The Integration of … Modeling, Statistics, Computation and Calculus at East Tennessee State University

1. The Integration of … Modeling, Statistics, Computation and Calculus at East Tennessee State University Jeff Knisley — East Tennessee State University Project Mosaic Kickoff Event – June 28, 2010

2. Integrative Projects at ETSU • Focus on What we have been up to • The Symbiosis Project • General Education Statistics Course • Quantitative Modeling Track of the Math Major • Later today / this week: Focus on How we’ve done what we done • (And just as valuable – What we’ve learned from what hasn’t worked)

3. Symbiosis: An Introductory Integrated Mathematics and BiologyCurriculum for the 21st Century (HHMI 52005872) • Team-taught by Biologists (6), Mathematicians (3), and Statisticians (1) • Biologists progress to needs for analyses, models, or related concepts (e.g., optimization) • A complete intro stats and calculus curriculum via the needs and contexts provided by the biologists • More Recently … extensive computational activities featuring R, Maple, and Netlogo

4. Goals of the Symbiosis Project • Implement a large subset of the recommendations of the BIO2010 report in an introductory lab science sequence • Semester 1: Statistics + Precalculus, Limits, Continuity • Semester 2: Calculus I course + Statistics (Our focus on Semesters 1 and 2) • Semester 3: Modeling, BioInformatics, reinforcement of previous ideas, More Statistics

5. Goals of the Symbiosis Project • Use Biological contexts to motivate mathematical and statistical concepts and tools • Analysis of data used to inform and interpret • Models and inference used to predict and explain • Use Mathematical concepts and Statistical Inference to produce biological insights • Insights often need to be quantified if only to predict the scale on which the insight is valid • Especially useful are insights that cannot be obtained without resorting to mathematics or statistics

6. Table of Contents • Symbiosis I and II • List of “modules” with topics selected by biologists • Mathematical and Statistical Highlights included(Not enough time to explore Symbiosis III) • Logistics: 5 + 1 format, student populations between 7 and 30, and 3 or 4 faculty per course

7. Symbiosis I The Scientific Method: Numbers, models, binomial, Randomization Test, Intro to Statistical Inference The Cell: Descriptive Statistics and Correlation Size and Scale: Lines, power laws, fractals, Poisson, exponentials, logarithms, and linear regression Mendelian Genetics: Chi-Square, Normal, Goodness of Fit Test, Test of Independence DNA: Conditional Probability, the Markov Property, Sampling distributions Proteins and Evolution: Limits, continuity, approximations, and the t-test

8. Symbiosis II Population Ecology: Derivatives, Rates of Change, Power, Product, Quotient rules, Differential Equations Species-Species Interactions: Chain rule, Properties of the Derivative, Differential Equations Qualitatively, Equilibria, Parameter Estimation Behavioral Ecology: Optimization, curve-sketching, L’hopital’s rule Chronobiology: Trigonometric functions and their derivatives, Periodograms Integration and Plant Growth: Antiderivatives, Definite Integrals, and the Fundamental Theorem Energy and Enzymes: Applications of the Integral, differential equations methods, Nonlinear Regression

9. Major Outcomes • Complete and/or Comprehensive Biological Investigations • Traditional Bio Curriculum: Biological questions pursued to a point short of quantitative analysis • Symbiosis: Data and Models used to explore biological questions and predict answers • Mendelian genetics via chi-square analysis of data • rK strategists based on logistic model and importance/stability of equilibria

10. Aspects of Integration • Biologists need or can use almost all the math and stats we can provide • But their goals are radically different • Statistical inference as a tool for justifying classification of organisms into different categories • Models as a means of separating different phenomena • And the results are used to address their (often non-quantitative) questions • E.g.: Simple epidemiological models used to suggest whether or not mosquito’s can carry the aids virus

11. Aspects of Integration • Statisticians and Mathematicians can contribute to biology in a variety of ways • But transparency is paramount • Examples of concepts/techniques “Transparent” to our biologists: The Randomization test, p-values, normal distribution, Chi-square, Periodograms, logarithms, power laws, Nonlinear Regression, phase-plane analysis • Examples of concepts/techniques that are NOT “Transparent” to our biologists: the limit concept, the exponential function, Poisson distribution, conditional probability, t-test, degrees of freedom

12. Aspects of Integration • Statisticians and Mathematicians can contribute to biology in a variety of ways • And time/effort must be devoted to important subtleties – within biological contexts • Example: Logarithms and exponentials with base e. (Why not just use base 10 for everything?) • Example: Number of offspring, which is an important bio-quantity – as Poisson-distributed • Example: The approximation (1+x)n≈ enx occurs in numerous applications and contexts in biology, but it takes a long time before it “sinks in”

13. Observation • Issues preventing “downstream” usage of math and stats • Start as small issues at the most elementary levels • Nearly all of module 1 addresses the difference between a scientific hypothesis and a statistical hypothesis • Surface area to volume ratio: First we must agree on notation (i.e., A or S or SA or … ). • And grow into major obstacles • If insufficient time spent developing the hypotheses, result may be “Doing the test” without really knowing what they are testing. • E.g.: If time is not spent exploring what a biologist means by a population density, ecological models may become impossible to interpret biologically.

14. Further Insights • Computing and Computational Science have emerged as major components • Informatics, genetics, proteomics, … • And Even in Ecology! • Programming in R • Need is for math/stat informed algorithms • Not for elaborate structures or sophisticated programming languages

15. Further Insights • Logistics are a challenge • Transcripts are important!!! • Course sizes / delivery methods differ significantly • Biology lectures can be huge • Biology labs are typically smaller than math/stat sections • (I had never had to consider how to combine a lab grade with a lecture grade) • Communication is very important, especially about the “little issues” that tend to grow

16. Future Directions for Symbiosis • More emphasis on computation • Algorithms as method to address biological inquiries • Algorithms as statistical tools • Inference via bootstrapping, • Predictions via clustering • Informatics • Avoiding reliance on “off-the-shelf” approaches • Symbiosis IV: A Gen Ed “Intro to Computational Science” course for math and bio majors

17. General Education Statistics • In 1996, ETSU began requiring every non-calculus student take an introductory statistics course in their first year • To enable students to understand and participate in a data-driven world • To prepare students for the stats they would see in their respective majors • In 2001, the Gen Ed Stats course moved into the “Stat Cave” – a 45 station computer lab • To make the course technology-driven and data-intensive • Approx 1200 students per semester (100 in summer) continuously using Minitab, applets, etc.

18. math.etsu.edu/stats/

19. Some Features of the Course • Teaching multiple sections • Extensive training of instructors • Highly structured course content • Online/Off-campus sections may use calculators for some activities • Two part Final Exam • A comprehensive data analysis project due the week before the in-class Final Exam • A standardized M/C final exam common to all sections of the course

20. Quantitative Modeling Track in the Math Major • In conjunction with our Statistical Literacy and Quantitative Biology emphases • Features many different modeling courses • Statistical modeling • Mathematical modeling • Predictive modeling (data mining, machine learning) • Survival models (with computational emphasis) • Computational/Discrete Modeling • (students take 2 to 4 of these) • Future: Integrate with other sciences, Public Health, Medicine, Pharmacy, etcetera…

21. Thank you! Any questions