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MATH 399: Independent Study in Mathematics
3.00 Credits
Shippensburg University of Pennsylvania
Independent study affords students the opportunity to engage in independent study related to their major field, a supporting area, or specialized interest.
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MATH 399 - Independent Study in Mathematics
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MATH 400: History of Mathematics
3.00 Credits
Shippensburg University of Pennsylvania
Focuses on the development of mathematical ideas relevant to K-12 mathematics. Some examples include episodes in the development of number systems, algebra, geometry, trigonometry, number theory, and analytic geometry. Some time spent on multicultural issues, sometimes referred to as 'ethnomathematics.' Must be at least junior standing to enroll. This class is available for graduate credit.
Prerequisite:
MATH 320
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MATH 400 - History of Mathematics
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MATH 410: Numerical Analysis
3.00 Credits
Shippensburg University of Pennsylvania
Primarily methods of numerical approximation to the value of functions, polynomials, and systems of equations. Topics include accuracy of approximate calculations, interpolation and interpolating polynomials, solution of algebraic and transcendental equations. Numerical solution of simultaneous linear and nonlinear equations, principle of least squares, difference equations, and quadrature formulas are studied. This class is available for graduate credit.
Prerequisite:
MATH 212 and (CMSC 110, CMSC 180, or SWEN 100)
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MATH 410 - Numerical Analysis
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MATH 421: Number Theory and Cryptography
3.00 Credits
Shippensburg University of Pennsylvania
Introduction to a selection of topics from the related fields of Number Theory and Cryptography. Topics may include congruence arithmetic, primitive roots, quadratic residues, perfect numbers, Pythagorean triples, sums of squares, Fermat's Last Theorem, and primality testing, various substitution ciphers including affine, Vigenere, and Hill ciphers and the RSA public key encryption system with several variations. Algorithms for each encryption scheme discussed will be introduced and implemented. This class is available for graduate credit.
Prerequisite:
MATH 320
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MATH 421 - Number Theory and Cryptography
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MATH 422: Partial Differential Equations
3.00 Credits
Shippensburg University of Pennsylvania
Introduction to Partial Differential Equations, a fundamental branch of applied mathematics. Three classical equations from mathematical physics are discussed: the wave equation, the heat equation and Laplace's equation. Techniques which include separation of variables, Fourier series and fundamental solutions are introduced to address these equations. An introduction to numerical methods is also included. This class is available for graduate credit.
Prerequisite:
MATH 213 and MATH 320
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MATH 422 - Partial Differential Equations
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MATH 425: Advanced Algebraic Structures
3.00 Credits
Shippensburg University of Pennsylvania
Detailed study of one or more of the higher level algebraic structures such as groups, rings, fields, or abstract vector spaces. Emphasis on structure theorems such as the fundamental theorem of group homomorphisms and uses the sophistication developed in MAT 320. This class is available for graduate credit.
Prerequisite:
MATH 318 and MATH 320
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MATH 425 - Advanced Algebraic Structures
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MATH 430: Complex Analysis
3.00 Credits
Shippensburg University of Pennsylvania
Introductory course in the theory of functions of a complex variable. Topics include complex numbers, analytic functions, contour integration, Cauchy's Theorem, and infinite series. Methods of a logical proof are developed and used throughout. This class is available for graduate credit.
Prerequisite:
MATH 213 and MATH 320
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MATH 430 - Complex Analysis
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MATH 441: Real Analysis I
3.00 Credits
Shippensburg University of Pennsylvania
Designed to give a fundamental understanding of the concepts used in elementary calculus. Methods of a logical proof are developed and used throughout. Topics include real numbers, sequences, limits, continuity, derivatives and the Riemann integral. This class is available for graduate credit.
Prerequisite:
MATH 212 and MATH 320
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MATH 441 - Real Analysis I
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MATH 450: Combinatorics
3.00 Credits
Shippensburg University of Pennsylvania
Concerned with computing within discrete mathematical structures and combinatorial problem solving. Topics include sets and graphs; counting and enumeration techniques including recurrence relations and generating functions; and graph theory algorithms. This class is available for graduate credit.
Prerequisite:
MATH 225
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MATH 476: Probability
3.00 Credits
Shippensburg University of Pennsylvania
In-depth development of probability and distribution theory. Topics include counting techniques, Bayes' Theorem, random variables, moment-generating functions, univariate and multivariate probability distributions, and the Central Limit Theorem. This class is available for graduate credit.
Prerequisite:
MATH 213 and MATH 318
Corequisite:
MATH 213
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MATH 476 - Probability
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