Course Descriptions

Course Information
Mathematics (SM) Course Information

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. Prereq: Coreq: Prereq: Coreq: Prereq:
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:Prereq: Coreq: Prereq: Coreq: Prereq: Coreq:
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 Prereq: SM121 Coreq: Prereq: SM121 Coreq:
Course:SM122X
Title:Multivar Calculus W/ Review
Credits: 4—0—4
Description:For those who have had a year of prior calculus study but did not validate Calculus I. Introduction to multivariable calculus topics from the first part of Calculus III with embedded review of topics and skills from first-year calculus. Participation in SM122X entails validation credit for SM131. Completion of SM122X counts as credit for SM122.
Requisites:Prereq: Placement by department chair. Prereq: Coreq: Prereq: Coreq: Prereq:
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 OR SM221P OR SM223 Coreq: Prereq: SM221 OR SM221P OR SM223 Coreq:
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 Coreq: Prereq: SM221 OR SM221P OR SM223 Coreq:
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 Coreq: Prereq: SM122 OR SM122R Coreq: Prereq: SM122 OR S
Course:SM221X
Title:Multivariable Calculus With Infinite Series
Credits: 4—0—4
Description:For those who have completed SM122X. Introduction to multivariable and vector calculus topics from the second part of Calculus III and introduction to infinite sequences and series with embedded review of topics and skills from first-year calculus. Completion of SM221X counts as credit for SM221.
Requisites:Prereq: SM122X Prereq: SM122 Coreq: Prereq: SM122 Coreq: Prereq: SM122 Coreq:
Course:SM222
Title:Differential Equations With Matrices
Credits: 4—0—4
Description:A more rigorous treatment of material from SM212, the course uses basic ideas from linear algebra. Intended for mathematics and quantitative economics majors. [fall, spring]
Requisites:Prereq: Calculus III (SM221 or SM223); Coreq: SM261. Prereq: Coreq: Prereq: C
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 Coreq: Prereq: SM122 OR SM122R Coreq: Prereq: SM122 OR S
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 or SM162). Prereq: Coreq: Prereq: Coreq: Prereq: C
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 SM22 Coreq: Prereq: (SM221 OR SM221P OR SM22 Coreq:
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:Prereq: Coreq: SM221 OR SM221P OR SM223 Prereq: Coreq: SM221 OR SM221P OR SM22
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 or SM162 Prereq: Coreq: Prereq: Coreq: Prereq: Coreq:
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 Prereq: SM261 OR SM263 Coreq: Prer
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 or SM162). Prereq: Coreq: Prereq: Coreq: Prereq: C
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 Coreq: Prereq: SM122 Coreq: Prereq: SM122 Coreq:
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. Coreq: Calc III Prereq:
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:Prereq: Coreq: Prereq: Coreq: Prereq: Coreq:
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. Prereq: Coreq: Prereq: Coreq: Prereq: Cor
Course:SM291
Title:Fundamentals Of Mathematics
Credits: 3—0—3
Description:Introduction to mathematical reasoning and the written and oral presentation of mathematical concepts, theory, and application of sets and relations. [spring] Cannot received credit for both SM291 and SM244.
Requisites:Prereq: Calculus II. SQE majors may not take both SM291 and SM222. Prereq: SM29
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). Prereq: Coreq: Prereq: Coreq:
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. Prereq: Coreq: Prereq: Co
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.
Requisites:Prereq: permission of department chair. Prereq: Coreq: Prereq: Coreq: Prereq:
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.
Requisites:Prereq: permission of department chair. Prereq: Coreq: Prereq: Coreq: Prereq:
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 Coreq: Prereq: SM291 Coreq: Prereq: SM291 Coreq:
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 Coreq: Prereq: SM333 OR SM331H Coreq: Prereq: SM333 OR S
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. Prereq: SM239 AND SM261 Coreq: 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 Coreq: Prereq: SM122 Coreq: Prereq: SM122 Coreq:
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:SM291 Prereq: SM291 Coreq: Prereq: SM291 Coreq: Prereq: SM291 Coreq:
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. Prereq: Coreq: Prereq: Coreq: Prereq:
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. Prereq: Coreq: Prereq: Coreq: Prereq:
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 Coreq: Prereq: SM261 Coreq: Prereq: SM261 Coreq:
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 Coreq: Prereq: SM261 AND SM291 Coreq: Prereq: SM261 AND
Course:SM364
Title:Intro Scientific Computing
Credits: 3—0—3
Description:Computer arithmetic and errors; algorithms and programs for: function approximations, numerical integration, and the numerical solution of ordinary differential equations; an introduction to programming. [spring]
Requisites:Prereq: SM361 or permission of department chair. Prereq: Coreq: Prereq: Coreq:
Course:SM411
Title:Intro To Complex Variables
Credits: 3—0—3
Description:This course extends the techniques of differential and integral calculus to the complex numbers. Highlights include Cauchy's theorem on integration, the residue theorem, and power series expansions. Applications to real analysis and physical problems will be discussed. [fall]
Requisites:Prereq: SM331 or SM331H or SM333 Prereq: Coreq: Prereq: Coreq: Prereq: Coreq:
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 or permission of instructor. Prereq: Coreq: Prereq: Coreq: Prere
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. Prereq: Coreq: Prereq: Coreq: Prereq:
Course:SM425
Title:Advanced Numerical Analysis
Credits: 3—0—3
Description:Numerical solution of equations in one and several variables, direct and iterative algorithms, rate of convergence. Computer methods emphasized.
Requisites:Prereq: (SM212 or SM222) and (SM233 or MATLAB) and (SM331 or SM331H or SM333 or
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 (SM331 or SM331H or SM333 or
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 SM31 Coreq: Prereq: SM239 AND (SM339 OR SM31 Coreq:
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. Prereq: SM339 Coreq: Prereq: SM339 Coreq: Prereq: SM339 Coreq:
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. Prereq: Coreq: Prereq: Coreq:
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 Coreq: Prereq: SM342 Coreq: Prereq: SM342 Coreq:
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. Prereq: Coreq: Prereq: Coreq: Prereq:
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. Prereq: Coreq: Pre
Course:SM462
Title:Modern Algebra Ii
Credits: 3—0—3
Description:This course will cover groups, rings, fields, Galois theory.
Requisites:Prereq: SM362 Coreq: Prereq: SM362 Coreq: Prereq: SM362 Coreq:
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. Prereq: Coreq: Prereq: Coreq: Prereq:
Course:SM464
Title:Topology
Credits: 3—0—3
Description:A mathematical analysis of topological spaces, separation axioms, covering properties, and metric spaces.
Requisites:Prereq: SM331 or SM331H or SM333 Prereq: Coreq: Prereq: Coreq: Prereq: Coreq:
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. Prereq: Coreq: Prereq: Coreq:
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. Prereq: Coreq: Prereq:
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. Prereq: Coreq: Prereq
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. Prereq: Coreq: Prereq: