Apr 30, 2024  
2016-2017 Graduate Catalog (as of 08-31-16) 
    
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2016-2017 Graduate Catalog (as of 08-31-16) [ARCHIVED CATALOG]

Course Descriptions

 

Environmental Studies
  

  • EVSS 538 Introduction to Hydrogeology (4)

    Introduction to quantitative nature of water flow within geologic media. Discuss the significance of water flow theory and the dynamics of many natural flow systems in geologic settings. Quantitative analysis of water resources in a decision-making format. Lectures three hours per week; laboratory three hours per week.
    Prerequisite(s): MATH 120 or 220 or equivalent; or permission of the instructor.
    Course Frequency: Spring
    Cross-Listing: GEOL 438
  

  • EVSS 659 Environmental Statistics (3)

    This course provides an introduction to environmental statistics and risk assessment. Topics include probability, correlation, regression, hypothesis testing, analysis of variance, model testing, residual analysis, and nonparametric models. Environmental applications will be provided throughout the course.
    Prerequisite(s): Math 250: Statistical Methods I (or an equivalent college-level statistics course) or pass an entrance exam.
    Course Frequency: Spring

Foundations, Secondary, and Special Education
  

  • EDFS 691 Use of Technology in Math and Science (3)

    Designed to expose participants to skills and techniques for using technology, software, and hardware to improve the instruction of mathematics and science. Participants review current mathematics and science software, develop activities to incorporate technology into the mathematics and science curriculum and design problem-solving activities.
    Prerequisite(s): EDFS 687  or equivalent or permission of the instructor.
    Course Frequency: Occasional

Mathematics
  

  • MATH 502 Advanced Linear Algebra (3)

    This course provides the linear algebra background necessary for a variety or applied fields as well as advanced work in algebra and analysis. Topics include vector spaces, linear transformations, dual spaces, matrices, matrix factorizations, matrix norms, determinants, eigenvalues and diagonalization, bilinear forms, projections, orthogonal and unitary transformations, Jordan canonical form, and infinite dimensional linear spaces. Applications such as an approximation theory, positive matrices, computation, multilinear algebra, and spectral theory will be selected by the instructor.
    Prerequisite(s): Students must have a working knowledge of undergraduate Linear Algebra and proof techniques of Abstract Algebra and Analysis.
    Course Frequency: Fall
    Cross-Listing: MATH 402
  

  • MATH 503 Applied Algebra I (3)

    This course introduces basic concepts of abstract algebra and its applications. Topics include sets, relations, functions; introduction to graphs, group theory, LaGrange’s theorem, the homomorphism theorems, applications to coding theory and connections with graph theory; Boolean algebra, with applications to combinatorial circuits.
    Prerequisite(s): MATH 303 (Abstract Algebra). S
    Course Frequency: Spring
  

  • MATH 511 Real Analysis I (3)

    Topics include set theory and metric spaces, topological properties, local and uniform convergence criteria, properties of continuous functions and differentiation of vector valued functions.
    Prerequisite(s): MATH 411 (Advanced Calculus II). F
    Course Frequency: Fall
  

  • MATH 515 Complex Analysis (3)

    This course provides a proof-based introduction to Complex Analysis. Topics include the complex number system, analytic and harmonic functions, power series, integrations, residue theory, analytic continuation, conformal mapping, and applications.
    Prerequisite(s): Students must have a working knowledge of proof techniques of analysis.
    Course Frequency: Spring
    Cross-Listing: MATH 415
  

  • MATH 523 Partial Differential Equations I (3)

    This course provides an introduction to the three main classes of partial differential equations (hyperbolic, parabolic, and elliptic) that arise in the description of wave motion, diffusion processes, and potential theory. Topics include the study of initial and boundary value problems, and solution methods such as fundamental solutions and separation of variables. Additional topics may include the method of characteristics, Sturm-Liouville theory, Green’s functions, integral transformations, and nonlinear partial differential equations.
    Prerequisite(s): Students must have a working knowledge of Vector Calculus and Ordinary Differential Equations.
    Course Frequency: Fall
    Cross-Listing: MATH 423
  

  • MATH 530 Mathematical Statistics I (3)

    This is a calculus based probability and statistics course. Topics will include probability functions and densities, mathematical expectations, sums of random variables, and sampling distributions.
    Prerequisite(s): Students must have a working knowledge of Vector Calculus.
    Course Frequency: Fall
    Cross-Listing: MATH 430
  

  • MATH 531 Mathematical Statistics II (3)

    This is the second course in a two-semester course on Mathematical Statistics. Topics include decision theory, estimation, hypothesis testing, regression, correlation, and analysis of variance.
    Prerequisite(s): MATH 530  or equivalent
    Course Frequency: Spring
    Cross-Listing: MATH 431
  

  • MATH 540 Statistical Learning I (3)

    This course provides an introduction to various approaches to statistical learning including empirical processes, classification and clustering, nonparametric density estimation and regression, model selection and adaptive procedures, bootstrapping and cross-validation.
    Prerequisite(s): Students must have a working knowledge of undergraduate Linear Algebra, Multivariate Calculus, and Statistics.
    Course Frequency: Fall
    Cross-Listing: MATH 440
  

  • MATH 541 Statistical Learning II (3)

    Neural networks, nearest neighbor procedures, Vapnik Chervonenkis dimension, support vector machines, structural risk minimization induction, regularization methods and boosting and bagging in classification and regression.
    Prerequisite(s): MATH 540  
    Course Frequency: Spring
    Cross-Listing: MATH 441
  

  • MATH 545 Numerical Analysis I (3)

    This course is a study of numerical methods and analysis of their accuracy, robustness, and speed. Topics include numerical solution of ordinary differential equations, approximations of functions, solving simultaneous linear equations by direct and iterative methods, computing eigenvalues and eigenvectors, and solving systems of non-linear equations. Standard computer software will be used.
    Prerequisite(s): Students must have a working knowledge of Linear Algebra, Ordinary Differential Equations, and some computer programming skills.
    Course Frequency: Occasional
    Cross-Listing: MATH 545
  

  • MATH 550 Linear Models (3)

    This course provides an introduction to the theory of linear models for analyzing data. Topics include analysis of variance and regression models, as well as Bayesian estimation, hypothesis testing, multiple comparison, and experimental design models. Additional topics such as balanced incomplete block designs, testing for lack of fit, testing for independence, and variance component estimation are also treated. The approach taken is based on projections, orthogonality, and other vector space concepts.
    Prerequisite(s): Students must have a working knowledge of undergraduate Linear Algebra and Statistics.
    Course Frequency: Fall
    Cross-Listing: MATH 449
  

  • MATH 551 Linear Programming and Optimization (3)

    This course provides an introduction to deterministic models in operations research. Topics include linear programming, network analysis, dynamic programming, and game theory.
    Prerequisite(s): Students must have a working knowledge of Linear Algebra, Vector Calculus, and some computer programming.
    Course Frequency: Fall
    Cross-Listing: MATH 451
  

  • MATH 552 Operations Research (3)

    This course provides an introduction to probabilistic models in operations research. Topics include queueing theory, applications of Markov chains, simulation, integer programming and nonlinear programming.
    Prerequisite(s): Students must have a working knowledge of Linear Algebra, Vector Calculus, and some computer programming skills.
    Course Frequency: Spring
    Cross-Listing: MATH 452
  

  • MATH 555 Bayesian Statistical Methods (3)

    Posterior distributions using observed data are calculated and used for inferences about model parameters. Classical statistical methods are compared with the Bayesian methods and classical models such as linear regression, ANOVA, and generalized linear models are extended to include the Bayesian paradigm. Monte Carlo methods, Gibbs sampling and Metropolis-Hastings algorithms.
    Prerequisite(s): MATH 530  or equivalent
    Course Frequency: Spring
    Cross-Listing: MATH 455
  

  • MATH 560 Stochastic Processes (3)

    Stochastic Processes are sequences of random variables indexed in either discrete or continuous time unit. They can be used to model systems that involve random elements as they evolve over time. In this course we will study Poisson processes, Markov chains, renewal processes, martingales, random walks, and Brownian motion.
    Prerequisite(s): MATH 530  or equivalent
    Course Frequency: Occasional
    Cross-Listing: MATH 460
  

  • MATH 561 Time Series Analysis (3)

    Time series are sequences of data points measured typically at successive uniform time intervals. They are used in signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, and control engineering. Time series analysis is a collection of methods for analyzing time series data in order to extract meaningful characteristics of the data. In this course we will study stationary processes, forecasting techniques, ARMA models, spectral analysis, non-stationary and seasonal models, and multivariate time series.
    Prerequisite(s): MATH 530  or equivalent
    Course Frequency: Occasional
    Cross-Listing: MATH 461
  

  • MATH 580 Topics in Applied Mathematics (3)

    This course is a one-semester introduction to an advanced topic in applied mathematics with generally only undergraduate mathematics prerequisites.
    Course Frequency: Occasional
    Repeatable: For up to 6 credit hours.
  

  • MATH 585 Topics in Pure Mathematics (3)

    This course is a one-semester introduction to an advanced topic in pure mathematics with generally only undergraduate mathematics prerequisites.
    Course Frequency: Occasional
    Repeatable: For up to 6 credit hours.
  

  • MATH 589 Special Topics in Probability and Statistics (3)

    This course is a one-semester introduction to an advanced topic in Probability and Statistics with generally only undergraduate mathematical prerequisites.
    Course Frequency: Occasional
    Repeatable: For up to 6 credit hours.
  

  • MATH 601 General Topology (3)

    This course provides an introduction to general topology. Topics include the generation of topological spaces, continuity, connectedness, compactness, separation and countability.
    Prerequisite(s): MATH 311 (Advanced Calculus I), MATH 411 (Advanced Calculus II) recommended.
    Course Frequency: Occasional
  

  • MATH 604 Applied Algebra II (3)

    This course is a continuation of MATH 503 . Topics include rings and fields with applications to block designs, BCH and difference codes, public key crytography; semigroups and monoids, with applications to automata and languages.
    Prerequisite(s): MATH 503 .
    Course Frequency: Occasional
  

  • MATH 607 Discrete Mathematics (3)

    This course is an introduction to the theory and applications of discrete mathematics. Topics include enumeration techniques, combinatorial identities, matching theory, basic graph theory, combinatorial designs and related topics.
    Prerequisite(s): MATH 203 (Linear Algebra).
    Course Frequency: Occasional
  

  • MATH 612 Real Analysis II (3)

    This course is a continuation of MATH 511 . Topics include the Riemann-Stieltjes integral, equicontinuous families of functions, Lp spaces, linear transformations, the inverse and implicit function theorems and elementary measure theory.
    Prerequisite(s): MATH 511 .
    Course Frequency: Occasional
  

  • MATH 623 Partial Differential Equations II (3)

    Topics include first-order equations and the Cauchy problem, canonical forms of second order equations, the Cauchy-Kowalevski Theorem, separation of variables and eigenfunction expansions, Green’s functions, maximum principles and numerical methods. Special topics such as the calculus of variations, the Galerkin method, perturbations, bifurcations and group methods will be selected by the instructor.
    Prerequisite(s): MATH 523 . oS
    Course Frequency: Occasional
  

  • MATH 624 Dynamical Systems (3)

    This course provides an introduction to the qualitative theory of ordinary differential and difference equations. Topics include existence uniqueness, stability theory, limit cycles, Poincaré maps, structural stability and bifurcation theory. Applications will be provided throughout the course. Special topics such as Hamiltonian systems, gradient systems, perturbations, symbolic dynamics, strange attractors and chaos will be selected by the instructor.
    Prerequisite(s): MATH 323 (Differential Equations) and MATH 502 .
    Course Frequency: Occasional
  

  • MATH 645 Numerical Analysis II (3)

    This course is a continuation of MATH 545 . Topics include finite difference and finite element methods for partial differential equations and numerical optimization. Other topics will be selected by the instructor.
    Prerequisite(s): MATH 545 . oF
    Course Frequency: Occasional
  

  • MATH 650 Statistical Quality Control (3)

    This course is an introduction to basic methods of statistical process control. Topics include control charts, cumulative sum control charts, lot acceptance sampling plans and related topics.
    Prerequisite(s): MATH 350 (Statistical Methods) or permission of the instructor. eSu
    Course Frequency: Occasional
  

  • MATH 651 Design of Experiments (3)

    This course is an introduction to how and why scientific experiments should be designed. The most commonly used designs and their variations along with resulting analysis will be covered.
    Prerequisite(s): MATH 350, or equivalent, or permission of the instructor. oSu
    Course Frequency: Occasional
  

  • MATH 680 Special Topics in Applied Mathematics (3)

    This course is a semester study of an advanced topic in applied mathematics.
    Prerequisite(s): Permission of the instructor.
    Course Frequency: Occasional
    Note: Since the content changes, this course may be repeated for credit. Note: Since the content changes, this course may be repeated for credit.
  

  • MATH 685 Special Topics in Pure Mathematics (3)

    This course is a semester study of an advanced topic in pure mathematics.
    Prerequisite(s): Permission of the instructor.
    Course Frequency: Occasional
    Note: Since the content changes, this course may be repeated for credit.
  

  • MATH 690 Graduate Teaching Seminar (1-3)

    This seminar is designed for graduate students in the mathematical sciences who are interested in teaching in higher-education settings. The seminar is customizable with a range of activities addressing practical and theoretical aspects of teaching in higher-education settings. The seminar is customizable with a range of activities addressing practical and theoretical aspects of teaching and learning: from constructing and teaching a class, including syllabus preparation and time management, to learning effective approaches to college-level teaching. Students will have the opportunity to work closely with a faculty member in an undergraduate classroom environment.
    Prerequisite(s): Admission into the Mathetmatics Graduate Program
    Course Frequency: Fall and Spring
    Repeatable: For up to 3 credit hours
    Restriction: Does not count toward the 30-credit-hour requirement for the M.S. in Mathematical Sciences
  

  • MATH 699 Independent Study in Mathematics (3)

    This course is designed to provide graduate students with an opportunity to study an area of mathematics of interest to them that is not generally offered.
    Prerequisite(s): Depends on the particular topic being studied.
    Course Frequency: Occasional
    Repeatable: For up to 12 credit hours.
  

  • MATH 700 Thesis (3)

    This course is an individual study in mathematics directed by a faculty member.
    Prerequisite(s): Approval of the Graduate Steering Committee and the instructor.
    Course Frequency: Occasional
    Note: This course may be taken for credit twice when the nature of the study warrants it. The following courses, regularly taught in the Department of Biometry and Epidemiology at the Medical University of South Carolina, may also be used as part of the curriculum for students emphasizing statistics. Students enroll in these courses using the cross-registration procedures. At least 18 credit hours must be earned from graduate courses of the College of Charleston.
  

  • MATH 900 Continuous Research Enrollment (1-9)

    Students who are nearing the end of their coursework for their degree and who have begun work on their master’s thesis topic may need to utilize the Continuous Research Enrollment course to maintain a suitable level of enrollment for their programs. Linked directly to students’ research on a thesis topic and must be considered as a progress report toward that end when graded by the thesis advisor. The course will be graded on a pass-fail basis.
    Prerequisite(s): Form submission and program approval.
    Course Frequency: Occasional
    Repeatable: May be repeated when taken within the program’s time limit requirements.
    Restriction: Continuous Research Enrollment hours cannot be used as part of a program of study towards a degree. Continuous Research Enrollment hours may not be taken in lieu of thesis hours, but may be taken in combination with thesis hours, if no additional hours are available or necessary.

Science and Math for Teachers
  

  • SMFT 518 Applications of Calculus for Teachers (4)

    A course designed primarily for secondary science and math teachers to investigate applications of calculus in science and technology. Topics will include a review of limits, derivatives and integration techniques, as well as applications to physics, geology, chemistry, biology and technology. Investigative labs, utilizing data collection, and interdisciplinary projects will be major components of the course.
    Prerequisite(s): One undergraduate calculus course and the student teaches secondary science or mathematics.
    Course Frequency: Occasional