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MTH 347: Number Theory
4.00 Credits
CUNY College of Staten Island
4 hours; 4 credits Mathematical induction, divisibility, prime numbers, Euclidean algorithm, factorization methods, Diophantine equations, congruences, Chinese remainder theorem, systems of congruences, Fermat’s little theorem, multiplicative functions, public key cryptography, primitive roots, primality tests, quadratic reciprocity, Pythagorean triples, Fermat’s last theorem, and sums of squares. Other topics may include continued fractions and partitions. Prerequisite: MTH 232
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MTH 347 - Number Theory
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MTH 350: Mathematical Logic
4.00 Credits
CUNY College of Staten Island
(Also PHL 321) 4 hours; 4 credits The calculus of propositions. Existential and universal quantifiers. Turing machines and computability theory. Non-computable functions. The decision problem for arithmetic. Axiomatizing arithmetic. The Godel Incompleteness theorem. Prerequisite: MTH 233 or MTH 236
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MTH 350 - Mathematical Logic
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MTH 360: Actuarial Science
2.00 Credits
CUNY College of Staten Island
2 hours; 2 credits Intensive review of concepts from calculus and linear algebra with special attention to actuarial applications. This course may not be used to satisfy the requirements for the Mathematics major. Prerequisite: MTH 330 or MTH 338
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MTH 360 - Actuarial Science
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MTH 370: Operations Research
4.00 Credits
CUNY College of Staten Island
4 hours; 4 credits Use of linear programming in minimization and maximization problems and the solution of such problems by computer. Topics will include convex sets, linear inequalities, the simplex method, duality, degeneracy procedures, and the transportation model. Prerequisites: MTH 338 and CSC 126 or CSC 270
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MTH 370 - Operations Research
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MTH 410: Mathematical Statistics I
4.00 Credits
CUNY College of Staten Island
4 hours; 4 credits A course in the basic concepts of applied mathematical statistics: parametric models, estimation, confidence intervals, hypotheses testing. Prerequisite: MTH 311
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MTH 410 - Mathematical Statistics I
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MTH 411: Mathematical Statistics II
4.00 Credits
CUNY College of Staten Island
4 hours; 4 credits A continuation of MTH 410, topics in applied mathematical statistics including regression and correlation, the linear model, analysis of variance, randomized block designs, non-parametric methods. Prerequisite: MTH 410
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MTH 411 - Mathematical Statistics II
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MTH 415: Mathematical Biology
4.00 Credits
CUNY College of Staten Island
(Also BIO 415) 4 hours; 4 credits This course will address the growing interaction between mathematics and the biological sciences and will provide a practical context for the mathematical description and analysis of biological processes. The emphasis will be on the construction and analysis of models consistent with empirical data. Biological problems in ecology and conservation, epidemiology, cell biology, and neuroscience will be used to illustrate the equations, including especially nonlinear equations. The computer program MATLAB will be used extensively. Prerequisites: MTH 230 and MTH 231 or equivalent, MTH 229, and one BIO 300-level course
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MTH 415 - Mathematical Biology
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MTH 416: Mathematics of Finance
4.00 Credits
CUNY College of Staten Island
(Also FNC 416) 4 hours; 4 credits Introduction to the mathematical theory of derivative pricing; binomial trees and martingales; Black-Scholes formula; stochastic differential equations and Ito calculus; Girsanov theorem Prerequisite: MTH 311
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MTH 416 - Mathematics of Finance
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MTH 431: Complex Analysis
4.00 Credits
CUNY College of Staten Island
4 hours; 4 credits Functions of a complex variable; Cauchy integral theorem; power series, residues, and poles; elementary conformal mapping. Applications to problems in physics and engineering will be considered. Prerequisite: MTH 330
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MTH 431 - Complex Analysis
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MTH 435: Nonlinear Dynamics and Chaos
4.00 Credits
CUNY College of Staten Island
4 hours; 4 credits An introduction to nonlinear problems in mathematics. Subjects to be covered include bifurcation theory, nonlinear oscillation, phase plane analysis, limit cycles. Poincare and Lienard theorems. Lorenz equations and chaos, strange attractors, the logistic equation, period doubling, fractals. Applications are to problems in biological and physical systems and engineering science. The course will make extensive use of computers. Prerequisite: MTH 330
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MTH 435 - Nonlinear Dynamics and Chaos
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