Course Information

MATHEMATICS DEPARTMENT


Course: SA302
Title: ANALYSIS OF NAVAL TACTICS
Credits: 3-2-4
Description: An introduction to the techniques of modeling and quantitative analysis applied to specific naval operational problems, including search and patrol, screening, anti-air warfare, mining, equipment reliability and decision rules. Does not count as a major elective for Mathematics majors.
Offered: Fall 2013-2014
Requisites: Prereq: SM219, SM239 or SM230.
Course: SA305
Title: LINEAR PROGRAMMING
Credits: 3-0-3
Description: An introduction to linear programming. Topics include: extensive linear programming modeling techniques, the Simplex method, sensitivity analysis, and basic linear programming theory. Midshipmen cannot receive credit for both SA305 and SA401.
Offered: Spring 2012-2013
Requisites: Prereq: SM261 or permission of department chair.
Course: SA367
Title: INTRODUCTION TO MATHEMATICAL MODELING
Credits: 3-0-3
Description: 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.
Offered: Spring 2012-2013
Requisites: Prereq: SM219, SM239 or SM230.
Course: SA402
Title: DYNAMIC & STOCHASTIC MODELS
Credits: 3-0-3
Description: Investigation of quantitative analysis of decision options, including dynamic programming, decision trees, Markov chains and queuing theory. Applications to typical operations are stressed.
Offered: Fall 2013-2014
Requisites: Prereq: (SM239 or SM230) and SM261.
Course: SA403
Title: GRAPH AND NETWORK ALGORITHMS
Credits: 3-0-3
Description: This course introduces graph algorithms for problems in network and combinatorial optimization. Topics include: minimum spanning trees, matchings, shortest paths, maximum flows and minimum cost flows. Students will also be expected to program algorithms on a computer.
Offered: Fall 2013-2014
Requisites: Prereq: SM233 or permission of department chair.
Course: SA405
Title: ADVANCED MATH PROGRAMMING
Credits: 3-0-3
Description: This course covers a range of advanced topics in mathematical programming. Topics include integer programming modeling, branch-and-bound methods, integer programming theory and nonlinear optimization theory and algorithms. Students will also learn to use a set-based modeling language for an advanced integer programming solver. Topics will vary with instructor.
Offered: Fall 2013-2014
Requisites: Prereq: SA305 or permission of department chair.
Course: SA410
Title: APPLICATIONS OF SEARCH AND DETECTION THEORY
Credits: 3-0-3
Description: 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.
Offered: Spring 2012-2013
Requisites: Prereq: SM239 or SM230.
Course: SA412
Title: PROJECTS IN OPERATIONS ANALYSIS
Credits: 3-0-3
Description: Operations research techniques are applied using student projects, case studies and visiting lecturers. Topics include current military and industrial problems.
Offered: Spring
Requisites: Prereq: permission of department Chair.
Course: SA421
Title: SIMULATION MODELING
Credits: 3-0-3
Description: Discrete simulation of systems using a simulation language. Includes random variate generation, validation and verification of simulations, input and output data analysis. Semester projects are done as part of an analysis team.
Offered: Spring 2012-2013, Fall 2013-2014
Requisites: Prereq: SM233. Coreq: SM339.
Course: SA430
Title: LOGISTICS
Credits: 3-0-3
Description: Investigation of techniques of operations analysis applicable to the solution of problems in reliability, maintainability, availability and inventory.
Offered: Fall 2013-2014
Requisites: Prereq: SM239 or SM230.
Course: SA442
Title: APPLIED STATISTICS II
Credits: 3-0-3
Description: 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.
Offered: Spring
Requisites: Prereq: SM339.
Course: SA475
Title: OPERATIONS RESEARCH CAPSTONE
Credits: 3-0-3
Description: This course is a capstone course for the Operations Research 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.
Offered: Spring
Requisites: Prereq: 1/C SMO Major or permission of department chair.
Course: SA475E
Title: RESEARCH SEMINAR IN QUANTITATIVE ECONOMICS
Credits: 3-0-3
Description: Directed research on a specific topic. Capstone course for Quantitative Economics majors. Emphasis on empirical work using computers.
Offered: Spring 2012-2013
Requisites: Prereq: 1/C SQE major.
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
Offered: Fall 2013-2014
Requisites: Prereq: placement by department chair.
Course: SM121
Title: CALCULUS I
Credits: 4-0-4
Description: The first of a traditional two course sequence covering differential and integral calculus of one real variable and infinite series.
Offered: Fall 2013-2014
Requisites: Prereq: None.
Course: SM122
Title: CALCULUS II
Credits: 4-0-4
Description: Continuation of Calculus I.
Offered: Spring 2012-2013, Summer 2013-2014, Fall 2013-2014
Requisites: Prereq: Calculus I (SM131 or SM121 or SM161).
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.
Offered: Fall 2013-2014
Requisites: Prereq: Placement by department chair.
Course: SM131
Title: CALCULUS I
Credits: 3-0-3
Description: The first of a traditional two course sequence covering differential and integral calculus of one real variable and infinite series for students who had prior differential calculus experience.
Offered: Fall 2013-2014
Requisites: Prereq: placement by department chair.
Course: SM161
Title: CALCULUS WITH COMPUTERS I
Credits: 5-0-5
Description: The first of a two course sequence presenting an algorithmic development of the differential and integral calculus of one real variable and an introduction to programming.
Offered: Fall
Requisites: Prereq: permission of department chair.
Course: SM162
Title: CALCULUS WITH COMPUTERS II
Credits: 5-0-5
Description: A continuation of SM161.
Offered: Spring 2012-2013
Requisites: Prereq: SM161.
Course: SM212
Title: DIFFERENTIAL EQUATIONS
Credits: 4-0-4
Description: Linear and simultaneous differential equations; solution by Laplace transform; partial differential equations and Fourier series.
Offered: Spring 2012-2013, Summer 2013-2014, Fall 2013-2014
Requisites: Prereq: Calculus III (SM221 or SM223).
Course: SM219
Title: INTRODUCTORY STATISTICS
Credits: 3-0-3
Description: 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.
Offered: Spring 2012-2013, Fall 2013-2014
Requisites: Prereq: SM122 or SM162.
Course: SM221
Title: CALCULUS III WITH VECTOR FIELDS
Credits: 4-0-4
Description: Differential and integral calculus of several real variables; vector analysis including integral theorems.
Offered: Spring 2012-2013, Fall 2013-2014
Requisites: Prereq: Calculus II (SM122 or SM162).
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.
Offered: Spring 2012-2013
Requisites: Prereq: SM122X
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.
Offered: Spring 2012-2013, Fall 2013-2014
Requisites: Prereq: Calculus III (SM221 or SM223); Coreq: SM261.
Course: SM223
Title: CALCULUS III WITH OPTIMIZATION
Credits: 4-0-4
Description: Differential and integral calculus of several real variables; vector analysis; optimization techniques for functions of several variables.
Offered: Fall 2013-2014
Requisites: Prereq: Calculus II (SM122 or SM162).
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.
Offered: Spring 2012-2013, Summer 2013-2014, Fall 2013-2014
Requisites: Prereq: Calculus II (SM122 or SM162).
Course: SM233
Title: INTRODUCTION TO APPLIED MATHEMATICS
Credits: 2-2-3
Description: This course introduces students to several fundamental topics in applied mathematics: simulation and statistical modeling, applications of linear algebra, partial differential equation models, and computational tools and topics. Appropriate computer software will be introduced.
Offered: Spring 2012-2013
Requisites: Prereq: Calculus III; Coreq: SM261.
Course: SM239
Title: PROBABILITY AND STATISTICS I
Credits: 3-0-3
Description: An applied study of a variety of discrete and continuous probability models. Probability models covered include binomial, Poisson, exponential, gamma, normal, Student-t, and chi-squared. Methods for calculating probabilities and estimating parameters are included. The Law of Large Numbers and the Central Limit Theorem are included. This course is both a stand-alone course and a prerequisite for Applied Statistics I (SM339). Credit will not be given for both SM239 and SM230.
Offered: Fall 2013-2014
Requisites: Prereq/Coreq: Calculus III (SM221 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.
Offered: Fall 2013-2014
Requisites: Prereq: SM122 or SM162
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.
Offered: Fall
Requisites: Prereq: Calculus II (SM122 or SM162).
Course: SM261
Title: MATRIX THEORY
Credits: 3-0-3
Description: Matrices, transformations, linear equations, vector spaces, characteristic matrix, eigenvalues, orthogonality.
Offered: Spring 2012-2013, Fall 2013-2014
Requisites: Prereq: Calculus II (SM122 or SM162).
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.
Offered: Spring 2012-2013
Requisites: Prereq: (SM221 or SM223) and SM261.
Course: SM280
Title: TOPICS IN MATHEMATICS
Credits: 1-0-1
Description: An overview and sampling of topics from a variety of mathematical disciplines including both tracks of the Mathematics Major. Students will be exposed to the power, beauty, and utility of Mathematics.
Offered: Fall
Requisites: Prereq: Calculus II and SMA or SMP major or permission of department chair.
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.
Offered: Spring 2012-2013
Requisites: Prereq: Calculus II. SQE majors may not take both SM291 and SM222.
Course: SM311
Title: ENGINEERING MATHEMATICS I
Credits: 3-0-3
Description: Vector analysis, Fourier analysis, partial differential equations, Sturm-Liouville problems, Legendre polynomials, determinants, and matrices.
Offered: Fall, Spring
Requisites: Prereq: Differential Equations (SM212 or SM222).
Course: SM312
Title: ENGINEERING MATHEMATICS II
Credits: 3-0-3
Description: Laplace and Fourier transforms, selected topics from complex variables.
Offered:
Requisites: Prereq: Differential Equations (SM212 or SM222).
Course: SM313
Title: PROBABILITY WITH APPL TO EE
Credits: 3-0-3
Description: A first course in probability with many examples and exercises drawn from electrical engineering. Knowledge of calculus (including multivariable) is assumed. The course covers basic counting techniques, properties of probabilities, discrete and continuous random variables, expectation values, variance, covariance, joint probability distributions, functions of random variables, moment generating functions, the Central Limit Theorem, random sampling, and sampling distribution of means. The emphasis is on understanding the random variable concept.
Offered: Fall 2013-2014
Requisites: Prereq: Differential Equations (SM212 or SM222).
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.
Offered: Fall 2013-2014
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 both SM239 and SM316.
Offered: Spring 2012-2013, Fall 2013-2014
Requisites: Prereq: Differential Equations (SM212 or SM222).
Course: SM321
Title: TOPICS IN APPL MATHEMATICS
Credits: 3-0-3
Description: Junior level topics in applied mathematics. The content will vary in order to keep abreast of new ideas and approaches.
Offered:
Requisites: Prereq: permission of department chair.
Course: SM331
Title: ADVANCED CALCULUS I
Credits: 4-0-4
Description: Real numbers, sequences, limits of sequences, limits of functions, continuity, properties of continuous functions, differentiability, Riemann integral, series, power series.
Offered: Fall
Requisites: Prereq: SM261 and SM291.
Course: SM331H
Title: REAL ANALYSIS I
Credits: 4-0-4
Description: Honors versions of SM331.
Offered: Fall 2013-2014
Requisites: Prereq: permission of department chair.
Course: SM332H
Title: REAL ANALYSIS II
Credits: 4-0-4
Description: Honors version of SM334.
Offered: Spring 2012-2013
Requisites: Prereq: permission of department chair.
Course: SM333
Title: SEQUENCES, SERIES & FUNCTIONS
Credits: 4-0-4
Description: This course deals with the convergence properties of sequences and series, including: limit theorems and convergence tests, power series, sequences and series of functions, pointwise and uniform convergence, and the analytic operations preserved by the convergence process. Midshipmen may not receive credit for both SM333 and any of SM331, SM331H, and SM332H.
Offered: Fall 2013-2014
Requisites: Prereq: SM261 and SM291, or permission of department chair.
Course: SM334
Title: ELEMENTS OF ADVANCED CALCULUS
Credits: 3-0-3
Description: This course is a continuation of SM333. Together the courses cover logic, induction, sequences, limits, real numbers, series, continuity, differentiability, properties of continuous functions, the Riemann Integral, and power series.
Offered: Spring 2012-2013
Requisites: Prereq: SM331 or SM331H or SM333
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.
Offered: Spring 2012-2013
Requisites: Prereq: SM239 and SM261.
Course: SM342
Title: DISCRETE STRUCTURES
Credits: 3-0-3
Description: Foundations and methods of proof. Combinatorics, graph theory, group theory. Selected topics. Counts as track elective for the SMA and the SMP majors.
Offered: Spring 2012-2013
Requisites: Prereq: SM122 or SM162.
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.
Offered: Fall, Spring
Requisites: Prereq: permission of department chair.
Course: SM361
Title: INTERMEDIATE LINEAR ALGEBRA
Credits: 4-0-4
Description: This course deals with 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, and numerical linear algebra. Applications will be chosen by the instructor, but might include: image compression, principal components analysis, and applications to physics.
Offered: Fall 2013-2014
Requisites: Prereq: (SM233, SM261 and SM291) or permission of department chair.
Course: SM362
Title: MODERN ALGEBRA
Credits: 3-0-3
Description: Integers, groups, mappings, rings, fields.
Offered: Fall 2013-2014
Requisites: Prereq: SM261 and SM291.
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.
Offered: Spring 2012-2013
Requisites: Prereq: SM361 or permission of department chair.
Course: SM365
Title: INTRO SCIENTIFIC COMPUTING
Credits: 4-0-4
Description: Computer arithmetic and errors; algorithms and programs for: iterative solution of equations, linear systems of equations, function approximations, numerical integration, and the numerical solution of ordinary differential equations; an introduction to programming.
Offered: Fall
Requisites: Prereq: SM261.
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.
Offered: Spring 2012-2013
Requisites: Prereq: SM331 or 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.
Offered: Spring 2012-2013
Requisites: Prereq: SO414 or permission of instructor.
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.
Offered: Fall 2013-2014
Requisites: Prereq: permission of department chair.
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.
Offered: Fall 2013-2014
Requisites: Prereq: (SM212 or SM222) and (SM233 or MATLAB) and (SM331 or SM331H or SM333 or approval of department chair) and (SM364 or SM365).
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.
Offered:
Requisites: Prereq: (SM212 or SM222) and (SM233 or MATLAB) and (SM331 or SM331H or SM333 or approval of department chair) and (SM365 or SM365).
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.
Offered: Spring 2012-2013
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.
Offered: Fall 2013-2014
Requisites: Prereq: SM339 or permission of department chair.
Course: SM444
Title: DISCRETE STRUCTURES 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.
Offered: Fall 2013-2014
Requisites: Prereq: SM342.
Course: SM450
Title: TOPICS IN PURE&APPLIED MATH2
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.
Offered: Fall 2013-2014
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.
Offered: Spring 2012-2013
Requisites: Prereq: (SM261 and SM291) or permission of department chair.
Course: SM462
Title: ALGEBRAIC STRUCTURES
Credits: 3-0-3
Description: Groups, rings, fields, Galois theory.
Offered:
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.
Offered: Fall 2013-2014
Requisites: Prereq: permission of department chair.
Course: SM464
Title: TOPOLOGY
Credits: 3-0-3
Description: A mathematical analysis of topological spaces, separation axioms, covering properties, and metric spaces.
Offered: Fall 2013-2014
Requisites: Prereq: SM331 or SM331H or SM333
Course: SM465
Title: ADVANCED DIFFERENTIAL EQUATIONS
Credits: 3-0-3
Description: Existence and uniqueness of solutions to ordinary differential equations. Stability, oscillation, dynamical systems.
Offered:
Requisites: Prereq: (SM212 or SM222) and (SM331 or 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.
Offered: Spring 2012-2013
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.
Offered: 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.
Offered: 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.
Offered: Spring 2012-2013
Requisites: Prereq: 1/C SMP Major or permission of department chair.