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Course Criteria
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4.00 Credits
An introduction to both the principles and practice of cryptography and its application to network security. Topics include symmetric-key encryption (block ciphers, modes of operations, AES), message authentication (pseudorandom functions, CBCMAC), public-key encryption (RSA, ElGamal), digital signatures (RSA, Fiat-Shamir), and authentication applications (identification, zero-knowledge).
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4.00 Credits
Introduction to the main concepts, constructs, and applications of modern algebra. Groups, transformation groups, Sylow theorems, and structure theory; rings, polynomial rings, and unique factorization; introduction to fields and Galois theory. Although not acceptable for the mathematics majors, it is accepted toward the mathematics minor and is a strongly recommended course for the Steinhardt mathematics education major.
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4.00 Credits
Divisibility and prime numbers. Linear and quadratic congruences. The classical number-theoretic functions. Continued fractions. Diophantine equations.
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4.00 Credits
Introduction to the mathematics of finance. Topics: linear programming with application to pricing. Interest rates and present value. Basic probability, random walks, central limit theorem, Brownian motion, log-normal model of stock prices. Black- Scholes theory of options. Dynamic programming with application to portfolio optimization.
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4.00 Credits
Formulation and analysis of mathematical models. Mathematical tools include dimensional analysis, optimization, simulation, probability, and elementary differential equations. Applications to biology, economics, and other areas of science. The necessary mathematical and scientific background is developed as needed. Students participate in formulating models as well as in analyzing them.
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4.00 Credits
In numerical analysis, one explores how mathematical problems can be analyzed and solved with a computer. As such, numerical analysis has very broad applications in mathematics, physics, engineering, finance, and the life sciences. This course introduces the subject to mathematics majors. Theory and practical examples using Matlab are combined to explore topics ranging from simple root-finding procedures to differential equations and the finite element method.
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4.00 Credits
Intended primarily for premedical students with interest and ability in mathematics. Topics of medical importance using mathematics as a tool, including Department of Mathematics control of the heart, optimal principles in the lung, cell membranes, electrophysiology, countercurrent exchange in the kidney, acid-base balance, muscle, cardiac catheterization, and computer diagnosis. Material from the physical sciences is introduced as needed and developed within the course.
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4.00 Credits
Introduces the student of biology or mathematics to the use of computers as tools for modeling physiological phenomena. The student constructs two computer models selected from the following list: circulation, gas exchange in the lung, control of cell volume, and the renal countercurrent mechanism. The student then uses the model to conduct simulated physiological experiments.
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4.00 Credits
First- and second-order equations. Series solutions. Laplace transforms. Introduction to partial differential equations and Fourier series.
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4.00 Credits
Many laws of physics are formulated as partial differential equations. This course discusses the simplest examples of such laws as embodied in the wave equation, the diffusion equation, and Laplace's equation. Nonlinear conservation laws and the theory of shock waves. Applications to physics, chemistry, biology, and population dynamics.
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