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MATH 346: Number Theory
3.00 Credits
University of Scranton
(Prerequisite: MATH 299 or permission of instructor)Topics include divisibility, the Euclidean algorithm, linear diophantine equations, prime factorization, linear congruences, some special congruences, Wilson’s theorem, theorems of Fermat and Euler, Euler phi function and other multiplicative functions, and the Mobius Inversion Formula.
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MATH 346 - Number Theory
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MATH 351: Linear Algebra
3.00 Credits
University of Scranton
(Prerequisite: MATH 221)Vector spaces, matrices, determinants, linear transformations, eigen values, eigenvectors, inner products, and orthogonality.
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MATH 351 - Linear Algebra
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MATH 360: Coding Theory
3.00 Credits
University of Scranton
(Prerequisite: MATH 351)A study of algebraic coding theory. Topics include: linear codes, encoding and decoding, hamming, perfect, BCH cyclic and MDS codes, and applications to information theory.
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MATH 360 - Coding Theory
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MATH 361: Numerical Analysis
3.00 Credits
University of Scranton
(Prerequisites: MATH 222, MATH 351)Introductory numerical methods. Topics include: root finding, matrix factorizations, numerical linear algebra, polynomial interpolation, numerical integration, numerical solution of differential equations. Appropriate computation tools will be used.
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MATH 361 - Numerical Analysis
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MATH 384: Special Topics
1.00 - 4.00 Credits
University of Scranton
Topics, prerequisites, and amount of credit will be announced prior to preregistration.
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MATH 384 - Special Topics
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MATH 410: Introduction to Stochastic Processes
3.00 Credits
University of Scranton
(Prerequisites: MATH 310, MATH 351)An introduction to stochastic processes studying Markov chains, stationary distributions, birth and death processes, pure jump processes, second order continuity, integration and differentiation, and stochastic differential equations.
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MATH 410 - Introduction to Stochastic Processes
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MATH 446: Real Analysis I
3.00 Credits
University of Scranton
(Prerequisites: MATH 222, MATH 299)Topics include: the algebra and topology of the real numbers, functions, sequences of numbers, limits, continuity, absolute and uniform continuity, and differentiation.
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MATH 446 - Real Analysis I
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MATH 447: Real Analysis II
3.00 Credits
University of Scranton
(Prerequisite: MATH 446)Selections from: integration theory, infinite series, sequences and infinite series of functions, and related topics.
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MATH 447 - Real Analysis II
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MATH 448: Modern Algebra I
3.00 Credits
University of Scranton
(Prerequisites: MATH 299, MATH 351)Fundamental properties of groups, rings, polynomials, and homomorphisms.
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MATH 448 - Modern Algebra I
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MATH 449: Modern Algebra II
3.00 Credits
University of Scranton
(Prerequisite: MATH 448)Further study of algebraic structures.
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MATH 449 - Modern Algebra II
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