20212022 Florida Tech Catalog [ARCHIVED CATALOG]
Course Descriptions


Courses are listed alphanumerically. The 1000, 2000, 3000 and 4000 series are undergraduate courses. The 5000 series are graduate courses that can also be taken by undergraduates with cumulative grade point averages of 2.75 or higher, who have satisfied all listed prerequisites and whose registration is approved by the department head or program chair responsible for the course. The 6000 series courses are restricted to graduate students only. Courses below 1000 are developmental in nature, are not counted in GPA calculations and do not count toward any Florida Tech degree.
Courses that may be taken in fulfillment of Undergraduate Core Requirements are designated as follows: CL: computer literacy requirement, COM: communication elective, HU: humanities elective, LA: liberal arts elective, Q: scholarly inquiry requirement, SS: social science elective, CC: crosscultural, Hon: course may include honors sections during some semesters. These designations follow the course descriptions. Other courses that satisfy Undergraduate Core Requirements are identified by the course prefix: any MTH course can be used toward meeting the mathematics requirement; and any AVS, BIO, CHM or PHY course, or EDS 1031 or EDS 1032 , toward meeting the physical/life sciences requirement.


Marine Biology 


MAR 5517 Modeling for Ecology and Biology Credit Hours: 3 Presents graduatelevel modeling and applications for ecology and biology. Includes allometry, growth and healing of wounds, population dynamics, competition and symbiosis, predatorprey relations, community and diversity models, models in biogeography, evolution and conservation. Prerequisite: MAR 3410



MAR 5573 Scientific Analysis, Writing and Presentation Credit Hours: 3 Gives indepth consideration to recent literature related to various marine biology areas. Teaches how to critically read, evaluate, review and present marine science papers. Also teaches skills for writing abstracts, papers and grants, and for making professional presentations. 


MAR 5621 Marine Mammal Studies in the Pacific Northwest Credit Hours: 3 Explores the biology of marine mammals and how that biology has been shaped by the marine environment. Focuses on current techniques for collecting behavioral, spatial and physiological data in different habitats. Requires a field trip to the San Juan Islands, Washington. Meets with MAR 3621 . 


MAR 5899 Final Semester Thesis Credit Hours: 02 Variable registration for thesis completion after satisfaction of minimum registration requirements. Requirement(s): Accepted petition to graduate and approval by Office of Graduate Programs 


MAR 5904 Field Biology and Evolution of the Galapagos Islands Credit Hours: 3 Field biology course in the Galapagos Islands. Emphasizes climate and evolution processes and patterns. Includes both terrestrial and marine investigations of the unique biota of the islands. Requirement(s): Instructor approval 


MAR 5990 Biological Sciences Seminar Credit Hours: 0 Presents and discusses current research by visiting scientists, university faculty and graduate students. 


MAR 5991 Biological Research Seminar Credit Hours: 1 Presents and discusses thesis or dissertation research. 


MAR 5995 Biological Research Credit Hours: 39 Research under the guidance of a faculty member of the marine sciences in a selected area of biology. Requirement(s): Considered a fullload course. 


MAR 5999 Thesis Credit Hours: 36 Research and preparation for the master’s thesis. 




MAR 6999 Dissertation Credit Hours: 312 Research and preparation for the doctoral dissertation. Requirement(s): Admission to candidacy for the doctoral degree 
Mathematical Science 


MTH 0002 Final Program Examination Credit Hours: 0 Requires registration in order to sit for the final program examination. 


MTH 0003 Basic Algebra Credit Hours: 3 Builds a foundation for algebra. Includes algebraic expressions, order of operations, linear equations and inequalities. Introduces graphing, polynomials, exponents and factoring. Requirement(s): Must be enrolled in Florida Tech Online and credit cannot be applied to any Florida Tech degree 


MTH 0004 Final Program Examination 2 Credit Hours: 0 Requires registration in order to sit for the final program examination. Prerequisite: MTH 0002 Corequisite: MTH 0002



MTH 0005 Final Program Examination 3 Credit Hours: 0 Requires registration in order to sit for the final program examination. Prerequisite: MTH 0004 Corequisite: MTH 0004



MTH 0111 Intermediate Algebra Credit Hours: 3 Basic operations on real numbers, algebraic expressions, linear equations, inequalities, exponents, polynomials, factoring, rational functions, roots, radicals, quadratic equations and quadratic functions. Requirement(s): Credit cannot be applied toward any Florida Tech degree 


MTH 1000 Precalculus Credit Hours: 4 Algebra and trigonometry that are used to develop the skills needed in calculus. Required for students who have minimal algebra and/or trigonometry preparation, or whose placement test indicated such a need. Requirement(s): Must take placement exam. 


MTH 1001 Calculus 1 Credit Hours: 4 Functions and graphs, limits and continuity, derivatives of algebraic and trigonometric functions, chain rule; applications to maxima and minima, and to related rates. Exponential logarithmic, circular and hyperbolic functions: their inverses, derivatives and integrals. Requirement(s): High school algebra and trigonometry and a passing score on the placement test, or prerequisite course Prerequisite: MTH 1000



MTH 1002 Calculus 2 Credit Hours: 4 Integration and applications of integration, further techniques of integration, improper integrals, limits, l’Hospital’s rule, sequences and series, numerical methods, polar coordinates and introductory differential equations. Prerequisite: MTH 1001 or MTH 1010



MTH 1003 Calculus 2 for Natural Sciences Credit Hours: 4 Covers the integration and applications of integration, further techniques of integrations, improper integrals, limits, l’Hospital’s rule and numerical methods. Also includes introductory differential equations, multivariable derivatives and multivariable integrals. Prerequisite: MTH 1001 or MTH 1010



MTH 1010 Honors Calculus 1 Credit Hours: 4 Provides a rigorous treatment of differential calculus. Emphasizes proofs. Includes functions and graphs, limits and continuity, differentiation, chain rule, Taylor’s formula, calculation of the limit of a differentiable function, applications to maxima and minima, constructing the graph of a function and the Riemann integral. Prerequisite: MTH 1000



MTH 1011 Precalculus A Credit Hours: 3 Includes a review of operations on real numbers, algebraic expressions, linear equations, inequalities, exponents, polynomials, factoring, rational functions, roots, radicals, quadratics, graphing and difference functions. 


MTH 1012 Precalculus B Credit Hours: 3 Includes exponential and logarithmic functions including properties and graphs, and trigonometric functions including properties and graphs, and inverses and identities. Prerequisite: MTH 1011 or MTH 1701



MTH 1020 Honors Calculus 2 Credit Hours: 4 Provides a rigorous treatment of integral calculus. Emphasizes proofs. Includes integration and applications of integration, further techniques of integration, improper integrals, integrals depending on a parameter, sequences and series, uniform convergence of series and improper integrals. Prerequisite: MTH 1010



MTH 1051 Introductory Discrete Mathematics Credit Hours: 3 Elementary coverage of discrete mathematics. Includes logical arguments, mathematical induction in proofs, sets and relations (extension to functions and their properties), elementary counting principles (inclusionexclusion), permutations and combinations. Requirement(s): Must be enrolled in Florida Tech Online and credit can only be applied toward business, communication, humanities, management, psychology or computer information systems degrees at Florida Tech Prerequisite: MTH 1701



MTH 1603 Applied Calculus and Statistics Credit Hours: 3 Includes derivatives and integrals, and their applications, and probability and statistics, and their applications. Requirement(s): Credit cannot be applied toward any Florida Tech degree that requires MTH 1001 Calculus 1 Prerequisite: MTH 1000



MTH 1701 College Algebra Credit Hours: 3 Realnumber system; arithmetic operations with polynomials, special products and factoring; linear, fractional and quadratic equations; inequalities, exponents, radicals and absolute values; functions and graphs; and complex numbers, logarithms, logarithmic and exponential functions. Credit can only be applied toward business, communication, humanities, management, psychology or computer information systems degrees at Florida Tech. Requirement(s): Must take placement exam. 


MTH 1702 Applied Calculus Credit Hours: 3 Elements of differential and integral calculus with application to business, economics, management and the social and life sciences, as well as maxima, minima, rates, exponential growth and decay, and some techniques of integration. Prerequisite: MTH 1000 or MTH 1701



MTH 1703 Finite Mathematics Credit Hours: 3 Studies topics in mathematics especially applicable to business, such as linear models, linear programming, mathematics of finance, counting methods, probability and statistics. Requirement(s): Must be enrolled in Florida Tech Online Prerequisite: MTH 1701



MTH 1801 Trigonometry Review Credit Hours: 1 Reviews trigonometric topics necessary for calculus, including trigonometric functions, graphs, identities and solving trigonometric equations. Requirement(s): High school trigonometry, appropriate score on placement test and may be taken with MTH 1001 Calculus 1 


MTH 2001 Calculus 3 Credit Hours: 4 Cylindrical and spherical coordinates, vectors, functions of several variables, partial derivatives and extrema, multiple integral, vector integral calculus. Prerequisite: MTH 1002 or MTH 1020



MTH 2010 Honors Calculus 3 Credit Hours: 4 Provides a rigorous treatment of multivariable differential and integral calculus. Emphasizes proofs. Includes vector functions, functions of several variables, partial derivatives and extrema, implicit function theorem, multiple integrals, Fubini’s theorem, GaussGreen theorem, and Stokes’ theorem. Prerequisite: MTH 1020



MTH 2051 Discrete Mathematics Credit Hours: 3 Formulation of precise definitions and their negations using propositional and predicate logic; argument analysis and proof techniques including induction; number theory; and sets, relations, functions, directed graphs and elementary counting arguments. Requirement(s): Passing score on placement test or prerequisite course Prerequisite: MTH 1000 or MTH 1001 or MTH 1010 or MTH 1702



MTH 2201 Differential Equations/Linear Algebra Credit Hours: 4 Firstorder differential equations, linear differential equations with constant coefficients, firstorder systems of differential equations with constant coefficients, numerical methods, Laplace transforms, series solutions, algebraic systems of equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors. Prerequisite: MTH 1002 or MTH 1003 or MTH 1020



MTH 2202 Linear Algebra for Differential Equations Credit Hours: 1 Includes systems of equations, matrices, determinants, vector spaces, eigenvalues, and eigenvectors. Supplements differential equations. Requirement(s): Instructor approval Prerequisite: MTH 1002 or MTH 1020



MTH 2332 Primer for Biomath Credit Hours: 1 Introduces the separate languages of mathematics and biology such that students from the different disciplines can efficiently develop a biomath glossary to communicate with one another. Focuses on the current research projects in biology and ecology, and the relevant mathematical analysis. Requirement(s): Instructor approval Prerequisite: MTH 1000



MTH 2401 Probability and Statistics Credit Hours: 3 Random variables, expectations, sampling and estimation of parameters, normal and other distributions and centrallimit theorem, tests of hypothesis, linear regression and design experiments. Prerequisite: MTH 1002 or MTH 1003 or MTH 1020



MTH 3010 Functions and Modeling Credit Hours: 3 Provides prospective secondary education teachers discussions of case studies from different applications. Emphasizes the formulation of models and their analysis using mathematical tools from calculus, differential equations, linear algebra and probability statistics. Minimum student level  junior Requirement(s): Instructor approval Prerequisite: MTH 2201 or MTH 3200 Corequisite: MTH 3102



MTH 3051 Combinatorics and Graph Theory Credit Hours: 3 Elementary and advanced counting techniques including permutations, combinations, multisets, inclusionexclusion, generating functions, recurrence relations and topics in graph theory including graphs, trees, binary tree, graph traversals and network flow. Prerequisite: (MTH 1001 or MTH 1010 ), and (CSE 1400 or MTH 2051 )



MTH 3101 Complex Variables Credit Hours: 3 Algebra of complex numbers, elementary analytic functions, complex integration, series representations for analytic functions, residue theory and conformal mapping and its applications. Prerequisite: MTH 2001 or MTH 2010



MTH 3102 Introduction to Linear Algebra Credit Hours: 3 Includes vectors and matrices, linear equations, vector spaces and subspaces, orthogonality, determinants, eigenvalues and eigenvectors, and linear transformations. Introduces students to solution and manipulation of matrix equations using a standard package of mathematical software. Prerequisite: MTH 1002 or MTH 1020



MTH 3107 Optimization Credit Hours: 3 Provides a rigorous introduction to the fundamental theory of optimization. Includes linear programming, duality, sensitivity, convex analysis, nonlinear optimization, optimal control and Pontryagin’s maximum principle. Emphasizes problem formulation, analytical theory, algorithmic methods and recent applications. Prerequisite: (MTH 2001 or MTH 2010 ) and (MTH 2201 or MTH 3200 )



MTH 3200 Honors Differential Equations Credit Hours: 4 Provides analytical and computational methods for solving ordinary differential equations (ODEs), analysis of obtained solutions with applications to modeling problems. Includes matrix analysis for systems of linear equations, firstorder linear/nonlinear and higherorder linear ODEs, firstorder linear ODE systems, solutions by Laplace Transform. Prerequisite: (MTH 1002 or MTH 1003 or MTH 1020 )



MTH 3210 Introduction to Partial Differential Equations and Applications Credit Hours: 3 Includes heat, wave and Laplace equations, initial and boundary value problems of mathematical physics and Fourier series. Also covers Dirichlet problem and potential theory, Dalambert’s solutions for wave equation, Fourier and Laplace transforms, and Poisson integral formula. Also includes PDEs in higher dimensions and special functions of mathematical physics. Prerequisite: (MTH 2001 or MTH 2010 ) and (MTH 2201 or MTH 3200 )



MTH 3220 Honors Partial Differential Equations Credit Hours: 3 Rigorously analyzes partial differential equations of mathematical physics, initial and boundary value problems for diffusion, waves and Laplace equations. Covers Fourier series, Fourier and Laplace transforms and Green’s functions. Emphasizes proofs. Also includes PDEs in higher dimensions, special functions and general eigenvalue problems. Prerequisite: MTH 2010 and MTH 3200



MTH 3301 Finite Differences and Finite Elements Credit Hours: 3 Numerical methods for BVPs in one and two dimensions; finite difference methods for solving PDEs, finite element methods, variational formulation and Galerkin approximations for ODEs and twodimensional PDEs, and writing programs. Prerequisite: (CSE 1502 or CSE 1503 or CSE 2050 ), and MTH 3210



MTH 3312 Scientific Computing Credit Hours: 3 Introduces the basic concepts and tools in scientific computing relevant to computational science and engineering. Includes basic computer programming and data processing, interpolation and approximation, solution of linear/nonlinear systems of equations, numerical differential equations and stochastic simulation. Prerequisite: MTH 2201 or MTH 3200



MTH 3401 Introduction to Number Theory Credit Hours: 3 Covers divisibility, prime numbers, unique factorization, congruencies. quadratic reciprocity, Diophantine equations, properties of rational numbers, polynomials and dynamical systems. Includes computation, formulating conjectures, writing proofs and extended projects. Prerequisite: MTH 1002 or MTH 1020



MTH 3663 Mathematical Methods for Biology and Ecology Credit Hours: 3 Examines biological processes and mathematically reformulates the biological information into linear and nonlinear systems, and differential equations, and studies these formulations via matrix algebra, numerical techniques, approximation theory, stability and bifurcation analysis. Requirement(s): Instructor approval Prerequisite: (BIO 2332 or MTH 2332 ), and (MTH 1002 or MTH 1020 )



MTH 3773 Deterministic Methods and Models in Biomathematics Credit Hours: 3 Quantitatively investigates problems in population dynamics, biochemical reactions, infectious diseases and neurobiology with deterministic math models. Introduces the model formulation and analysis through matrix algebra, difference/differential equations, stability and bifurcation analysis, and computational simulations. Prerequisite: MTH 2201



MTH 3993 Selected Topics on Biostochastics Credit Hours: 3 Studies the influence of stochasticity on biological processes using statistical methods and Markov processes to analyze vital biological rates, including mutation rates for diseaseassociated DNA repeats, organismal growth and percapita survival. Requirement(s): Instructor approval Prerequisite: (MTH 1002 or MTH 1020 ), and (BIO 2332 or MTH 2332 )



MTH 4051 Abstract Algebra Credit Hours: 3 Groups, cyclic groups, permutation groups, isomorphisms, cosets and Lagrange’s theorem, rings, integral domains, vector spaces, and fields. Prerequisite: MTH 3102



MTH 4082 Introduction to Parallel Processing Credit Hours: 3 Introduces parallel algorithm development, architectures for parallel computers, programming paradigms SIMD and MIMD for shared and distributed memory computers. Presents parallel algorithms for matrix computations, sorting and searching, and various numerical algorithms. Includes analysis of performance of parallel algorithms and scalability of algorithms. Recommended: Programming ability in Fortran or C. Prerequisite: CSE 1001 or CSE 3312 or MTH 3312



MTH 4101 Introductory Analysis Credit Hours: 3 Rigorous treatment of calculus. Includes sequences and series of real numbers, limits of functions, topology of the real line, continuous functions, uniform continuity, differentiation, Riemann integration, sequences and series of functions, Taylor’s theorem; uniform convergence and Fourier series. Prerequisite: MTH 2001 or MTH 2010



MTH 4105 Topology Credit Hours: 3 Metric and topological spaces, continuity, homeomorphism connectedness, compact spaces, separation axioms, product spaces, homeotypic and fundamental group. Prerequisite: MTH 2051 and MTH 3102



MTH 4111 Honors Analysis Credit Hours: 3 Covers topologies and metric spaces, continuous and semicontinuous functions, measures, Vitali and Besicovitch covering theorems and Lebesgue integration. Also covers Jordan decomposition of measures, RadonNikodym Theorem and Lpspaces. Prerequisite: MTH 2010 and MTH 3200



MTH 4201 Models in Applied Mathematics Credit Hours: 3 Allows students to formulate and construct mathematical models that are useful in engineering, physical sciences, biological sciences, environmental studies and social sciences. Minimum student level  junior Requirement(s): Instructor approval Prerequisite: MTH 2201 or MTH 3200



MTH 4202 Stochastic Modeling Credit Hours: 3 Includes discrete and continuous time parameter Markov processes and their applications to genetics, biology, ecology, Poisson and renewal processes and applications to reliability and queueing, time series, Brownian motion, martingales, Îto calculus and applications to finance. Prerequisite: (MTH 2001 or MTH 2010 ) and MTH 2401



MTH 4224 Introduction to Machine Learning Credit Hours: 3 A broad introduction to machine learning and data mining. Topics include supervised learning(feature selection, Bayesian classifier, nearest neighbors, logistic regression, decision trees,support vector machines) and unsupervised learning (dimensionality reduction, kmeans clustering, hierarchical clustering, principal component analysis) methods. Prerequisite: (CSE 1001 or CSE 1502 or CSE 1503 ) and (MTH 2201 or MTH 2202 or MTH 3102 or MTH 3200 )



MTH 4311 Numerical Analysis Credit Hours: 3 Includes interpolation and approximation, solution of linear systems (basic iterative methods, conjugate gradient and preconditioner) and linear least square problems (QR and SVD), fast Fourier transform, numerical solution of ODEs, and boundary values problems (finite difference/finite element). Prerequisite: CSE 3312 or MTH 3312



MTH 4320 Deep Learning Credit Hours: 3 A projectbased introduction to deep learning architectures, algorithms and applications. Includes multilayer perceptrons, convolutional neural networks, recurrent neural networks and transformers; theory and implementation of learning algorithms, training and tuning procedures; and
applications to computer vision and natural language processing. Prerequisite: (CSE 1002 or CSE 1502 or CSE 1503 ) and (MTH 2201 or MTH 2202 or MTH 3102 or MTH 3200 )



MTH 4324 Statistical Modeling Credit Hours: 3 Provides an indepth introduction to statistical modeling and inference with linear models, Bayesian statistics, and related methods including simple linear regression, multiple regression, ANOVA, polynomial regression, Bayesian linear regression, MCMC algorithm, and sampling methods. Prerequisite: MTH 2401



MTH 4801 Advanced Geometry Credit Hours: 3 Topics in Euclidean and nonEuclidean geometry with an emphasis on proofs and critical thinking. Satisfies the state of Florida requirement for teacher certification in mathematics. Requirement(s): Instructor approval Prerequisite: MTH 2001 or MTH 2010



MTH 4920 Special Topics in Applied Mathematics Credit Hours: 3 Selected topics from mathematics. Content varies from year to year depending on the needs and interests of the students and expertise of the instructor. Requirement(s): Instructor approval 


MTH 4990 Undergraduate Research Credit Hours: 3 Participation in a research project under the direction of a faculty member. (Q) Requirement(s): Instructor approval 


MTH 5007 Introduction to Optimization Credit Hours: 3 An applied treatment of modeling, analysis and solution of deterministic (e.g., nonprobabilistic) problems. Topics include model formulation, linear programming, network flow, discrete optimization and dynamic programming. Recommended: At least one upperlevel undergraduate math course. 


MTH 5009 Introduction to Probabilistic Models Credit Hours: 3 An applied treatment of modeling, analysis and solution of problems involving probabilistic information. Topics chosen from decision analysis, inventory models, Markov chains, queuing theory, simulation, forecasting models and game theory. Recommended: Background knowledge equivalent to MTH 2401 Probability and Statistics . 


MTH 5050 Special Topics Credit Hours: 3 Contents may vary depending on the needs and interests of the students and the fields of expertise of the faculty. Requirement(s): Instructor approval 


MTH 5051 Applied Discrete Mathematics Credit Hours: 3 Logic fundamentals, induction, recursion, combinatorial mathematics, discrete probability, graph theory fundamentals, trees, connectivity and traversability. Applications from several fields of science and engineering, including computer science, operations research, and computer and electrical engineering. Recommended: Background knowledge equivalent to MTH 2051 Discrete Mathematics . 


MTH 5070 Educational Statistics Credit Hours: 3 Includes sampling procedures, frequency distributions, measures of central tendency, estimation of variability, the normal distribution, differences between two groups, analysis of variance and correlation. Also includes nonparametric techniques, multivariate techniques and computer analysis of educational data. 


MTH 5102 Linear Algebra Credit Hours: 3 Linear algebra, systems of linear equations and Gauss elimination method; inverses, rank and determinants; vector spaces; linear transformations, linear functional and dual spaces; eigenvalues, eigenvectors; symmetric, Hermitian and normal transformations; and quadratic forms. Recommended: Undergraduate course in multivariable calculus or linear algebra. 


MTH 5107 Optimization Models and Methods Credit Hours: 3 Surveys popular optimization models and algorithms. Topics chosen from linear, integer, nonlinear, dynamic and combinatorial optimization. Recommended: At least one upperlevel undergraduate math course. 


MTH 5110 Real Analysis 1 Credit Hours: 3 Sequences and series of functions, uniform convergence, approximation by polynomials, real analytic functions, differential calculus of functions of several variables, inverse function and implicit function theorems, Lebesgue measure, measurable functions, Lebesgue integration, absolutely integrable functions, comparisons with Riemann integral. Background knowledge equivalent to MTH 4101 Introductory Analysis . 


MTH 5111 Real Analysis 2 Credit Hours: 3 Studies basic topology, continuous and semicontinuous functions, metric spaces, differentiation, measures, product measure, Lebesgue integration, RadonNikodym Theorem, Lpspaces and measures on topological spaces. Prerequisite: MTH 5101



MTH 5115 Functional Analysis Credit Hours: 3 Banach spaces, Hilbert spaces, topological vector spaces, bounded and unbounded linear operators, spectral theory. Prerequisite: MTH 5110



MTH 5125 Applied Complex Variables Credit Hours: 3 Analytic functions, CauchyReimann equations, contour integration, Cauchy theorem, Cauchy integral formula, Taylor and Laurent series, residue theorem and applications, linear fractional transformations, conformal mapping, SchwarzChristoffel transformation. Inversion integral for Laplace transform with complex argument; inverse Laplace transforms. Recommended: Background knowledge equivalent to MTH 2001 Calculus 3 and MTH 2201 Differential Equations/Linear Algebra . 


MTH 5130 Theory of Complex Variables Credit Hours: 3 Topology of the complex plane, analytic functions, Cauchy’s integral formula, Liouville’s theorem, maximum modulus theorem, Taylor and Laurent series, singularities, residue theorem, analytic continuation, entire functions, infinite product representation and conformal mapping. Recommended: Background knowledge equivalent to MTH 2201 Differential Equations/Linear Algebra and MTH 4101 Introductory Analysis . 


MTH 5201 Mathematical Methods in Science and Engineering 1 Credit Hours: 3 Fourier series and their convergence properties; SturmLiouville eigenfunction expansion theory; Bessel and Legendre functions; solution of heat, wave and Laplace equations by separation of variables in Cartesian coordinates. Recommended: Background knowledge equivalent to MTH 2001 Calculus 3 and MTH 2201 Differential Equations/Linear Algebra . 


MTH 5202 Mathematical Methods in Science and Engineering 2 Credit Hours: 3 Solution of heat, wave and Laplace equations by separation of variables in cylindrical and spherical coordinates. Associated Legendre functions, hypergeometric functions and spherical harmonics. Fourier transforms and separation of variables for heat and wave equations on infinite intervals. Vector integral calculus. Prerequisite: MTH 5201



MTH 5203 Mathematical Methods in Science and Engineering 3 Credit Hours: 3 General perturbation techniques for linear and nonlinear ordinary differential equations, boundary layer theory, WKB methods, multiple scale analysis, approximate methods of solution, asymptotic expansion of integrals, asymptotic power series solutions of linear ODEs near irregular singular points. Prerequisite: MTH 5125 and MTH 5201





MTH 5225 Linear Optimization Models and Methods Credit Hours: 3 Provides theory and applied treatment of linear programming problems including network and transportation problems and integer programming. Includes formulation of deterministic linear models, analysis and solution methods for linear optimization problems, applicability to complex systems in realworld problems. Background knowledge in linear algebra and multivariable calculus. 






MTH 5305 Numerical Linear Algebra Credit Hours: 3 Includes numerical solution of linear systems and linear least square problems, eigenvalue algorithms, and matrix factorization/ decomposition. Presents analysis of numerical algorithms in linear algebra and their applications in Image Analysis, Signal Processing, Software Engineering, and Fluid Mechanics. Recommended background knowledge in linear algebra. 


MTH 5310 Numerical Methods for Ordinary Differential Equations Credit Hours: 3 Numerical methods for initial value problems, boundary value problems and eigenvalue problems for ordinary differential equations. RungeKutta methods, multistep and adaptive methods, stiff equations and Astable methods, collocation. Prerequisite: MTH 5301





MTH 5320 Deep Learning Credit Hours: 3 A projectbased introduction to deep learning architectures, algorithms and applications. Includes multilayer perceptrons, convolutional neural networks, recurrent neural networks and transformers; theory and implementation of learning algorithms, training and tuning procedures; and
applications to computer vision and natural language processing.
Crosslisted with MTH 4320 . Prerequisite: Background knowledge equivalent to MTH 2202 and CSE 1002 .



MTH 5324 Statistical Modeling Credit Hours: 3 Provides an indepth introduction to statistical modeling and inference with linear models. Bayesian statistics, and related methods including simple linear regression, multiple regression, ANOVA, polynomial regression, Bayesian linear regression, MCMC algorithm, and sampling methods. Background knowledge in probability and statistics. 


MTH 5335 Nonlinear Optimization Models and Methods Credit Hours: 3 Covers fundamentals of nonlinear continuous unconstrained and constrained optimization, methods for solving nonlinear programming problems. Includes analysis of widely used iterative algorithms and their convergence, convexity and optimality conditions, gradient methods, Lagrangian functions, elements of duality theory and implementing constraints. Background knowledge in linear algebra and multivariable calculus. 


MTH 5401 Applied Statistical Analysis Credit Hours: 3 Covers statistical distributions, statistical tests for data, least squares and regression, estimations, tests of hypotheses, analysis of variance, planning and designing research experiments, randomized blocks, Latin and GraecoLatin squares and data reduction, analysis using ANOVA (analysis of variance) and other methods. Recommended: Background knowledge equivalent to MTH 2001 Calculus 3 . 


MTH 5411 Mathematical Statistics 1 Credit Hours: 3 Covers discrete and continuous random variables, generating and moment generating functions, multivariate distributions, covariance and correlation, sums of independent random variables, conditional expectation, Central Limit Theorem, Markov and Chebyshev inequalities and the Law of Large Numbers. Recommended: Undergraduate courses in multivariable calculus and linear algebra. 


MTH 5412 Mathematical Statistics 2 Credit Hours: 3 Includes maximum likelihood and Bayes estimators, confidence intervals, testing hypotheses, uniformly most powerful tests, nonparametric methods (chisquare and KolmogorovSmirnov goodnessoffit tests) and regression analysis. Prerequisite: MTH 5411



MTH 5415 Regression Models for Machine Learning Credit Hours: 3 Describes how to implement regressionbased machine learning models for prediction and inference using available data. Presents algorithms, techniques, and applications of regressionbased machine learning models at an advanced level by building on the knowledge of probability and statistics. Background knowledge in probability and statistics. 


MTH 5420 Theory of Stochastic Processes Credit Hours: 3 Includes discrete and continuoustime stochastic processes, point and counting processes and Poisson counting process; as well as compound Poisson process, nonstationary Poisson process, renewal theory, regenerative processes and Markov chains. Prerequisite: MTH 5411



MTH 5425 Theory of Stochastic Signals Credit Hours: 3 Covers univariate and multivariate distributions, generating and moment generating functions; autocorrelation, widesense, strictsense stationary, voltage, Poisson, Wiener, random telegraph signal and white noise processes; Dirac delta function, Fourier transform, system response, transfer function and spectral analysis. Requirement(s): Instructor approval 


MTH 5430 Queuing Theory Credit Hours: 3 Includes queuing processes; imbedded and continuous time parameter processes; Markov, semiMarkov and semiregenerative processes; singleserver and multiserver queues; and processes of servicing unreliable machines. Controlled stochastic models. Prerequisite: MTH 5411



MTH 5434 Stochastic Analysis of Financial Markets 1 Credit Hours: 3 Lays the foundation for mathematical concepts widely applied in financial markets. Uses economical theory with stochastics (martingales, Wiener, Markov, Ito processes, stochastic differential equations) to derive fair option prices and to hedge call options. Also uses fluctuation theory to predict stocks’ crossing of critical levels. Prerequisite: MTH 5411 or MTH 5425



MTH 5436 Stochastic Analysis of Financial Markets 2 Credit Hours: 3 Offers multidimensional stochastics applied to financial markets. Continues with multivariate Ito processes and multidimensional FeynmanKac theorems, hedging of American and exotic call options and forward exchange rates. Introduces timesensitive analysis of stocks, and risk theory. Prerequisite: MTH 5434 or ORP 5025



MTH 5899 Final Semester Thesis Credit Hours: 0  2 Variable registration for thesis completion after satisfaction of minimum registration requirements. Requirement(s): Approval by Office of Graduate Programs and accepted petition to graduate 

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