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

Ecology

**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

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

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