56:645:503-504Theory of Functions of a Complex Variable I,II (3,3) Analytic functions and the Cauchy Integral Theorem. Conformal mappings. Laplace transforms.
56:645:505-506Analysis I,II (3,3) Infinite series, especially Fourier series. Epsilon-delta proofs of continuity and differentiability. Convergence tests. Measure theory and integration.
56:645:508Mathematical 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.
56:645:527-528Methods 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.
56:645:531Geometry (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.
56:645:532Differential Geometry (3) Curves and surfaces in Euclidean space. Riemannian manifolds, connections, and curvature.
56:645:540Computational 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.
56:645:545Topology (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.
56:645:549-550Linear Algebra and Applications (3,3) Finite dimensional vector spaces, matrices, and linear operators. Eigenvalues, eigenvectors, diagonalizability, and Jordan canonical form. Applications.
56:645:551-552Abstract Algebra I,II (3,3) Introductory topics in rings, modules, groups, fields, and Galois theory. Pre- or corequisite: 56:645:549.
56:645:554Applied 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.
56:645:556Data 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.
56:645:557Regression and Time Series (3) Time series regression is a statistical method for predicting a future response based on the response history (known as autoregressive dynamics) and the transfer of dynamics from relevant predictors. The regression method of forecasting means studying the relationships between data points, which can help you to: Predict sales in the near and long term. Understand inventory levels. Understand supply and demand. Review and understand how different variables impact all of these factors.
56:645:558Probability Theory and Stochastic Processes (3)This course provides a mathematically precise introduction to the basic concepts of probability theory, whose aim is the description and study of random phenomena. The following basic principles are introduced: stochastic modeling, conditional probabilities and independence of random variables, as well as their expectation and variance, two fundamental limit theorems for long-time averages of independent identically distributed random variables. The course concludes with an introduction to Markov chains and their long time behavior.
56:645:560Industrial Mathematics (3) Monte Carlo methods, wavelets, data acquisition and manipulation, filters, frequency domain methods, fast Fourier transform, discrete Fourier transform.
56:645:562Mathematical Modeling (3) Perturbation methods, asymptotic analysis, conservation laws, dynamical system and chaos, oscillations, stability theory. Applications may include traffic flow, population dynamics, and combustion.
56:645:563Statistical Reasoning (3) Random variables, uniform, Gaussian, binomial, Poisson distributions, probability theory, stationary processes, central limit theorem, Markov chains, Taguchi quality control.
56:645:570Special Topics in Pure Mathematics (3) Topics vary from semester to semester. Prerequisite: Permission of instructor. Course may be taken more than once.
56:645:571-572Computational 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.
56:645:575Qualitative 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.
56:645:578Mathematical 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.
56:645:580Special Topics in Applied Mathematics (3) Topics vary from semester to semester. Prerequisite: Permission of instructor. Course may be taken more than once.
56:645:581Mathematical 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.
56:645:698Independent Study in Pure Mathematics (3) Study of a particular subject independently but with frequent consultations with a faculty member.
56:645:699Independent Study in Applied Mathematics (3) Study of a particular subject independently but with frequent consultations with a faculty member.
56:645:700Thesis in Pure Mathematics (3) Expository paper written under the close guidance of a faculty member.
56:645:701Thesis in Applied Mathematics (3) Expository paper written under the close guidance of a faculty member.
56:645:800Matriculation 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.
Graduate School-Camden 
