5th International Symposium 2015 – IntSym 2015, SEUSL
THE ROLE OF MATHEMATICS IN BIOLOGY
P. Elango
Department of Mathematical Sciences, Faculty of Applied Sciences, South Eastern
University of Sri Lanka
ABSTRACT: Mathematics plays a key role in many disciplines of science, primarily as a
mathematical modeling tool. New innovations and developments in physics are by the influence
of mathematics. Calculus was invented entirely for the use of physics. The importance of the role
of mathematics in physics is understood by the existing discipline “mathematical physics” or
"theoretical physics". One can think is mathematics has that same important role or even lesser
important role in the field of biology and is mathematics and biology could possibly have
anything in common. Even though physics and biology are very different sciences,
mathematicians and biologists developed the "mathematical biology" or "biomathematics" as a
recent discipline for the mathematical representation in biology to the theoretical and practical
applications in biological, biomedical and biotechnology researches. In this paper we study the
role played by mathematics in biology and analysis weather a considerable amount of
mathematics courses need to be teach for biological science graduates.
Keywords: Mathematics, Biology, Mathematical models, Biomathematics.
1. INTRODUCTION
In early days an attempt was made to establish the mathematical biology as a new
discipline, but it did not succeed (Keller,2002). There were initiatives by
mathematicians but there were no precedents. For example, theoretical models to
describe the spread of diseases had been discussed by Bernouilli and the flow of
blood in veins was the uppermost in Euler’s mind when he performed his seminal
work on fluid mechanics (Euler,1775).
Mathematical biology or biomathematics is a fast-growing well-recognized and the
most exciting modern application of mathematics. This is an interdisciplinary
research area with a range of applications in biology, biotechnology and biomedical
science. The filed may be referred to as mathematical biology or biomathematics to
stress the mathematical side or theoretical biology to stress the biological side. A
variety of mathematical techniques are used in mathematical biology to model
biological researches. Mathematical areas such as calculus, probability theory,
statistics, linear algebra, graph theory, combinatorics, algebraic geometry, topology,
dynamical systems, differential equations and coding theory are now being applied
in this field.
215
, 5th International Symposium 2015 – IntSym 2015, SEUSL
Many topics from biosciences have been high priority on the global agenda; the
fights against cancer and degenerative diseases of the brain, such as Alzheimer’s,
Parkinson’s and ALS and the management of health threats such as AIDS. Society
is waiting to get the research results for their better life. The emergence of models
and the existence of large data sets that require quantitative analysis in biology
gives a great opportunity for mathematics. The existing or already established
methods in mathematics can be used to support biological problems but the
quantitative analysis of the fundamental problems in bioscience definitely require
new ideas and new techniques from mathematics. The most significant biological
achievement of the 20thCentury is the identification of the DNA. This work was
essentially done by Physicists, Chemists and Crystallographers. There has already
been evidence of effective contribution between biology and mathematics. For
instance, the modeling of epidemics and the study of signal propagation in nerves
are the growing works of differential equations and studies of dynamical system in
this century.
There are several biomathematics research groups already established in the
departments of mathematics, statistics, computer science and biology and also
biostatistics centers around the world. The current size of the mathematical
bioscience research groups and researchers is relatively small compared the
important and need of mathematics for biological sciences.
2. THE ROLE OF MATHEMATICS TO BIOLOGY
Mathematical biology or biomathematics is a fast growing, well recognized and the
most exciting modern application of mathematics. The use of mathematics in
biology is important since biology becomes more quantitative. This new discipline
has applications in biology, biomedical and biotechnology. The aim of this new
discipline is the mathematical representations and modeling of the biological
problems using a variety of mathematical theories and techniques. The
mathematical biology has both theatrical and practical applications in research on
biological, biomedical and biotechnological fields.
One significant work is currently done by Dr. Aver Friedman, distinguished
Professor of mathematics and his research team at the Oberlin center for
computation and modeling in Ohio State university is to find a cure for cancer
(Margaret Putney, 2005). The objective of the research is to use a virus that attacks
just the tumor while leaving the healthy cells alone. The cancer which mostly
affected by research is a particular type of brain tumor known as glioma. The
researchers are trying to find a virus that reproduces fast enough is able to avoid
enough of the immune system to reduce the tumor. The researchers of this center
found some parameters that would cause the tumor to be reduced. They passed
their result to the biologists to create a virus that matches such parameters.
216
THE ROLE OF MATHEMATICS IN BIOLOGY
P. Elango
Department of Mathematical Sciences, Faculty of Applied Sciences, South Eastern
University of Sri Lanka
ABSTRACT: Mathematics plays a key role in many disciplines of science, primarily as a
mathematical modeling tool. New innovations and developments in physics are by the influence
of mathematics. Calculus was invented entirely for the use of physics. The importance of the role
of mathematics in physics is understood by the existing discipline “mathematical physics” or
"theoretical physics". One can think is mathematics has that same important role or even lesser
important role in the field of biology and is mathematics and biology could possibly have
anything in common. Even though physics and biology are very different sciences,
mathematicians and biologists developed the "mathematical biology" or "biomathematics" as a
recent discipline for the mathematical representation in biology to the theoretical and practical
applications in biological, biomedical and biotechnology researches. In this paper we study the
role played by mathematics in biology and analysis weather a considerable amount of
mathematics courses need to be teach for biological science graduates.
Keywords: Mathematics, Biology, Mathematical models, Biomathematics.
1. INTRODUCTION
In early days an attempt was made to establish the mathematical biology as a new
discipline, but it did not succeed (Keller,2002). There were initiatives by
mathematicians but there were no precedents. For example, theoretical models to
describe the spread of diseases had been discussed by Bernouilli and the flow of
blood in veins was the uppermost in Euler’s mind when he performed his seminal
work on fluid mechanics (Euler,1775).
Mathematical biology or biomathematics is a fast-growing well-recognized and the
most exciting modern application of mathematics. This is an interdisciplinary
research area with a range of applications in biology, biotechnology and biomedical
science. The filed may be referred to as mathematical biology or biomathematics to
stress the mathematical side or theoretical biology to stress the biological side. A
variety of mathematical techniques are used in mathematical biology to model
biological researches. Mathematical areas such as calculus, probability theory,
statistics, linear algebra, graph theory, combinatorics, algebraic geometry, topology,
dynamical systems, differential equations and coding theory are now being applied
in this field.
215
, 5th International Symposium 2015 – IntSym 2015, SEUSL
Many topics from biosciences have been high priority on the global agenda; the
fights against cancer and degenerative diseases of the brain, such as Alzheimer’s,
Parkinson’s and ALS and the management of health threats such as AIDS. Society
is waiting to get the research results for their better life. The emergence of models
and the existence of large data sets that require quantitative analysis in biology
gives a great opportunity for mathematics. The existing or already established
methods in mathematics can be used to support biological problems but the
quantitative analysis of the fundamental problems in bioscience definitely require
new ideas and new techniques from mathematics. The most significant biological
achievement of the 20thCentury is the identification of the DNA. This work was
essentially done by Physicists, Chemists and Crystallographers. There has already
been evidence of effective contribution between biology and mathematics. For
instance, the modeling of epidemics and the study of signal propagation in nerves
are the growing works of differential equations and studies of dynamical system in
this century.
There are several biomathematics research groups already established in the
departments of mathematics, statistics, computer science and biology and also
biostatistics centers around the world. The current size of the mathematical
bioscience research groups and researchers is relatively small compared the
important and need of mathematics for biological sciences.
2. THE ROLE OF MATHEMATICS TO BIOLOGY
Mathematical biology or biomathematics is a fast growing, well recognized and the
most exciting modern application of mathematics. The use of mathematics in
biology is important since biology becomes more quantitative. This new discipline
has applications in biology, biomedical and biotechnology. The aim of this new
discipline is the mathematical representations and modeling of the biological
problems using a variety of mathematical theories and techniques. The
mathematical biology has both theatrical and practical applications in research on
biological, biomedical and biotechnological fields.
One significant work is currently done by Dr. Aver Friedman, distinguished
Professor of mathematics and his research team at the Oberlin center for
computation and modeling in Ohio State university is to find a cure for cancer
(Margaret Putney, 2005). The objective of the research is to use a virus that attacks
just the tumor while leaving the healthy cells alone. The cancer which mostly
affected by research is a particular type of brain tumor known as glioma. The
researchers are trying to find a virus that reproduces fast enough is able to avoid
enough of the immune system to reduce the tumor. The researchers of this center
found some parameters that would cause the tumor to be reduced. They passed
their result to the biologists to create a virus that matches such parameters.
216
