Open Questions: Mathematics and Biology
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See also:
Chaos theory and dynamical systems 
Selforganization and complex systems 
Protein chemistry and biology 
Systems biology
Introduction
Differential equations
Dynamical systems
Knot theory
Swarming behavior

Site indexes

Math Forum Internet Mathematics Library: Biology
 Alphabetized list of links with extensive annotations.

Open Directory Project: Mathematical Biology
 Categorized and annotated mathematical biology links. A version of this
list is at
Google, with entries sorted in "page rank" order.

Links to Mathematical Biology Sites
 A substantial, categorized list of links, by
Jason Matthiopoulos. Also has a good bibliography of
textbooks in mathematical biology.

Mathematical Biology
 Extensive categorized but unannotated list of links, at the
Mathematical BBS.

Galaxy: Mathematical Biology
 Categorized site directory. Entries usually include
descriptive annotations.
More
here.

Society for Mathematical Biology: Other Sites of Interest
 Unannotated links.
Sites with general resources

Mathematics in Biology
 Site hosted at Brandeis University. Deals with all aspects of use
of mathematics in the life sciences. There is a lot of substantial
content, but much of it requires sophisticated mathematics.

Geometric models of biological phenomena
 An outline (literally) and lecture notes related to combinatorial,
statistical, and geometric issues in mathematical models of
biological phenomena.
Part of the
Workshop Website Network of the
American Institute of Matheamtics.

The Society for Mathematical Biology
 Professional society which aims "to provide a forum for
discussion of research in biology, mathematicalbiology, and
mathematics applied to or motivated by biology." Site includes
useful external links.
Surveys, overviews, tutorials

Mathematical biology
 Article from
Wikipedia.

Mathematics and Biology: The Interface
 This workshop report is an excellent summary
of the current interfaces between mathematics and biology. It
describes the impact of each field on the other. On the mathmematics
side, nonlinear dynamics, topology, and knot theory are especially
important. In biology, many areas are affected, but especially
molecular biology and evolutionary biology.

Genome Multimedia Site
 Interactive course on the analysis of the genetic sequence using
information theory, probability, and statistics.
Special topics

Magical numbers in nature
 October 12, 2001 interview from Nature Science Update
with mathematician Ian Stewart on the use of mathematical ideas
in biology. Topics include symmetry, dynamics, chaos theory,
fractals, and pattern formation.

Professor Bonnie Berger
 Home page of MIT professor specializing in computational
biology. Site includes information on research, publications, and
course notes.

Biomedical Models of Cellular and Physiological Systems
and Disease
 Research project led by Leah Keshet.

Mathematical Modelling in Pharmaceutical Development
 Research Project led by Jack Tuszynski. Site contains project
information and minitutorials.
 Mathematical Challenges from Genomics and Molecular Biology
Richard M. Karp
Notices of the AMS, May 2002, pp. 544553
 A fundamental goal of biology is to understand the functioning
of cells. Genomics and molecular biology have yielded a whole new
kind of insight into this question. Among the biological questions
most amenable to mathematical analysis are genome
sequencing, gene finding, construction of evolutionary
phylogenies, analysis of data from DNA microarrays, and understanding
the process of gene expression. The most useful mathematical
techniques are in the areas of probability, optimization, and
computational theory.
[Article in PDF format]
 The Unreasonable Effectiveness of Mathematics in Molecular
Biology
Arthur M. Lesk
Mathematical Intelligencer, Spring 2000, pp. 2837
 The article presents an examination of the notion that
mathematics can be as useful for (some) biological problems as it
is in physics. One example is the study of protein folding and
structure.
 We Got Rhythm: Dynamical Systems of the Nervous System
Nancy Kopell
Notices of the AMS, January 2000, pp. 616
 A mamalian nervous system is always active and exhibits a
variety of periodic, rhythmical phenomena. Some of these "brain
waves" are associated with mental processes and cognitive states,
which are of great interest but poorly understood. The article
presents mathematical ways to model such dynamical systems.
[Article in PDF format]
 Using Mathematics to Understand HIV Immune Dynamics
Denise Kirschner
Notices of the AMS, February 1996, pp.191202
 Much effort has been expended in modeling the interaction of
HIV and the immune system. A model is presented here involving the
interaction of HIV with one type of immune system cell, using a
system of three first order differential equations governing
three dependent variables.
[Article in PDF format]
 Getting Started in Mathematical Biology
Frank Hoppensteadt
Notices of the AMS, September 1995, pp. 969975
 The general nature of mathematical models in biology is
discussed using examples from neurobiology. Advice is offered on
how to do collaborative research in mathematical biology.
[Article in PDF format]
 Mapping Heredity: Using Probabilistic Models and Algorithms to
Map Genes and Genomes
Eric S. Lander
Notices of the AMS, July 1995, pp. 747753; August 1995, pp. 854858
 Elements of genome mapping are presented, and appropriate
statistical techniques are described.
[Article in PDF format] (Part one)
[Article in PDF format] (Part two)
 Lifting the Curtain: Using Topology to Probe the Hidden Action
of Enzymes
De Witt Sumners
Notices of the AMS, May 1995, pp. 528537
 Because DNA consists of two entwined and very long linear
molecules, the processes of transcription and replication of DNA
by enzymes must satisfy geometric and topological conditions.
Understanding these constraints can help determine otherwise
unobservable details of how various enzymes perform their tasks.
Sophisticated results of knot theory play an important role in
this analysis.
[Article in PDF format]
 Nicholas F. Britton – Essential Mathematical Biology
SpringerVerlag, 2003
 The book provides a selfcontained introduction to
mathematical biology for students with a mathematical
background (calculus and differential equations). Topics
include population dynamics, infectious diseases, population
genetics and evolution, molecular and cellular biology, and
cancer modeling.
 Iam Stewart  Life's Other Secret: The New Mathematics of the
Living World
John Wiley & Sons, 1998
 The author, a professional mathematician presents ways in
which some mathematical concepts are applicable to biology.
Since almost no formulas or equations are used in the whole
book, this limits what can be offered. The main concept that
is applied heavily is symmetry. Topic covered include DNA and
the genetic code, artificial life, the Fibonacci sequence,
and neural networks.
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Copyright © 2002 by Charles Daney, All Rights Reserved