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Course Criteria
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3.00 Credits
Methods of applied mathematics concentrating on techniques for the analysis of differential and integral equations. Topics include: Integral equations, differential operators, Fredholm alternative, distribution theory and Green's function methods. Graduate students will be given an extra assignment not required of undergraduate students.
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3.00 Credits
Methods of applied mathematics concentrating on techniques for the analysis of differential and integral equations. Topics include: integral equations, differential operators, Fredholm alternative, distribution theory and Green's function methods. Graduate students will be given an extra assignment not required of undergraduate students.
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3.00 Credits
The study of differential equations involving functions of more than one variable. Topics include: Laplace, heat and wave equations, boundary value problems, methods of separation of variables and eigenfunction expansions, Fourier series, Green's functions, maximum principle and computational methods. Graduate students will be given an extra assignment not required of undergraduate students.
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3.00 Credits
The study of differential equations involving functions of more than one variable. Topics include: Laplace, heat and wave equations, boundary value problems, methods of separation of variables and eigenfunction expansions, Fourier series, Green's functions, maximum principle and computational methods. Graduate students will be given an extra assignment not required of undergraduate students.
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4.00 Credits
No course description available.
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3.00 Credits
An introduction to applications of mathematics to various biological, ecological, physiological, and medical problems, which will be analyzed both analytically and numerically. Graduate students will be given additional assignments that will not be completed by undergraduate students.
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3.00 Credits
An introduction to applications of mathematics to various biological, ecological, physiological, and medical problems, which will be analyzed both analytically and numerically. Graduate students will be given additional assignments that will not be completed by undergraduate students.
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3.00 Credits
The course covers basic theory and applications of combinatorics and graph theory. Combinatorics is a study of different enumeration techniques of finite but large sets. Topics that will be studied include principle of inclusion and exclusion, generating functions and methods to solve difference equations. Graph theory is a study of graphs, trees and networks. Topics that will be discussed include Euler formula, Hamilton paths, planar graphs and coloring problem; the use of trees in sorting and prefix codes; and useful algorithms on networks such as shortest path algorithm, minimal spanning tree algorithm and min-flow max-cut algorithm. Graduate students will be given extra assignments determined by the instructor that undergraduates will not be required to do.
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3.00 Credits
The course covers basic theory and applications of combinatorics and graph theory. Combinatorics is a study of different enumeration techniques of finite but large sets. Topics that will be studied include principle of inclusion and exclusion, generating functions and methods to solve difference equations. Graph theory is a study of graphs, trees and networks. Topics that will be discussed include Euler formula, Hamilton paths, planar graphs and coloring problem; the use of trees in sorting and prefix codes; and useful algorithms on networks such as shortest path algorithm, minimal spanning tree algorithm and min-flow max-cut algorithm. Graduate students will be given extra assignments determined by the instructor that undergraduates will not be required to do.
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3.00 Credits
Differential geometry uses tools from calculus and linear algebra to study the geometric properties of smooth curves and surfaces in Euclidean spaces. Topis include: arc length, surface area, geodesics, curvature, first and second fundamental forms, Gauss-Bonnett formula. Graduate students will be assigned additional assignments and/or project.
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