# Biology and the Quantitative Sciences

Listed below are links to exemplary courses and other initiatives designed to educate undergraduates about the connections between biology and mathematics, statistics, and computer science.

## Bibliography

BIO2010: Transforming Undergraduate Education for Future Research Biologists, National Academies Press

http://www.nap.edu/catalog/10497.html

## Introductory Courses

### Introductory Mathematics and Applied Mathematics Courses that Replace/Revise Standard Calculus

*University of California, Davis
Calculus for Biology and Medicine (MAT 17A/17B/17C)*

This year-long, three-quarter sequence of courses provides an introduction to differential calculus via applications in biology and medicine. It covers important topics such as limits, derivatives of polynomials, trigonometric, and exponential functions, graphing, and applications of the derivative to biology and medicine. Each course requires a three-hour lecture and a one-hour discussion section. It currently uses the text Calculus for Biology and Medicine (Prentice Hall, 2nd edition, 2003).

Target Audience: Prospective majors in biology and other biologically related fields

Prerequisites: Two years of high school algebra, plane geometry, plane trigonometry, and analytical geometry, and satisfaction of the Mathematics Placement Requirement.

http://www.math.ucdavis.edu/courses

Contact: Vice Chair for Undergraduate Matters, Department of Mathematics, vicechair-undergrad@math.ucdavis.edu

*University of Tennessee
Mathematics for the Life Sciences (MATH 151/152)*

This year-long sequence provides an introduction to a variety of mathematical topics of use in analyzing problems arising in the biological sciences. The general aim is to show how mathematical and analytical tools may be used to explore and explain a wide variety of biological phenomena that are not easily understood with verbal reasoning alone. The course has an accompanying computer laboratory component where students use the software packages Matlab and Maple for their assignments.

Target Audience: Undergraduates in biology, agriculture, forestry, wildlife, pre-medicine and other pre-health professions. (Not for students who desire a strong mathematical grounding and who plan to take more advanced math courses.)

Prerequisites: 2 years of high school algebra; 1 year of geometry; half a year of trigonometry.

http://www.tiem.utk.edu/~gross/math151.html

http://www.tiem.utk.edu/~gross/math152.html

Contact: Louis J. Gross, Professor of Ecology and Evolutionary Biology and Mathematics, gross@tiem.utk.edu

### Other Introductory Mathematics Courses

*University of California, Davis
Applied Statistics for Biological Sciences (STA 100)*

The one-quarter course introduces biology majors to applied statistics. It covers such topics as probability computation/modeling, estimation, hypothesis testing, contingency tables, ANOVA, regression, and implementation of statistical methods using computer packages. It currently uses the text Statistics for the Life Sciences (Third Edition). Course completion can satisfy general education requirements in science and engineering.

Target Audience: Majors in biology and other biologically related fields.

Prerequisites: Second-quarter calculus.

http://www.stat.ucdavis.edu/courses/

Contact: Christiana Drake, Associate Professor and Undergraduate Advisor, Department of Statistics, drake at wald.ucdavis.edu

*University of South Carolina
Mathematical Modeling for the Life Sciences (MATH 172)*

This one-semester course is less concerned with the mechanical aspects of computation and more concerned with why we want to do these calculations. Students form a mathematical model of a changing real world situation, use a variety of methods to analyze it, and then interpret the calculated results in the context of the original problem. Students solve problems by using a blend of numerical, graphical, and analytic methods (manipulation of formulas), and then communicate the solutions effectively, both in writing and orally.

Target Audience: Anyone, particularly biology majors, who have taken the first semester of calculus and desire (require) a second calculus-level mathematics course.

Prerequisites: A grade of C or better in the first semester of calculus.

http://www.math.sc.edu/~miller/172/

Contact: Douglas B. Meade, Undergraduate Director of Mathematics, Dept. of Mathematics, (803) 777-6183, meade@math.sc.edu; Matt Miller, Professor, Dept. of Mathematics, (803) 777-3690, miller@math.sc.edu

### Introductory Science Courses

*University of California, Davis
Modeling in Biology (BIS 20Q)*

This two-unit course introduces students to quantitative concepts and techniques using Mathcad, a software tool that can be used to do routine computations and modeling. The course centers on downloadable modules that have to be completed by the student every week. Class meetings consist of weekly lectures and optional two-hour computer labs. The modules themselves present biological problems that require quantitative thinking.

Target Audience: Majors in biology and other biologically related fields.

Prerequisites: Completion of, or concurrent enrollment in, second-quarter calculus.

http://quantbio.ucdavis.edu/courses.html (includes downloadable example modules)

Contact: Carole Hom, Academic Coordinator, Biological Invasions IGERT and Quantitative Biology, Department of Biological Sciences, clhom at ucdavis.edu

*Utah State University
Integrated Life Science (USU 1350)*

This interdisciplinary course focuses on basic concepts of life science. It demonstrates the role of modeling, prediction, and observation in the process of scientific discovery, which occurs within an historical and social context. The course fulfills the university's General Education Life Sciences Breadth Requirement.

Target Audience: Non-science majors.

Prerequisites: None.

http://www.uintahbasin.usu.edu/riche/live1350opener.htm

Contact: Richard Etchberger, Associate Professor, Natural Resources, (435) 789-6100, richarde@ext.usu.edu

### Other Introductory Courses

*Stony Brook University
Laboratory Methods in Biomedical Engineering (BME 212)*

This course provides students with the opportunity to gain insight into the research process in biomedical engineering, the result of which may lead to scientific discoveries and technological advances. The class relies heavily on hands on experience and uses laboratory experiments to teach experimental design as well as the collection, analysis, interpretation, and presentation of data. Importantly, the design of all labs is discovery-based rather than purely instruction-based. Particular emphasis is placed on the statistical analysis of the collected data. The course also provides students with the opportunity to write and defend reports based on the laboratory work, consistent with formats and standards found in scientific journals in biomedical engineering.

Target Audience: Biomedical Engineering sophomores.

Prerequisites: 1 semester of calculus; 1 semester of freshman biology; 1 semester of biomedical engineering.

http://www.bme.sunysb.edu

http://bme.sunysb.edu/bme/ugrad/courses.html

Contact: Stefan Judex, Assistant Professor in Biomedical Engineering, (631) 632-1549, stefan.judex@sunysb.edu

## Advanced Courses

### Advanced Courses in Computational Biology, Undergraduate

*University of California, Davis
Theory and Practice of Bioinformatics (ECS 124)*

This course focuses on the fundamental biological, mathematical, and algorithmic models underlying bioinformatics. Students will learn a set of common bioinformatics tools, such as sequence analysis, database search, gene prediction, molecular structure comparison and prediction, phylogenetic trees, high throughput biology, massive datasets. Topics will include biological applications in molecular biology and genetics.

Target Audience: Majors in biology and other biologically related fields, or minors in quantitative biology and bioinformatics

Prerequisites: One computer programming course, one statistics course, one introductory biology course, some calculus.

http://www.cs.ucdavis.edu/courses/exp_course_desc/124.html

Contact: Daniel M. Gusfield, Professor of Computer Science, gusfield at cs.ucdavis.edu

*University of Pennsylvania
*

*Computational Biology (BIOL 536/CIS 535)*

Advanced Computational Biology (BIOL 537/CIS 635)

Advanced Computational Biology (BIOL 537/CIS 635)

This two-semester sequence provides a rigorous hands-on introduction to the biological side of computational biology. It covers fundamentals of algorithms, statistics, and mathematics as applied to biological problems. Particular emphasis is given to biological problem modeling and theoretical perspectives. Students are expected to learn basic algorithm principles, basic mathematical and statistical proofs, and molecular biology. Lectures are supplemented with demonstrations and computer laboratory assignments. The course is team-taught by faculty from Biology, Computer & Information Sciences, and the Center for Bioinformatics.

Target Audience: Computer science and engineering students who require a better grasp of molecular biology and bioinformatics and biology students interested in becoming skilled users of molecular genetic analysis applications.

Prerequisites: College level introductory biology; undergraduate or graduate level statistics; molecular biology and/or genetics (encouraged); familiarity with computers (encouraged).

http://www.bio.upenn.edu/courses/S01/BIOL536/

http://www.bio.upenn.edu/courses/S04/BIOL536/

http://www.bio.upenn.edu/courses/F02/BIOL537/

Contact: Warren Ewens, Professor of Biology, (215) 898-7109, wewens@sas.upenn.edu

### Advanced Courses in Mathematical Biology, Undergraduate

*University of California, Davis
Mathematical Biology (MAT 124)*

This quarter-long course focuses on the methods of mathematical modeling of biological systems including such topics as difference equations, ordinary differential equations, stochastic and dynamic programming models. Students will also learn computer simulation methods as applied to biological systems. Biological applications will cover population growth, cell biology, physiology, evolutionary ecology, and protein clustering.

Target Audience: Majors in biology and other biologically related fields

Prerequisites: Knowledge of a computer language or Matlab, one year of calculus, and differential equations.

http://www.math.ucdavis.edu/courses

Contact: Vice Chair for Undergraduate Matters, Department of Mathematics, vicechair-undergrad@math.ucdavis.edu

*University of Washington
Techniques for Mathematical Biology (BIOL 428)*

This course equips students to use, rather than prove, many applied mathematics techniques essential in mathematical biology. Students use symbolic computation software (Mathematica, Macsyma) to do by computer the kind of mathematical formula manipulation that mathematicians formerly performed by hand.

Target Audience: Biology majors.

Prerequisites: Calculus (recommended); linear algebra (recommended).

http://www.washington.edu/students/crscat/biology.html

Contact: Garrett M. Odell, Professor, Dept. of Biology, Center for Cell Dynamics, Friday Harbor Laboratories, (206) 616-0895, odellgm@u.washington.edu

*Utah State University
Applied Mathematics in Biology (BIOL/MATH 4230)*

This capstone course for the BioMath Minor is team-taught by faculty in the Departments of Biology and Mathematics & Statistics. The course revolves around formulation, analysis, and experimental tests of mathematical models in biology. Students use mathematical, computational and statistical approaches to investigate biological problems in theoretical and laboratory settings. The goals are to illustrate the importance of dynamical concepts in real-world, especially biological, circumstances, to discover some of the important mathematical results which apply to biological situations, to give students as realistic an experience as possible in interdisciplinary mathematical science, and to provide a scientific experience in which the primary aim is quality of output, not quantity.

Target Audience: Bio-Mathematics minors.

Prerequisites: 2 semesters of biology; 1 semester of linear algebra/differential equations; programming experience (recommended).

http://www.math.usu.edu/~powell/biomath/index.html

Contact: James W. Haefner, Professor, Dept. of Biology and Ecology Center, (435) 797-3553, jhaefner@biology.usu.edu; James Powell, Professor, Dept. of Mathematics & Statistics, (435) 797-1953, powell@math.usu.edu

### Advanced Courses in Modeling, Undergraduate

*North Carolina State University
Mathematical Models in Life and Social Sciences (MA 432)*

This course includes topics from differential and difference equations, probability, and matrix algebra applied to the formulation and analysis of mathematical models in biological and social science (e.g., population growth).

Target Audience: Primarily mathematics majors, but others are welcome.

Prerequisites: 1 semester of differential equations; 1 semester of linear algebra; programming language proficiency.

Corequisites: 1 semester of probability.

http://www2.acs.ncsu.edu/reg_records/crs_cat/MA.html#MA432

Contact: Mette Olufsen, Assistant Professor, Dept. of Mathematics, msolufse@math.ncsu.edu

*University of California, Davis
Introduction to Dynamic Modeling in Biology (BIS 132)*

This course gives an overview of models based on the notion that biological entities change over time. It will cover various approaches for dynamic modeling in the biological sciences, including matrix models, difference equations, and differential equations and simulation, with emphasis on understanding the models, their assumptions, and implications.

Target Audience: Majors in biology and biologically related fields, or minors in quantitative biology and bioinformatics.

Prerequisites: One year of calculus and at least one class in biology.

http://biosci.ucdavis.edu/undergrad/minors/qbb/courses/BIS_132.html

Contact: Carole Hom, Academic Coordinator, Biological Invasions IGERT and Quantitative Biology, Department of Biological Sciences, clhom at ucdavis.edu

*University of Minnesota
The Modeling of Nature and the Nature of Modeling (EEB 3963/5963)*

This course provides hands-on modeling experiences in the context of biological applications. Students carry out modeling steps, from developing the model, to analytical analysis, to developing computer code, to running the models.

Target Audience: Prospective biology majors and beginning biology graduate students.

Prerequisites: 1 year of calculus including some familiarity with differential equations.

http://cbs.umn.edu/class/fall2003/eeb/3963/

Contact: Claudia Neuhauser, Professor, Head, and Director of Graduate Studies, Ecology, Evolution, and Behavior, (612) 624-6790, cneuhaus@cbs.umn.edu

### Other Advanced Courses, Undergraduate

*Stony Brook University
Linear Systems Analysis with Biomedical Applications (BME 461)*

The goal of this course is to offer students an opportunity to learn and model and simulate static and dynamic physiological systems using linear systems theory. Simulations and estimation are performed using Matlab and already developed software.

Prerequisites: 1 semester of Laboratory Methods in Biomedical Engineering; 1 semester of Bioelectricity.

http://www.bme.sunysb.edu

http://bme.sunysb.edu/bme/ugrad/courses.html

Contact: Ki H. Chon, Associate Professor of Biomedical Engineering, Physiology & Biophysics, Dept. of Biomedical Engineering, (631) 444-7286, ki.chon@sunysb.edu

## Research Opportunities

*University of California, Davis
Collaborative Learning at the Interface of Mathematics and Biology (CLIMB)*

The NSF-funded CLIMB program emphasizes hands-on training using mathematics and computation to answer state-of-the-art questions in biology. Davis juniors in mathematical and biological sciences can participate in a paid, year-long research experience, which includes coursework, seminars, and mentoring during the academic year and full-time collaborative research during the summer. CLIMB trainees enroll in a series of courses in quantitative techniques, biological modeling, and research methods that give them a foundation for applying these techniques to real biological problems in the research lab.

http://climb.ucdavis.edu/

## Links to Other Resources

*University of North Carolina at Chapel Hill
Bioinformatics Programs Summary*

This page lists summaries of the major bioinformatics programs that are currently operating in the United States.

http://ils.unc.edu/bmh/bioinfo/bioinformatics_programs_summary

*BioQUEST Curriculum Consortium*

This consortium works for the reform of undergraduate biology.

http://www.bioquest.org/

*Program in Mathematics and Molecular Biology (PMMB)*

A multi-university interdisciplinary national research and training
consortium whose goal is the continued expansion of the applications of
mathematics to molecular biology.

http://www.math.fsu.edu/~pmmb/

*University of Tennessee
Quantitative Education for Life Scientists*

The goal of this NSF-supported project is to produce a curriculum of quantitative courses for undergraduate life science students. These quantitative courses integrate with the biological courses and utilize examples from recent biological research. The two main components of this project include: an entry-level mathematics for the life sciences sequence that incorporates a diversity of mathematical concepts in a biological context (MATH 151/152), and a set of more than 50 modules designed to enhance the quantitative components of the entry-level general biology sequence. This project appears as a case study in the BIO2010 Report.

http://www.tiem.utk.edu/bioed/

Contact: Louis J. Gross, Professor of Ecology and Evolutionary Biology and Mathematics, gross@tiem.utk.edu