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Graduate School-Camden
Actuarial and Statistical Analysis
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Biology 120
Biology, Computational and Integrative 121
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Chemistry 160
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English 350, 352, 354, 615, 842
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Mathematical Sciences 645
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Applied and Computational Mathematics
Certificate in Statistics
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World Languages and Cultures 410
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  Camden Graduate Catalog 2021-2023 Graduate School-Camden Mathematical Sciences 645 Graduate Courses  

Graduate Courses

56:645:503-504 Theory of Functions of a Complex Variable I,II (3,3) Analytic functions and the Cauchy Integral Theorem. Conformal mappings. Laplace transforms.
56:645:505-506 Analysis I,II (3,3) Infinite series, especially Fourier series. Epsilon-delta proofs of continuity and differentiability.  Convergence tests. Measure theory and integration.
56:645:507 Contemporary Issues--Teaching beyond Regurgitation (3) Discusses traditional as well as contemporary approaches to teaching mathematics. Comparisons within these contexts are investigated. The intricate connections between geometry and algebra serve as a segue to a deeper analysis of calculus and linear and abstract algebra. Selected readings from NCTM publications are a course requirement.
56:645:508 Mathematical Reasoning (3) This course develops two fundamental components of writing mathematics: reasoning (thinking about the proof) and writing (formulating and writing the ideas precisely using logical statements). The course begins with illustrative examples and general guidelines.
56:645:527-528 Methods of Applied Mathematics I,II (3,3) Derivation of the heat and wave equations. Existence theorems for ordinary differential equations, series solutions. Bessel and Legendre equations. Sturm-Liouville Theorem. Pre- or corequisite: 56:645:549. 
56:645:531 Geometry (3) Review and reevaluation of Euclid's geometry. Axiomatic development of Euclidean and hyperbolic geometries. The parallel postulate. The impossibility of trisecting an angle or duplicating a cube.
56:645:532 Differential Geometry (3) Curves and surfaces in Euclidean space. Riemannian manifolds, connections, and curvature.
56:645:533-534 Introduction to the Theory of Computation I,II (3,3) 645:533: Introduction to formal languages, automata, and computability: regular languages and finite state automata; context-free grammars and languages; pushdown automata; the Church-Turing thesis; Turing machines; decidability and undecidability; Rice's theorem. 645:534: Second course in the sequence; addresses key topics in computability and complexity theory, such as recursive and recursively enumerable sets; the Recursion Theorem; Turing reductions and completeness; Kolmogorov complexity; space and time complexity; NP-completeness; hierarchy theorems; probabilistic complexity classes, and interactive proof systems.
56:645:535-536 Algebra for Computer Scientists I,II (3,3) Linear and abstract algebra, including group theory, with applications to image processing, data compression, error correcting codes, and encryption.
56:645:537 Computer Algorithms (3) Algorithm design techniques: divide-and-conquer, greedy method, dynamic programming, backtracking, and branch-and-bound. Advanced data structures, graph algorithms, and algebraic algorithms. Complexity analysis, complexity classes, and NP-completeness. Introduction to approximation algorithms and parallel algorithms.
56:645:538 Combinatorial Optimization (3) Algorithmic techniques for solving optimization problems over discrete structures, including integer and linear programming, branch-and-bound, greedy algorithms, divide-and-conquer, dynamic programming, local optimization, simulated annealing, genetic algorithms, and approximation algorithms.
56:645:540 Computational Number Theory and Cryptography (3) Primes and prime number theorems and numerical applications; the Chinese remainder theorem and its applications to computers and Hashing functions; factoring numbers; cryptography; computation aspects of the topics emphasized. Students required to do some simple programming.
56:645:541 Introduction to Computational Geometry (3) Algorithms and data structures for geometric problems that arise in various applications, such as computer graphics, CAD/CAM, robotics, and geographical information systems (GIS). Topics include point location, range searching, intersection, decomposition of polygons, convex hulls, and Voronoi diagrams.
56:645:545 Topology (3) Point set topology, fundamental group and coverings. Singular homology and cohomology, the Brouwer degree and fixed-point theorems, the sphere retraction theorem, invariance of domains.
56:645:549-550 Linear Algebra and Applications (3,3) Finite dimensional vector spaces, matrices, and linear operators. Eigenvalues, eigenvectors, diagonalizability, and Jordan canonical form.  Applications.
56:645:551-552 Abstract Algebra I,II (3,3) Introductory topics in rings, modules, groups, fields, and Galois theory. Pre- or corequisite: 56:645:549.
56:645:554 Applied Functional Analysis (3) Infinite dimensional vector spaces, especially Banach and Hilbert vector spaces. Orthogonal projections and the spectral decomposition theorem. Applications to differential equations and approximation methods.
56:645:556 Data Visualization (3) This is a one-semester introduction to data visualization techniques. Students will learn and work through the data science pipeline, focusing on how to effectively and efficiently transform and visualize their data. Techniques will be applied to produce publication-quality graphics, as well as interactive tools for exploratory analysis. Mathematical techniques for transforming data to address common data problems in today's industries will be covered. The Python programming language along with popular data science packages are used extensively. Prerequisite: Linear Algebra.
56:645:557 Signal Processing (3) Signal modeling: periodic, stationary, and Gaussian signals. System representation: Volterra representation, state space representation, simulation. Themes in system design: least square estimation, system identification, adaptive signal processing. Representation of discrete causal signals: role of Fourier analysis, convolutions, fast Fourier transforms. Realization of linear recurrent structures: controllability, observability and minimal realization, frequency domain analysis of signals, and the role Laplace transforms. Stability analysis: Lyapunov and linearization methods. Prediction, filtering, and identification: linear prediction, the LQR problem, Kalman filter.
56:645:558 Theory and Computation in Probability and Queuing Theory (3) Basic probability structures, probability distributions, random number generations and simulations, queuing models, analysis of single queue, queuing networks, applications of queuing theory.
56:645:560 Industrial Mathematics (3) Monte Carlo methods, wavelets, data acquisition and manipulation, filters, frequency domain methods, fast Fourier transform, discrete Fourier transform.
56:645:561 Optimization Theory (3) Linear programming: optimization, simplex algorithm, nonlinear programming, game theory.
56:645:562 Mathematical Modeling (3) Perturbation methods, asymptotic analysis, conservation laws, dynamical system and chaos, oscillations, stability theory. Applications may include traffic flow, population dynamics, and combustion.
56:645:563 Statistical Reasoning (3) Random variables, uniform, Gaussian, binomial, Poisson distributions, probability theory, stationary processes, central limit theorem, Markov chains, Taguchi quality control.
56:645:570 Special Topics in Pure Mathematics (3) Topics vary from semester to semester. Prerequisite: Permission of instructor. Course may be taken more than once.
56:645:571-572 Computational Mathematics I,II (3,3) Newton's method, curve and surface fitting. Numerical solutions of differential equations and linear systems, eigenvalues and eigenvectors. Fast Fourier transform.
56:645:574 Control Theory and Optimization (3) Controllability, observability, and stabilization for linear and nonlinear systems. Kalman and Nyquist criteria. Frequency domain methods, Liapunov functions.
56:645:575 Qualitative Theory of Ordinary Differential Equations (3) Cauchy-Picard existence and uniqueness theorem. Stability of linear and nonlinear systems. Applications to equations arising in biology and engineering.
56:645:578 Mathematical Methods in Systems Biology I (3) Introduction to computational and system biology, focusing on advanced mathematical tools. In particular, ordinary and partial differential equations, control theory and discrete mathematics (networks) will be used to address a wide set of biological and biomedical applications. The latter will range from classical prey-predator populations examples to cancer immuno and drug therapies, from evolutionary math to gene networks. Prerequisite: 56:645:508.
56:645:579 Celestial Mechanics (3) In this course we examine the orbits of planets, satellites, asteroids, and spacecraft. The first part of the course deals with classical astrodynamics, as practiced by space agencies before 1990. The second part of the course will explore features of three-body systems that cannot be approximated by two-body conic sections. Topics include Lagrange points, hyperbolic maps, and stable and unstable manifolds. We will see how these concepts have in recent years been used to find spacecraft orbits, which require less fuel than the classical piecewise conic section orbits.
56:645:580 Special Topics in Applied Mathematics (3) Topics vary from semester to semester. Prerequisite: Permission of instructor. Course may be taken more than once.
56:645:581 Mathematical Methods in Systems Biology II (3) The course will focus on mathematical methods, which are of particular relevance for biological systems. Building up on Mathematical Methods in System Biology I, the course will first develop the theory of ordinary differential equations, dealing with equilibrium analysis, phase portraits, and stability. Then links between properties of networks and systems of ODEs will be explored. Finally, network dynamics will be addressed. Prerequisite: 56:645:508.
56:645:698 Independent Study in Pure Mathematics (3) Study of a particular subject independently but with frequent consultations with a faculty member.
56:645:699 Independent Study in Applied Mathematics (3) Study of a particular subject independently but with frequent consultations with a faculty member.
56:645:700 Thesis in Pure Mathematics (3) Expository paper written under the close guidance of a faculty member.
56:645:701 Thesis in Applied Mathematics (3) Expository paper written under the close guidance of a faculty member.
56:645:800 Matriculation Continued (0) Continuous registration may be accomplished by enrolling for at least 3 credits in standard course offerings, including research courses, or by enrolling in this course for 0 credits. Students actively engaged in study toward their degree who are using university facilities and faculty time are expected to enroll for the appropriate credits.
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