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Undergraduate Research in Mathematical Biology: A Collaboration Between ASU and SCC

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. J. Marty Andries. Carlos Castillo-Chaves. Yang Kuang. School of Life Sciences.

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Undergraduate Research in Mathematical Biology: A Collaboration Between ASU and SCC

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  1. 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

  2. ASU Program Directors J. Marty Andries Carlos Castillo-Chaves Yang Kuang School of Life Sciences Dept. Mathematics and Statistics Dept. Mathematics and Statistics ASU PIs/Mentors SCC Program Director Hal Smith Ron Rutowski Jim Elser Dept. Mathematics and Statistics School of Life Sciences John Nagy School of Life Sciences Dept. Life Sciences

  3. 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.

  4. UBM Program Organization ASU Program SCC Program Formal Coursework Formal Coursework Summer Workshops “Mini-Thesis” Graduate Student Mentoring Research Project/Thesis

  5. 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

  6. 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).

  7. 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

  8. 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

  9. 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

  10. BIO 298 Course Outline 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 already-existing 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

  11. UBM Program Organization ASU Program SCC Program Formal Coursework Formal Coursework “Mini-Thesis”

  12. 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

  13. 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

  14. 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

  15. UBM Program Organization ASU Program SCC Program Formal Coursework Formal Coursework Summer Workshops “Mini-Thesis”

  16. Summer Workshops Summer Workshop Options: ASU with Marty and Yang Los Alamos with Carlos

  17. 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

  18. 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

  19. UBM Program Organization ASU Program SCC Program Formal Coursework Formal Coursework Summer Workshops “Mini-Thesis” Research Project/Thesis

  20. 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

  21. UBM Program Organization ASU Program SCC Program Formal Coursework Formal Coursework Summer Workshops “Mini-Thesis” Graduate Student Mentoring Research Project/Thesis

  22. Graduate Student Mentoring Develop curriculum for summer skill-building exercises Active mentoring of undergraduate research projects

  23. 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?

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