2017-2018: 1400 students! no calculus prerequsite

The leading voices in US biology and medicine have called for drastic changes in math education for biology and pre-med students In their view, the traditional “Calculus for Life Sciences” should be replaced by a course that enables students to – “Quantify and interpret changes in dynamical systems” – “Explain homeostasis in terms of positive or negative feedback.” * In such a course, – “Mathematical/computational methods should be taught, but on a need-to know basis.” – “The emphasis should not be on the methods per se, but rather on how the methods elucidate the biology” – “ordinary differential equations (made tractable and understandable via Euler’s method without any formal course in differential equations required)”.**

MODEL

“CHANGE EQUATION”

STATE SPACE

VECTORFIELD

EULER’S METHOD

TRAJECTORY

Equilibrium Points Moose-Deer Competition Model

Equilibrium Points Spruce Budworm Outbreak

Positive Feedback: Bistable ‘switch”

if n > 8, system exhibits stable oscillations Negative Feedback: Homeostasis OR Oscillations if n > 8, system exhibits stable oscillations

hormone data (normal female)

Linear Algebra repeated iteration of a matrix with 2 negative eigenvalues, converts the circle of black points into the red line, visualizing the principal eigenvector of the matrix

Google Pagerank weighted ‘points to’ diagram ‘points to’ matrix

Python - Sagemath

Student Outcomes Interest in Math before and after course