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Course Criteria
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3.00 Credits
Polynomial interpolation; numerical solution of initial value problems for ordinary differential equations by single and multi-step methods, Runge-Kutta, Predictor-Corrector; numerical solution of boundary value problems for ordinary differential equations by shooting method, finite differences and spectral methods. Credit may not be granted for both MATH 578 and MATH 478. Prerequisite: An undergraduate numerical course, such as MATH350 or instructor's consent. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
MATH 471 This course is concerned with a branch of complexity theory. It studies the intrinsic complexity of numerical problems, that is, the minimum effort required for the approximate solution of a given problem up to a given error. Based on a precise theoretical foundation, lower bounds are established, i.e. bounds that hold for all algorithms. We also study the optimality of known algorithms, and describe ways to develop new algorithms if the known ones are not optimal. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
The geometry of the various elements, the element matrices, assembly of stiffness matrices, analysis of error estimates and convergence proofs. Applications. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This course is a continuation of Math 485/548. It introduces the student to modern continuous time mathematical finance. The major objective of the course is to present main mathematical methodologies and models underlying the area of financial engineering, and, in particular, those that provide a formal analytical basis for valuation and hedging of financial securities. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
The course covers basics of the modern interest rate modeling and fixed income asset pricing. The main goal is to develop a practical understanding of the core methods and approaches used in practice to model interest rates and to price and hedge interest rate contingent securities. The emphasis of the course is practical rather than purely theoretical. A fundamental objective of the course is to enable the students to gain a hand-on familiarity with and understanding of the modern approaches used in practice to model interest rate markets. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This is an advanced course in the theory and practice of credit risk and credit derivatives. Students will get acquainted with structural and reduced form approaches to mathematical modeling of credit risk. Various aspects of valuation and hedging of defaultable claims will be presented. In addition, valuation and hedging of vanilla credit derivatives, such as credit default swaps, as well as vanilla credit basket derivatives, such as collateralized credit obligations, will be discussed. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This course introduces numerical methods, especially the finite difference method for solving different types of partial differential equations. The main numerical issues such as convergence and stability will be discussed. It also includes introduction to the finite volume method, finite element method and spectral method. Prerequisite: An undergraduate numerical course such as MATH 350 and MATH 489 or consent of instructor. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Fundamentals of multivariate meshfree radial basis function and moving least squares methods; applications to multivariate interpolation and least squares approximation problems; applications to the numerical solution of partial differential equations; implementation in Matlab. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Prerequisite: Instructor permission required. 1. 000 TO 20.000 Credit Hours 1. 000 TO 20.000 Other hours Levels: Graduate Business, Graduate Schedule Types: Independent Study/Research College of Science & Letters College Applied Mathematics Department
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0.00 Credits
Current research topics presented in the department colloquia and seminars. 0. 000 Credit Hours 1. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate Schedule Types: Seminar College of Science & Letters College Applied Mathematics Department
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