Mathematics, Pure & Applied Mathematics Concentration (M.S.)  Graduate (Combined B.S. Math/M.S.)  2015 University Catalog
MATHEMATICSw/CONC:Pure&AplMath(ComBS/MS)
Complete 33 semester hours including the following 3 requirements (12 hours will be applied from the UG program):

PURE MATHEMATICS
Complete 4 courses for 12 semester hours: .
MATH 521 Real Variables I (3 hours lecture) 3 MATH 525 Complex Variables I (3 hours lecture) 3 MATH 531 Abstract Algebra I (3 hours lecture) 3 MATH 535 Linear Algebra I (3 hours lecture) 3 
APPLIED MATHEMATICS
Complete 4 courses for 12 semester hours: .
MATH 530 Mathematical Computing (3 hours lecture) 3 MATH 560 Numerical Analysis (3 hours lecture) 3 MATH 584 Operations Research (3 hours lecture) 3 MATH 591 Applied Industrial Mathematics (3 hours lecture) 3 
ELECTIVES
Complete 6 semester hours from the following:

If equivalent courses haven't been previously taken, take the following. Only 6 hours can be used for credit.
MATH 515 Intermediate Analysis I (3 hours lecture) 3 MATH 516 Intermediate Analysis II (3 hours lecture) 3 MATH 518 Foundations of Abstract Algebra (3 hours lecture) 3 
Complete 3 semester hours9 semester hours from the following:


THESIS

Complete for 3 semester hours.
MATH 698 Master's Thesis 3 
Submit the completed Thesis original and one copy to the Graduate Office. See Thesis Guidelines for details.

Course Descriptions:
CMPT576: ObjectOriented Software Development (3 hours lecture)
Introduction to the major features of the objectoriented paradigm and their realization in an objectoriented programming language. Introduction to major methods and tools used in objectoriented analysis and design. Implementation and testing issues. 3 sh.
Prerequisites: CMPT 581, CSIT 571 and departmental approval for students with Deferred or Conditional status.
CMPT578: Introduction to Artificial Intelligence (3 hours lecture)
An introduction to artificial intelligence including representations of knowledge, problem solving, games, heuristics and backtracking, expert systems, theorem proving, the language LISP and PROLOG. 3 sh.
Prerequisites: CSIT 571 and departmental approval for students with Deferred or Conditional status.
CMPT581: Systems Software Design (3 hours lecture)
Assemblers, macroprocessors, linkers and loaders, introduction to compilers and run facilities. Required of majors. 3 sh.
Prerequisites: CSIT 545 and departmental approval for students with Deferred or Conditional status.
CMPT587: Microcomputers and Computer Interfaces (3 hours lecture)
Introduction to geneology, manufacture and hardware design of microprocessors, microcomputer architecture, instruction sets and programming, microcomputer peripherals and interfaces. 3 sh.
Prerequisites: CSIT 545 and departmental approval for students with Deferred or Conditional status.
CMPT588: Fundamentals of Programming Languages (3 hours lecture)
A comparative approach to modern programming languages with emphasis on nonimperative languages, and an introduction to parallel languages. 3 sh.
Prerequisites: Departmental approval for students with Deferred or Conditional status.
CMPT589: Computer Simulation of Discrete Systems (3 hours lecture)
Introduction to simulation and discrete simulation models. Queuing theory and stochastic processes. Simulation methodology including generation of random numbers and variates, design of simulation experiments, analysis of data generated by simulation experiments and validation of models. Survey of current simulation languages and selected applications. 3 sh.
Prerequisites: CSIT 545 and departmental approval for students with Deferred or Conditional status.
CMPT593: Structured System Design and Analysis (3 hours lecture)
A study of the design of large scale computer systems relative to the constraints imposed by hardware, software and particular types of applications. Recent work in automated system design will be discussed. 3 sh.
Prerequisites: CSIT 555 and departmental approval for students with Deferred or Conditional status.
CMPT678: Neurocomputing (3 hours lecture)
Basic neural network concepts, definitions, and building blocks; learning laws; simple implementations; associative networks; mapping networks; survey of applications. 3 sh.
Prerequisites: CSIT 571 and departmental approval for students with Deferred or Conditional status.
MATH515: Intermediate Analysis I (3 hours lecture)
Properties of the real number system, limits, continuous functions, intermediate value theorem, derivative, mean value theorem, Riemann integral. 3 sh.
Prerequisites: Permission of graduate program coordinator.
MATH516: Intermediate Analysis II (3 hours lecture)
This course is a continuation of MATH 515. Topics include functions of several variables, partial derivatives, Green's theorem, Stoke's theorem, divergence theorem, implicit function theorem, inverse function theorem, infinite series, uniform convergence. 3 sh.
Prerequisites: MATH 515 or MATH 425 or equivalent, permission of graduate program coordinator.
MATH518: Foundations of Abstract Algebra (3 hours lecture)
Fundamental concepts of algebra including groups, rings, integral domains and fields, with important examples. 3 sh.
Prerequisites: Permission of graduate program coordinator.
MATH521: Real Variables I (3 hours lecture)
Real number system, Lebesgue measure and integration, differentiation, Fourier series, LP, metric, normed vector, Banach and Hilbert spaces. 3 sh.
Prerequisites: MATH 426 and permission of graduate program coordinator.
MATH522: Real Variables II (3 hours lecture)
Real number system, Lebesgue measure and integration, differentiation, Fourier series, LP, metric, normed vector, Banach and Hilbert spaces. 3 sh.
Prerequisites: MATH 521, permission of graduate program coordinator.
MATH525: Complex Variables I (3 hours lecture)
Integration and differentiation in the complex domain, Cauchy's theorem, Cauchy's integral formula, Laurent expansion, residues, elements of conformal mapping, series and product representations. 3 sh.
Prerequisites: MATH 426 and permission of graduate program coordinator.
MATH526: Complex Variables II (3 hours lecture)
Integration and differentiation in the complex domain, Cauchy's theorem, Cauchy's integral formula, Laurent expansion, residues, elements of conformal mapping, series and product representations. 3 sh.
Prerequisites: MATH 525, permission of graduate program coordinator.
MATH530: Mathematical Computing (3 hours lecture)
Introduction to mathematical computing techniques using a computer algebra system and algorithmic approach to solving mathematical problems. Mathematical applications taken from various areas of mathematics, the sciences, engineering, and business. 3 sh.
Prerequisites: Permission of the graduate program coordinator or consent of the instructor.
MATH531: Abstract Algebra I (3 hours lecture)
Basic algebraic structures including groups, rings, fields, modules and lattices. 3 sh.
Prerequisites: MATH 431 and permission of graduate program coordinator.
MATH532: Abstract Algebra II (3 hours lecture)
Basic algebraic structures including groups, rings, fields, modules and lattices. 3 sh.
Prerequisites: MATH 531, permission of graduate program coordinator.
MATH535: Linear Algebra I (3 hours lecture)
Vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. 3 sh.
Prerequisites: MATH 335 and permission of graduate program coordinator.
MATH536: Linear Algebra II (3 hours lecture)
Vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. 3 sh.
Prerequisites: MATH 535, permission of graduate program coordinator.
MATH540: Probability (3 hours lecture)
Sample spaces and events, combinatorial analysis, conditional probability and stochastic independence, random variables and probability distributions, expected value and variance, probability generating functions, continuous random variables. 3 sh.
Prerequisites: MATH 340 and permission of graduate program coordinator.
MATH551: Topology (3 hours lecture)
Basic pointset topology, topological spaces, homeomorphisms, compactness, connectedness, separation properties, uniformities, metrizability, introductory algebraic topology, homology groups and homotopy. 3 sh.
Prerequisites: MATH 425, and permission of graduate program coordinator.
MATH554: Projective Geometry (3 hours lecture)
Projective planes and spaces are studied by synthetic and analytic approaches. Topics covered include the theorems of Desargues and Pappus, harmonic sequences, projectivities, coordinatization, finite planes, and conics. 3 sh.
Prerequisites: MATH 335 and permission of graduate program coordinator.
MATH560: Numerical Analysis (3 hours lecture)
Error analysis, interpolation and approximation theory, numerical solution of linear and nonlinear equations, numerical differentiation and integration, numerical solution of differential equations. 3 sh.
Prerequisites: MATH 335, and permission of graduate program coordinator.
MATH564: Ordinary Differential Equations (3 hours lecture)
Linear and nonlinear equations, Green's functions, power series solutions, autonomous systems, existence and uniqueness, singularities, SturmLiouville systems. 3 sh.
Prerequisites: MATH 335, and 420, and permission of graduate program coordinator.
MATH566: Partial Differential Equations (3 hours lecture)
First order equations, separation of variables, series solutions, hyperbolic, parabolic and elliptic equations, characteristics, transform methods. 3 sh.
Prerequisites: MATH 335, and 420, and permission of graduate program coordinator.
MATH568: Applied Mathematics: Continuous (3 hours lecture)
Formulation, manipulation and evaluation of mathematical models of continuous systems. Topics selected from: conservation principles and the classical equations of mathematical physics, applications of the qualitative and quantitative theory of ordinary and partial differential equations, optimization, calculus of variations, stability theory, stochastic models. 3 sh.
Prerequisites: MATH 335, and 340, and 420, and 425, and permission of graduate program coordinator.
MATH569: Applied Mathematics: Discrete (3 hours lecture)
Introduction to the basic ideas of discrete mathematics and its applications. Counting principles, permutations, combinations, algorithms, complexity, graphs, trees, searching and sorting, recurrence relations, generating functions, inclusionexclusion, the pigeonhole principle, chromatic number, eulerian chains and paths, hamiltonian chains and paths, flows in networks, finite Markov chains. 3 sh.
Prerequisites: MATH 335, and 340, and 425, and permission of graduate program coordinator.
MATH580: Combinatorial Mathematics (3 hours lecture)
Arrangements and selections, binomial coefficients, Stirling numbers, generating functions, recurrence relations, inclusionexclusion, Polya enumeration formula, combinatorial graph theory, combinatorial geometries. 3 sh.
Prerequisites: MATH 222 and graduate program coordinator's permission.
MATH581: Graph Theory (3 hours lecture)
Graphs, digraphs, and trees. Connectivity, separability, planarity, and colorability. Cliques, independent sets, matchings, flows and tours. Graphs as mathematical models; graph algorithms. 3 sh.
Prerequisites: MATH 222, and 335, and graduate program coordinator's permission.
MATH584: Operations Research (3 hours lecture)
An indepth study of one or at most two topics in operations research, selected from linear programming and game theory, linear and nonlinear programming, queuing theory, inventory theory, simulation models. 3 sh.
Prerequisites: MATH 425 and STAT 440 and permission of graduate program coordinator.
MATH585: Fundamentals of Scientific Computing (3 hours lecture)
Theory and implementation of mathematical computing techniques. This course will present basic programming and graphing techniques to analyze mathematical models. Students will learn basic algorithm design, programming paradigms, simulation techniques, visualization software, and typesetting software for science and mathematics. 3 sh.
Prerequisites: MATH 420 and permission of the Graduate Program Coordinator.
MATH586: Fundamentals of Mathematical Models (3 hours lecture)
The course investigates meaningful and practical problems across various industry related disciplines including mathematical sciences, engineering, economics, operation research and life sciences. Students will learn how to identify problems, construct or select developed models, collect and analyze data, and draw appropriate conclusions. The development of appropriate mathematical models used to study applied case problems originating from industry interest will be stressed as well as interpretation of mathematical results in that context. 3 sh.
Prerequisites: MATH 585 and STAT 583 and permission of graduate program coordinator.
MATH587: Fundamentals of Optimization (3 hours lecture)
Introduction to applied optimization in various settings, both continuous and discrete. Topics selected from linear programming, nonlinear programming, network optimization models, and feedback control with an emphasis on applications to business management, economics, game theory, and finance. The course will be teamtaught, with the various areas of optimization introduced by faculty with expertise in that field. 3 sh.
Prerequisites: MATH 585 and STAT 583 and permission of Graduate Coodinator.
MATH588: Professional Science Master MiniProjects (6 hours lecture)
Students working in teams will be assigned problems selected from professional case studies and may include problems of current interest supplied by collaborating industries and/or advisory board members. Solution methodology will vary from problem to problem and will require the wide breadth of mathematical tools covered in the prerequisite courses. These include discrete and continuous modeling, optimization methods, and data analysis. Central to the professional experience, students will present problem statement, solution methodology, and results during class time. Emphasis will be placed on incorporating the skills developed in the PSM plus courses. Specifically, these skills involve understanding goals, leadership and teamwork, communication skills, marketing the project, discipline, flexibility, innovation, special appropriate technologies, quality of project outcomes, ethics (as applicable), and meeting potential employer expectations. 6 sh.
Prerequisites: MATH 585, MATH 586, MATH 587, STAT 583 and permission of the Graduate Program Coordinator.
MATH590: Advanced Topics (3 hours lecture)
An indepth study of a topic or topics selected from areas such as algebra, analysis, geometry, probability and statistics, and applied mathematics, with special emphasis upon recent developments in the field. May be repeated once for a maximum of 6.0 credits as long as the topic is different. 3 sh.
Prerequisites: Graduate program coordinator's permission.
MATH591: Applied Industrial Mathematics (3 hours lecture)
Formulation, modeling, and solution of mathematical problems from engineering, science and business. Topics include statistical distributions, Monte Carlo method, function fitting, transforms optimization, regression analysis, costbenefit analysis, ordinary differential equations, partial differential equations, numerical methods, divided differences, splines, Galerkin's method, and finite elements. 3 sh.
Prerequisites: MATH 335, MATH 425, MATH 530, STAT 440 or permission of graduate program coordinator.
MATH595: Seminar (14 hours seminar)
Guided study of selected topics in major field of interest. May be repeated once for a maximum of 6.0 credits as long as the topic is different. 1  4 sh.
Prerequisites: Graduate program coordinator's permission.
MATH690: Independent Study in Mathematics
Independent study under the direction of a faculty member, offering the opportunity to pursue topics in mathematics which may be outside the scope of regular curricular offerings or may be an extension of an existing course or courses. Approval must be obtained from the graduate coordinator and faculty advisor. May be repeated once for a maximum of 6.0 credits during the graduate program. 3 sh.
Prerequisites: Permission of graduate program coordinator. Departmental approval.
MATH697: Culminating Experience for PSM (6 hours lecture)
Students will work in teams to solve problems originating in the industry or to deliver industry related case studies. Each group will produce a written report of their work and give a PowerPoint presentation summarizing their report. Projects will require background knowledge in the PSM mathematical and technical core content and the communication/business plus course training. Each project will be mentored by a PSM faculty or advisory board member. 6 sh.
Prerequisites: Completion of 27 credits including MATH 585 and MATH 586 and MATH 587 and MATH 588 and STAT 583 and permission of the Graduate Program Coordinator.
MATH698: Master's Thesis
Independent research project done under faculty advisement. Students must follow the MSU Thesis Guidelines, which may be obtained from the Graduate School. Students should take MATH 699 if they don't complete MATH 698 within the semester. 3 sh.
Prerequisites: Permission of graduate program coordinator.
STAT541: Applied Statistics (3 hours lecture)
Review of estimation and hypothesis testing for one sample and two sample problems; introduction to nonparametric statistics and linear regression; fundamental principles of design, completely randomized design, randomized block design, latin square, and 2 factor design. 3 sh.
Prerequisites: STAT 330 or STAT 443 and permission of graduate program coordinator.
STAT542: Statistical Theory I (3 hours lecture)
Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chisquared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, NeymanPearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. 3 sh.
Prerequisites: STAT 541 and permission of graduate program coordinator.
STAT543: Statistical Theory II (3 hours lecture)
Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chisquared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, NeymanPearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. 3 sh.
Prerequisites: STAT 542 and permission of graduate program coordinator.
STAT544: Statistical Computing (3 hours lecture)
Computer systems for data analysis and data graphics, and intermediate level statistical methodology are investigated. Several statistical computing packages are utilized and evaluated. 3 sh.
Prerequisites: STAT 541 or STAT 548, and CMPT 183, and permission of graduate program coordinator.
STAT545: Practicum in Statistics I
An applied experience in which students work with practitioners in industry, government or research organizations utilizing statistical techniques in a research setting. Students will work with statisticians on projects involving experimental design and data collection as well as the analysis and interpretation of the data. May be repeated once. 3 sh.
Prerequisites: STAT 541, STAT 544, and STAT 547 or STAT 548, and permission of graduate program coordinator.
STAT546: NonParametric Statistics (3 hours lecture)
Selected distributionfree tests and estimation techniques including sign, KolmogorovSmirnov, Wilcoxon signed rank, MannWhitney, Chisquare, rank correlation, Kendall's Tau, KruskalWallace, Friedman, McNemar, and others. 3 sh.
Prerequisites: STAT 330 and permission of graduate program coordinator.
STAT547: Design and Analysis of Experiments (3 hours lecture)
Fundamental principles of design; fixed, random and mixed models; factorial designs; designs with restricted randomization; splitplot design; confounding; fractional replication; experimental and sampling errors. 3 sh.
Prerequisites: STAT 541 or STAT 548, and permission of graduate program coordinator.
STAT548: Applied Regression Analysis (3 hours lecture)
Fitting equations to data; matrices, linear regression; correlation; analysis of residuals; multiple regression; polynomial regression; partial correlation; stepwise regression; regression and model building; regression applied to analysis of variance problems; introduction to nonlinear regression. 3 sh.
Prerequisites: STAT 330 or STAT 443, and permission of graduate program coordinator.
STAT549: Sampling Techniques (3 hours lecture)
Sampling and survey methodology; basic sampling theory; simple, stratified, random, cluster, systematic and area sampling. Sampling errors and estimation procedures. 3 sh.
Prerequisites: STAT 330 or STAT 443, and permission of graduate program coordinator.
STAT595: Topics in Statistics (3 hours lecture)
Topics such as exploratory data analysis, statistical graphics, statistical quality control and statistical quality assurance, Bayesian methods and Markov chain Monte Carlo studies. May be repeated twice for a total of 9.0 credits. 3 sh.
Prerequisites: Permission of graduate program coordinator.
STAT597: Research Methods in Statistical Science (3 hours lecture)
Preparation for research in statistical science. Application of mathematics and computing science to the development, modeling, validation and evaluation of statistical research methods. Identification of statistical issues in real world problems and novel applications of statistical methods to these problems. Development of research proposals in statistical science. 3 sh.
Prerequisites: STAT 552 or equivalent and departmental approval.
STAT640: Biostatistics I (3 hours lecture)
Fundamental statistical concepts and methods used by statistical scientists in the health, biological, medical and pharmaceutical industries. Categorical data analysis, logistic regression, generalized linear models, nonparametric regression techniques. 3 sh.
Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.
STAT641: Biostatistics II (3 hours lecture)
Fundamental statistical concepts and methods used by statistical scientists in the health, biological, medical and pharmaceutical industries. Survival analysis and designs for clinical trials. 3 sh.
Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.
STAT642: Introduction to Stochastic Processes (3 hours lecture)
Generating functions, convolutions, recurrent events, random walk models, gambler's ruin problems, Markov chains and processes, time dependent stochastic processes, queuing theory and epidemic models. 3 sh.
Prerequisites: MATH 540 and permission of graduate program coordinator.
STAT645: Advanced Topics in Statistics (3 hours lecture)
Recent developments in statistical science. Topics such as data mining, statistical genomics, computationally intensive dataanalytic methods, statistical consulting, dynamic statistical graphics and visualization, applied time series analysis. May be repeated with no limit as long as the topic is different. 3 sh.
Prerequisites: Permission of graduate program coordinator.
STAT646: Multivariate Analysis (3 hours lecture)
Analysis of multiple response variables simultaneously; covariance and the multivariate normal distribution; manova, discriminant functions; principle components and canonical correlations. 3 sh.
Prerequisites: STAT 541, STAT 548 and permission of graduate program coordinator.
STAT647: Practicum in Statistics II
An applied experience in which students work with practitioners in industry, government or research organizations utilizing advanced statistical techniques in a research setting. Students will be expected to exhibit the ability to work independently on projects involving advanced techniques in experimental design, analysis and interpretation of data. May be repeated once. 3 sh.
Prerequisites: STAT 542, STAT 545, at least one 600level course, and permission of graduate program coordinator.
STAT648: Advanced Statistical Methods (3 hours lecture)
Advanced statistical concepts and methods used by statistical scientists in the analysis of designed experiments and observational studies. Response surface methodology, analysis of covariance, the general linear model, the cell means model and the analysis of variance of unbalanced or messy data. 3 sh.
Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.
STAT649: Independent Study in Statistics
Independent study under the direction of a faculty member, offering the opportunity to pursue topics in statistics which may be outside the scope of regular curricular offerings or may be an extension of an existing course or courses. Approval must be obtained from the graduate coordinator and faculty advisor. May be repeated once for a maximum of 6.0 credits during the graduate program. 3 sh.
Prerequisites: Permission of graduate program coordinator and departmental approval.