The Graduate Program


The research faculty in mathematical biology is very interested in training Ph.D students. For that purpose they have received a large Research Training Grant from the National Science Foundation. This grant provides academic year stipends so that graduate students studying mathematical biology have reduced teaching responsibilities and the grant also provides summer stipends. The Director of the Research Training Grant is Michael Reed and the Assistant Director is Anita Layton.

The program in mathematical biology is part of the Graduate Program of the Mathematics Department. Students apply to become graduate students in the Mathematics Department, indicating their interest in mathematical biology in their applications. When they complete the requirements of the program, they receive the Ph.D. in Mathematics.

What is mathematical biology?

The faculty takes a very broad view of the field of mathematical biology and the training of graduate students. In their thesis research, students can:
  • Apply mathematics to specific important biological or medical problems.
  • Develop new analytical or computational tools for biological problems.
  • Prove theorems and develop areas of pure mathematics inspired by biology.

Many mathematical biology faculty members are both pure and applied mathematicians, and thus they are well qualified to advise students and help them formulate a program of study based on their own interests.

The breadth of research topics can be seen on the list of current graduate students interested in mathematical biology.

This video is taken from a 16-mm movie made in the 1950s by the late David Rogers. It depicts a human polymorphonuclear leukocyte (neutrophil) on a blood film crawling among red blood cells. The neutrophil is "chasing" Staphylococcus aureus microorganisms.


Training in Mathematics.

The faculty believes that all graduate students in mathematical biology should have excellent training in core mathematics. Thus each student should take a variety of graduate courses during their first two years selected from some of the following fields, analysis, dynamical systems, partial differential equations, probability, algebra, geometry, topology, statistics, discrete mathematics, depending on the student's particular interests. All students interested in mathematical biology should take Math 790-77. All students supported by the Research Training Grant are required to attend the colloquium seminar and the colloquium each week.

Sign up for Mathematics 790-77. Current Research in Mathematical Biology. The colloquium seminar is designed to introduce students to the work and career of the next colloquium speaker. Typically, RTG faculty and students study two recents papers of the colloquium speaker and two students are assigned to lead the discussion. After the colloquium, RTG postdocs and graduate students take the speaker to lunch. Each term, the colloquium has a theme, though not all speakers necessarily fit within the theme. Last year and this year the themes and organizers are as follows:

  • Fall 2011. Bio-fluid Mechanics, organized by Anita Layton and Karin Leiderman
  • Spring 2012. Applications of Geometry and Topology to Biology, organized by Jon Harer and Elizabeth Munch.
  • Fall 2012. Mathematical and Computational Neuroscioence, organized by Michael Reed and Mainak Patel.
  • Spring 2013. Cancer Modeling. Organized by Rick Durrett.

Training in Biology. The amount of training in biology that is appropriate depends on whether the student's research plan is in area (1), (2), or (3) indicated above under What is Mathematical Biology?. Students may, if they wish, take courses in a very large number of different departments and schools (see The Duke Environment).

Students supported by the Research Training Grant will normally do a project with a biologist in the summer after their second year of graduate study. Projects will be arranged by the the Director, Michael Reed, and the the members of the Biology Advisory Committee, a group of distinguished biologists at Duke. Students can be supported more than once (and earlier in their careers) if appropriate to their interests.

Responsibilities of RTG students. Graduate students supported by the Research Training Grant benefit because they have fewer teaching responsibilities and therefore can concentrate on their research program. They do have some other responsibilities, however. The RTG grant has a large number of stipends to support undergraduate research projects in mathematical biology. RTG graduate students will sometimes be asked to help faculty members mentor these projects. Each year, the TG faculty will hold a 10 day workshop in May for students from small colleges in the southeast to tell them about mathematical biology and to encourage them to go to graduate school. RTG students will occasionally be asked to assist with the workshop.

Training in Teaching and Presentation Skills. All mathematical biology students must participate in the teacher-training program of the Mathematics Department. Jack Bookman, who developed this pioneering program at Duke, helps graduate students become excellent teachers. Students also receive training in in delivering research lectures and grant writing. Excellent presentation skills are particularly important for mathematical biologists who often have to give lectures to mathematicians who know little biology or to biologists who know little mathematics.

Mentoring and Advising. All students entering the graduate program of the Mathematics Department are assigned a faculty mentor who helps them with course selection and discusses with them their career goals. Once the graduate student selects a thesis advisor these duties are taken on by the advisor. All graduate students interested in mathematical biology will be assigned a mentor who does research in mathematical biology.

Talk to Current Students. Prospective graduate students can find out what our current students think about mathematics training, teacher-training, biology training, mentoring and advising, and the atmosphere in the Department. Simply consult the list of current students interested in mathematical biology and send emails.

Financial Support.

All students admitted to the Ph.D. program in mathematics are guaranteed five years of financial support, assuming that they make satisfactory progress towards the degree. The Research Training Grant provides student funding in the form of research assistantships (open to US Citizens and permanent residents) for students pursuing research in mathematical biology. Additional (unrestricted) student support is available through fellowships, faculty research grants and departmental teaching assistantships.Thus all students, regardless of nationality, are encouraged to apply to study mathematical biology at Duke.

What if I'm not sure? That is not unusual. Most students go to graduate school to earn the Ph. D. because they love mathematics, but very few know exactly what they want to work on. You may be driven to study pure mathematics or you may be excited by seeing mathematics in action in the real world, but you may be unsure whether you want to specialize in applications to economics, or biology, or physics, or computer science. That's fine.

During your first two years of graduate study you will take lots of courses, attend lots of seminars and talk to lots of mathematicians and mathematics graduate students. Because of this immersion, you will know much much more about mathematics and applied mathematics than you do now and you will choose what is right for you. You can decide as late as your third year that you want to do mathematical biology. Or, perhaps if you came to Duke intending to specialize in mathematical biology you will decide in your third year that you want to do something else. That's ok too. Such mid-course corrections are not unusual. Our faculty will help you to figure out what you want and then will help you achieve your career goals.

How do I apply?

This part is easy. You simply go to the application information for graduate study in mathematics at Duke, where you will find directions and a discussion of the admissions process and financial support. You can also email directly Michael Reed, Director of the Research Training Grant Program or Tom Witelski, Director of Graduate Studies.

Graduate Students Interested in Mathematical Biology

Ph.D in 2013

* Indicates support from the NSF Research Training Grant



Shishi Luo

webpage
Advisor: Michael Reed

"I work with the Koelle Lab (Biology department) on modelling rapidly evolving infectious diseases. Understanding the overall dynamics of such viruses requires interfacing disease dynamics, traditionally modeled by nonlinear systems of differential equations, with molecular sequence evolution, traditionally studied using the tools of population genetics."

 

Elizabeth Munch *

webpage
Advisor: John Harer

"My research mostly focuses on computational topology and applications to biology. I am currently working on a project which uses algebraic topology and persistent homology to create a model of animal swarming."

Ph.D in 2012

* Indicates support from the NSF Research Training Grant



Tiffany Kolba *

webpage
Advisor: Jonathan Mattingly

"I study issues of stability for stochastic differential equations. Since randomness is inherently present in nature, many biological phenomena can be modelled using stochastic differential equations. A few of these biological phenomena which I am interested in are neuron firing, the spread of epidemics, and molecular motors."

 


Sarah Schott

webpage
Advisor: Mark Huber

"I am interested in probability and Monte Carlo Methods, in particular. Monte Carlo algorithms have proven useful in the analysis of protein folding, phylogenetic trees and population genetic models."

Ph.D in 2011

* Indicates support from the NSF Research Training Grant

 

Matt Bowen *

webpage
Advisor: David Schaeffer

Thesis: A Spectral Deferred Correction Method for Computing the Cardiac Two-Cycle

 




Richard Hahn *

webpage
Advisor: Sayan Mukherjee

Thesis: Probability Models for the Targeted Borrowing of Information

 


Kevin Gonzales

webpage
Advisor: David Schaeffer

"My current research focuses on building and analyzing a differential equationmodel that describes the cAMP-PKA pathway in Saccharomyces cervisiae (buddingyeast)."

Current Students Interested in Mathematical Biology

* Indicates current support from the NSF Research Training Grant

 

Erin Beckman
ebeckman@math.duke.edu
webpage
Advisor:

"Mathematical biology."

 

 

Michael Bell
mikebell@math.duke.edu
webpage
Advisor:

"Mathematical biology."

 

 

Michael Casey

webpage
Advisor: Michael Reed

"I am currently interested in incorporating more geometric methods in biological modeling, particularly in problems with a strong biophysics flavor. Past projects have included numerical simulations of swarm dynamics (fish, birds, wildebeests, etc.) under natural selection, and geometric models of the motion of cilia."

 

 

Chris Castorena

webpage
Advisor: Katia Koelle

"I'm interested in the effect that incorporating demographic and behavioral heterogeneities into mathematical disease models has on the effectiveness of control strategies. I'm also interested in developing optimization models for allocating disease control funding."

 

 

Miles Crosskey *

webpage
Advisor: Mauro Maggioni

"I'm currently working with Mauro Maggioni on a project that uses diffusion maps for dimensionality reduction on molecular dynamics systems."

 

 

Ian Drayer *

webpage
Advisor:

"I am most interested in mathematical simulation development and mathematical modeling, particularly utilizing stochastic methods to develop and test algorithms. At the moment, my interests lie in applications to models of Biological systems, as well as sports rankings."

 

 

Jack Enyeart *

webpage
Advisor: Michael Reed

"I'm interested in mathematical modeling of biological phenomena--particularly those that involve stochastic processes."

 

 

Shalla Hanson
s-hanson@math.duke.edu
webpage
Advisor:

"Mathematical biology."

 



Sean Lawley *

webpage
Advisor: Michael Reed

"I am currently developing a mathematical model of arsenic detoxification with Mike Reed and Fred Nijhout to study how nutritional supplements can increase arsenic detoxification in humans."

 




Yi Li

webpage
Advisor: Anita Layton

"I work on numerical methods for computing fluid motion driven by immersed interfaces."

 



HwaYeon Ryu *

webpage
Advisor: Anita Layton

"I am interested in probability closely related with PDE problem andbiology. Especially, I am trying to study how probability theory in thetheoretical sense could be used and applied in biology in order to explain"why and how" something happens."

 

 

Joseph Schmitt *

webpage
Advisor: Anita Layton

"I've worked with Anita Layton to model how cilia move debris out of the lungs. We used PDEs to model the beating motion of the cilia."

 



Ioannis Sgouralis

webpage
Advisor: Anita Layton

"My interest is in Analysis and its applications, especially in Biology. Currently, I am working with Professors Anita Layton and Harold Layton on the renal physiology. I am developing new mathematical models and incorporating experiment data to study the myogenic response of the afferent arteriole."

 



Ezgi Temamogullari

webpage
Advisor:

"Mathematical biology."

 



Chi Zhang *

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Advisor: