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Associate Dean for Academic Affairs Frederic I. Davis Comments to: fid@nadn.navy.mill |
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SM121 & SM122 Calculus I & II (4-0-4 & 4-0-4). Differential and integral calculus of one real variable; infinite series. SM121 Prereq: None & SM122 Prereq: SM121 or SM131. [SM121: fall, spring] & [SM122: fall, spring, summer]
SM131 Calculus I (3-0-3). Same as SM121 for students with prior differential calculus experience. [fall]
SM161 & SM162 Calculus with Computers I & II (5-0-5 & 5-0-5). Programming using MATLAB and a computer algebra package, algorithmic development of the integral and differential calculus of one real variable. SM161 Prereq: permission of department chair & SM162 Prereq: SM161. [SM161: fall] & [SM162: spring]
SM212 Differential Equations (4-0-4). Linear and simultaneous differential equations; solution by Laplace transform; partial differential equations and Fourier series. Prereq: SM221, SM223, or SM251. [fall, spring, summer]
SM219 Statistics and Probability (3-0-3). Nature of statistical methods, description of data, probability, distributions, estimation, tests of hypothesis, correlation, regression. Credit cannot be given for SM219 if credit has been given for SM230 or SM239. Prereq: SM122 or SM162. [spring]
SM221 Calculus III with Vector Fields (4-0-4). Differential and integral calculus of several real variables; vector analysis including integral theorems. Prereq: SM122 or SM162. [fall, spring]
SM222 Differential Equations with Matrices (4-0-4). A more rigorous treatment of material from SM212, the course uses basic ideas from linear algebra. Intended for mathematics majors. Prereq: SM221, SM223, or SM251; coreq: SM261. [spring]
SM223 Calculus III with Optimization (4-0-4). Differential and integral calculus of several real variables; vector analysis; optimization techniques for functions of several variables. Prereq: SM122 or SM162. [fall]
SM230 Probability with Naval Applications (3-0-3). An elementary treatment of the basic concepts of probability with an emphasis on naval applications. Sample spaces, discrete and continuous random variables and standard distributions. Selected topics of naval applications of probability theory such as random search, minefields and lateral range curves. Conditional probability and Bayes' theorem. Prereq: SM122 or SM162. [spring, summer]
SM239 Probability and Statistics I (3-0-3). A more rigorous treatment of material in SM230 for advanced work in mathematics, operations research, science and engineering. Credit cannot be given for both SM230 and SM239. Prereq: SM221, SM223, or SM251. [fall, spring]
SM251 Calculus with Computers III (4-0-4). Course content includes and extends that of SM221 with extensive computer applications. Prereq: SM162. [fall]
SM259 Mathematical Logic (3-0-3). Mathematical languages, formal logic, propositional calculus and truth tables, first order predicate calculus, proof theory, axiomatic systems and model theory. Applications to logical networks and nonstandard analysis. Prereq: SM122 or SM162. [fall]
SM261 Matrix Theory (3-0-3). Matrices, transformations, linear equations, vector spaces, characteristic matrix, eigenvalues, orthogonality. Prereq: SM122 or SM162. [fall]
SM271 Linear Programming (3-0-3). Simplex and dual simplex methods, minimax theorem, transportation problems and game theory. Prereq: SM122 or SM162. [as required]
SM279 Multivariable Calculus (3-0-3). An introduction to the geometry and analysis of n-dimensional space, including topics on multidimensional curves, inner products, linear functions, real valued functions, Taylor approximations, optimization, inverse function theorem, implicit function theorem, and change of variables in integration. Applications to economics and physics will be discussed. Prereq: SM221 or SM223, SM261. [spring]
SM291 Fundamentals of Mathematics I (2-2-3). Introduction to mathematical reasoning and the written and oral presentation of mathematical concepts, theory, and application of sets and relations. Prereq: SM122 or SM162. [spring]
SM311 Engineering Mathematics I (3-0-3). Vector analysis, Fourier analysis, partial differential equations, Sturm-Liouville problems, Legendre polynomials, determinants, and matrices. Prereq: SM212 or SM222. [fall, spring]
SM311O Engineering Mathematics I (3-0-3). Vector analysis, Fourier analysis, partial differential equations with emphasis on stream and potential functions, conservation of mass, conservation of linear momentum (Navier-Stokes Equations) in rectangular and rotating coordinate systems. Prereq: SM212 or SM222.
SM311P Mathematical Methods for Physics (3-0-3). A course in mathematics applicable to physics. Includes topics from the following areas: linear (vector) algebra, linear (vector) analysis, boundary value problems, and variational calculus. Prereq: Calculus III and Differential Equations.
SM312 Engineering Mathematics II (3-0-3). Laplace and Fourier transforms, selected topics from complex variables. Prereq: SM212 or SM222. [as required]
SM313 Engineering Mathematics III (3-0-3). Fundamental topics from calculus based probability theory (discrete and continuous random variables, multivariate distributions, expected values, and the Central Limit Theorem) and from linear algebra and matrix theory (matrix operations, Gaussian elimination, linear independence, eigenvalues, and solutions to systems of ordinary differential equations) suitable for applications in engineering. Prereq: SM212 or SM222. [fall]
SM314 Engineering Mathematics with Statistics (4-0-4). Basic concepts in probability and statistics, Laplace transforms, Fourier analysis, and complex variables with applications. Prereq: SM212 or SM222. [fall, spring]
SM315 Introduction to Partial Differential Equations (3-0-3). Linear equations, Cauchy problems, Laplace and Poisson equations, boundary value problems, heat equations, Sturm-Liouville problems, and orthonormal expansions. Prereq: SM212 or SM222. [fall]
SM331 & SM332 Advanced Calculus I & II (4-0-4, 4-0-4). Logic, induction, sequences, limits, real numbers, series, continuity, differentiability, properties of continuous functions, the Riemann Integral, power series. Prereq: SM261, SM291. [fall & spring]
SM331H & SM332H Real Analysis I & II (4-0-4, 4-0-4). Honors versions of SM331 and SM332. Prereq: Permission of mathematics department honors committee. [fall & spring]
SM339 Applied Statistics I (3-0-3). An applied study of a variety of statistical methods used in obtaining, presenting, summarizing and analyzing statistical information. Included are strategies for data collection and presentation, and techniques of statistical inference for population, parameters based on the concepts of sampling, probability and distribution theory. Prereq: SM239, SM261. [fall]
SM342 Discrete Structures I (3-0-3). Foundations and methods of proof. Combinatorics, graph theory, group theory. Selected topics. Prereq: SM122 or SM162. [spring]
SM362 Modern Algebra (3-0-3). Integers, groups, mappings, rings, fields. Prereq: SM261, SM291. [spring]
SM365 Introduction to Scientific Computing (4-0-4). Computer arithmetic and errors, algorithms and programs for iterative solution of equations, linear systems, function approximations, numeric integration, ordinary differential equations, use of scientific software libraries and introduction to MATLAB. Prereq: SM261 or SM311. [fall]
SM411 Introduction to Complex Variables (3-0-3). Algebra and topology of complex numbers. Elementary functions. Complex derivative and integral. Theorems of Cauchy. Analytic functions, conformal mappings, Taylor and Laurent series, singularities, residue theory, analytic continuation. Applications to real analysis and physical problems. Prereq: SM331. [fall]
SM425 Advanced Numerical Analysis (3-0-3). Numerical solution of equations in one and several variables, direct and iterative algorithms, rate of convergence. Computer methods emphasized. Prereq: SM212 or SM222, SM331 or permission of department chair. [as required]
SM426 Numerical Methods for Differential Equations (3-0-3). Interpolation and polynomial approximation, numerical integration and differentiation, numerical algorithms for initial value and boundary value problems. Prereq: SM212 or SM222, SM331 or permission of department chair. [as required]
SM439 Seminar in Statistics (3-0-3). This course examines statistics as it occurs in actual research practice. The students read and review research articles from a variety of fields and evaluate the statistical analysis used to arrive at conclusions. Prereq: SM339. [fall]
SM444 Discrete Structures II (3-0-3). Topics in combinatorics and graph theory, with applications. Latin squares, linear algebra and combinatorics, finite projective planes, topological graph theory, Ramsey theory, trees. Prereq: SM342. [as required]
SM461 Linear Algebra (3-0-3). Vector spaces, linear transformations, Jordan canonical form, inner product spaces. Prereq: SM261, SM331. [as required]
SM462 Algebraic Structures (3-0-3). Groups, rings, fields, Galois theory. Prereq: SM362, SM331. [as required]
SM464 Topology (3-0-3). A mathematical analysis of topological spaces, separation axioms, covering properties, and metric spaces. Coreq: SM332. [as required]
SM465 Advanced Differential Equations (3-0-3). Existence and uniqueness of solutions to ordinary differential equations. Stability, oscillation, dynamical systems. Prereq: SM212 or SM222; coreq: SM332. [as required]
SA367 Introduction to Mathematical Modeling (3-0-3). Realistic problems, often of military interest, are formulated mathematically and solved using techniques from probability, statistics, calculus and differential equations. The analysis is carried out by students working in small teams and individually. Solutions are presented in oral nontechnical briefings and in written technical reports. Prereq: SM239 or SM230. [fall]
SA401 Linear Models and Optimization (3-0-3). Investigation of fundamentals of linear optimization subject to constraints, including construction and analysis of linear programming and network problems. Prereq: SM261. [fall, spring]
SA402 Dynamic and Stochastic Models (3-0-3). Investigation of quantitative analysis of decision options, including PERT/CPM, dynamic programming, Markov chains and queuing theory. Applications to typical operations are stressed. Prereq: SM239 or SM230, SM261. [fall, spring]
SA410 Applications of Search and Detection Theory (3-0-3). Considerations in picking a measure of effectiveness (MOE) for use in analyzing decision options and decision criterion are studied. The focus of the course is the analysis of search and detection operations, particularly as they arise in anti-submarine operations, using probability models. Barrier detection, area search and parallel sweep operations models are developed. Additional topics in mine warfare, target coverage models, anti-air warfare, and target motion analysis may be picked for study by the instructor. Credit cannot be given for both SA302 and SA410. Prereq: SM239 or SM230. [spring]
SA412 Projects in Operations Analysis (2-2-3). Operations research techniques are applied using student projects, case studies and visiting lecturers. Topics include current military and industrial problems. Prereq: permission of department chair. [spring]
SA421 Simulation Modeling (3-0-3). Discrete simulation of systems using a simulation language. Includes random number generation, validation and verification of simulations, input and output data analysis. Semester projects are done as part of an analysis team. Prereq: SM339. [spring]
SA430 Logistics (3-0-3). Investigation of techniques of operations analysis applicable to the solution of problems in reliability, maintainability, availability and inventory. Prereq: SM239. [fall]
SA442 Applied Statistics II (3-0-3). A continuation of SM339 that includes examination, evaluation and application of advanced statistical methods. Techniques studied include sampling, nonparametric analysis, simple and multiple regression, correlation, analysis of variance and decision theory. Prereq: SM339. [spring]
SA475E Research Seminar in Quantitative Economics (3-0-3). Directed research on a specific topic. Capstone course for Quantitative Economics majors. Emphasis on empirical work using computers. Prereq: 1/C SQE major. [spring]
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Associate Dean for Academic Affairs Frederic I. Davis Comments to: fid@nadn.navy.mill |
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