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Undergraduate Research in
Mathematical Biology: A Collaboration
Between ASU and SCC
John Nagy (SCC) and Yang Kuang (ASU)
ECMTB/SMB, Dresden, Germany
July 18, 2005
ASU Program Directors
Carlos Castillo-Chaves
J. Marty Andries
Dept. Mathematics
and Statistics
School of Life
Sciences
ASU PIs/Mentors
Hal Smith
Ron Rutowski
Dept. Mathematics
and Statistics
School of Life
Sciences
Yang Kuang
Dept. Mathematics
and Statistics
SCC Program
Director
Jim Elser
School of Life
Sciences
John Nagy
Dept. Life Sciences
Program Objectives
1) Formulate and implement a well structured multi-year long
undergraduate mathematical/quantitative biology program.
2) Provide first-class practical training for ASU and SCC
undergraduates pursuing research posts in theoretical and
mathematical biology.
3) Provide training in theoretical and mathematical biology
for students pursuing posts in empirical or clinical biology.
4) Support ASU’s graduate program in mathematical biology
by providing graduate students opportunities to mentor
undergraduates.
UBM Program Organization
Formal
Coursework
Summer
Workshops
Graduate
Student
Mentoring
ASU
Program
Formal
Coursework
SCC
Program
“Mini-Thesis”
Research
Project/Thesis
SCC Course Curricula
BIO 198—Introduction to Research in Biology (2 cr.)
Prerequisites:
General Biology for Majors I (BIO 181 or 187)
Algebra/Functions/Structures (MAT 122 or141 or 151)
Course Objectives:
1) Ethics in research
2) Using literature to answer specific questions
3) Empirical research methods—experiments and surveys
4) Theoretical research methods—mathematical and computer
modeling
BIO 198 Course Outline
Ethics:
Case studies
Using the literature:
Read and discuss primary research and review articles
Group activity—find numbers (e.g., lymphocyte reproduction
rate, ion flux through membrane channel, etc)
Independent project—Write short literature review on approved
topic (continuing, in support of mini-thesis).
BIO 198 Course Outline
Empirical research:
Read and discuss example of a fully crossed, factorial design experiment from
the primary literature
Read and discuss example of a survey study
Group activity—Design study to test efficacy of fad diet
Group activity—Design study to determine if chemistry prerequisite is
required for Gen. Bio. for Majors I.
Theoretical research:
Introduce discrete-time and continuous time population models—Logistic,
Lotka-Volterra competition and predation
Group activity—study population genetics model
Group activity—study model of cardiovascular system (computer)
Read and discuss literature—mathematical models of tumor growth
SCC Course Curricula
BIO 298—Introduction to Theoretical Biology
Prerequisites:
Introduction to research in biology (BIO 198)
First semester calculus (MAT 220)
Course Objectives:
1) Introduction to theory
2) Applications of difference/differential equations to biology
3) Applications of stochastic processes to biology
BIO 298 Course Outline
Introduction to theory:
Case studies—What does a theoretician do?
Read and discuss primary empirical and theory papers.
Study and discuss a computer-based model
Read and discuss a wicked-ish analysis paper
Difference/Differential equations:
Case studies—Building a dynamical system model
Activity—Build your own model (1 dimension, assigned topic)
Activity—Build your own model (2+ dimensions, assigned topic)
Discuss the concept of a solution to the above models
Introduction to the phase space
Activity—Find nullclines and general behavior of 2-D systems
BIO 298 Course Outline
Stochastic Processes:
Case studies—Need for models based on probability
Introduction to basic definitions and properties of randomness
Activity—Model sex ratio as Bernoulli process, compare to Laplace’s data
Mini-Thesis
Requirements:
Literature review
Study must include analysis of a model, usually by computer of an alreadyexisting model
Study must have a novel component
Student must produce a standard thesis-style document
Student must present thesis either as poster or talk, in any approved venue
UBM Program Organization
Formal
Coursework
ASU
Program
Formal
Coursework
SCC
Program
“Mini-Thesis”
ASU Course Curricula
BIO/MAT 2xx: Numeracy in the Life Sciences*
Lectures presented by several ASU faculty
Associated computer-aided activities
Minimal hands-on mathematics—lots of reading, writing, synthesis
Designed to convince traditional biology undergrads that mathematics is
useful and enjoyable and traditional math undergrads that biology is
a great playland.
BIO/MAT 35x: Mathematical models in biosciences*
Construction and interpretation of models in ecology, epidemiology, genetics
Introduce simple, standard difference and differential equation models
Numerical methods and simulation
Introduction to local stability analysis
ASU Course Curricula
BIO/MAT 35y: Advanced mathematical models in
biosciences*
Dynamical systems theory applied to biological problem-solving
Probability theory and stochastic processes
Game theory
Intermediate to advanced techniques in MatLab and Maple
Gateway to a guided research project
BIO/MAT 424: Mathematical models in ecology
Predator/prey dynamics
Host-parasite and host-parasitoid dynamics
Population dynamics in fluctuating environments
Evolutionary dynamics
Natural resource management
ASU Course Curricula
BIO/MAT 450: Topics in mathematical biology
Advanced and current applications of mathematics in biology
Curriculum varies with expertise of instructors and guest lecturers
BIO/MAT 591: Topics in computational biology
Comparison of biological sequences
Phylogeny reconstruction
Prediction of RNA and protein structural/functional biology
UBM Program Organization
Formal
Coursework
Summer
Workshops
ASU
Program
Formal
Coursework
SCC
Program
“Mini-Thesis”
Summer Workshops
Summer Workshop Options:
Los Alamos with Carlos
ASU with
Marty and Yang
Summer Workshops
Format:
Taken by students just entering the program or finishing their first year
Students meet 2 hours per day, 5 days per week for 8 weeks total
MWF – Skill building taught by graduate students
Introduce DEs, phase plane methods, stability analysis
Discrete-time dynamical systems
Stochastic processes
Computer applications in MatLab, XPP (WinPP), Maple
Introduction to standard mathematical models in biology
Summer Workshops
TTh – Survey lectures taught by faculty
Predator-prey dynamics (Kuang)
Bioeconomics models (Anderies)
Nutrient stoichiometry in ecology (Elser)
Microbial growth and the chemostat (H. Smith)
Stochastic models in molecular biology (Nagy)
Last 2 weeks—Student presentations
20-30 minutes long
Presenting research proposal for guided research project, or previous results
UBM Program Organization
Formal
Coursework
Summer
Workshops
ASU
Program
Formal
Coursework
SCC
Program
“Mini-Thesis”
Research
Project/Thesis
Guided Research Projects
1-2 years plus 1 summer
Mentoring:
One faculty member in Biology
One faculty member in Mathematics
At least one graduate student in either mathematics or biology
When appropriate, learning community with advanced undergraduates
Requirements:
Develop integrative research question and plan with primary mentor
Conduct research program guided by mentors
Produce a research report in style suitable for publication
Quality of research report must satisfy faculty mentors
Students are encouraged to present their research at undergraduate conferences
UBM Program Organization
Formal
Coursework
Summer
Workshops
Graduate
Student
Mentoring
ASU
Program
Formal
Coursework
SCC
Program
“Mini-Thesis”
Research
Project/Thesis
Graduate Student Mentoring
Develop curriculum for summer skill-building exercises
Active mentoring of undergraduate research projects
Assessment
Planning evaluation and assessment procedures in coordination with strong
mathematical education community at ASU
Annual evaluations of course work, summer workshops and mentoring by
students and faculty
Staff support for database on participants and subsequent success:
How many under-represented minorities completed at least one year of the
UBM program, and comparison of how they perform on end-of-year math
reasoning test compared to pre-test given during recruitment
How many continue in second year in this or similar program?
How many complete bachelor’s degrees within 4 years?
How many enter graduate or medical school, or obtain relevant
employment?