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Course Criteria
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0.00 - 4.00 Credits
Systems of linear equations, Gaussian elimination, matrices, and determinants. Differential multivariable calculus. Constrained optimization, and the Kuhn-Tucker conditions.
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0.00 - 4.00 Credits
Vectors in the plane and in the space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields and Stokes's theorem.
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0.00 - 4.00 Credits
Euclidean spaces, vector spaces, systems of linear equations, matrices and linear transformations, determinants, orthogonality, Eigen values and applications to systems of differential equations, symmetric matrices and Quadratic forms.
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0.00 - 4.00 Credits
This course is an introduction to multivariable calculus and its applications. Its goal is to cover the fundamental results of Vector Calculus known as Green's, Stokes' and Gauss' theorems, and to show how to use them to solve problems. We attempt to explain the theory behind the techniques so that "WHY" they work is understood. The level of rigor is midway between MAT 201 and 217. The course is designed for science and engineering students with a good mathematical aptitude and for mathematicians with applied math interests.
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0.00 - 4.00 Credits
This is the linear algebra part of the MAT 203-204 sequence, which is harder and more theoretical than the 201-202 sequence.
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0.00 - 4.00 Credits
An introduction to classical number theory, to prepare for higher-level courses in the department. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions and quadratic reciprocity. There will be a topic, chosen by the instructor, from more advanced or more applied number theory: possibilities include p-adic numbers, cryptography, and Fermat's Last Theorem. This course is suitable both for students preparing to enter the Mathematics Department and for non-majors interested in exposure to higher mathematics.
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0.00 - 4.00 Credits
The rigorous epsilon-delta treatment of limits, convergence, and uniform convergence of sequences and series. Continuity, uniform continuity, and differentiability of functions. The Heine-Borel Theorem. The Rieman integral, conditions for integrability of a function and term by term differentiation and integration of series of functions, Taylor's Theorem.
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0.00 - 4.00 Credits
Rigorous introduction to linear algebra and matrices, with emphasis on proofs rather than on applications.
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0.00 - 4.00 Credits
Rigorous introduction to calculus in several variables.
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0.00 - 4.00 Credits
Introduction to mathematical foundations of the theory of ordinary differential equations. In the first part of the course, we will discuss elementary methods of solutions of ordinary differential equations. There will be a lengthy discussion of solutions of systems of linear differential equations with constant coefficients and its relation to eigenvalues of matrices. We will also discuss existence and uniqueness theorems for ordinary differential equations and differentiable dependence on initial data and parameters and methods of numerical solution of equations. This course assumes knowledge of multivariable calculus and linear algebra.
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