Welcome to the UTK Mathematical Life Sciences Page for Education

This collection of Pages has been organized by Susan Harrell and Monica Beals under the supervision of Louis Gross at the University of Tennessee, Knoxville, with support from the National Science Foundation Undergraduate Course and Curriculum Program through Award DUE-9752339, "Alternative Routes to Quantitative Literacy for the Life Sciences".

General Biology Modules

****** These pages are drafts and should not be modified or reproduced in any way ******

Cell Structure and Growth

Cell Division and Rates of Population Growth -- exponential and geometric equations, sequences

Cell Division and the Presence of a Growth Factor -- exponential and hyperbolic equations

Doubling Time of Tumors -- ratios, linear regression

Maintenance of Cell Shape -- simple algebra, reading a chart

Mechanisms of Cell Attachment -- simple equations, geometry, interpreting graphs

Mitotic Index and Cell Division -- ratios, reading a chart

Nuclear and Cytoplasmic Viscosity -- linear equations

Nucleo-cytoplasmic Transport -- exponential equations

Nucleoplasmic Index -- ratios, interpreting graphs

Permeability of Molecules through the Cell Membrane -- linear regression, log-log plots

Cell Aggregation and Sphere Packing -- geometry, ratios, inequalities


Cellular Processes 

Antibody Binding -- hyperbolic and linear equations

Chemoreception -- hyperbolic and linear equations

Diffusion Through a Cell Membrane -- calculus, rates of change, linear and hyperbolic equations

Enzymes and the Rate of Chemical Reactions -- calculus, rates of change, hyperbolic equations

Gibb's Free Energy -- ratios, logarithms, exponents

Efficiency of ATP Production -- ratios

Maintaining Cellular Conditions: pH and Buffers -- logarithms, exponents, ratios

Metabolism for Energy and the Respiratory Quotient -- quotients, ratios

Water Movement through a Membrane: The Van't Hoff Equation --inequalities, simple algebra


Genetic Information

Amino Acid Frequency -- probability, linear regression

DNA and Knot Theory -- topology

Half Life of mRNA -- exponential and logarithmic equations


Genetics and Evolution

Body Size Constraints in Xylem Feeding Insects: Allometric Relationships -- exponential equations, ratios, logarithmic scales

The Chi-Square Test -- probability, statistical testing

Hardy-Weinberg Equilibrium -- frequencies

Population Bottlenecks: Heterozygosity vs. Allelic Diversity-- basic algebra, ratios, exponential functions

Population Genetics: Limits to Adaptation-- basic algebra, logarithms



Cohort Life Tables -- functions

Diversity Indices: Simpson's D -- functions

Diversity Indices: Shannon's H -- functions

Estimating Tree Heights: Right Triangle Trigonometry -- trigonometric functions

Interspecific Competition: the Lotka-Volterra Model -- differential equations, state-space graphs

Optimal Foraging Theory -- inequalities

Predator-Prey Dynamics: the Lotka-Volterra Model -- differential equations

Species-Area Relationships -- exponential and logarithmic equations

Type I Functional Response -- linear functions

Type II Functional Response -- Holling's Disk Equation


Biomechanics, Structure, and Function

Sizes of Organisms: The Surface Area to Volume Ratio -- geometry, ratios

Stress-Strain Curves and Young's Modulus -- ratios



Plant Physiology

Energy Absorbed From Light During Photosynthesis -- ratios, hyperbolic equations

Coordinating Photosynthetic Activity: Circadian Rhythms -- trigonometry, sine waves

Nastic Movements in Plants --hyperbolic equations, interpreting models

Plant Cell Expansion and Plant Hormones -- hyperbolic equations

Phototropism and Gravitropism: Quantifying Stem Curvature -- geometry, trigonometry

Quantitative Cytological Characteristics: Photorespiration - ratios, reading a chart

Translocation of Nutrients in the Phloem: Dixon's Paradox -- linear equations, linear regression

Translocation of Nutrients in the Phloem: Poiseuille's Equation -- hyperbolic equations, calculus, rates of change


Animal Physiology

Cardiac Output -- proportions, linear equations, linear regression

Hemoglobin Evolution -- parabolic and hyperbolic equations, calculus, finding maxima

Lung Capacity and Rhythms in Breathing -- trigonometry, sine waves

Muscle Contraction -- hyperbolic functions, plotting data

Osmoregulation -- logarithmic equations

Oxygen Diffusion in Simple Organisms -- parabolic and linear equations

Sperm Motility -- square roots, parabolic equations

Synapse Transmission and Action Potentials -- inequalities,

Tension in Blood Vessels: LaPlace's Equation -- linear equations


You can also check out our General Biology Reform links

and the working version of our Glossary of Biology Terms


Return to Math Education for the Life Sciences Project Home Page

Copyright 1999 M. Beals, L. Gross, S. Harrell









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