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Incorporating Biology into Math Courses at the University of Richmond

Discover how the University of Richmond incorporates biology into math courses, including new courses on Scientific Calculus and Biomedical Modeling, to help science students understand the role of math in scientific investigation. Learn about the development process, topics covered, and the importance of relevant illustrations and examples.

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Incorporating Biology into Math Courses at the University of Richmond

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  1. Incorporating Biology into Math Courses at the University of Richmond Lester Caudill Kathy Hoke University of Richmond Department of Mathematics and Computer Science lcaudill@richmond.edu khoke@richmond.edu

  2. New Math Courses at UR • Two-semester science-based calculus: Scientific Calculus I – II • One-semester Upper-division biomedical modeling course: Mathematical Models in Biology and Medicine

  3. Main Goals • Sci Calc: • Rethink and revise course content to underscore relevance to the sciences • Help science students understand and utilize the role of math modeling in scientific investigation • Modeling: • Teach students to construct and analyze math models of scientific processes

  4. Development of Sci Calc • Step 1:Identify the most relevant math topics for the sciences • Step 2: Make some room in our mainstream two-semester calculus sequence • Step 3: Fill resulting room with new topics (from Step 1), and organize in a logical and coherent order

  5. Step 1: Absent/Underrepresented Topics • Consultation with science faculty AND • Researching modern uses of math modeling in the sciences LED TO • Some changes

  6. Step 1: Absent/Underrepresented Topics • Multivariate calculus

  7. Example: Chemical reaction data S2O82- + 2I-→ 2SO42- + I2

  8. Step 1: Absent/Underrepresented Topics • Multivariate calculus • More emphasis on worst-case error estimates and practical estimation • Responsible data set management, including regression techniques • Discrete probability • Linear algebra and dynamical systems • Modern and relevant illustrations, examples, and applications

  9. Step 2: Make room in mainstream calculus • Omit some less-relevant (to the sciences and to modern applied mathematicians) math topics: • Endpoint convergence tests for Taylor series • Old traditional physics/geometry applications (e.g. volumes of solids of revolution)

  10. Step 2: Make room in mainstream calculus • Open course only to students who already have a good calculus background. • Relegate some simpler (review) topics to outside readings and assignments • Functions and other pre-calculus review, derivative shortcut formulas, vector basics, single-variable optimization SHOW FIVEFOLDPATHI.DOC

  11. Step 3: Combine and Organize • Sci Calc I: • Fitting models to data • Fitting models to data and theory via ROC • AROC, IROC, and derivative • Multivariate differential calculus • Definite integrals

  12. Step 3: Combine and Organize • Sci Calc II: • Applications of definite integrals • MIC-hour calculations • Distribution and density functions • Survival-renewal models • Probability and uncertainty • Polynomial approximation • Dynamical systems models • Difference equation models • Differential equation models • Discrete dynamical systems and linear algebra

  13. Text for Sci Calc • Start with Calculus: Concepts and Contexts by Stewart • Heavily supplemented with • Handouts • Computer labs • Data sets • Assignments • Examples SHOW SURV-RENEW READING

  14. Text for Sci Calc • ~40% of the material covered in the two semesters is not supported by the current text

  15. Biomedical Modeling Course • Upper-level math course • Open to Sci Calc grads (and others) • Goal:Teach math-inclined science students to construct and analyze math models, using difference and differential equations, of scientific processes.

  16. Biomedical Modeling Course • Strategy: Teach some modeling principles, then study DE and dfE models in various areas of biology and medicine. • Topics and their sequencing carefully planned to introduce successively higher-level model-building and analysis skills.

  17. Biomedical Modeling Topics • Biological control of pest populations • Spotlight #1: Tumor growth dynamics • Pharmacokinetics • Spotlight #2: Models of chemotherapy • Epidemiology • Interacting populations • Spotlight #3: Leukemia dynamics • Immunology of the HIV virus • Enzyme kinetics

  18. Biomedical Modeling Topics • Each unit begins with biomedical background info SHOW CANCERSPOTLIGHT1.DYN

  19. Illustrating Concepts • Prey processing time and saturation effects

  20. Modeling Projects • Antibiotic treatment of bacterial infections (including antibiotic resistance) • Drug dosing regimens • Spread of nosocomial infections (including infection-control methods) • Dynamic instability of microtubules (cytoskeleton components)

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