Computational Mathematics Courses

CPMA 511 Logic and Proof 
1.5 cr.

Mathematical truth, axioms and theorems, propositional truth tables, quantifiers, predicate calculus, decision procedures, and mathematical induction. Example syllabus. 
CPMA 512 Linear Algebra 
1.5 cr.

Matrices, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, and orthogonality. Example syllabus. 
CPMA 515 Advanced Discrete Math 
1.5 cr.

Introduction to number theory, recursively defined functions, analyzing algorithm performance, recurrence relations, generating functions, permutations and combinations, Inclusion/Exclusion, introduction to Graph Theory, and Boolean algebra. Prerequisite: 511. Example syllabus. 
CPMA 518 Vector Calculus 
1.5 cr.

Three dimensional geometry, directional derivatives, gradient, divergence, curl, maximumminimum problems, multiple integrals, parametric surfaces and curves, and line integrals. 
CPMA 521 Probability and Markov Chains 
1.5 cr.

Review of random variables, discrete and continuous distributions, expectation, conditional probability, and limit theorems. Introduction to Markov chains, finite absorbing and nonabsorbing chains, limiting distributions, and infinite chains. 
CPMA 522 Statistical Inference 
1.5 cr.

Review of statistical estimation and hypothesis testing. Introduction to nonparametric methods, analysis of variance, statistical modeling and Bayesian inference. Prerequisite: 521. 
CPMA 525 Linear Models 
1.5 cr.

Review of simple linear regression and multiple linear regression. Topics further covered include Type I and Type III SSQ, various residual diagnostics measures, effects of outliers and influential measures, estimation distinctions when dependent and independent variables are either nominal or continuous, introduction to fixed/random effects and components of variance, 1way ANOVA with multiple comparisons techniques, and ANACOVA models for the common slope and separate slope form. All models are demonstrated using JMP and SAS. 
CPMA 526 Experimental Design 
1.5 cr.

Continuation of CPMA 525. Begins with the concepts about the principles of experimental design, randomization and blocking. Topics covered are 2way and multiway ANOVA models, orthogonal contrasts, factorial designs, balanced and unbalanced designs, repeated measures, nesting effect within models, mixed models analyses, and estimation comparing the EMS and REML approaches. Corequisite: 525. 
CPMA 531 Programming Language: Java 
1.5 cr.

Classes, objects, instances, messages, methods, inheritance, interfaces, polymorphism, software life cycle, variables, expressions, data objects, control structures, strings, arrays, files, searching, sorting, applets, toolkits, threads, and graphical user interfaces. Example syllabus. 
CPMA 532 Data Structures 
1.5 cr.

Abstract data types, stacks, queues, databases, priority queues, trees, linked lists, hashing, balanced trees, selforganizing data structures, and advanced sorting. Corequisite: 531. Example syllabus. 
CPMA 535 Introduction to Computer Systems 
1.5 cr.

Computer representation and hardware, system programming, prototyping and development, memory and data organization, communications and networking, human/computer interactions, and performance analysis and improvement. Prerequisite: 532. Example syllabus. 
CPMA 536 Software Engineering 
1.5 cr.

Software development processes and the software life cycle, software architecture and design, emphasizing objectoriented design, user interface design, validation and verification, testing methods, systems analysis and requirements definition, software management and personnel issues. Prerequisite: 532.Example syllabus. 
CPMA 550 Computer Networks 
3 cr.

Network technologies, protocols, and management. Programming networked applications. The effects of the Internet and World Wide Web on computing and society. 
CPMA 551 Digital Image Processing 
3 cr.

Introduction to the mathematics of images and image processing, as well as computational methods for real data manipulation. Topics include image acquisition, image enhancement and restoration in both the spatial and frequency domains, the Fourier transform, wavelets, image compression, image segmentation, and morphological processing algorithms. Example syllabus. 
CPMA 560 Algorithms/Graph Theory 
3 cr.

Graph theory, graph algorithms, coloring, network flows, computational geometry, compression, randomized algorithms, parallel algorithms, and NPcompleteness. 
CPMA 563 Numerical Differential Equations 
3 cr.

Finite difference methods, stability, boundary value problems, ordinary differential equations, integral equations, and partial differential equations. Prerequisites: 511, 512. 
CPMA 565 Numerical Methods 
3 cr.

Linear systems, interpolation, functional approximation, numeric differentiation and integration, and solutions to nonlinear equations. 
CPMA 566 Operations Research 
3 cr.

An introduction to the background of operations including example problems and a brief history. An extensive discussion of the theory and applications of linear programming will follow. Other topics will include integer programming, transportation and network flow models, and dynamic programming. Prerequisite: CPMA 512. 
CPMA 571 Optimization 
3 cr.

Linear programming, transportation problem, network flow, nonlinear convex programming, dynamic programming, geometric programming, game theory, and gradient methods. 
CPMA 573 Statistical Computing 
3 cr.

Generating pseudorandom numbers, Monte Carlo integration, simulation, Bayesian inference, Gibbs sampling, Metropolis sampling, MetropolisHastings sampling, the EM algorithm, multivariate NewtonRaphson maximization. 
CPMA 574 Prediction and Classification Modeling 
3 cr.

Classification rates, ROC curves, crossvalidation techniques, modern regression methods, data reduction/principle components, stages of biomarker development, and study design issues in cancer and occupational research 
CPMA 575 Introduction to Elementary Data Mining 
3 cr.

The emphasis of this course is to understand the beginning concepts in building either a predictive or a classification model using data mining techniques. Special topics covered are: distinction between supervised and unsupervised learning; issues in data exploration; steps in data cleaning including missing data, transformations and methods of imputation; training vs. testing sets; determining model accuracy (ROC curves, lift and cumulative lift charts): crossvalidation, bootstrapping estimations; partitioning and classification tree analyses. Software used for demonstrating procedures incorporate JMP and SAS algorithms. 
CPMA 577W Applied Stats with Regression 
3 cr.

This course begins with a review of inferential statistics. Emphasis on data collection methods, stating hypotheses, confidence intervals and bootstrapping methods for estimating parameters are introduced. Both traditional and resampling methods are demonstrated for testing hypotheses. Additional topics covered are graphical methods for exploring distributions and determining outliers, 1way and 2way analysis of variance models using a linear models approach, and linear and multiple regression methods. JMP software is used for demonstrating methods. 
CPMA 580 Artificial Intelligence/Cognitive Science 
3 cr.

Computational and statistical modeling of human cognitive processes and their implementation: modularity of mind, rulebased vs. distributed vs. prototype models, search techniques, story understanding, and statistical models of language. 
CPMA 582 Machine Learning 
3 cr.

Basic tools, including statistical significance testing, overview of theory, algorithms, and applications, concept learning, reinforcement learning, clustering, advanced concept learning, neural networks, perceptrons, decision trees, generalpurpose algorithmic methods, data mining, and collaborative filtering. 
CPMA 584 Formal Languages and Automata 
3 cr.

Formal languages and their relation to automata. Regular expressions and languages, context free languages, recognition of languages by automata, Turing machines, decidability, and computability. 
CPMA 585 Computer Security 
3 cr.

Network, database, and Web security, threat models, elementary and advanced cryptology, protocol analysis, covert channels, access control and trust issues, legal and ethical issues in security. 
CPMA 586 Computer Graphics 
3 cr.

Geometric generation of two and threedimensional graphics. Theory of affine transformations. Scan conversion, geometric transformation, clipping, interaction, curves and surfaces, and animation. 
CPMA 587 Database Management 
3 cr.

The use, design, and implementation of database management systems. Topics include data models, current DBMS implementations, and data description, manipulation, and query languages. 
CPMA 590 Special Topics 
3 cr.

Various subjects in computational mathematics. May be repeated for credit when content changes. Prerequisite: Permission of the instructor. 
CPMA 591 ST: Linguistic Forensics: Computational Analysis of Language 
3 cr.

Computational analysis of language, with specific reference to techniques for inferring authorship properties. 
CPMA 595 Independent Study 
3 cr.

Directed study on a topic related to computational mathematics. May be repeated once for credit. Prerequisite: Permission of the instructor and Graduate Director. 
CPMA 599 Internship 
3 cr.

Internship suitably related to the program as determined by the Program Director. May be repeated for a total of up to six credits. 
CPMA 601 Project 
16 cr.

Prerequisite: Permission of the Graduate Director. 
CPMA 700 Thesis 
16 cr.

Prerequisite: Permission of the Graduate Director. 
