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Biological Mathematics Graduate Degree Programs

More and more, scientists are turning to mathematical modeling to help them advance their biology research. This article provides background information on admissions requirements and core courses for a biological mathematics master's degree.

How to Earn a Biological Mathematics Master's Degree

Applications of mathematics in biology research range from applying fluid mechanics to living systems (biofluid mechanics) to building mathematical models to organize vast amounts of genetic data. Because biological mathematics is such a broad field, graduate students can tailor their coursework and take unique blend of advanced mathematics and biological science courses they need to pursue their research goals. In a biological mathematics master's degree, students spend about two years taking academic classes before completing a research project or taking a comprehensive exam. For a PhD program, students spend up to five years taking core courses and then prepare to defend their dissertation on a research topic of their choice.

Mathematical Modelling

Mathematical modeling forms the core of biological mathematics coursework. In introductory biomathematics courses, students learn about when and how mathematical models and computing can be used in fields as diverse as genetics, toxicology, natural resource management, ecology, pharmacology, and immunology. As part of this course, students may learn a programming or data analytics language to practice working with mathematical models.

Differential Equations

One important mathematical concept that pervades nearly every application of mathematics in biology research, is differential equations. Thus, mathematical biology programs often require students to take this course early on in their studies. Students study case studies to better understand the range of techniques and approaches that researchers can use to apply partial differential equation modeling in biology research. Topics may include spatially distributed systems, solid and fluid systems, scaling, perturbations, and asymptotics.

Modeling in Biology

This class helps students integrate their knowledge of biology with their growing mathematical and computational tool kit. Students will likely practice using computer simulations (among other technical skills) to apply quantitative modeling in answering a research question. Through the semester, professors may introduce applications of modelling in different subdisciplines of biology, like population health or toxicology. Topics may include compartment models, forrester diagrams, probabilistic and deterministic descriptions of dynamic processes and the development of model equations. In some cases, students will complete an independent project related to their chosen area of research to demonstrate their competency using technological tools in research.

Stochastic Processes

Stochastic processes, particularly stochastic modeling, helps scientists give mathematical descriptions of biological relationships, particularly ones that involve randomness. In this course students are introduced to stochastic modeling techniques. They learn how scientists and mathematicians apply these techniques in various settings, including genetics, physiology, ecology, engineering and medicine.

Biostatistics

Biostatistics is the use of statistics to study living organisms. In this course students learn biostatistics techniques commonly used in biological research. Topics include principal components, factor analysis, cluster analysis, recursive partitioning and multilevel and longitudinal analysis.

Computational Methods

This class builds on biomathematics courses and prepares students with advanced computational modelling techniques that can be applied to explore research questions. Topics in this course may include implementing numerical algorithms, conditioning, interpolation, quadrature, approximation theory, direct and iterative solution of linear systems and least squares, systems of nonlinear equations and numerical optimization.

Biomathematics Seminar

Many programs include seminar programs that give graduate students the opportunity to present their research progress to other students and faculty members. This course gives students a place to practice their research presentation skills. They also have the opportunity to critique other projects and engage with experts in the field.

Thesis

Some students choose to write a thesis in lieu of completing the final comprehensive exam. When entering the program, admitted students work with faculty to devise a research plan and choose an academic advisor based on their unique research interests. Throughout their time taking academic classes, students also pursue their independent research. Advisors monitor a student's progress and offer some assistance. At the end of their studies, students must defend their thesis before a panel of academic experts.

Admissions Requirements for a Biological Mathematics Degree

Admissions officers expect applicants to have an undergraduate degree in either biology or mathematics. Applicants send in their undergraduate transcripts to showcase their achievement in multivariate calculus, linear algebra, statistics and biology. Applicants also send in GRE test scores, letters of recommendation from previous professors, and a statement of purpose explaining their research interests and goals. In addition, PhD applicants may have to complete a qualifying examination near the beginning of their program (wherein they discuss and defend their proposed research project).

Biological mathematics graduate degrees allows students to develop their own course of study based on their unique research goals. Graduates are well-prepared to integrate their enhanced mathematical skill-set with biological research.