an arsenal of skills enabling them to perform quantitative analyses.

The success of SYMBIOSIS requires a rethinking of both math and biology pedagogy, including the “breaking down” of barriers between individual mathematical courses like Calculus and Linear Algebra; between mathematics and statistics; between empirical and theoretical biology; and between mathematics and the biological sciences.

COURSES (to be implemented starting Fall 2007)

SYMBIOSIS I Introductory Biology and Statistics (IBMS 1100) will cover the topics of Introduction to Biology and Math, Scientific Enquiry, central concepts in Biology and Math; The Cell, statistical tables and graphs, descriptive statistics, correlation; Allometry and Functional Models, precalculus coverage of functions along with curve fitting and regression, scaling in biological systems; Mendelian Genetics, probability trees, the binomial distribution, the Chi-square test, limits as a tool to define probability in terms of relative frequency; DNA Genetics, structure and function of DNA and genomes, discrete probability distributions, test of hypothesis for proportions, simple Markov models, limits as a tool to justify the Central Limit Theorem; Evolution, introduction, basic math, linear algebra, Hardy-Weinberg.

SYMBIOSIS II Introductory Biology and Calculus (IMBS 1200) will cover the basics of the Calculus I so that students will be ready for Calculus II. Populations, rates of change, tangents, derivatives, exponential, estimating population size; Ecology, qualitative analysis of differential equations, differentiability, continuity, difference to continous, limits, curve-sketching; Behavioral Ecology, optimization and curve-sketching; Circadian Rhythms, trig functions, derivatives of trig functions, periodograms; Structured Populations, definition of the integral, areal under a curve, age distributions and densities, antiderivatives, Fundamental Theorem of Calculus; Energy and Enzymes, non-linear regression.

SYMBIOSIS III Introductory Biology, Statistics and Discrete Math (IBMS 1300). (Still under development) Membranes, volume and surface area, separable differential equations; Neurons, Fundamental Theorem, differential models, matrix theory, limits and L’hopital’s Rule; Endocrine; Development and Growth; Introduction to BioInformatics, algorithms, BLAST, Genbank; Discrete Models, graph theory, protein folding; Evolution, part II.

STRATEGIC PLANNING

Along with the curriculum changes embodied with SYMBIOSIS, we will be planning to introduce and enhance a Concentration in Quantitative Biology for biology and math students. Additional resources are also being sought to expand our undergraduate research infrastructure to go along with our curriculum changes

Haverford College

Mathematics and Biology at Haverford College Rob Manning, Dept of Mathematics and Phil Meneely, Dept of 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. Few students from one department take advanced courses in the other, and a program in computational biology has not yet developed. The applications of math to biology and biology to math have tended to be isolated examples and could be more rigorous and more extensive. Because our biology department focuses on molecular and cellular approaches, some familiar applications of mathematical biology such as population dynamics and physiology are not included in our curriculum. On the other hand, bioinformatics and network biology fit easily in our curriculum. 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.

Point Loma Nazarene University

Mathematics and Biology at Point Loma Nazarene University by Greg Crow–Mathematics and 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.

University of Arizona

Interdisciplinary educational opportunities for University of Arizona undergraduates at the interface of the life sciences and quantitative sciences

Interdisciplinary graduate educational activities have a long tradition at the University of Arizona. Presently, the University has 15 graduate interdisciplinary programs. (See http://gidp.arizona.edu/). Several of them involve the life sciences and the quantitative sciences, e.g., applied mathematics, biomedical engineering, cancer biology, genetics, insect science, neuroscience, physiological sciences, and statistics.

In addition, the University’s BIO5 Institute is designed to promote interdisciplinary research in the life sciences. Through its Quantitative Biology Consortium (QBC), (See http://bio5.org/research/research_qbc.php) BIO5 coordinates existing research and educational activities, as well as developing new initiatives in quantitative biology. The Consortium emphasizes approaches using mathematical modeling and experimental biophysics; statistics and biostatistics; and bioinformatics and biological computing. The QBC looks to support educational activities form kindergarten through postdoctoral education.

As a consequence, undergraduate educational activities at the interface of the life sciences and quantitative sciences have been developed and are being developed by researchers and educators with a long tradition of collaborative work.

In the past few decades, as interdisciplinary approaches become increasingly central in recent achievements in basic science, the research community has witnessed a significant change from traditional reductionist methods to a more holistic approach. The need to solicit expertise in engineering, the physical sciences and the quantitative sciences is being driven, in part, by advances in many fields including biological imaging, genomics, proteomics, and drug design. This fundamental change in perception by researchers is now impacting the educational emphases for the next generation of life scientists.

In response, the University of Arizona is conducting at least 5 endeavors in undergraduate interdisciplinary education.

1. HHMI Biomath. This project is designed to develop 3 semester long courses – one in integral calculus, one in differential equations, and one in statistics. These courses will begin in the fall of 2007 with an initial group of 25 biochemistry majors. These courses will be comparable in rigor to the courses traditionally taken by mathematics, physics, and engineering majors. Students who make this curricular choice can continue to earn a major or minor in mathematics. When these three course curricula and materials are set, used, and evaluated, we will look to integrate them in the university’s larger mathematics education goals and to expand the use of this course sequence beyond the initial scholarly interests. This project is funded by the Howard Hughes Medical Institute (2006 grant: 52005889).

2. Q-Bio: Integration of Quantitative Concepts into Introductory Biology. The broad goal of this project is to better prepare undergraduate biology students for successful participation in upper level biology courses and the increasingly quantitative work required by current careers in biology. The project works towards this goal by developing and refining student-learning modules for instructional use in introductory courses for biology majors. For example, the first module. Diffusion: Why are cells so small? is designed to demonstrate the role of diffusion in the movement of molecules within cells, and in constraining cell size. This program is funded in 2006 by a grant to the University of Arizona from the National Science Foundation (DUE-0633379).

3. Integrated Science Course. The Integrated science course has been approved (Physics 301) and will be taught in the spring semester of 2008. The course will be a combined lab and lecture course, meeting twice a week for three hour sessions in a chemistry laboratory equipped with computers and lecture space. Students will participate in four interdisciplinary science modules – protein folding, multiscale modeling, biological motion, and entropy. The course will feature multiple modes of inquiry – lecture, laboratory experiments, computer simulation, data collection and analysis, and “just in time” introduction to mathematics and computational tools.

4. Mathematical Modeling. The Department of Mathematics offers two courses in mathematical modeling. Mathematics 380 and Mathematics 485. Math 380, jointly taught with the ecology department, is designed primarily for life science students who have completed a year of calculus. Since 2002, Math 485 combines formal lectures with computer laboratories and simulations of dynamical systems and models. Undergraduates work in teams on modeling projects, under the supervision of graduate or post-graduate mentors. Each team writes a midterm and a final report and gives oral presentations of its work and presents their projects in a poster session held in a public venue. For more details, go to http://math.arizona.edu/~lega/485-585/mh.html . The course was developed with support from TRIF (Technology and Research Initiative Fund) of the University of Arizona.

5. Interdisciplinary Undergraduate Biology Research Project. The Interdisciplinary Biomedical Research Program for Undergraduates in the Quantitative and Physical Sciences and Engineering, established in 2005, (https://ubrp.arizona.edu/interdisciplinary/default.cfm) enables undergraduate students majoring in engineering, mathematics and the physical sciences to apply their knowledge to biologically and biomedically related problems. To date 29 students have participated. Some students are involved for multiple years and this is encouraged. Thirteen (45%) were engineering majors, 10 (34%) were mathematics majors, 4 (14%) were computer science majors, and 2 (7%) were physics majors. While it is too soon to tell what impact this program will have on the educational and career paths of participants, faculty mentors found the students’ quantitative skills to be very useful in advancing their research agendas. This program is funded by a grant to the University of Arizona from the National Institutes of Health (# 1 R25 GM072733) and BIOS.

University of Delaware

Stimulating Attitudes of Enquiry is the theme that has permeated our Howard Hughes Medical Institute Undergraduate Science Education initiatives since 1992. Faculty, regardless of their discipline, ask “How can I get my students to think?” Problem-based learning (PBL) is an instructional method that challenges students to “learn to learn,” working cooperatively in groups to seek solutions to real world problems. These problems are used to engage students’ curiosity and initiate learning the subject matter. PBL prepares students to think critically and analytically, and to find and use appropriate learning resources. Starting in 1994 with an NSF grant and with subsequent assistance from HHMI, FIPSE, and the PEW Charitable Trusts, the University of Delaware has become a leader in the implementation of PBL in undergraduate education. It provides multi-day workshops once or twice a year through the Institute for Transforming Undergraduate Education <http://www.udel.edu/inst/>. PBL problems are available through a password-protected site accessible to instructors at: <https://chico.nss.udel.edu/Pbl/>. Samples of PBL course syllabi and links to PBL-related materials are available at: <http://www.udel.edu/pbl/>.

To stimulate attitudes of enquiry we have extensively revised our biology curriculum. This has included an emphasis on real-time data collection and basic statistical analyses in introductory biology laboratories and the development of Investigative Laboratories in Ecology, Physiology, Cell Physiology, Molecular Biology and Genetics. Our current initiative is focused on developing a student appreciation for the value of quantitative analysis. We are proceeding on four major fronts:

• Introductory calculus: To bring more mathematical rigor to the Biological Sciences major, we are offering a special section of our most comprehensive first semester calculus course for those students interested in the life sciences. This special section covers the same mathematical topics required by Engineering, Physics, Chemistry and Mathematics majors, but the material is motivated by processes in the life sciences. For instance, rather than introducing differentiation as a means of relating forces and accelerations, we introduce derivatives as changes in concentrations or thermal energy flux. To support student learning across the disciplines, the new lecture includes high-quality problems that integrate biology and mathematics. Faculty members from Biological Sciences, Biochemistry, Chemical Engineering, and Mathematics are collaborating on module and course design.

• Math Fellows: To strengthen further the connection between biology and mathematics, we have created Math Fellow positions to aid faculty in the Introductory and Core Investigative Laboratories. These upper level math majors help biology students understand how to analyze data collected from their experiments and develop simple mathematical models to help explain their results.

• Bioinformatics Minors: For math majors who want more intense training in biology or for biology majors who want more intense training in database design, we have developed two minors. Both these minors require the student to participate in interdisciplinary undergraduate research.

• Quantitative Biology Major: We have created an interdisciplinary major program in Quantitative Biology leading to the Bachelor of Science degree. The major provides a strong background in mathematics, biology, chemistry and physics appropriate for students who wish to pursue a career or graduate studies the biomedical and life sciences. The major requires students to attend interdisciplinary lecture and seminar courses each year, complete a newly developed course in Systems Biology, and to participate in research leading to a senior thesis.

   
   

University of Florida

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 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 a new HHMI Core Laboratory.

The course, MAC4930 “Mathematical methods in the natural sciences” is a 3 credit, one-semester course that will be taught in association with the Science-for-Life core laboratory. The core laboratory is an integrated sequence of advanced early-undergraduate laboratory courses that covers physics, chemistry, and biology in an integrated fashion, in a new state-of-the-art laboratory located in the UF Health Science Center. MAC4930 adds a fourth discipline – mathematics – to this integrated program.

MAC4930 is a calculus-level, MATLAB-based introduction to mathematical modeling and quantitative/statistical analysis of data. The course will cover the following topics:

Data representation – discrete (vectors & matrices), continuous (functions), graphical (plots, histograms), vectors spaces, metrics, complex numbers

Data analysis – averages, variance & covariance, errors, noise

Probability and statistics – probability distributions, random variables, conditional probability, independence, correlation, confidence, likelihood, linear regression, least squares

Linear models – stochastic (transition probabilities, random walks) and deterministic (exponential growth and decay)

Linear algebra – solving linear systems, matrix operations, linear transformations, projections, eigenvalues & eigenvectors

Nonlinear deterministic models – positive & negative feedback, predator-prey, logistic growth, enzyme kinetics, homeostatic regulation, linearization, dynamical systems

University of Maryland

Since 2002, with support from a Howard Hughes Medical Institute Undergraduate Science Education grant, we have been developing a team-based approach to curriculum reform throughout the biological sciences at the University of Maryland. Teams consist of faculty, postdoctoral fellows and graduate students that are revising linked sequences of courses at all levels of our undergraduate curriculum, infusing them with current research approaches and increased emphasis on interdisciplinary connections. Two complementary efforts have been addressing the need for increased quantitative training for biology students. The first, MathBench, is developing web-based educational modules that introduce essential quantitative skills in introductory biology coursework, with the ultimate goal of helping students develop the skills necessary for careers in modern biology. These modules use humor, references to popular culture and interactive elements to engage students, but they also build upon the students’ intuitive understanding to help them explore biological concepts using fairly sophisticated mathematical approaches. The modules focus on ten major quantitative skills identified by University of Maryland faculty as being essential for a comprehensive understanding of modern biology. Twenty-six modules are already being developed and piloted in five fundamental biology courses (Introductory Biology: Cell and Molecular Biology, Introductory Biology: Ecology and Evolution, Introductory Biology: Organismal Diversity, Principles of Genetics, and General Microbiology).

The second initiative is the development of a new calculus and advanced mathematics course sequence for biology majors to replace our existing courses, which were originally designed for business and social sciences majors. The new two-semester sequence, to be piloted in 2007-2008, will introduce calculus using biologically-meaningful contexts, and will go beyond the typical calculus course to include a variety of other mathematical tools, such as probability theory, differential equations, and mathematical modeling, all of which are essential for understanding complex biological phenomena.

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.

University of Montana

The approach that we will employ in integrating more quantitative skills into our biology curriculum is a combination of new courses and revamped existing courses that, collectively, provide a breadth of material in Mathematics, Computer Science, Visualization and Modeling. These courses will be combined with our unified lower division curriculum and with more traditional upper division offerings to offer a defined Biology B.S. emphasis in Quantitative Biology. This elective will be recommended by our Biology Advising Office to those interested in pursuing advanced studies and careers in areas such as Disease Ecology, Climatology, Climate Change Ecology, Genetics and Evolution, and Biogeography.

While still in our first year of activity in this area, we have advanced far in defining our curricular goals. The courses that are planned for this Quantitative Biology emphasis are described briefly below in approximate order of the sequence in which they might be taken. Based on conversations with heads of other units, several of the courses will be cross-listed in other relevant departments.

Biology 110; Principles of Biology (existing course). BIOL 110 is one of the lower-division core courses and is generally taken in the spring semester of the freshman year. This course teaches essential concepts in the areas of genetics/molecular biology, evolution, physiology and metabolism and microbiology. Under the auspices of the previous HHMI grant, this course was revamped to include a mandatory laboratory component for all students (9 sections of 25 – 30 students). Included ion the lab exercises are a module on bacterial diversity that uses bacterial colony morphology classification to teach students to predict and calculate species richness estimates, species evenness estimates, and Shannon Weaver Diversity indices. Another module uses insect parasitism on invasive plants as a model for inter-species interactions and teaches students to perform some basic statistical analyses that are fundamental to ecology.

Biology 221; Cell and Molecular Biology is another of the lower-division core courses and is generally taken in the spring semester of the sophomore year. One of the faculty instructors is attending an NAS-HHMI workshop this summer to learn about advances in teaching Cell and Molecular Biology and plans to integrate some computational content into the curriculum and lab exercises (e.g. measuring and calculating mutation rates).

Computer Science 271; Programming for non-majors (new course). This course will be offered by the Computer Science Department and will teach fundamentals of computer programming to non-majors, especially promoting enrollment from biology majors. This course would represent an elective for biology majors (typically sophomore - junior). The course will teach relevant computer languages and fundamentals of programming for those engaged in biological studies. Assigned problems and exercises will focus on case studies and data sets from biology.

Computer Science/Biology 331; Bioinformatics (revamped course). This Computer Science course is being revamped to be more inclusive of biology majors and to not require programming skills that only a Computer Science major would have (as in its previous iteration). This Bioinformatics course is highly relevant to biology students interested in phylogenetics, diversity, evolution, and population genetics.

Biology/Math 395; Quantitative Biology (new course). This new course is being developed by and will be co-taught by two professors (Population Genetics and Applied Math) for offering this fall. The elective course will be targeted at biology students (junior-level) specifically wanting to employ more quantitative approaches into their preparation. The course will teach some of the fundamental statistical and computational tools that are widely used in the biological sciences using case studies and data from biology.

Math/Biology 414; Deterministic Models (revamped course). This is course introduces Biology and Math majors (junior- senior level) to comparatively simple mathematical models in biology. Considerable parts of the course are devoted to discussion of host-parasite systems, as well as to mathematical models of infectious diseases (susceptible-infected-recovered systems).

Biology/Microbiology 495; Phylogenetics and Evolution (revamped course for seniors and graduate students). This course on Phylogenetic and Evolutionary analysis relies heavily on tools of Bioinformatics such as genetic algorithms, PERL programming, pattern-matching and similarity analyses. The course will be further developed to include the conceptual principals that underlie the computational tools to develop a fuller appreciation of how they work and how they might be further manipulated to provide more analytical power.

Math 444/445; Statistical Methods and Data Analysis (existing course). These courses cover basic exploratory data analysis, one-sample and two-sample inferences, nonparametric methods, linear and nonlinear regression, and experimental design and analysis. Much of the course focuses on problems based in biology and ecology.

Math 549; Applied Sampling Methods (existing course). This graduate-level course will also accept advanced undergraduates (by permission of instructor). The course focuses on standard sampling designs (simple random, stratified, cluster, systematic, double sampling), ratio and regression estimation, and more modern sampling methodologies, such as transect sampling, distance sampling, detection functions, adaptive sampling, and spatial sampling.

University of Richmond

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:

• Math 231 Scientific Calculus I
• Math 232 Scientific Calculus II
• 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, and after researching modern uses of mathematical modeling in the sciences, we identified important mathematical topics that have been absent or underrepresented in standard calculus courses. These topics include

• 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.)
• more emphasis (than is typical in calculus courses) on worst-case error estimates and practical estimation
• responsible data set management, including regression techniques
• discrete probability
• linear algebra, as it relates to dynamical systems models
• modern and relevant examples and applications

To make room for these new topics, while keeping Scientific Calculus to two semesters, we did two things:

• 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.
• 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.
  Having found no text that adequately covers all of the topics, we decided to use the same book that is used in the general calculus sequence ( Calculus: Concepts and Contexts by James Stewart) heavily supplemented with handouts, computer labs, data sets, assignments, and examples for the science applications. In fact, approximately 40% of the material covered in the two semesters is not supported by our current text, so a great deal of supplementary material was needed. This course was offered for the first time during the 2005-6 academic year, and a substantially revised version was offered during 2006-7

This course 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:

• Biological control of pest populations
• Tumor growth dynamics
• Pharmacokinetics
• Models of chemotherapy
• Epidemiology
• Interacting populations
• Leukemia dynamics
• Immunology of the HIV virus
• Enzyme kinetics

The students, working in pairs, completed a final modeling project, in which they create, validate, analyze, and interpret an original model. Each pair presented their results in a written report, as well as an in-class presentation. For the Fall 2006 initial offering of this course, the project topics were:

• Antibiotic treatment of bacterial infections. This included the possibility of antibiotic-resistant mutations in the bacterial population, and the resulting dynamics.
• Drug dosing regimens. This project focused on developing a treatment plan for a patient that required periodic drug injections. It also expanded to include oral administration of the medicine.
• Spread of nosocomial (i.e. hospital) infections. This project includes an analysis of methods to control infection that is spread on medical instruments, as well as on the hands of healthcare workers. (The introduction to this project opens with the memorable line, “Hospitals are full of sick people.”)
• Dynamic instability of microtubules. This project, on certain cytoskeleton components, was proposed by the student team, consisting of two biochemistry/molecular biology majors.
   

BIOL 351: Bioimaging

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)
   

The 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).