| Course: | SM005 |
| Title: | Pre-Calculus Mathematics |
| Credits: | 4—1—4 |
| Description: | Basic review of algebraic and arithmetic operations, analysis of functions and their graphs, and trigonometry. This course may be required in addition to stated graduation requirements for certain midshipmen |
| Requisites: | Prereq: placement by department chair. |
| Course: | SM121 |
| Title: | Calculus I |
| Credits: | 4—0—4 |
| Description: | The first of a traditional three course sequence covering differential and integral calculus in one or more variables. This course focuses on limits and differential calculus. After a quick refresher in precalculus, this course covers limits (instantaneous rate of change, definition of the derivative), techniques of differentiation (derivatives of basic functions, product rule, quotient rule, chain rule), and applications (optimization, curve sketching, linear approximations, Taylor polynomials). |
| Requisites: |
| Course: | SM122 |
| Title: | Calculus II |
| Credits: | 4—0—4 |
| Description: | Continuation of Calculus I. The second of a traditional three course sequence covering differential and integral calculus in one or more variables. This course focuses on integral calculus and covers antiderivatives/integrals (Riemann sums, techniques for integration, applications), separable differential equations (modeling, Euler's method, direction fields), infinite series including Taylor series, and vector arithmetic. |
| Requisites: | Prereq: SM121 |
| Course: | SM208 |
| Title: | Data Science For Decision-Making |
| Credits: | 3—0—3 |
| Description: | An introduction to using probabilistic and statistical tools to support decision makers. Topics include: descriptive statistics, requirements for causal inference, data manipulation, data visualization and exposition, data generation via probability models, hypothesis testing and confidence intervals via resampling techniques, the Central Limit Theorem and its implications, regression for prediction and inference, additional machine learning methods, ethical issues in machine learning, and critical thinking in the context of data science. Midshipmen will make extensive use of appropriate computer tools. |
| Requisites: | Prereq: SM221, SM221P, or SM223 |
| Course: | SM212 |
| Title: | Differential Equations |
| Credits: | 4—0—4 |
| Description: | An introduction to solving and applying different types of differential equations. Topics include: explicitly solving both first and higher-order differential equations; systems of differential equations using matrix techniques; Laplace transforms; numerical methods to approximate solutions to differential equations; partial differential equations via Fourier series and separation of variables; modeling physical phenomena using differential equations and interpreting their solutions, and writing well-organized, coherent solutions to problems. |
| Requisites: | Prereq: SM221 OR SM221P OR SM223 |
| Course: | SM221 |
| Title: | Calculus III With Vector Fields |
| Credits: | 4—0—4 |
| Description: | One possible follow-on course to Calculus II. Topics include: describing basic curves and space motion using vector functions and their derivatives and integrals; describing basic surfaces using rectangular, cylindrical, and spherical coordinates; describing basic surfaces using parametrizations; finding partial derivatives, directional derivatives, and gradient vectors; demonstrating proficiency in relating these to the changes in a function; demonstrating intuitive understanding of the curl, divergence, and the main theorems in vector calculus (Green's Theorem, Stokes' Theorem, Divergence Theorem); classifying critical points; demonstrating proficiency in evaluating double and triple integrals in various coordinate systems; demonstrating proficiency in evaluating line integrals and surface integrals of vector fields and interpreting the results in connection to work, potential, or flux for the field; writing well-organized, coherent solutions to application problems. |
| Requisites: | Prereq: SM122 OR SM122R |
| Course: | SM222 |
| Title: | DIFFERENTIAL EQUATIONS WITH MATRICES |
| Credits: | 4—0—4 |
| Description: | An introduction to differential equations. Topics include solution of first order differential equations (separable, linear), direction fields, numerical solution of first order differential equations via Euler's method, and modeling; solution of second order linear homogeneous and non-homogeneous equations with applications to mass-spring systems; solution of linear homogeneous systems of equations with constant coefficients (includes ALL cases of eigenvalues) and applications, phase plane, solution of non-homogeneous linear systems, matrix exponential; almost linear systems with phase plane; solution to partial differential equations (heat equation with Dirichlet and Neumann b.c.), and Fourier series. |
| Requisites: | Prereqs: Calculus III (SM221 or SM223); Coreq: SM261 |
| Course: | SM223 |
| Title: | Calculus III With Optimization |
| Credits: | 4—0—4 |
| Description: | One possible follow-on course to Calculus II. Topics include describing basic curves and space motion (including projectile motion) using vector functions and their derivatives and integrals; drawing and interpreting level sets and graphs of a real valued function; computing partial derivatives, directional derivatives and gradient vectors; solving extreme value problems by finding and classifying critical points and by the method of Lagrange multipliers; evaluating double and triple integrals in various coordinate systems and using integrals to find centers of mass; and writing well-organized, coherent solutions to application problems. |
| Requisites: | Prereq: SM122 OR SM122R |
| Course: | SM230 |
| Title: | Probability With Naval Applications |
| Credits: | 3—0—3 |
| Description: | 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. Credit will not be given for both SM230 and SM239. [fall, spring, summer] |
| Requisites: | Prereq: Calculus II (SM122). |
| Course: | SM233 |
| Title: | Intro To Computational Math |
| Credits: | 2—2—3 |
| Description: | This course introduces various topics in computational mathematics with a focus on MATLAB programming. Topics include basic programming constructs, computation of sequences and series, numerical integration, Monte Carlo simulation, linear algebra applications, and numerical solution of differential equations. Additional topics, selected at the instructor's discretion, may include root-finding methods, Markov chains, fractals, and PageRank computation. |
| Requisites: | Prereq: (SM221 OR SM221P OR SM223) & SM261 |
| Course: | SM239 |
| Title: | Intro To Probability And Statistics |
| Credits: | 3—0—3 |
| Description: | An applied study of discrete and continuous probability models. Topics include: understanding and applying basic probability axioms and counting techniques; expressing probability statements in terms of the probability mass or density function, or the cumulative distribution function of random variables; modeling phenomena and quantifying uncertainty using key distributions (including but not restricted to normal, binomial, geometric, exponential, and Poisson); computing joint, marginal, and conditional distributions and understanding correlation; performing basic random variable transformations; solving problems using basic probability inequalities, the Law of Large Numbers, and the Central Limit Theorem. |
| Requisites: | Coreq: SM221 OR SM221P OR SM223 |
| Course: | SM242 |
| Title: | Discrete Math & Probability |
| Credits: | 4—0—4 |
| Description: | Introduction to first order logic, set theory, proof techniques, counting principles, graph theory, matrix operations, discrete random variables and analysis of algorithms. Credit cannot be given for SM242 if credit has been given for SM342. [fall, spring] |
| Requisites: | Prereq: SM122 |
| Course: | SM244 |
| Title: | Discrete Math For Ops Res |
| Credits: | 3—0—3 |
| Description: | An introduction to discrete mathematics, with an emphasis on its applications to operations research. Topics include: logic and proofs, set theory, graph theory and its connections to matrix theory. Cannot receive credit for both SM244 and SM291. |
| Requisites: | Prereq: SM261 or SM263 or Dept Chair approval |
| Course: | SM259 |
| Title: | Mathematical Logic |
| Credits: | 3—0—3 |
| Description: | 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. [fall] |
| Requisites: | Prereq: Calculus II (SM122). |
| Course: | SM261 |
| Title: | Linear Algebra I |
| Credits: | 3—0—3 |
| Description: | This course explores the foundational concepts of linear algebra in R^n, including matrices, linear transformation, linear equations, determinants, eigenvalues, bases of vector spaces, and orthogonality. |
| Requisites: | Prereq: SM122 |
| Compendium: | SM261 |
| Course: | SM263 |
| Title: | Applied Linear Algebra |
| Credits: | 3—0—3 |
| Description: | The course covers: systems of equations, matrix arithmetic and factorizations, the rank-nullity theorem, eigenvectors and eigenvalues, the singular value decomposition, the discrete Fourier transform and other filters, regression, and optimization aimed at predictive analytics. Computer programming language will be used throughout the course. Credit will not be be given for both SM261 and SM263. |
| Requisites: | Prereq: Calc II and SD211, or permission of Dept Chair. |
| Course: | SM275 |
| Title: | Mathematical Methods For Economics |
| Credits: | 3—0—3 |
| Description: | Primarily for Economics majors. Presents mathematical methods for economics and associated applications. Matrix operations, simple equilibrium models with matrix methods, difference equations and growth models, constrained optimization for utility maximization or cost minimization. (Fall) |
| Requisites: |
| Course: | SM279 |
| Title: | Multivariable Calculus |
| Credits: | 3—0—3 |
| Description: | 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. [spring] |
| Requisites: | Prereq: (SM221 or SM223) and SM261. |
| Course: | SM291 |
| Title: | FUNDAMENTALS OF MATHEMATICS |
| Credits: | 3—0—3 |
| Description: | This course introduces the fundamental techniques of mathematical proofs, including direct proof, proof by contradiction, induction, and contrapositive. Topics covered include logic, set theory, functions, and basic number theory. Emphasis is placed on developing clear and rigorous reasoning skills essential for advanced mathematics. Credit cannot be received for both SM291 and SM244. |
| Requisites: | Prereq: CALC III (SM221 or SM223) |
| Compendium: | SM291 |
| Course: | SM315 |
| Title: | Intro To Partial Diff Eqns |
| Credits: | 3—0—3 |
| Description: | Linear equations, Cauchy problems, Laplace and Poisson equations, boundary value problems, heat equations, Sturm-Liouville problems, and orthonormal expansions. [fall] |
| Requisites: | Prereq: Differential Equations (SM212 or SM222). |
| Course: | SM316 |
| Title: | Engr Math With Prob & Stats |
| Credits: | 3—0—3 |
| Description: | Basic concepts in probability and statistics, arithmetic of complex numbers, and Fourier analysis. Credit cannot be given for either SM219, SM230, or SM239 and SM316. [fall, spring] |
| Requisites: | Prereq: Differential Equations (SM212 or SM222). Prereq: Coreq: Prereq: Coreq: |
| Course: | SM317 |
| Title: | Statistical Learning |
| Credits: | 3—0—3 |
| Description: | This course covers a variety of statistical learning topics, including: function estimation with data, bias-variance tradeoff, classification, linear regression, resampling methods, linear model selection and regularization, non-linear modeling, and tree-based methods, support vector machines, and unsupervised learning. |
| Requisites: | Prereq: SM230 or SM239, or permission of Dept Chair. |
| Course: | SM331H |
| Title: | Honors Real Analysis I |
| Credits: | 4—0—4 |
| Description: | A proof based course covering the properties of the real line, the completeness axiom, Euclidean spaces, cardinality, topology of Euclidean, normed and/or metric spaces, connectedness, compactness, the Heine-Borel theorem, convergence of sequences, limsup and liminf, the Bolzano-Weierstrass theorem, completeness, numerical series, limits and continuity of functions, the intermediate value theorem, the extreme value theorem, uniform continuity, fixed point theorems. Midshipmen may not receive credit for both SM333 and SM331H. |
| Requisites: | Prereq: SM291 & permission of department chair. |
| Course: | SM332H |
| Title: | Honors Real Analysis II |
| Credits: | 4—0—4 |
| Description: | A continuation of SM331H. The course covers differentiability, the mean value theorem, Taylor's theorem, the Riemann integral, sequences and series of functions, modes of convergence, power series, Taylor series, Weierstrass approximation, the Stone-Weierstrass theorem, applications. Midshipmen may not receive credit for both SM334 and SM332H. |
| Requisites: | Prereq: SM331H & permission of department chair. |
| Course: | SM333 |
| Title: | Real Analysis I |
| Credits: | 4—0—4 |
| Description: | This course introduces the rigorous foundations of real analysis, focusing on the structure of the real number system, sequences, limits, continuity, and differentiation. Midshipmen may not receive credit for both SM333 and SM331H. |
| Requisites: | Prereq: SM291 |
| Course: | SM334 |
| Title: | Real Analysis II |
| Credits: | 3—0—3 |
| Description: | Building on Real Analysis I, this course explores integration, infinite series, and sequences and series of functions. Midshipmen may not receive credit for both SM334 and SM332H. |
| Requisites: | Prereq: SM333 OR SM331H |
| Course: | SM339 |
| Title: | Applied Statistics I |
| Credits: | 3—0—3 |
| Description: | 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. [fall, spring] |
| Requisites: | Prereq: SM239 and SM261. |
| Course: | SM342 |
| Title: | Discrete Mathematics |
| Credits: | 3—0—3 |
| Description: | This course covers select topics in discrete mathematics, focusing on combinatorics (permutations, generating functions, recurrence relations, counting techniques, graph theory) and foundations and methods of proof. |
| Requisites: | Prereq: SM122 |
| Course: | SM349 |
| Title: | Number Theory |
| Credits: | 3—0—3 |
| Description: | Number theory (the study of integers, in particular primes) is one of the oldest branches of math. It uses tools from algebra, geometry, analysis, and topology. Its primary application is cryptography. Topics include divisibility, primes, unique prime factorization, Diophantine equations, congruences, the Chinese Remainder Theorem, polynomials and their roots, and quadratic reciprocity. Optional topics may include quadratic forms, multiplicative functions, continued fractions, elliptic curves, Pick's Theorem, and Geometry of Numbers. |
| Requisites: | Prereq: SM291 |
| Course: | SM350 |
| Title: | Topics In Pure & Applied Math |
| Credits: | 3—0—3 |
| Description: | Junior-level topics in pure and applied mathematics. The content will vary in order to keep abreast of new ideas and approaches. [fall, spring] |
| Requisites: | Prereq: permission of department chair. |
| Course: | SM350A |
| Title: | Topics In Pure & Applied Math |
| Credits: | 3—0—3 |
| Description: | Junior-level topics in pure and applied mathematics. The content will vary in order to keep abreast of new ideas and approaches. [fall, spring] |
| Requisites: | Prereq: permission of department chair. |
| Course: | SM361 |
| Title: | Linear Algebra II |
| Credits: | 4—0—4 |
| Description: | This course covers abstract linear algebra and its applications. Topics include: abstract vector spaces, linear transformations, inner products and norms, orthogonal bases, projections, singular value decomposition and other matrix factorizations. Additional topics will be chosen by the instructor, but might include: image compression, principal components analysis, applications to physics, numerical linear algebra. |
| Requisites: | Prereq: SM261 |
| Course: | SM362 |
| Title: | Modern Algebra |
| Credits: | 3—0—3 |
| Description: | This course provides an introduction to group theory, covering group structures, subgroups, cosets, homomorphisms, normal subgroups, and group actions. |
| Requisites: | Prereq: SM261 AND SM291 |
| Course: | SM364 |
| Title: | INTRO TO SCIENTIFIC COMPUTING |
| Credits: | 3—0—3 |
| Description: | Computer arithmetic and errors; rootfinding algorithms; interpolation and polynomial approximation; numerical integration and differentiation; error in solutions of systems of linear equations via direct methods; solutions of systems of linear equations via iterative methods; numerical solution of ordinary differential equations. |
| Requisites: | Prereq: SM361 or Dept Chair approval |
| Course: | SM411 |
| Title: | INTRO TO COMPLEX VARIABLES |
| Credits: | 3—0—3 |
| Description: | An introduction to complex valued functions of a single complex variable: complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, Taylor and Laurent series, singularities, the residue theorem, and applications. |
| Requisites: | Prereq: SM331H or SM333 |
| Course: | SM415 |
| Title: | Math Model Ocean & Atmos |
| Credits: | 3—0—3 |
| Description: | Mathematical Modeling of the Ocean and Atmosphere. 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. Use of MATLAB to solve applied problems in oceanography and meteorology. [spring] |
| Requisites: | Prereq: SO414, SO513, or Dept Chair approval. |
| Course: | SM421 |
| Title: | Topics In Applied Mathematics II |
| Credits: | 3—0—3 |
| Description: | Senior level topics in applied mathematics. The content will vary in order to keep abreast of new ideas and approaches. |
| Requisites: | Prereq: permission of department chair. |
| Course: | SM425 |
| Title: | ADVANCED NUMERICAL ANALYSIS |
| Credits: | 3—0—3 |
| Description: | Solution of Linear Systems. Direct Methods: efficient implementation, Cholesky decomposition, sparse matrices, permutation and ordering strategies. Iterative Methods: conjugate gradient method, Krylov subspace methods, introduction to multigrid methods. Linear Least Squares Problems: QR factorization and Gram-Schmidt orthogonalization, Householder transformations. Eigenvalues and Singular Values: power method and variations, singular value decomposition, other methods for computing eigenvalues and singular values. Nonlinear Systems & Optimization: Newton's method for nonlinear systems, unconstrained and constrained optimization. Fourier transforms: The Fourier, Discrete & Fast Fourier transform, and trigonometric interpolation. |
| Requisites: | Prereq: (SM212 or SM222) and (SM233 or MATLAB) and (SM331H or SM333) and SM364 |
| Course: | SM426 |
| Title: | Numerical Methods For Diff Eq |
| Credits: | 3—0—3 |
| Description: | Interpolation and polynomial approximation, numerical integration and differentiation, numerical algorithms for initial value and boundary value problems. |
| Requisites: | Prereq: (SM212 or SM222) and (SM233 or MATLAB) and (SM331H or SM333) |
| Course: | SM435 |
| Title: | Sports Statistics |
| Credits: | 3—0—3 |
| Description: | An introduction to the statistical analysis of sports data via a case studies approach. Statistical topics include linear and logistic regression, maximum likelihood estimation, bootstrapping, the multivariate normal distribution, random forests, Markov chains, and simulation. Sports topics include: player valuation, game outcome prediction, the hot hand controversy, and cheating detection. |
| Requisites: | Prereq: SM239 AND (SM339 OR SM317) |
| Course: | SM437 |
| Title: | Experimental Design |
| Credits: | 3—0—3 |
| Description: | This is an advanced applied statistics course focusing on the collection and analysis of data arising from either sampling finite populations or arising from scientific experiments. Emphasis is placed on simple random sampling, stratified sampling, cluster sampling, ratio estimation, randomized block designs, factorial designs, and confounding. [spring] |
| Requisites: | Prereq: SM339. |
| Course: | SM439 |
| Title: | Topics In Statistics |
| Credits: | 3—0—3 |
| Description: | Senior level topics in statistics. The content will vary in order to keep abreast of new ideas and approaches. [fall] |
| Requisites: | Prereq: SM339 or permission of department chair. |
| Course: | SM444 |
| Title: | Discrete Mathematics II |
| Credits: | 3—0—3 |
| Description: | Topics in combinatorics and graph theory, with applications. Latin squares, linear algebra and combinatorics, finite projective planes, topological graph theory, Ramsey theory, trees. |
| Requisites: | Prereq: SM342 |
| Course: | SM450 |
| Title: | Topics In Pure & Applied Math |
| Credits: | 3—0—3 |
| Description: | Senior-level topics in pure and applied mathematics. The content will vary in order to keep abreast of new ideas and approaches. [fall, spring] |
| Requisites: | Prereq: permission of department chair. |
| Course: | SM461 |
| Title: | Linear Algebra |
| Credits: | 3—0—3 |
| Description: | Vector spaces, linear transformations, Jordan canonical form, inner product spaces. [fall, spring] |
| Requisites: | Prereq: (SM261 and SM291) or permission of department chair. |
| Course: | SM462 |
| Title: | Modern Algebra II |
| Credits: | 3—0—3 |
| Description: | This course will cover groups, rings, fields, Galois theory. |
| Requisites: | Prereq: SM362 |
| Course: | SM463 |
| Title: | Topics In Analyt/Discr Math |
| Credits: | 3—0—3 |
| Description: | Senior level topics in pure mathematics. The content will vary in order to keep abreast of new ideas and approaches. |
| Requisites: | Prereq: permission of department chair. |
| Course: | SM464 |
| Title: | TOPOLOGY |
| Credits: | 3—0—3 |
| Description: | An introduction to topological spaces (including metric spaces), open and closed sets, bases, continuous functions, homeomorphisms, separation properties, compactness by open covers, connectedness, product spaces, and quotient spaces. Some optional topics include local properties, metrization theorems, homotopy theory, universal covers, fixed point theorems, topological manifolds, and properties of nets. |
| Requisites: | Prereq: SM331H or SM333 |
| Course: | SM468 |
| Title: | Crypto, Codes & Info Security |
| Credits: | 3—0—3 |
| Description: | Cryptography, Codes, and Information Security investigates the mathematics of secret and error-correcting codes. [spring] |
| Requisites: | Prereq: SM261 or permission of department chair. |
| Course: | SM472 |
| Title: | Projects In Mathematics |
| Credits: | 3—0—3 |
| Description: | This course is a capstone course for the the mathematics major. Students will read and make presentations on topics determined by the instructor. Each student will complete a project on a topic to be agreed upon by the instructor and student. Students will present their results in writing and orally. [spring] |
| Requisites: | Prereq: 1/C SMA Major or permission of department chair. |
| Course: | SM473 |
| Title: | Projects In Math & Applied Math |
| Credits: | 3—0—3 |
| Description: | This course is a capstone course for the mathematics and applied mathematics majors. Students will read and make presentations on topics determined by the instructor. Each student will complete a project on a topic to be agreed upon by the instructor and student. Students will present their results in writing and orally. [spring] |
| Requisites: | Prereq: 1/C Math Major or permission of department chair. |
| Course: | SM474 |
| Title: | Projects In Applied Mathematics |
| Credits: | 3—0—3 |
| Description: | This course is a capstone course for the applied mathematics major. Students will read and make presentations on topics determined by the instructor. Each student will complete a project on a topic to be agreed upon by the instructor and student. Students will present their results in writing and orally. [spring] |
| Requisites: | Prereq: 1/C SMP Major or permission of department chair. |