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Course Criteria
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3.00 Credits
This is an introductory course in number theory. The topics covered begin with divisibility and factorization, the Fundamental Theorem of Arithmetic, prime numbers, greatest common divisor, and least common multiples. The course continues with congruences and arithmetic functions. The remainder of the course introduces one or more advanced topics such as quadratic residues, primitive roots, Diophantine equations, continued fractions, and cryptography.
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3.00 Credits
Numerical methods fundamental to scientific computing are developed. Topics include finite difference calculus; zeros of a function; matrix computations; solutions to systems of linear equations; approximation by polynomials; numerical differentiation and integration; numerical solutions of ordinary differential equations; rounding errors and other types of errors. Selected algorithms will be run on the computer. Students will be required to use appropriate computer software.
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3.00 Credits
The course is an introduction to cryptography, the study of securing communication and information. This course will cover the mathematical, algorithmic, and historical aspects of classical and modern cryptography. We will also introduce students to personal encryption software as well as programming libraries and computer algebra systems that allow one to perform large computations necessary for cryptographic applications. Topics will include classical and modern symmetric ciphers, public-key cryptography (e.g. RSA), various cryptographic protocols, and any other topics of interest to the instructor and students. All necessary theoretical background will be reviewed, but some background in number theory, abstract algebra, probability, or computer science will be expected.
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3.00 Credits
In this course students will develop an understanding of the basic theory, applications and connections of linear algebra and differential equations. Topics include: first, second, and higher order ordinary differential equations; methods of solutions include exact, substitution reduction, undetermined coefficients, variation of parameters, power series solutions, the Laplace Transform, and system of linear differential equations. Consideration is given to applications to the physical and natural sciences. Students will be required to use appropriate computer software.
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3.00 Credits
This course is meant to provide an introduction to nonlinear dynamics and chaos theory. An emphasis will be placed on qualitative analysis for both continuous and discrete dynamical systems. Key concepts will include fixed/ equilibrium points and periodic solutions, linear stability analysis and asymptotic behavior, bifurcation analysis for parameterized families, and existence of periodic orbits. The latter part of the course will focus on chaos theory with topics including period-doubling bifurcations, strange attractors, and Lyapunov exponents. Classic and real-world models will be stressed. Throughout the course, programming in scientific computing software (e.g. MATLAB) will be introduced and reinforced.
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3.00 Credits
Introduction to the structure of the real number system and its topology; metric space and its topology; basic theorems of real analysis; differentiable functions.
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3.00 Credits
Introduction to the theory of Reimann-Stieltjes integration; functions of bounded variation; Lebesgue measure and Lebesgue integrals; uniform convergence of sequences and series of functions.
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3.00 Credits
Operations Research uses quantitative methods to determine the best decision for an operating system. A mathematical approach to studying methods as applied to the decision process in industry is taken. The methods studied are selected from among: linear programming; game theory; graph theory and network analysis. Students will be required to use appropriate computer software.
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3.00 Credits
Operations Research uses quantitative methods to determine the best decision for an operating system. A mathematical approach to studying methods as applied to the decision process in industry is taken. The methods studied are selected from among: linear programming; game theory; integer programming; graph theory and network analysis; nonlinear programming; and metaheuristics. Students will be required to use appropriate computer software.
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1.00 - 6.00 Credits
MAT PROBLEM SEMINAR
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