School of Mathematical Sciences
College of Science
School of Mathematical Sciences
College of Science
BS, University of New Hampshire; MS, Ph.D., University of Delaware
This capstone experience introduces students to mathematical problems and situations not encountered in previous courses of study. The class will primarily revolve around student-directed,collaborative efforts to solve a given problem using rigorous mathematical analysis and (as appropriate) computational methods. Significant work outside the classroom will be required of students. Students will write a formal report of their solution methods, and produce a poster for presentation at an end-of-term conference-style event.
0 - 9 Credits
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
This course will introduce graduate students to the logical methodology of mathematical modeling. They will learn how to use an application field problem as a standard for defining equations that can be used to solve that problem, how to establish a nested hierarchy of models for an application field problem in order to clarify the problem’s context and facilitate its solution. Students will also learn how mathematical theory, closed-form solutions for special cases, and computational methods should be integrated into the modeling process in order to provide insight into application fields and solutions to particular problems. Students will study principles of model verification and validation, parameter identification and parameter sensitivity and their roles in mathematical modeling. In addition, students will be introduced to particular mathematical models of various types: stochastic models, PDE models, dynamical system models, graph-theoretic models, algebraic models, and perhaps other types of models. They will use these models to exemplify the broad principles and methods that they will learn in this course, and they will use these models to build up a stock of models that they can call upon as examples of good modeling practice.
This course is principally a study of the calculus of functions of two or more variables, but also includes the study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, and includes applications in physics. Credit cannot be granted for both this course and MATH-221.
This course covers the algebra of complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of real-valued integrals by complex-variable methods.
May 11, 2016
Summer camp for girls recognized by STEM groupRIT’s SMASH Experience for Girls has been recognized by the Finger Lakes STEM Hub as an exemplary K-12 program in science, technology, engineering and math.
Maki, Kara L. and David S. Ross. "A New Model for the Suction Pressure Under A Contact Lens." Journal of Biological Systems. (2014). Print.
Li, Longfei, et al. "Tear Film Dynamics with Evaporation, Wetting, and Time-dependent Flux Boundary Condition on an Eye-shaped Domain." Physics of Fluids 26. 5 (2014): 52101. Print.
Maki, Kara L. and David S. Ross. "Exchange of Tears under a Contact Lens Is Driven by Distortions of the Contact Lens." Integrative and Comparative Biology 54. 6 (2014): 1043-1050. Print.
Lee, S. H., et al. "Gravity-driven Instability of a Thin Liquid Film Underneath a Soft Solid." Physical Review E 90. 5 (2014): 53009. Print.
Huang, J., et al. "Phantom Study of Tear Film Dynamics with Optical Coherence Tomography and Maximum-likelihood Estimation." Optics Letters 38. (2013): 1721-1723. Print.
Huang, J., et al. "Maximum-likelihood Estimation in Optical Coherence Tomography in the Context of the Tear." Biomedical Optics Express 4. (2013): 1806-1816. Print.
Maki, Kara L. and Yuriko Renardy. "The Dynamics of a Viscoelastic Liquid which Displays Thixotropic Yield Stress Behavior." Journal of Non-Newtonian Fluid Mechanics 181. (2012): 30-50. Print.
Maki, Kara L. and Satish Kumar. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." Langmuir 27. (2011): 11347-11363. Print.
Maki, Kara L. "Mechanics of the Contact Lens." Indo-American Frontiers of Science Symposium. Indo-US Science & Technology Forum and National Academy of Sciences. Agra, India. 7 Apr. 2013. Conference Presentation.
Maki, Kara L. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." 1st Int. Workshop on Wetting and Evaporation: Droplets of Pure and Complex Fluids. Aix Marseille Universite. Marseilles, France. 18 Jun. 2013. Lecture.
Maki, Kara Lee and David S. Ross. "Settling Dynamics of the Contact Lens." Applied and Computational Math Seminar. George Mason University. Fairfax, VA. 26 Oct. 2012. Lecture.
Maki, Kara Lee and David Ross. "Settling Dynamics of the Contact Lens." Workshop on Thin Liquid Films and Fluid Interfaces: Models, Experiments and Applications. Banff International Research Station. Banff, Alberta, Canada. 13 Dec. 2012. Conference Presentation.
Maki, Kara Lee and Yuriko Rendary. "Dynamics of a Thixotropic Yield Stress Fluid: A Mathematical Perspective of Ketchup?" Applied Mathematics Seminar. University of Delaware. Newark, DE. 27 Jun. 2012. Lecture.
Maki, Kara Lee and David Ross. "Settling Dynamics of a Contact Lens." Minisymposium on Dynamics and Applications of Thin Liquid Flims. Society for Industrial and Applied Mathematics Annual Meeting. Minneapolis, MN. 12 Jul. 2012. Conference Presentation.
Maki, Kara Lee and Satish Kumar. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." Workshop on Surfactant Driven Thin Film Flows. Fields Institute for Research in Mathematical Sciences. Toronto, Ontario. 22 Feb. 2012. Conference Presentation.
Maki, Kara Lee and Satish Kumar. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." Special Session on Mathematics in Industry. Joint Mathematic Meeting. Boston, MA. 4 Jan. 2012. Conference Presentation.
Maki, Kara L. "Skin Formation in Drying Droplets of Colloidal Suspensions." NSF Mathematics Institutes' Modern Math Workshop. The Society for Advancement of Chicanos and Native Americans in Science Annual Conference. San Jose Convention Center, San Jose, CA. 26 Oct. 2011. Conference Presentation.